NeuroPhysics
NeuroPhysics Corporation is a medical RD company specializing in NeuroSPECT imaging techniques and equipment, as well as other non-invasive in-vivo monitoring devices
ProPhysics Innovations, Inc.
ProPhysics Innovations, Inc. (PPI) provides a broad range of physics solutions in medicine, research, academia and industry.
Home Page ProPhysics Innovations, Inc. "Physics Solutions in Medicine Industry" Welcome... ProPhysics Innovations, Inc. is a medical and health physics consulting group based in the Research Triangle area of North Carolina. Our central location makes us easily accessible to client facilities throughout the southeast while off-site consulting services are provided nationwide. ProPhysics provides high quality, professional physics services to an expanding base of medical, research, academic and industrial client facilities. Please, click around our website and see how we can meet your needs. To get back here (home), click onto the ProPhysics symbol. web prophysics.com Contact Us Services News About Us Client Page Physicist Page FAQ Copyright 1996-2004 ProPhysics Innovations, Inc. All rights reserved. Site Last Updated: 10 01 2004 04:48 PM
Physicsweb.org
Listings of physics openings for all degree levels.
PhysicsWeb - Employment Centre - Latest Jobs Advanced site search job seekers Latest jobs Search jobs Job alerts Add a CV resume Update a CV resume Employer profiles employers Recruitment advertising Latest CVs Search CVs CV alerts quick search Search by job title, organization name, description, keyword or location Jobs CVs VIEW JOBS Search Selection jobs are currently filtered out. Include Search Selection jobs . Physics Jobs is the definitive online resource for job announcements, career enhancing courses or calls for proposals accessed globally by the physics and engineering community. All advertisements placed in Physics World are complimented by their online presence. NEW for 2004 - Physics Jobs has joined forces with two other world wide renowned leading scientific websites; cerncourier.com and nanotechweb.org. Your positions can be added to these sites at your request, but only when you have placed your advertisement in Physics World or CERN Courier. 1-20 21-40 41-60 61-80 81-96 Next Applied Researchers GCHQ, Cheltenham, United Kingdom View Employer Profile Posted: Oct 25 2005 Closing Date: not specified Editor Physics World IOP Publishing, Bristol, United Kingdom Posted: Nov 16 2005 Closing Date: Dec 19 2005 Several positions - Grid Computing LIGO VO Center for Gravitational Wave Physics, University Park, PA, United States Posted: Nov 15 2005 Closing Date: not specified University Lecturer in Theoretical Particle Physics (to $47078) The Rudolf Peierls Centre for Theoretical Physics, Oxford, United Kingdom Posted: Nov 15 2005 Closing Date: Jan 16 2006 Faculty Position in Theoretical Elementary Particle Physics SLAC, Stanford, CA, United States Posted: Nov 15 2005 Closing Date: Feb 1 2006 Experimental Research Associates SLAC, Menlo Park, CA, United States Posted: Nov 15 2005 Closing Date: not specified Director of Elementary Particle Physics Cornell University, Ithaca, NY, United Kingdom Posted: Nov 15 2005 Closing Date: Jan 15 2006 Research Fellows (20235 to 30607) Brunel University West London, London, United Kingdom Posted: Nov 15 2005 Closing Date: not specified Research Infrastructures Istituto Nazionale di Fisica Nucleare - Laboratori Nazionali di Frascati, Frascati, Italy Posted: Nov 15 2005 Closing Date: not specified Faculty Position in Experimental Particle Physics Drexel University, Philadelphia, PA, United States Posted: Nov 15 2005 Closing Date: Jan 15 2006 Shape classified projects at the cutting edge of science. QinetiQ, Hants, United Kingdom Posted: Nov 15 2005 Closing Date: Nov 4 2005 Assistant Professor University of California, Los Angeles, CA, United States Posted: Nov 15 2005 Closing Date: Jan 1 2006 We Highlight Science ESRF, Cedex 9, Grenoble, France Posted: Nov 15 2005 Closing Date: not specified NUCLEAR PHYSICIST Nuclear Physicist, Paris, France Posted: Nov 15 2005 Closing Date: not specified Science Director - Australian Synchrotron Australian Synchrotron, Melbourne, Australia Posted: Nov 14 2005 Closing Date: not specified Applications Physicist I Fermilab, Batavia, IL, United States Posted: Nov 14 2005 Closing Date: not specified Experimental particle and astroparticle physics FOM - NIKHEF, Amsterdam, 1009 DB, Netherlands Posted: Nov 14 2005 Closing Date: Jan 15 2006 Assistant Professor Niagara University, Niagara, New York, United States Posted: Nov 11 2005 Closing Date: not specified Postdoctoral Researchers (26401 to 25401) The University of Liverpool, L69 3BX, United Kingdom Posted: Nov 8 2005 Closing Date: Nov 25 2005 Schrdinger Fellowship (47131 to 52578) DIAS, Dublin, Ireland Posted: Nov 8 2005 Closing Date: Dec 16 2005 To receive regular careers advice, industry profiles, the latest opportunities and our movers and shakers news, please subscribe to Physics World. Each issue will provide you with invaluable career information, as well as the latest recruitment opportunities. 1-20 21-40 41-60 61-80 81-96 Next e-mail job alerts Sign up to our e-mail job alerting service, alter your alert settings or unsubscribe . employer spotlights AWE plc GCHQ Qinetiq Home | News | Physics World | PhysicsJobs | Resources | Events | Best of PhysicsWeb Buyer's Guide | Contact us | Advertising | IoP members | Products press | Advanced site search Tel +44 (0)117 929 7481 | Fax +44 (0)117 925 1942 | E-mail info@physicsweb.org Copyright IOP Publishing Ltd 1996-2005. All rights reserved. Legal Notice
High-energy physics jobs
Search a High-energy Physics employment database maintained by the Stanford Linear Accelerator Center.
Jobs Search Hep :: HepNames :: Institutions :: Conferences :: Experiments :: Jobs :: Videos Jobs Search High-Energy Physics Employment Database Field: Any Type Accelerator Astro Cosmo Astro Particle Computing Experiment Phenomenology Theory Math ------------ astro-ph gr-qc hep-ex hep-lat hep-ph hep-th nucl-ex nucl-th physics.acc-phys physics.ins-det physics-other Region: All regions Africa Asia Australasia Europe Middle East North America South America Rank: Show all Ph.D. Student Postdoc Tenure-track Tenured Staff (non-research) Visiting Scientist Country: Albania Algeria Argentina Armenia Australia Austria Azerbaijan Bangladesh Barbados Belarus Belgium Benin Bolivia Bosnia-Herzegovina Botswana Brazil Bulgaria Burma Burundi Cameroon Canada Chad Chile China (PRC) Colombia Costa Rica Croatia Cuba Czech Republic Denmark Dominican Republic Ecuador Egypt El Salvador Estonia Ethiopia Finland France Georgia Germany Ghana Greece Guadeloupe Honduras Hong Kong Hungary Iceland India Indonesia Iran Iraq Ireland Israel Italy Jamaica Japan Jordan Kazakhstan Kenya Korea Kuwait Kyrgyzstan Latvia Lebanon Lesotho Libya Liechtenstein Lithuania Macedonia Malagasy Republic Malaysia Malta Mexico Moldova Mongolia Morocco Namibia Nepal Netherlands New Zealand Niger Nigeria North Korea Norway Oman Pakistan Palestine Papua New Guinea Peru Philippines Poland Portugal Qatar Romania Russia Rwanda Saudi Arabia Senegal Singapore Slovakia Slovenia South Africa Spain Sri Lanka Sudan Swaziland Sweden Switzerland Syria Tadzhikstan Taiwan Tanzania Thailand Trinidad Tunisia Turkey Uganda Ukraine United Arab Emirates United Kingdom United States Uruguay Uzbekistan Vatican Venezuela Vietnam Yemen Yugoslavia Zambia Sort by: Newest first Deadline - Descending Deadline - Ascending Institution Country Region Keyword: Search Help :: Standard Search :: About Jobs :: List of All Jobs Tip of the Moment Mailing List We offer a Mailing List to keep you up to date, or you can try RSS feeds Jobs Add a Posting Join Mailing List List of All Jobs Quick Searches Corrections Email Us SPIRES TopCites HEP Reviews SPIRES News Playground Biblio. Tools Preprint listing Resources arXiv HEPDATA PDG SLAC Books About SPIRES :: SLAC :: SLAC Library :: Contact SPIRES HEP is a joint project of SLAC, DESY FNAL as well as the worldwide HEP community. Mirrors: DESY (Germany), Fermilab (US), IHEP (Russia), Durham U. (UK), SLAC (US), YITP (Japan); Last Updated: 09 12 2005
Science careers database
Search a database of jobs maintained by Science magazine.
Science Careers Science Careers Jump to: Page Content , Section Navigation , Section Search , Site Navigation , Site Search , Account Information , or Site Tools . You are seeing this message because your web browser does not support basic web standards. Find out more about why this message is appearing and what you can do to make your experience on this site better. Site Tools Site Search Site Area Science Magazine News STKE SAGE KE Science Careers All HighWire Journals Terms Account Information Site Navigation Readers Members Authors Librarians Advertisers Jobs Funding Meetings and Events Career Development For Advertisers About ScienceCareers Home ScienceCareers Home Jobs Search Jobs Biotechnology Jobs Faculty Jobs Postdoctoral Jobs Jobs Posted Today Job Search Help Job Tools Login Create an Account Account Profile Job Alerts Resumes Cover Letters For Advertisers Post a Job Post a Meeting List your Event in Science's 2006 Event Calendar To Advertise Contact Us Also in ScienceCareers Science Careers Forum Get your questions answered by our experts. Career Development Resources Search 2,426 Jobs Search Keywords: Match: All Words Any Words Search: All Text Job Title Only Sort By: Relevance Date Removing items from your search. This can be done by using the minus function in the keyword field. Example: Faculty -postdoc This would exclude postdoc ads being returned in the search results. Select a Location: City or US Zip Code: State: State AK AL AR AZ CA CO CT DC DE FL GA HI IA ID IL IN KS KY LA MA MD ME MI MN MO MS MT NC ND NE NH NJ NM NV NY OH OK OR PA RI SC SD TN TX UT VA VT WA WI WV WY Country: Afghanistan Africa Albania Algeria Andorra Angola Anguilla Antarctica Antigua Barbuda Argentina Armenia Aruba Australia Austria Azerbaijan Bahamas Bahrain Bangladesh Barbados Belarus Belgium Belize Benin Bermuda Bhutan Bolivia Bosnia Herzegovina Botswana Bouvet Island Brazil Brunei Bulgaria Burkina Faso Burundi Cambodia Cameroon Canada Cape Verde Cayman Islands Chad Chile China Christmas Island Cocos Islands Colombia Comoros Congo Cook Islands Costa Rica Cote D'ivoire Croatia Cuba Cyprus Czech Republic Denmark Djibouti Dominica Dominican Republic East Timor Ecuador Egypt El Salvador England Equatorial Guinea Eritrea Estonia Ethiopia Falkland Islands Faroe Islands Fiji Finland France French Polynesia Gabon Gambia Georgia Germany Ghana Gibraltar Greece Greenland Grenada Guam Guatemala Guinea Guinea-Bissau Guyana Haiti Honduras Hong Kong Hungary Iceland India Indonesia Iran Iraq Ireland Israel Italy Jamaica Japan Jordan Kazakhstan Kenya Kiribati Korea, North Korea, South Kuwait Kyrgyzstan Laos Latvia Lebanon Lesotho Liberia Libya Liechtenstein Lithuania Luxembourg Macau Madagascar Malawi Malaysia Maldives Mali Malta Marshall Islands Mauritania Mauritius Mayotte Mexico Micronesia Moldovia Monaco Mongolia Montserrat Morocco Mozambique Myanmar Namibia Nauru Nepal Netherlands New Caledonia New Zealand Nicaragua Niger Nigeria Niue Norway Oman Pakistan Palau Panama Papua New Guinea Paraguay Peru Philippines Pitcairn Poland Portugal Puerto Rico Qatar Romania Russia Rwanda Saint Helena Saint Kitts Nevis Saint Lucia Samoa, African Samoa, American San Marino Sao Tome Principe Saudi Arabia Scotland Senegal Seychelles Sierra Leone Singapore Slovakia Slovenia Solomon Islands Somalia South Africa Spain Sri Lanka Sudan Suriname Swaziland Sweden Switzerland Syria Taiwan Tajikistan Tanzania Thailand Togo Tokelau Tonga Trinidad Tobago Tunisia Turkey Turkmenistan Tuvalu Uganda Ukraine United Arab Emirates United Kingdom United States Uruguay Uzbekistan Vanuatu Vatican City State Venezuela Vietnam Virgin Islands Wallis Futuna Isl. Wales Western Sahara Yemen Yugoslavia Zaire Zambia Zimbabwe Radius: 10 mile radius 20 mile radius 30 mile radius 40 mile radius 50 mile radius 75 mile radius 100 mile radius 125 mile radius OR Select a Region: Northeast (CT,MA,ME,NH,NJ,NY,PA,RI,VT) Midatlantic (DC,DE,MD,VA) Southeast (AL,FL,GA,KY,MS,NC,SC,TN,WV) Midwest (IA,IN,IL,KS,MI,MN,MO,ND,NE,OH,SD,WI) Southwest (AR,AZ,LA,NM,OK,TX) West (AK,CA,CO,HI,ID,MT,NV,OR,UT,WA,WY)
CERN jobs portal
Human resources portal for CERN, the world's largest particle physics laboratory. (this replaces a broken link in the current category list)
Jobs at CERN and Recruitment Programs for Students, Fellows and Associates Human Resources External Pages [ CERN Home ] [ HR Home ] [ Search ] [ Sitemap ] [ Feedback ] [ Contact ] [ Printable ] General Links Young People Staff Fellows Associates Students Special Programmes Contact Us Welcome to the CERN Recruitment Service ! Are you interested in joining the World's leading laboratory for particle physics and working in an international, multicultural environment ? Special Programmes Trainees (France, Portugal and Spain), Programmes on Israeli funds, CERN-Asia programmes, European Community Fellowships , Austrian Doctoral studentships Marie Curie EST positions in Theoretical Physics Marie-Curie Early Stage Training positions at CERN Local Staff employment Emploi de Personnel Local Direct access to e-recruitment system (ERT) Accs direct au systme de recrutement lectronique (ERT) [ CERN Home ] [ HR Home ] [ Search ] [ Sitemap ] [ Feedback ] [ Contact ] [ Printable ] Last modified Wed, 5 Oct 2005 HR Webmaster Copyright CERN If you have any feedback regarding this page, please contact - Recruitment Service
Careers with Physics
Advice and resources from the UK Institute of Physics.
Careers with Physics - Institute of physics, Career development, Professional development To access the navigation menu, please use the text links at the bottom of the page: Text Menu Students Graduate With a 2:2 or a 3rd? Start Your Own Business Becoming Chartered Career Support Email Alert - Sign Up E-Guidance Redundancy CVs Career Break Grants Careers Fair Statement of Service Meet the careers adviser Choose an option from the menus to continue The AA-Standard refers to all pages within the domain for which this is the home page Copyright Institute of Physics and IOP Publishing Ltd. 2000-2002 Update: November 14, 2005 Home Page | Professional Development | Events | Resources Qualifications | Jobs | Why Physics? | Discussion Board | Site Map
Physics Astronomy REU reviews
Student-written reviews of REUs and other summer undergraduate research programs jobs, plus answers to FAQs and useful related links
Physics and Astronomy Research Experience Reviews Physics and Astronomy Research Experience Reviews: REU's and Other Undergraduate Summer Research What is an REU? Is summer research for me? Is it better to do research at my home institution or another school? Student reviews: European Laboratory for Particle Physics (CERN) - Geneva, Switzerland National Institutes of Standards and Technology (NIST) - MD Santa Fe Institute - Santa Fe, NM University of Minnesota - Minneapolis, MN Plasma Physics at UCLA - Los Angeles, CA Ecology Research - Costa Rica and Ontario, Canada The National Science Foundation has good documentation about the REU program and a list of all the sites. Also, an exhaustive list of REUs and other programs around the country is available from UPenn. The Harvard Math Club has a similar site for math REU's. Have you had a cool summer experience? Please dash off a quick summary and email it to Viva Horowitz '05 (vhorowi1-at-swarthmore.edu) or Robin Smith '03 (robinleslie-at-alum.swarthmore.edu). Include websites, email addresses, or other contact info for future students to learn about these programs. Don't be afraid to give an honest evaluation about whether the program offers an enjoyable and worthwhile experience; if you don't recommend the program to future students, be honest and say why it was not good. Add a technical abstract or link to relevant posters and presentations you've done if you like. Please have your review added to our site! back to top Website maintained by Swarthmore Women in Astronomy and Physics and updated 8 January 2004. Email comments to vhorowi1-at-swarthmore.edu. Thank you to all those who have submitted research experience reviews. Thanks go out to Prof. John Boccio, Prof. David Cohen, and Bo Hu '05 for providing valuable assistance coding and posting this webpage. The help of Kelsey Hollenback, Viva Horowitz '05, Matt Landreman '03, and Robin Smith '03 is also appreciated.
Spieworks
Maintained by the International Society for Optical Engineering. Includes job listings for related science and engineering posts, with a search function, as well as a list of conferences and some tips.
SPIEWorks :: Jobs for optics, photonics and imaging professionals. The employment resource for optics, photonics, and imaging professionals home view jobs view companies career fairs resources contact us username: password: Forgot username password? Advanced Search Featured Companies Coherent Technologies, Inc Crystal Fibre General Atomics Eastman Kodak Co. IPG Photonics Corp. Become a SPIEWorks Featured Company Newest Job Postings Observing Assistant C.A.R.A. W.M. Keck Observatory | View | Apply | Save Job | Optical Engineer Raydiance, Inc. | View | Apply | Save Job | Optical Engineer- Manufacturing Alcon Labs | View | Apply | Save Job | View All Career Expos UPCOMING Add your resume starting 26December2006 Photonics West Career Fair San Jose, California, USA On-site Career Fair : 24-25January2006 Online Career Expo : 23-29January2006 Conference : 21-26January2006 UPCOMING Add your resume starting 20March2006 Defense Security Career Fair Kissimmee, Florida , USA On-site Career Fair : 18-19April2006 Online Career Expo : 17-21April2006 Conference : 17-21April2006 View All home | view jobs | view companies | career expos | resources | contact us | post your resume cv 2005 SPIEWorks. A service of SPIEThe International Society for Optical Engineering. | privacy policy | copyright statement
Physics and Astronomy Job Openings
Search a database kept by the Chronicle of Higher Education.
Chronicle Careers: Jobs in Higher Education
Job Openings at the European Patent Office (EPO)
The EPO is an international authority whose task is to examine and grant patents on behalf of its 20 member states.
Job openings at the European Patent Office (EPO) European Patent Office (EPO) job openings homepage = general presentation = job openings D E F Patent examiner IS recruitment General Conditions Current Jobs Examiner We have currently many vacancies for patent examiner posts. Apply using our online application form [ more ] The European Patent Organisation, an intergovernmental organisation based in Munich, is in charge of the worlds fastest-growing regional patent system. An outstanding example of successful co-operation among European countries, the Organisation currently numbers 31MemberStates and is set to expand further soon. Its executive body, the European Patent Office, strives to stand out as a model international public service organisation. As the patent granting authority for Europe with a strong global orientation, it received 178.579 patent applications in 2004. Its mission is to support innovation, competitiveness and economic growth for the benefit of the citizens of Europe. With a budget of well over EUR 1 000 million and with a staff complement of over 5 918 at its headquarters in Munich and branches in The Hague, Berlin and Vienna, the Office is one of the largest international institutions in Europe. Latest additions Description Title Deadline for application Administrative Employee in The Hague (INT EXT 4235) (Support to User Services Mail Printing) Internal Services - 4.7.3.1 30.12.2005 Loaded 28.11.2005 Supervisor head of section in Munich (INT EXT 4228) in Directorate 5.2.1 (Patent Law) 27.12.2005 Loaded 25.11.2005 Administrative Employee in The Hague (INT EXT 4231) Department 1.3.2 (Documentation Biotechnology) 23.12.2005 Loaded 22.11.2005 Supervisor head of section in Munich (INT EXT 4226) Technical Facility Management, Isar building (4.4.2) 20.12.2005 Loaded 17.11.2005 Current vacancies We currently have vacancies in Munich , in Berlin (Germany), in Vienna (Austria), in The Hague (The Netherlands) and in Brussels (Belgium) Looking for a career at the forefront of technology within an international environment? We have many vacancies for patent examiners . In Information Systems (IS), the IT directorate of the EPO, we also have open posts. Learn about working in the EPO at one of our 'Recruitment Tours ' Other opportunities at the UK Patent Office . Munich (Germany) Description Title Deadline for application Administrator in Munich INT EXT 4216) (Budgeting Manager) in Dir. 4.2.1 (Planning and Budgeting) 29.11.2005 Loaded 18.10.2005 Administrator in Munich INT EXT 4206) (Accounting Manager) in Dir. 4.2.2 (Treasury and Accounts) 29.11.2005 Loaded 18.10.2005 Administrative employee in Munich (EURO 4212) in Department 3.0.40 (2 year contract) closed Loaded 25.10.2005 Administrative employee in Munich (INT EXT4220) DG 1 principal directorate Secretary in Principal Directorate "Pure and Applied Organic Chemistry (PAOC)" closed Loaded 25.10.2005 Technically qualified member of the Boards of appeal in 3.2.03 (Mechanics) 31.12.2005 Loaded 31.10.2005 Technically qualified member of the Boards of appeal in 3.3.01 (Chemistry) 31.12.2005 Loaded 31.10.2005 Technically qualified member of the Boards of appeal in 3.2.04 (Mechanics) LIKELY TO ARISE 31.12.2005 Loaded 31.10.2005 Director in Munich INT EXT 4157) Head of Directorate 5.4.2 - Knowhow 09.12.2005 Loaded 09.11.2005 Administrator in Munich INT EXT 4221) in 0.3.2 (Planning and Reporting) 11.12.2005 Loaded 11.12..2005 Supervisor head of section in Munich (INT EXT 4226) Technical Facility Management, Isar building (4.4.2) 20.12.2005 Loaded 17.11.2005 Supervisor head of section in Munich (INT EXT 4228) in Directorate 5.2.1 (Patent Law) 27.12.2005 Loaded 25.11.2005 The Hague (The Netherlands) Description Title Deadline for application Implementation Manager in Information Systems in the Hague (INT EXT 3907) Administrator until further notice Loaded 15.06.04 JAVA Analyst-Programmer Supervisor Supervisor Head of Section in Information Systems in the Hague (INT EXT 3906) Administrative employee until further notice Loaded 28.05.04 Network Analyst Supervisor Head of Section Operational Services in Information Systems in the Hague (INT EXT 3880) Administrative employee until further notice Loaded 2.04.04 Administrative employee in the Hague (INT EXT 4150) (multiple posts) in Patent Administration - Dir. 1.1.4 until further notice Loaded 01.09.05 Network Engineer Operational Services Information Systems IS in the Hague (INT EXT 4203) Administrator until further notice Loaded 09.09.05 Development Coordinator in Documentation Area Development and Maintenance - Patent Granting in Information Systems in the Hague (INT EXT 4204) Administrator until further notice Loaded 12.09.05 Director in The Hague (INT EXT 4218) Infrastructure Services (D.4.7.3) 28.11.2005 Loaded 28.10.2005 Administrative Employee in The Hague (INT EXT 4224) in Facility Management in Building Administration - 4.7.3.2 08.12.2005 Loaded 10.11.2005 Administrative Employee in The Hague (INT EXT 4234) Cluster Secretary 09.12.2005 Loaded 11.11.2005 Administrative Employee in The Hague (INT EXT 4231) Department 1.3.2 (Documentation Biotechnology) 23.12.2005 Loaded 22.11.2005 Open Source, Change- and Package Manager for epoline in Information Systems in the Hague (INT EXT 4227) Administrator until further notice Loaded 25.11.05 Administrative Employee in The Hague (INT EXT 4235) (Support to User Services Mail Printing) Internal Services - 4.7.3.1 30.12.2005 Loaded 28.11.2005 Berlin (Germany) Description Title Deadline for application There are currently no vacancies at this site Vienna (Austria) Description Title Deadline for application Administrative Employee in Vienna (INT EXT 4141) in Directorate 4.5.1 (Co-operation Programmes and INPADOC) 11.12.2005 Loaded 11.11.2005 Brussels Bureau Description Title Deadline for application There are currently no vacancies at this site General Conditions The attractive salaries are at a similar level to those of other international organisations. Candidates must be a national of one of the present or future member states of the European Patent Organisation: Current member states : Austria, Belgium, Bulgaria, Cyprus, the Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Liechtenstein, Lithuania, Luxembourg, Monaco, the Netherlands, Poland, Portugal, Romania, Spain, Slovakia, Slovenia, Sweden, Switzerland, Turkey, United Kingdom. Future member states: Malta The official languages are English, French and German. The posts are equally open to suitably qualified male and female applicants. Official application forms (available with each vacancy notice), are to be completed in full and should either accompany applications or be sent immediately afterwards. Useful Information More information on the EPO's working conditions and the recruitment procedure . Learn about working in the EPO at one of our 'Recruitment Tours ' EPO Home Page | Recent updates | Request info | Send comments | Index Copyright 1997-2005 European Patent Office . All Rights Reserved.
AIP Employment and Industry
American Institute of Physics career network for physics, engineering and related physical sciences.
Physics and engineering jobs - Physics Today Career Network ADVERTISING | CAREER NETWORK | BUYERS GUIDE | EVENT CALENDAR | REQUEST PRODUCT INFO | PHYSICS TODAY JOB SEEKERS: Search Jobs Post Your Resume Job Fairs Job Hunting Guide EMPLOYERS: Post a Job Search Resumes Job Fairs Job Banner Advertising Pricing Client List Contact Us Physics Today Home The Physics Today Career Network is considered by recruiters worldwide as the best resource either in print or online for posting open positions. This highly regarded, comprehensive classified section reaches more than 120,000 physicists, engineers and other scientists in a broad range of sectors from academia to industry to government and nonprofit organizations. Physics Today offers advertisers unmatched exposure and the best buy for their advertising dollar. JOB FAIRS A powerful way for employers and employees in physical sciences and engineering to come together. American Physical Society Annual March Meeting March 13-15, 2006 Baltimore Convention Center Baltimore, MD Employer registration Candidate registration "The AIP Career Network and Job Fair has been an outstanding resource for us to find candidates for our scientific job openings. We have received very good response from our job postings and the website is easy to use and to apply selective screening. We have also received great support from the AIP Career Network and Job Fair staff." Dwight Mitchell, Hamilton Sundstrand "During 2005 we did extensive recruiting and the APS fair was by far our most effective event of the year." Dan Rhodes HR Manager GE Consumer and Industrial, Lighting Technology RESOURCES Hunting for jobs at liberal arts colleges Landing Your First Job: A Guide for Physics Students What's a Physicist Worth? GradschoolShopper.com Career Guidance for High School and Undergraduate Students FEATURED JOBS GE Global Research - China Technology Center Shanghai, China X-ray Imaging Systems Engineer Northrop Grumman Van Nuys, CA Physicists, Mathematicians, Scientists Grinnell College Grinnell, IA Assistant Professor - 1 year term position 2006-07 IXI Corporation McLean, VA SAS Programmer Econometrician Contact us | About Physics Today | Privacy Policy | Terms Conditions Copyright 2004 by the American Institute of Physics All rights reserved
Physlink - Physics, Astronomy and Engineering Jobs
Job openings for physicists, engineers, scientists. Post and read job listings and follow links to various science employment sites.
Jobs in Physics, Engineering and Astronomy Not a member yet? Get Free Membership Username: Password: Remember me Forgotyourlogin? Askthe Experts Physics JobBoard University Departments Discussion Forums Online Chat Einstein eGreetings Science eStore Employers enter here Latest job update: November 9, 2005 Academic Positions Physics - Assistant Professor (tenure track) At the Niagara Unversity Western New York, USA (near Buffalo and Toronto, Canada) Committed to undergraduate teaching in support of the biology, chemistry, biochemistry, and pre-engineering programs more info Tenured or Tenure Track Positions in General Areas of Physics At the National Central University Chung-Li, Taiwan The Department of Physics invites aplications for tenured or tenure track positions in general areas of physics, starting August 2006. more info Tenure-track assistant professor in theoretical nuclear physics astrophysics At the Arkansas State University Arkansas State University, USA Faculty job at Arkansas State University more info Astrocamp Instructor - School year position At the Astrocamp Idyllwild, Ca. USA Instructor School Year Position more info Internships Student Positions PhysLink.com Forums Moderator At the Innovation Frontier, Inc. Anywhere Join the PhysLink.com team as a volunteer moderator for our discussion forums. Work from home at convenient times. more info Web Programming and Database Design At the Innovation Frontier, Inc. Long Beach, CA, USA Design and creation of a SQL database driven website sections of PhysLink.com. Experience with SQL and ColdFusion is required. more info go to the top Advertisement: All rights reserved. Copyright '1995-'2005 PhysLink.com
APS Careers in Physics
The American Physical Society Jobs careers page.
APS Careers in Physics search questions? comments? contact aps Careers Employment Employment Opportunities APS Career Center Internships - Information on a variety of physics-related opportunities Work at APS Job Fairs Student Guidance Resources Why study physics? What is a physicist? What do I do to become one? Our Student Guidance Resources section answers these questions and provides useful advice for planning your academic studies from middle school up through postdoctoral work. Educator Guidance Resources Our Educator Guidance Resources section is designed to help educators plan their academic coursework from kindergarten on up. Career Guidance Resources Our Career Guidance Resources section helps people at all stages of their careers in physics. View presentations from talks on physics careers, find a speaker for an event, or see what's happening in the Career and Professional Development Liaison program. Committee on Career and Professional Development The APS Committee on Careers and Professional Development (CCPD) is a nine member committee that works to monitor the changing nature of careers and the employment market for physicists and physics students at all levels.
AIP Education and Employment Statistics
The latest data regarding education and employment trends in physics and related science fields.
Education and Employment Data - American Institute of Physics home | contact us | join a society advanced search Publications AIP Journals | Conference Proceedings | Magazines | Books | Scitation Services Publishing | Careers Jobs | Exhibit Meeting Services Resources Government Relations | Education | History | Statistics | News Media About AIP Member Societies | Awards Prizes | Press Releases | Annual Report Government Relations Education History Center Statistical Research News Media Corporate Associates Physics Today Events Calendar AIP Store RSS News Feeds current issue The Statistical Research Center is your source for data on education and employment in physics, astronomy and allied fields. Statistics at a Glance For general information, click on the Full reports link beneath each main topic. To access a list of detailed tables and graphs, select from among the keywords under a main topic. High School Physics Full reports enrollments | teachers | teaching conditions | salaries | initiatives Undergrad Education Full reports 2-year college | degrees | women minorities | student goals | college choice | undergrad experience Graduate Education Full reports enrollments | degrees | subfields | support | women minorities | citizenship Faculty Full reports number | job market | women minorities | new faculty | 2-yr college Employment Full reports bachelors | masters | PhDs | faculty | salaries Women Full reports degrees | faculty | international | high school 2-year college International Full reports foreign students in U.S. | women | degrees abroad | international community Newest reports Physics Students from Abroad: Monitoring visa problems 2005 2004 Physics Roster. 2004 Astronomy Roster. Enrollments and Degrees Report, 2003. FAQ's about the Women in Physics and Astronomy Report. Initial Employment Report 2001 2002 International Students in Geoscience Graduate Programs Resources E-updates - free data alert service Download Physics Trends Flyers Who's Hiring physics Bachelors Career Guidance for Students Catalog of all current reports Physics and Related Societies Worldwide About the Research Center Research Center staff Contact us American Institute of Physics | privacy policy | site map
PhysicsJobs.com
Job site for Physics Professionals. Fee required to post vacancies.
Physics Jobs Sastha.com, Inc., USA. PhysicsJobs.com, PhysJobs.com, AstronomyJobs.com, PhysJobs.com, OpticsJob.com, EEjob.com, ElectronicsJob.com Job Ad Rate - $125 per ad for 120 days Pick upto 3 relevant sites Jobs Posting Info Here e-mail: sasthacom@comcast.net Job Site for Physics and related EE, Electronics, Optics Professionals FEATURED JOBS Date Position Company Website Contact Location 10 25 05 Physics Editor Writer Physics Today website aiphr@aip.org MD 6 23 05 Education Development Officer University of Bradford website jobs@bradford.ac.uk UK NicheJobs.com HRMJobs.com ChEjobs.com ChemistryJobs.com PurchasingJob.com MaterialsJobs.com PhysicsJobs.com MetallurgyJobs.com WeldingJobs.com SellingJobs.com BrandingJobs.com EconJobs.com FirmJobs.com BancJobs.com MedicoJobs.com SupplyJobs.com ManufacturingJob.com TradesJobs.com JournalismJob.com FacultyJob.com ManagerJobs.com CSJobs.com PharmacyJob.com MathJob.com BuyingJobs.com IEJobs.com EEJob.com CustomerJobs.com EnggJobs.com SciencesJobs.com TempsJobs.com MechanicalJob.com AdministratorJob.com BrasilJob.com IndonesiaJob.com MotorCityJob.com IndiaJob.com RussianJob.com EuropaJobs.com BeijingJob.com Mailing List Subscribers (14,500) Job Ad Rate - $125 per ad for 120 days Pick upto 3 relevant sites Jobs Posting Info Here e-mail: sasthacom@comcast.net PhysicsJobs.com launched in December 2001 will be targeting Jobs for Physics Professionals. Also a physics jobs and career discussion board PhysicsChat.com was introduced for the benefit of jobseekers. The synergy with other science related niche job sites: ChemistryJobs.com, MaterialsJobs.com, MedicoJobs.com and WeldingJobs.com will help build a strong job site. The site will also target Astronomy, Optics and other physics related professionals. Site Map Site News Clients Site Domains Sci Tech Links HRM Links Employers Info Buying Supply Links Jobseekers Info PhysicsChat.com To Get Your Job Ad Listed STEP 1 Email us the Ad in Word Format or in the email message. Provide complete contact information and billing information. email to Sasthacom@comcast.net STEP 2 We will invoice you at your billing address or email you an invoice (if you prefer). Payment Terms are Net 30. Ad Rate is $125 per AD for 120 days listing. STEP 3 We will notify you as soon as the Job is posted (typically within12 hours). If you need to make any changes or edit the ad, just email us the information. For More Details Click Here Our Clients include: J. Walter Thompson Bernard Hodes Intel Carrier Arthur D. Little Kraft Wal-Mart Forest Labs SmithKline Beecham Alcatel Motoman Motorola Western Digital Honeywell GE Capital Polaris Copeland AllState Sastha.com, Inc. Information : Job Posting Info Jobseekers Contact Us About Us Help Privacy Copyright 1998-2005 Sastha.com, Inc., All Rights Reserved.
TIPTOP Jobs On-Line
Bulletin-board for posting, searching, and finding physics job openings.
TIPTOP - Dynamic job list for physicists TIPTOP Jobs On-Line Dynamic job list for physicists Welcome to TIPTOP Jobs On-Line! Announce job openings here, completely free of charge! To submit an entry, simply register and your announcement(s) will appear on the bulletin board immediately. As a registered user, you'll be able to edit or delete your entry at your convenience. These lists are accurate and up-to-date. Old announcements will be removed automatically a week after the application deadline -- the extra time is there since in some cases late applications may be accepted. Job opportunities Open positions [ 74 entries ] Postdoc openings [ 113 entries ] PhD studentships [ 75 entries ] Summer jobs [ 2 entries ] Jobs wanted Jobs wanted [ 88 entries ] see also Physics Jobs List an announcement (job posting or wanted ad) Current deadlines and today's announcements Automated e-mail notification Receive weekly emails about new jobs and deadlines! [ Jobs Index | Register | Find member | Physics Jobs | PhysicsWeb ] The Internet Pilot TO Physics Copyright 1994-2005 IOP Publishing Ltd. All Rights Reserved. 23180319 page accesses since Feb. 25 1996. Last from 141.108.19.118. This site has been validated against the XHTML 1.1 DTD. All style sheets on this site validate as CSS 1. If you can see this message, your browser may not support Web standards .
Jobs in Physics, Astronomy and Other Fields
Links to career planning and job hunting information as well as to listings of available positions.
Jobs in Physics, Astronomy, and Other Fields Sonoma State University Department of Physics and Astronomy Jobs in Physics, Astronomy, and Other Fields Full-time employment opportunities in physics astronomy computers many fields . Part-time, temporary, and summer jobs for students . See also Steps Toward Grad School . Career planning aids Salaries of Scientists by Discipline Careers in Science and Engineering: A Student Planning Guide to Grad School and Beyond from the National Academy of Sciences. Careers Using Physics from the Society of Physics Students. Physical Sciences Career Exploration Links information on employment and grad schools in several sciences. Put Your Science to Work: The Take-Charge Career Guide for Scientists information about a book you can buyprimarily for Ph.D.'s. A Career in Acoustics? Careers in Aquatic Sciences How to Become an Astronaut Careers in Astronomy Frequently Asked Questions About Being an Astronomer A Guide Book to Astronomy what it's like being an astronomer, by Sten Odenwald. Opportunities and Resources for Research and Activism in Energy and Environmental Science Policy by Daniel Kammen. Careers in the Geosciences Careers in Oceanography Science, Math, and Engineering Career Resources information for scientists and would-be scientists at all levels, from high school students through Nobel laureates. Starting a job hunt ResumeTutor advice from the University of Minnesota. AIP Rsum Posting Service Its free to all physicists. The Job Hunters Bible: What Color Is Your Parachute a supplement to the famous book by Dick Bolles. Landing Your First Job: A Guide for Physics Students how to order a book published in 2002 by the American Institute of Physics. Whos Hiring Physics Bachelors a state-by-state listing of employers who recently hired new physics graduates to fill technical and professional positions, provided by the AIP. Jobs in physics and other fields Jobs posted at the American Institute of Physics . Jobs for Physicists and Engineers at all levels, from PhysLINK.com. Science Job Market jobs at all levels of teaching in the physical sciences, presented by the American Association of Physics Teachers. TIPTOP Jobs On-Line dynamic job list for physicists. PhysicsWeb mostly in Europe and mostly for Ph.D.'s. Job opportunities list at CERN mostly in Europe and mostly for physicists from CERN member countries. Job Openings advertised in the Chronicle of Higher Education mostly faculty positions. National Research Council Research Associateship Program postdoctoral positions at federal labs, including NASA and military labs, but excluding DOE labs. Jobs at the FOM Institute for Atomic and Molecular Physics in the Netherlands, for graduate students, postdocs, and Ph.D.'s. Physics and Hi-Tech positions in Israel Institute of Electrical and Electronics Engineers Employment Services job listings and more. Jobs in Accelerator Physics and Technology for Ph.D.'s. Jobs in Acoustics Jobs in Atomic and Plasma Physics mostly for Ph.D.'s. Jobs in Aviation and Aerospace from NationJob Network Jobs in Computational Fluid Dynamics Jobs in Crystallography posted by the American Crystallographic Association. Jobs in Engineering EngineeringJobs.com: A National Index of Engineering Jobs. Jobs in Engineering and Manufacturing from NationJob Network, includes programming jobs. Jobs in Environmental Engineering, Education, Advocacy, etc. Listings sent for a fee; samples online. Jobs in Environmental Fields from ejobs.org Jobs in GeoScience Jobs in High-Energy Physics Jobs in History of Science Jobs in Limnology and Oceanography Jobs in Materials Science includes metallurgy, polymers, ceramics. Jobs in Metallurgy mostly for Ph.D.'s. Jobs in Meteorology from the American Meteorological Society Jobs in Oil, Mining, Geoscience, Environmental, Agriculture, Forestry, Ecology, Meteorology, Oceanography, Hydrology, Soil, GIS and Related Subjects Jobs in Optics Optical Society of America Jobs in Optics optics.org Jobs in Optics SPIE Jobs in Science Technology Centers and Museums BrassRing jobs in technology. Data Processing Independent Consultant's Exchange (DICE) offers job listings and the opportunity to have your availability annnounced to 1000 companies. Mostly computer-related, but try searching on "physics" or whatever your field is. North Bay Technology Roundtable jobs with high tech companies in Sonoma and neighboring counties. SonomaCountyHelpWanted.com jobs in all fields. Jobs at Tellabs (formerly Advanced Fibre Communications) a telecommunications company in Petaluma, CA. Jobs at Advanced Micro Devices Jobs at Agilent One of Sonoma County's largest private employers, Agilent has employed several SSU Physics graduates . Jobs at Alcatel USA the telecommunications giant includes the former DSC, in Petaluma, CA. Jobs at Applied Physics Laboratory Large Baltimore employer. Jobs at Boeing Jobs at Compumotor a leader in the motion control industry, in Rohnert Park, CA. Jobs at GE Energy Jobs at Hewlett Packard . Jobs at ILX Lightwave Corp fiber optics and laser measurement in MT and CO. Jobs at Lockheed Martin Jobs at Medtronic includes Arterial Vascular Engineering, a large employer in Santa Rosa, CA. Jobs at Micro-Vu a manufacturer of precision optical measuring systems in Windsor, CA. Jobs at JDS Uniphase (includes the former Optical Coating Laboratory, Inc.) the largest employer of SSU physics grads . Jobs at the Office of Naval Research Jobs at Raytheon Information Technology and Scientific Services Jobs at Science and Technology Corp. Jobs at Science Applications International Corporation Jobs at SOLA Optical large maker of eyeglass lenses in Petaluma, CA and elsewhere. Jobs at Newport, including Spectra-Physics Lasers Photonics Jobs at SpectraSwitch a telecommunications company in Santa Rosa, CA. Jobs at Telcordia Technologies formerly Bellcore, this company provides software to the telecommunications industry. Jobs at Xerox Jobs at Brookhaven National Lab Jobs at Fermilab Jobs at Thomas Jefferson National Lab formerly CEBAF. Jobs at Lawrence Berkeley National Lab Jobs at Lawrence Livermore National Lab Jobs at Los Alamos National Lab Jobs at Sandia National Labs Jobs at the Stanford Linear Accelerator Center Jobs at the University Corporation for Atmospheric Research Jobs in astronomy and other fields American Astronomical Society Jobs Register the best list, updated monthly. Space Jobs mostly in the aerospace industry. Jobs at the Infrared Processing and Analysis Center (IPAC) in Pasadena Jobs at the European Southern Observatory Jobs at the W.M. Keck Observatory mostly engineering jobs. Jobs at NASA Jobs at the National Optical Astronomy Observatories Jobs at the National Radio Astronomy Observatory Jobs at the Smithsonian Astrophysical Observatory Jobs at the Space Telescope Science Institute Jobs at the Steward Observatory Jobs at the U.S. Naval Observatory Jobs in computers and other fields Bay Area Careers mostly computer-related. The Best Jobs In The USA Today mostly, but not all, computer-related. Job Search for Engineers Jobs at Apple Jobs at Autodesk Jobs at Cisco Jobs at IBM Jobs at Intel Jobs at Microsoft Jobs at the San Diego Supercomputer Center Jobs at Silicon Graphics, Inc. Jobs at Sun Microsystems Jobs at 3Com Jobs in many fields Academic Careers Online global academic job site to search jobs in education and academia. AllStarJobs.com includes links to many other sites. America's Job Bank about 100,000 jobs from 2000 state employment offices. Careerbuilder.com search jobs from more than 70 career sites. Careerjet an employment search engine for the USA, many listings. Careersite lots of listings in a variety of fields. College Grad Job Hunter mostly entry-level, includes several large, high-tech employers. Craig's List posted by Craig Newmark, includes sites for many cities in the U.S. and abroad. Employment Opportunities and Job Resources on the Internet The Riley guide The Entry Level Job Seeker Assistant Internet Career Connection mostly, but not all, computer-related. Jammin Jobs a national job board that lists thousands of open positions. Job Hunt extensive site with many resources. Jobs.net extensive site with many resources. JobStar California California job search guide by Bay Area public libraries. Job Web from the National Association of Colleges and Employers. Monster.com 150,000 job listings, a forum for jobseekers, and more. MonsterTRAK SSU participates in this program, so students may register and get additional help if they wish. Nation Job Network access to a huge database of jobs. NationJobSearch.com offers a wealth of industry and geography specific job search and career development resources Opportunity NOCs jobs with nonprofit organizations throughout the United States. Sonoma County Job Link SSU Career Services for SSU students and alumni. Teach for America the national teacher corps of outstanding recent college graduates. True Careers 125,000 job listings; post your rsum and get advice. U.S. Government Jobs EXCITE Careers Yahoo Jobs jobs, employment services, career planning, salaries, etc. Job Opportunity ads in the Chicago Tribune Job Opportunity ads in the Los Angeles Times Job Opportunity ads in the New York Times Job Opportunity ads in the San Francisco Chronicle Job Opportunity ads in the Santa Rosa Press Democrat Jobs at Sonoma State University Jobs at Stanford University Jobs at UC Berkeley Jobs at UC Davis Jobs in California Community Colleges 109 public community colleges. Jobs in the California State University system 23 universities. Jobs in the University of California System 10 campuses, 3 national labs, and the president's office. Northern California's Bay Area Higher Education Recruitment Consortium teaching and administrative jobs in 16 four-year colleges and universities and 10 community college districts. Part-time, temporary, and summer jobs for students Undergraduate Research Opportunities Do research and get paid for it. Summer Jobs on the Web part of JobStar California . Summer Jobs all types, worldwide. Seasonal Employment in national parks,resorts, etc. from Cool Works. Environmental Careers Organization free information on internships. Student Employment with NASA Student Jobs at Lawrence Livermore National Lab Summer jobs for students at the Stanford Linear Accelerator Laboratory SSU Career Services for SSU students and alumni. Net-Temps temporary and contract jobs in engineering and other fields, plus some permanent ones, free to jobseekers. Please send comments, additions, corrections, and questions to joe.tenn@sonoma.edu JST 2005-10-11
Semetrol
Producer of semiconductor characterization and analysis systems.
SEMETROL Home SEMETROL - Semiconductor Metrology Solutions New standards in resolution and sensitivity for characterization. SEMETROL Home DLTS Method DLTS Example Results Company Profile People - Contact SEMETROL Home DLTS Method DLTS Example Results Company Profile People - Contact Semiconductor Characterization and Analysis Products: Deep Level Transient Spectroscopy (DLTS) Current-Voltage-Temperature (I-V-T) Capacitance-Voltage (C-V) Thermal Admittance Spectroscopy (TAS) Photocapacitance (PC) Also: Customized systems Characterization and analysis services The SEMETROL Deep Level Transient Spectroscopy (DLTS) system is a result of several iterations in various hardware and software configurations, providing you with the best solution. The founder has over 20 years of experience with semiconductor characterization and analysis in both DoD and University laboratory environments, and has published extensively on characterization of materials such as GaAs, InGaAs, GaSb, AlGaSb, GaN, AlGaN, ZnO and SiC. The benefits of SEMETROL's DLTS system are shown at the right. Other characterization products are also available, such as Current-Voltage-Temperature (IVT), Capacitance-Voltage (CV), Thermal Admittance Spectroscopy (TAS), Photocapacitance (PC), as well as variations of DLTS (CC-DLTS, DDLTS for field dependence and spatial profiling). Each can be tailored to your particular requirements, including customized user interface and specialized analysis. High sensitivity: Detect defect concentrations five orders of magnitude lower than the shallow carrier concentration. User controlled sensitivity - average thousands of transients together. Accurate: With SEMETROL's DLTS system, Arrhenius plots are typically over more than three decades on e T^2 versus 1 kT plot - determined by number of points collected, and noise level. Efficient: Typically takes ~1 2 day from start to finish. Data collection is automated, freeing you for other activity. User Control: You set the data collection conditions. Interactive analysis. Graphical view of how well the transients are fit, as well as numerical figures of merit. Convenient: All data and analysis can be saved in a form useful for publication, or comparison to other data. Similar benefits implemented in other characterization systems available from SEMETROL. Current products: Deep Level Transient Spectroscopy Capacitance-Voltage Thermal Admittance Spectroscopy Current-Voltage-Temperature Photocapacitance Products to be developed in the next few months: Temperature Dependent Hall Photoluminescence Fourier Transform Infrared Spectroscopy User interface for DLTS data collection. User interface for Thermal Admittance Spectroscopy program. Systems can be customized by contacting Dan Johnstone to discuss your requirements and specifications: 804 590-0120, characterize@semetrol.com.
easyLab
Manufacturer of hydrostatic high-pressure cell modules for characterizing materials over a range of temperatures and applied magnetic fields.
easylab.co.uk The website for easylab.co.uk can be found by clicking here . easylab.co.uk is registered through Easily.co.uk - get web site hosting or domain name registration here
Labkron Instruments
Distributor of laboratory equipment and instruments.
::LABKRON Instruments:: Products Services We take utmost care in assembling each microscope ,which is then thoroughly inspected and tested at our manufacturing facilities. more... Click for Details Company Profile Manufacturers and exporters of Microscopes, Pathological Microscopes, Binocular Microscopes, Laboratory Glassware, Magnetic Stirrer. Click for Details Contact Info ::Quickies Home About Products Contact Query :: Featured Products Here are some best examples of our brilliant workmanship in Microscopes More . . . :: Your Query Name Email Query
Besocke Delta Phi GmbH
Manufacturer of instruments used in research and development in physics, chemistry, engineering and biology. Main products include Kelvin Probes, STM, AFM, Choppers and Gas sensors.
Besocke Delta-PHI
DCA Instruments
Manufacturer of UHV thin film deposition systems and components. The products include Molecular Beam Epitaxy (MBE) and Physical Vapor Deposition (PVD) equipment.
DCA Instruments :: Specialists in UHV and MBE thin film systems and components DCA News Recent news New UHV sputtering system January 2005 NTHU reports on high quality InN on Si August 2004 New Phosphorus Valved Cracker August 2004 First Scientific Advisory Board meeting held June 2004 More news 1989 - 2005 DCA Instruments Web design and hosting by Beetlebrow HOME PRODUCTS SLIDE SHOW SITE MAP ABOUT DCA NEWS CONTACT Molecular Beam Epitaxy UHV Magnetron Sputtering Pulsed Laser Deposition Effusion Cells and Valved Crackers
Danfysik
Since 1964 Danfysik have through development of products and technical expertise established the company's reputation as a supplier of high quality equipment for particle accelerator laboratories.
Welcome to Danfysik Latest news: May 2005 New transducer joins the 867 family... May 2005 Preparation for the 4th Generation Light Source ... 02.10.2004 Siemens and Danfysik collaborate in the area of particle therapy... DANFYSIK A S,Mollehaven 31,DK-4040 Jyllinge,Denmark. Phone: + 45 46 79 00 00,Fax: + 45 46 79 00 01. E-mail: sales@danfysik.dk - Copyright Danfysik A S 2004 - All rights reserved - Legal Disclaimer - Site overview
National Imports - Adhesive Products Division
Distributor and retailer of engineering and industrial adhesives; specializing in epoxy, acrylic, urethane, cyanoacrylate, and aerosol adhesives.
National Imports - Epoxy Adhesives 3M Scotch-Weld Adhesives - 3M Epoxy Adhesives - 3M Urethane Adhesives - 3M Acrylic Adhesives - 3M Instant Adhesives - 3M Aerosol Adhesives - 3M Primers - Applicator Systems - Bulk Orders Product Selection Guide - EpoxyAdhesives - UrethaneAdhesives - AcrylicAdhesives - AerosolAdhesives - InstantAdhesives - ProductDataSheets - MSDS Other Products - MAGCRAFT Permanent Magnets (Off-Site Link) National Imports LLC - Adhesive Products Division National Imports is a distributor of3M adhesives and MAGCRAFT permanent magnets. We carry an extensive line of 3M adhesives available for immediate delivery. Backed with more than 50 years of industrial adhesives experience, 3M provides one of the broadest lines of adhesives designed to meet almost any requirement. 3M adhesives will help you make your product lighter, longer lasting, stronger, less costly, better looking, and easier to manufacture. Meeting All of Your Adhesive Requirements In addition to providing an extensive line of adhesives, we also provide: A complete product selection guide Resources for understanding our adhesive products Downloadable product data sheets Downloadable Material Safety Data Sheets (MSDS). All of our stock products carry a complete money back guarantee. Just return your purchase to us within thirty days in original condition and we will refund your money including our regular ground shipping charges.We are committed to providing our customers the best service and personal attention on every order. 2005 - National Imports, LLC. All Rights Reserved.
FEMTO Messtechnik GmbH
Manufacturer of low-noise signal amplifiers, lock-in amplifier modules and photoreceivers for use in scientific applications.
FEMTO - Sophisticated Tools for Signal Recovery - Manufacturer of lock-in amplifiers, current amplifiers, transimpedance amplifiers , voltage amplifiers, photoreceivers, amplified photodiodes, low-noise amplifiers, logarithmic amplifiers, photodetectors.
Ansaldo Superconduttori
Manufacturer of conventional and superconductive magnets for research in high energy physics and thermonuclear fusion.
Ansaldo Superconduttori
SMI Lab Ltd.
Developer and manufacturer of photonic single crystalline materials and instruments.
Home Dear Ladies and Gentlemen's! Welcome to our Semiconductor Materials Instruments Laboratory home page! We are scientific research, developmentand manufacturing company. We develop, research, manufacture and sell A2B6, A3B5 photonic single crystalline materials and instruments, based on these materials. All our products: substrates ((111), (211), (001) orientations), plates, blanks, lenses, radiation detectors, IR-detectors, pixels arrays (for IR-, X- Y-rays sensitivity), based on CdZnTe, CdTe, HgCdTe, ZnSe, GaAs, InAs and others semiconductor compounds are ready for qualitative, low-cost imaging and others applications. Also we can offer new crystals for telecommunication and acousto optic, AgGaGeSe, Cs2HgCl4, Cs2HgBr4, Tl3PbCl5. If You desire, we can to develop for you new materials or instruments with specific properties. If You desire to have the modern growing technique (Low Pressure Modified Vertical Hybrid Bridgman Method, High Pressure Vertical Bridgman Method), technique for super high purification of Cd, Te, Zn, Hg ( 99.9999% purity) - we shell to develop and fabricate it for you. If You have others offers for us, we are ready to consider them. Our services and prices will be interesting for you. Visit to our Products pagefor viewing of our main products. Visit to our Contacts page, for contacting by us. |Home| | Products | | Services | | Contacts | Copyright 1999. Positive Software Corporation. All rights reserved Copyright 2004. SMI Lab Ltd. All rights reserved
S-DH GmbH
Developer of super-mirrors, neutron guide systems (ballistic, funnel) and several mechanical and optical devices like ELREBO (ElementReplacingBox).
S-DH GmbH Welcome to S-DH ! We manufacture and install neutron guides and supermirrors, continually improving our benchmark PRODUCTS to raise the international standard again and again. Permanent research and innovation goes toward ensuring the QUALITY of our products and maximising the benefit of our customers. This drive is what helps us remain UNIQUE in more than one way. Thank you for your interest in learning ABOUT S-DH , and if these pages inspire you to CONTACT us, please don't hesitate to ask for any further information or assistance. Kindly, Harald P. Haese and Andreas Knoepfler CEO
WITec GmbH
Manufacturer of equipment for scientific and industrial applications focused on new solutions for Optical and Scanning Probe Microscopy.
Please click to visit http: www.witec.de's web site. http: www.witec.de
Corporation Scientifique Claisse
Provides analytical fusion services, instrumentation and fine chemistry science services.
Claisse : Development of Analytical Fusion Techniques, Instrumentation and Fine Chemistry Science Acerca de Claisse Detecting Macromedia Flash 5 plug-in, please wait...
Surface Concept Oelsner Schnhense Ziethen GbR
Provides products and services for electron detection, electron optics and ultra-high vacuum compatible sensors for surface analysis.
Surface Concept Surface Concept offers products and services around electron detection, electron optics and ultra-high vacuum compatible sensors for surface analysis. High- speed delayline area detector for electrons, ions, X-rays Miniaturized electron optics Ultra- high vacuum sample manipulation Fast electronics devices Technology service Roadmap Delayline This site gives you an overview of our product range. You are welcome to contact us for discussing your application. News: Surface Concept is now Surface Concept GmbH Customer service Technical support Administrative support Surface Concept founders won Innovation Award 2004 BESSY New USB 2.0 electronics for all delayline detectors now available Board of management Dr. Andreas Oelsner 0049 (0)6131 392 3632 X -ray delayline detector successfully commissioned Unified Messaging 0049 (0)721 151468621 (answerphone+fax) Ultra -high vacuum sample manipulators n-hands joins roadmap consortium Adress SURFACE CONCEPT GmbH Staudingerweg 7, D-55128 Mainz, Germany Surface Concept presents interchangeable Delayline Detector for Electron Microscopes How to find us SPECS presents the Surface Concept Delayline Detector for PHOIBOS analyser Surface Concept + 10 Jahre Stiftung Innovation Rheinland Pfalz Thank you for visiting Surface Concept!
Vacuum Controllers, From Hastings Instruments
Hastings Instruments manufactures a complete line of Vacuum Instruments including Vacuum Controllers, for the precise measurement and control of vacuum and gas flows.
Vacuum Controllers, From Hastings Instruments Vacuum Controllers From Hastings Instruments Teledyne Hastings Instruments manufactures a complete line of Vacuum Instruments such as the Model 2002 OBE-2002 Vacuum Controllers, who's electronics module is available with Dual Analog, RS 232, RS 485-Half and Full Duplex, Dual 4-20 ma and DeviceNet output options. With more than 55 years of practical experience in vacuum technology, Hastings Instruments maintains a full line of quality digital and analog vacuum instruments and vacuum controllers to satisfy stringent requirements of every market within the vacuum industry such as the 760 Plus (Model HPM-760) Vacuum Controller. The 760 Plus is an exceptionally stable, accurate, repeatable absolute pressure gauge. The heart of this vacuum controller is the HPM-760S module, a stainless steel measurement volume attached to a small and rugged piezo-resistive transducer on a silicon chip. The most versatile vacuum instrument in the Teledyne Hastings product line is the Model 2002(r) Dual Vacuum Sensor. This device measures above atmospheric pressure to 10-4 Torr pressure using a small, dual sensor. The OBE is an economical OEM version of the successful Model 2002. Additional vacuum instruments offered by Teledyne Hastings Instruments include absolute pressure sensors which are independent of gas composition Teledyne Hastings products are used in government, industrial and academic RD labs throughout the world. Over the years, the Model VT and CVT instruments, together with the reliability of the rugged TC gauge tubes technology, have proven themselves as the standard in the industry by OEM and other equipment suppliers. For details please visit our Web Site and also view our Product Review Back To The Hastings Instruments Home Page (c) Copyright 2000 Teledyne Hastings Instruments
Teledyne Hastings Instruments
Manufacturer of vacuum and flow instruments for the measurement and control of vacuum and gas flows.
Teledyne Hastings Instruments Mass Flow and Vacuum Control Products Teledyne Hastings Instruments manufactures a complete line of Vacuum Instruments and Flow Instruments for the precise measurement and control of vacuum and gas flows. Hastings Instruments operates within the Teledyne Instruments Group, a group of specialty instrumentation companies providing innovative measurement devices to monitor critical manufacturing processes, improve productivity, facilitate energy exploration and protect the environment. Hastings Instruments News Press Releases Customer Service Visiting our Facility Contact Us Trade Shows World Wide Sales Product Introduction Product Review Application Notes Technical Papers Mass Flow Products Vacuum Products Information Request Product Manuals Product Bulletins Product Support Flow Service Plan Work With Us Submit Your Resume Of Sale Of Purchase Archive Teledyne Hastings Instruments Hastings Instruments has grown into one of the leading Vacuum Products and Thermal Mass Flow companies in America. Flow Instruments The current Models HFM Mass Flow Meters and HFC Mass Flow Controllers represent the culmination of more than 55 years experience in manufacturing quality Mass Flow Instruments. Vacuum Instruments Over the years, the Model VT and CVT instruments have proven themselves as the standard in the industry by OEM and other suppliers. One of the most versatile Hastings Vacuum Products is the Model 2002 Dual Vacuum Sensor. All Hastings Vacuum Instruments use precision sensing devices to provide maximum accuracy. European Union Regulatory Compliance Documentation Home | Terms of Use | Jobs | Maps | Contact Us Teledyne Technologies Incorporated 12333 West Olympic Boulevard - Los Angeles, CA 90064 Copyright 1999-2004 All rights reserved.
Kistler Instrument Corporation Kistler Instrumente AG
Design and manufacture of piezoelectric, piezoresistive and variable capacitance based sensors and signal electronics for measuring pressure, force, acceleration and strain . Der weltweit ttige Anbietern von Messtechnik und Sensoren auf Basis des piezoelektrischen Effekts fr Druck, Kraft und Beschleunigung. [CH-8408 Winterthur]
Kistler - measure. analyze. innovate. Kistler International Kistler Activities Products Services Choose your country: Europe France Germany Italy Switzerland United Kingdom more... Austria Belarus Belgium Bosnia and Herzegovina Bulgaria Croatia Czech Republic Denmark Finland Greece Hungary Iceland Ireland Liechtenstein Luxembourg Macedonia Netherlands Norway Poland Portugal Romania Russian Federation Slovakia Slovenia Spain Sweden Turkey Ukraine Yugoslavia Country not listed... Americas USA more... Argentine Brazil Canada Mexico Venezuela Country not listed... Asia China Japan Korea Singapore more... India Indonesia Iran Israel Kazakhstan Malaysia Philipines Taiwan Thailand Viet Nam Country not listed... Other Rest of the world Australia Botswana Lesotho Namibia New Zealand South Africa Swaziland Zimbabwe Country not listed... Welcome to the World of Measurement Technology Kistler is one of the world's leading suppliers of sensors and sensor electronics for measuringpressure, forceand acceleration. Kistler products are used in countless applications in research, development and production. A well developed international sales network with 18 Kistler Group Companies and more than 30 distributors enables us to provide our customers individual on-the-spot advice. Kistler's success is based on innovative technologies, a solid understanding of the market and a comprehensive range of services. Robust Piezoelectric measurement technology offers uncompromisingly robust high-resolution sensors. Print | Disclaimer | Webmaster | e-Contact | +41 52 224 11 11
Oxford Plasma Sources
Manufacturer of plasma sources of all types including RF (13.56MHz)and microwave (2.45GHz) in a range of sizes. Applications include MBE, surface science and thin film deposition.
plasma source plasma source Manufacturers and Designers of Scientific Instruments for the HV, UHV, MBE and Surface Science Communities Products Contact Us News Oxford Scientific Location Links Home Plasma Source - Ion Source, Atom Source, Hybrid Source Plasma sources from Oxford Scientific are examples of the classic microwave ECR plasma source and can be configured as broad beam ion sources, atom sources, hybrid or downstream plasma sources. Plasma sources on this page can be used to replace RF ion sources, RF atom sources or indeed Kaufmann ion sources. The Oxford Scientific Plasma source (OSPrey) is a truly UHV compatible source. Fully bakeable, with an all-welded stainless steel vacuum envelope, and outstanding cooling from a full length water-jacket, it is suitable for use in vacuum levels ranging from HV to those found in the most demanding MBE applications. Through the action of the well-known electron cyclotron resonance (ECR) phenomenon, a high density plasma is created by coupling a radially symmetric 2.45GHz microwave field to ions on the 86mT surface of a multi-polar magnetic array. A unique combination of features and options make this an extraordinarily versatile plasma source. User-configurable Oxford Scientific plasma sources can be user-configured to operate in one of several distinct modes. The basic unit common to all the operating modes is the plasma generator. By exchanging the beam optics, the energy, density and species emerging from the source can be tailored to suit a particular application. Energy and beam size The complete range of particle energies from neutral thermal atoms to 1500eV ions can be covered with a single source. Beam diameters from a 1mm to 2.5cm with useful beam sizes at the sample up to 10cm in diameter (standard 4" (NW63CF) flange source). Ask about sources with larger diameter beams and coverage. Operating Modes Atom source, hybrid, broad beam ion, and downstream plasma modes can all be achieved with a simple in-situ exchange of the one-piece beam optics. All optics and associated feedthroughs and power supplies may be retrofitted by the user as research needs change and at any future date. Customisation The range of options including custom grid designs and optimised differential pumping units, mean that most operating chamber pressures, sample sizes and working distances can be accommodated. Working pressures from 1x10-8 mbar to 10-1 mbar are obtainable, for applications from sub-monolayer second surface science studies to rapid bulk material growth. Features Filamentless design The absence of a hot filament to create the plasma, permits operation with most gases including reactive gases such as oxygen, chlorine, nitrogen and hydrogen. No microwave tuning required Simply turn the plasma on and off. Unique integrated shutter and current monitor option Allows beam density and residual current measurements to be made while the beam is shut off. Trivial bakeout preparation ~1minute Remove only the microwave generator and cables (no water-jacket disassembly). Built in microwave generator tuner Eliminates the need for waveguide installation. The sophisticated microwave tuner allows tuning to be optimised for each mode for maximum performance. Specifications Plasma Generator Microwave Frequency: 2.45GHz Microwave Power: 10 - 250W Magnetic Confinement: Permanent Magnets. Bakeable Mechanical Gases: Argon, Nitrogen, Chlorine, Hydrogen, Oxygen and most other gases with gaseous cracking products. Mounting Flange: 4" (NW63CF) In-vacuum length: 300mm (Standard. Other lengths on request) In-vacuum diameter: 57mm (at widest point) Suitable for all standard makes of 4" port. Cooling: Fully water cooled. Bakeout: Bakeable to 200C. Simple bakeout preparation. Plasma Chamber: Boron Nitride or alumina according to process gas. Ion Beam Mode Beam Diameter: 1mm - 25mm (at source) Beam Divergence: ~15 half-angle typical (Dependant on ion energy. Please ask for more details) Ion Energy: 25 - 1500eV (Ion beam mode) Total Beam Current: 20mA max. Ion Current Density: 2mA cm2 (Ion beam mode, focused optics) Gas Consumption: 10sccm - 100sccm typical (Lower flows possible. Please ask for more details) Grids: High transparency dual or triple molybdenum or graphite grids for broad beam ion mode. Huge range of other grids available (Please call to discuss your requirements) Chamber Working Pressure: 1x10-8 mbar to 1x10-1mbar (Depending on grids, pumps and process gas) Working Distance: 50mm - 300mm (150mm typical) Atom Source Downstream Modes Atom flux: 1x1016 atoms cm2 second at 10cm working distance (Atom source mode) Beam divergence: ~15 half-angle typical Aperture: Boron Nitride or alumina according to process gas. Beam diameter: 1mm - 25mm at source (To be specified) Chamber working-pressure: 1x10-8 mbar to 1x10-1mbar (Depending on grids, pumps, differential pumping and process gas) Working distance: 50mm - 300mm (150mm typical) Hybrid Atom flux: 1x1016 atoms cm2 second (Atom source mode) Ion Energy: 25 - 1500eV Total beam current: 50A max Aperture: Boron Nitride or alumina according to process gas Beam diameter: 1mm - 25mm at source (To be specified) Beam divergence ~15half-angle typical (Dependant on ion energy. Please ask for more details) Chamber working-pressure: 1x10-8 mbar to 1x10-1mbar (Depending on grids, pumps and process gas) Working distance: 50mm - 300mm (150mm typical) Power Supplies Microwave: 19" rack mount. 3U height. 230VAC, 50Hz (115V, 60Hz optional) Grid: 19" rack mount. 3U height. 230VAC, 50Hz (115V, 60Hz optional) Operating Modes The source can be operated in four distinct modes, according principally to the extraction optics fitted and covering a wide range of ion energies and particle types. Atom source: SUMMARY: Thermal energy neutrals. This mode is intended principally for low energy and low damage surface treatment and sample growth. A specially designed aperture inhibits the release of ions from the plasma while allowing neutral atoms and molecules to effuse out. The particles released are largely thermalised ( 1eV) by multiple collisions in the exit capillaries and are therefore suitable for use in sensitive semiconductor growth, cleaning and surface treatment applications. An residual ion current can be removed using the ion trap option where this may be of concern. Downstream plasma ECR mode SUMMARY: Low energy ions and neutrals. This mode reproduces classic ECR source characteristics. The optics here allow ions and higher energy plasma particles (~25eV) characterised by the plasma sheath potential to flood out into the chamber. The sample is typically placed some centimetres in front of the source and although more directly exposed to the plasma than in the atom mode above, it is "downstream" of the most energetic species in the ECR region. It is ideal for growth cleaning of tougher (higher bond energy) materials such as ceramic oxides where the increased kinetic energy of the particles, enhances the process dynamics without damage. Hybrid SUMMARY: Atom source ECR characteristics with controllable ions. This mode combines atom source and ion source behaviour to produce a source which behaves like the atom source at (1.) above until potentials are applied to the extraction grids when ions are then added to the beam. Because the ions are added by active extraction, their energy can also be controlled. This mode is ideal for applications where it is hoped that low damage reactive atoms will be adequate but higher kinetic energy ions are required as a back-up. It may also be used for adding a degree of anisotropy to the beam in, for example, in-situ etch processes. Broad Beam Ion source. SUMMARY: High density, large diameter ion beams. The use of high transparency dual and triple grid optics allows high current beams to be produced with energies ranging from 25eV to 1500eV and current densities up to 2mA cm2. The highest current and energy beam produced using the dual grid is therefore ideal for sputter deposition work, especially where reactive gas ions are required because of the filamentless construction. For ion assisted deposition, the triple grid on the other hand, allows currents in excess of 50A cm2 to be achieved even at ion energies below 100eV. Options Hardware 1 Shutter: Integrated into the source mounting flange, including rotary drive and shutter blade 2 Faraday cup: Built into the shutter. Allows beam and residual current measurements to be made while the beam is shut off. Requires the shutter option above. (An ammeter is required with nA or A range depending on application) 3 Plasma Igniter: A miniature electron gun integrated into the plasma source facilitates plasma ignition at lower pressures. 4 Differential pumping: Includes a chamber with 4 inch (NW63CF) pump port and aperture (or quartz beam tube, to be specified with order). Pump not included. 5 Immersed filament beam neutralisation: Including filament and power supply. For use with Ion Beam Mode. 6 Ion trap: Removes the residual ion current from the beam when the source is being used in atom source mode. 7 Custom source length: The length of the source can be ordered in the range of 100mm - 500mm. 8 Gasline adapter: Adapter from NW16CF to 1 4" Swagelok Grids and Apertures - Aperture plates are required for atom source modes. - Boron Nitride is used principally for nitrogen and hydrogen and alumina for oxygen - Dual grid sets are optimised for high energy ion extraction (1keV - 2keV) - Triple grid sets are optimised for low energy ion extraction (50eV- 1keV) 9 Boron Nitride aperture for atom source mode. Number and size of holes to be specified when ordering. Please call to discuss your application 10 Alumina aperture for atom source mode. Number and size of holes to be specified when ordering. Please call to discuss your application. 11 Hybrid grid set. For hybrid mode. Number and size of holes to be specified when ordering. Please call to discuss your application. 12 Dual grids: Molybdenum: Specify Plane, Focusing, or Divergent 13 Dual grids: Pyrolytic graphite: Specify Plane, Focusing, or Divergent 14 Triple grids: Molybdenum: Specify Plane, Focusing, or Divergent 15 Triple grids: Pyrolytic graphite: Specify Plane, Focusing, or Divergent Applications Gas Application Source Configuration Argon Ion Beam Deposition Ion Source - high energy optics Ion Beam Assisted Deposition (IBAD) Ion source - low energy optics Oxygen Oxide growth: HTc superconductors, optical coatings, dielectrics, Atom source - high flux aperture Reactive sputtering, laser ablation Downstream plasma source Ceramic growth, Al2O3 Atom source downstream plasma Oxygen cleaning Downstream plasma Oxidation kinetics Atom source with differential pumping Post growth oxidation low temperature: SiO2 Atom source downstream plasma Nitrogen Nitriding: GaN, AlN, InN, SiN Atom source - high flux aperture Doping: ZnSe Atom source - low flux apertures Alloying: GaAlAsN Atom source Hydrogen Cleaning Ion source hybrid source Atom source Growth enhancement surfactant Atom source Chlorine In-situ etching Ion source - low energy grid set Hybrid source Methane (carbon) SiC Downstream plasma Atom source "Instruments for Innovators" For more information or a quotation contact: Dr Christian Bradley Oxford Scientific Ltd Culham Innovation Centre D5 Culham Science Centre Abingdon Oxfordshire OX14 3DB U.K. Tel: +44 1865 408372 Fax: +44 1865 408301 email: info@oxsci.com Products | Contact Us | News | Oxford Scientific | Location | Links | Home 2002 Oxford Scientific Limited | Legal
Major Science Equipment Manufacturers
Directory of fax numbers, toll-free phone numbers, addresses and URLs for science equipment companies.
Major Science Equipment Manufacturers Major Science Equipment Manufacturers Arbor Scientific- P.O. Box 2750, Ann Arbor, MI, 48106-2750, Phone 1-800-367-6695, Fax 1-734-913-6201, www.arborsci.com Carolina Biological Supply Co.- 2700 York Rd., Burlington, NC 27215-3398, Phone 1-800-334-5551, Fax 1-800-222-7112, www.carolina.com Cole-Parmer- 625 E. Bunker Court, Vernon Hills, IL, 60061-1844, Phone 1-800-431-8948, Fax 1-847-247-2929, www.coleparmer.com Daedalon Corporation- 35 Congress St., P.O. Box 2028, Salem, MA, 01970-6228, Phone 1-800-233-2490, Fax 1-978-745-3065, daedalon@cove.com , www.daedalon.com Delta Education- P.O. Box 3000, Nashua, NH, 03061-3000, Phone 1-800-442-5444, Fax 1-800-282-9560, www.delta-education.com Edmund Scientific Co., Industrial Optics Division- 101 E. Gloucester Pike, Barrington, NJ, 08007-1380, Phone 1-609-573-6250, Fax 1-609-573-6295, www.edmundoptics.com Edmund Scientific Co., Consumer Science Division- 101 E. Gloucester Pike, Barrington, NJ, 08007-1380, Phone 1-800-728-6999, Fax 1-609-547-3292, www.edsci.com Educational Innovations Inc.- 151 River Road, Cos Cob, CT, 06807, Phone 1-203-629-6049, Fax 1-203-629-2739, www.teachersource.com Exploratorium- 3601 Lyon St., San Francisco, CA, 94123, Phone 1-800-359-9899, Fax 1-415-561-0307, www.exploratorium.edu Fisher Science Education- 485 S. Frontage Road, Burr Ridge, IL, 60521, Phone 1-800-955-1177, Fax 1-800-955-0740, www.fisheredu.com Frey Scientific, Beckley Cardy Group- 100 Paragon Parkway, Mansfield, OH, 44903, Phone 1-888-222-1332, Fax 1-888-454-1417, www.beckleycardy.com (look for Frey Scientific) or direct to www.freyscientific.com Information Unlimited- P.O. Box 716, Amherst, NH, 03031-0716, Phone 1-800-221-1705, Fax 1-603-672-5406, www.amazing1.com Kelvin - 280 Adams Blvd., Farmingdale, NY 11735 USA, Phone 1-800-535-8469, Fax 1-800-756-1025, www.kelvin.com Klinger Educational Products Corp. (Leybold Didactic GMBH)- 112-19 14th Rd., College Point, NY, 11356, Phone 1-800-522-6252, Fax 1-718-321-7756, www.klingereducational.com Learning Technologies Inc. (Project Star)- 40 Cameron Ave., Somerville, MA, 02140, Phone 1-800-537-8703, Fax 1-617-628-8606, www.starlab.com Nada Scientific- P.O. Box 1336, Champlain, NY, 12919, Phone 1-800-799-6232, Fax 1-518-298-3063, www.nadasci.com Metric Test Equipment 3486 Investment Boulevard, Hayward, CA 94545 Phone 800-432-3424 510-264-0887, www.metrictest.com Oxford Instruments Inc., (Oxford Tennelec Nucleus) Nuclear Measurements Group- 601 Oak Ridge Turnpike, Oak Ridge, TN, 37830-2560, Phone 1-800-769-3673, Fax 1-423-483-5891, www.oxinst.com Pasco Scientific- 10101 Foothills Blvd., P.O. Box 619011, Roseville, CA, 95678-9011, Phone 1-800-772-8700, Fax 1-916-786-8905, www.pasco.com Sargent-Welch Cenco (VWR Scientific Products)- P.O. Box 5229, Buffalo Grove, IL, 60089-5229, Phone 1-800-727-4368, Fax 1-800-676-2540, www.sargentwelch.com Science Stuff - 1104 Newport Avenue, Austin TX 78753-4019, Phone 1-800-795-7315, (512) 837-6020 www.sciencestuff.com TeachSpin - 45 Penhurst Park, Buffalo, NY 14222, Phone 1-800-819-3056, (716) 885-4701. www.teachspin.com Tel-Atomic Inc.- P.O. Box 924, Jackson, MI, 49204-0924, Phone 1-800-622-2866, Fax 1-517-783-3213, telatomic@mindspring.com , www.telatomic.com Thorlabs Inc.- 435 Route 206, Newton, NJ, 07860, Phone (973) 300-3079, Fax (973) 300-3679, www.thorlabs.com Other Suppliers of Science Equipment and Supplies Daigger- 199 Carpenter Ave., Wheeling, IL,60090, Phone 1-800-621-7193, Fax 1-800-320-7200, www.bcafreedom.com Educational Control Products- 5725 Ostin Ave., Woodland Hills, CA, 91367, Phone 1-800-486-0840, Fax 1-818-703-0802, ECPSYS@aol.com , www.ecpsystems.com Electro-Technic Products, Inc.- 4642 N. Ravenswood Ave., Chicago, IL, 60640-4592, Phone 1-312-561-2349, Fax 1-312-561-3130, www.electrotechnicproduct.com Flinn Scientific, Inc.- Flinn Scientific, Inc., P.O. Box 219, Batavia, IL 60510, Phone (800) 452-1261, Fax: (866) 452-1436, http: www.flinnsci.com The Learning Company - 500 Redwood Boulevard, Novato, CA 94947, Phone 1-800-825-4420, Fax 1-415-382-4406, http: www.learningcompanyschool.com Litiholo - A division of Liti Holographics, 813 Diligence Dr. Suite 123, Newport News, Virginia 23606, Telephone: 757-873-6460, http: www.litiholo.com hologram_film.htm Litiholo Hologram Kit with Instant Film. Schoolmasters Science- 745 State Circle, P.O. Box 1941, Ann Arbor, MI, 48106, Phone 1-800-521-3832, Fax 1-313-761-8711, www.school-tech.com scicat.html Science First- 95 Botsford Place, Buffalo, NY, 14216, Phone 1-800-875-3214, Fax 1-716-874-9853, www.sciencefirst.com Team Labs- 6390B Gunpark Drive, Boulder, CO, 80301, Phone 1-800-775-4357, Fax 1-303-530-4071, www.teamlabs.com Vernier Software Technology - 13979 S.W. Millikan Way, Beaverton, OR, 97005-2886, Phone 1-503-277-2299, Fax 1-503-277-2440, www.vernier.com Wale Apparatus Co., Inc. - 400 Front Street, P.O. Box D, Hellertown, PA 18055 Phone: (610) 838-7047 or (800) 334-WALE Fax: (610) 838-7440, www.waleapparatus.com Hardware Suppliers Century Spring Corp.- 222 East 16th Street, Los Angeles, CA 90015, Phone 1-800-237-5225, Fax 213-749-3802, http: www.centuryspring.com home.htm McMaster-Carr- http: www.mcmaster.com Small Parts, Inc.- Miami Lakes, FL 33014-0659, Phone 1-305-557-8222, 1-800-423-9009, http: www.smallparts.com Thomas Register- http: www.thomasnet.com General Radio -- Parts and Service for General Radio Products. QuadTech Inc.- 45 Mail ST. Bolton, MA, 01740-1107, Phone 1-800-253-1230, Fax 1-508-779-3222, www.quadtech.com Surplus Catalogs All Electronics P.O.Box 567, Van Nuys, CA 91408-0567 Phone: 1-888-826-5432 www.allelectronics.com American Science and Surplus- 3605 Howard St., Skokie, IL, 60076, Phone 1-847-982-0870, Fax 1-800-934-0722, www.sciplus.com Antique Electronic Supply- 6221 S. Maple Ave., Tempe, AZ, 85283, Phone 1-480-820-5411 Fax 1-800-706-6789, www.tubesandmore.com Bid-Service LLC- PO Box 6729, 225 Willow Brook Rd, Freehold, NJ 07728-6729, Phone 1-732-863-9500, Fax 1-732-836-1255, www.bidservice.com Edlie Electronics- 2700 Hempstead Turnpike, Levittown, L.I. NY, 11756-1443, Phone 1-800-647-4722, Fax 1-516-731-5125, www.edlieelectronics.com Herbach and Rademan- 16 Roland Ave., Mt. Laurel, NJ, 08054-1012, Phone 1-800-848-8001, Fax 1-609-802-0465, www.herbach.com Marlin P. Jones and Assoc. Inc.- P.O. Box 12685, Lake Park, FL, 33403-0685, Phone 1-800-652-6733, Fax 1-800-432-9937, www.mpja.com index.htm Pacific T.V.- 480 S. Joffre St., Victoria, British Columbia, Canada, V9A6C8, Phone 250-386-4283, Fax: 250-920-3517. http: members.shaw.ca pacifictv Surplus Shed 8408 Allentown Pike, Blandon, PA 19510, Phone: 1-877-7SURPLUS (78-7758), Fax: 610-926-0978 www.surplushed.com Toys HobbyTown USA- 6301 S. 58th Street, Lincoln, Nebraska, http: www.hobbytown.com Oriental Trading Company, Inc.- P.O. Box 2308, Omaha, NE 68103-2308, Phone 1-800-228-2269, http: www.oriental.com home.html U.S. Toy Co, Inc.-Constru ctive Playthings, 13201 Arrington Road, Grandview, MO 64030, Phone 1-800-832-0224, http: www.ustoy.com Electronics All Electronics- P.O. Box 567, Van Nuys, CA, 91408, Phone 1-800-826-5432, Fax 1-818-781-2653, www.allcorp.com Allied Electronics, Inc.- 7410 Pebble Drive, Fort Worth, TX 76118, Phone 1-800-433-5700, Fax 1-817-595-6444, www.alliedelec.com C and H Sales Co.- P.O. Box 5356, Pasadena, CA, 91117-9988, Phone 1-800-325-9465, Fax 1-818-796-4875, www.aaaim.com CandH Digi-Key Corp.- 701 Brooks Ave. South, P.O. Box 677, Thief River Falls, MN, 56701-0677, Phone 1-800-344-4539, Fax 1-218-681-3380, www.digikey.com Electronic Goldmine - P.O. Box 5408 Scottsdale, AZ 85261, Phone 1-800-445-0697, Fax 1-480-661-8259, www.goldmine-elec.com Hosfelt Electronics Inc.- 2700 Sunset Blvd., Steubenville, OH, 43952, Phone 1-800-524-6464, Fax 1-614-264-5414, www.hosfelt.com MCM Electronics- 650 Congress Park DR., Centerville, OH, 45459-4072, Phone 1-800-543-4330, Fax 1-513-434-6959, www.i-mcm.com welcome.jhtml Mouser Electronics- National Circulation Center, 2401 Highway 287 North Mansfield, TX, 76063-4827, Phone 1-800-633-2246, Fax 1-817-483-0931, www.mouser.com Newark Electronics- 4801 N. Ravenswood Ave., Chicago, IL, 60640-4496, Phone 1-800-463-9275, www.newark.com R and D Electronics- 5363 Broadway, Cleveland, OH, 44127, Phone 1-800-642-1123, Fax 1-216-441-8503, www.electronicsurplus.com U.S. Electronics Inc.- 1590 Page Industrial Blvd., St.Louis, MO-63132, Phone 1314-423-7550, Fax 314-423-0585, http: www.us-electronics.com Optics and Fiber Optics Corning Precision Lens- 4000 McMann Road, Cincinnati, Ohio 45245, Phone 1-800-877-0787, Fax 1-513-752-2841, http: www.uspl.com JML Direct Optics- 690 Portland Ave. Rochester, NY, 14621-5196, Phone 1-800-456-5462 Fax 1-716-342-6125, www.netacc.net ~jmlopt index.html Metrotek Industries, Inc.- 33 West Main St., Elmsford, NY, 10523-2413, Phone 1-914-347-4112, Fax 1-914-347-4203, www.metrotek.com Lasers Casix Inc.- 21822 Lassen St. G, Chatsworth, CA, 91311, Phone 1-818-709-7636, Fax 1-818-885-6926, www.casix.com Coherent, Inc., Laser Group- 5100 Patrick Henry Dr., Santa Clara, CA, 95054, Phone 1-800-527-3786, Fax 1-408-764-4800, www.cohr.com JDS Uniphase - 1768 Automation Parkway, San Jose, CA 95131, Tel 408 546-5000, Fax 408 546-4300 www.jdsu.com Kvant Ltd. - MFF UK Mlynska dolina, 842 48 Bratislava, Slovakia, Europe, Phone Fax +421 2 6541 1344, Fax +421 2 6541 1355, www.laser.sk EN DIDACTIC index.html Laseraim Tools Inc.- P.O. Box 3548, Little Rock, AR, 72203, Phone 1-501-375-2227, Fax 1-501-372-1445, www.laseraimtools.com Laserglow - 38 Cedar Springs Drive, Richmond Hill, Ontario, Canada, L4S2B1, Phone 1-416-729-7976, Fax 1-480-247-4864, www.laserglow.com Meredith Instruments- P.O. Box 1724, Glendale, AZ, 85301, Phone 1-800-722-0392, Fax 1-602-934-9482, www.mi-lasers.com MWK Industries- 1269 W. Pomona, No. 112, Corona, CA, 91720, Phone 1-909-278-0563, Fax 1-909-278-4887, www.mwkindustries.com Creative Technology- 4138 Coolidge Ave, Oakland, CA, 94402, Phone 1-510-531-4450, Fax 1-510-5314660, www.laser66.com Laser Dreams- 9616 Clyde Ave, Kenwood, CA, 95452, Phone 1-707-833-2302, Fax 1-888-830-2302, www.laserdreams.com Electronic Equipment ABRA Electronics- 1320 route 9, Champlain, NY 12919, Phone 1-800-717-ABRA, Fax 1-800-898-ABRA, http: www.abra-electronics.com Cadisco Electronics- 514-516 Ensor St., Baltimore, MD, 21202, Phone 1-410-685-1893, Fax 1-410-685-1723 Electronix Express- 365 Blair Ro, Avenel, NJ 07001, Phone 1-800-972-2225, Fax 1-732-381-1006, http: www.elexp.com Global Test Supply- 7906 Beaufort Ct., Wilmington, NC 28411, Phone 1-888-610-7664, Fax 1-910-401-1114, International Phone 1-910-221-9344, http: www.GlobalTestSupply.com Jameco Electronics- 1355 Shoreway Road, Belmont, CA 94002, Phone 1-800-831-4242, Fax 1-800-237-6948, http: www.jameco.com John Fluke Mfg. Co. Inc.- P.O. Box 9090, Everett, WA, 98206, Phone 1-800-443-5853, Fax 1-206-356-5116, www.fluke.com Naptech- P.O. Box 30, 12312 Hwy. 175, Cobb, CA, 95426, Phone 1-800-336-7723, Fax 1-707-928-1963, www.naptech.com Radio Shack- (visit the store nearest you!!!) www.tandy.com Ramsey Electronics, Inc.- 793 Canning Parkway, Victor, NY 14564, Phone 800-446-2295, http: www.ramseyelectronics.com Tektronix Inc.- Corporate Headquarters, P.O. Box 1000, Wilsonville, OR, 97070-1000, Phone 1-800-835-9433, www.tek.com TestMart - 550 TaylorAvenue, San Bruno, California, 94066, Phone 1-888-665-2765, www.testmart.com NetAquire - 733 7th Avenue, Kirkland, WA, 98033. Phone: (888)675-1122. Fax: (888) 670-1122 http: www.netacquire.com . Magnet Manufacturers Bunting Magnetics Co.- 500 S. Spencer AVE, Box 468, Newton, KS, 67114-0468, Phone 1-800-232-4359, Fax 1-847-593-2045, www.bunting-magnetics.com Cesco- 93 Utility Court, Rohnert Park, CA, 94928, Phone 1-877-624-8727, Fax 1-707-585-3886, www.cescomagnetics.com Dowling Miner Magnetics Corp.- 21707 8th ST E., P.O. Box 1829, Sonoma, CA, 95476, Phone 1-800-624-6381, Fax 1-707-935-1231 Dura Magnetics, Inc.- 5500 Schultz Dr., Sylvania, OH 43560, Phone 1-419-882-0591, Fax 1-419-882-4052, http: www.duramag.com Engineered Concepts - Birmingham, Al, Phone 1-205-837-4695, www.engconcepts.net magnets magnets.htm Magnetic Component Engineering, Inc.- 23145 Kashiwa Court, Torrance, CA, 90505, Phone 1-800-989-5656, Fax 1-310-539-4446, www.magneticcomponent.com Magnet Sales, Inc.- 11248 Playa Court, Culver City, CA 90230, Toll free phone: 800-421-6692, Telephone:310-391-7213, Fax: 310-390-4357, http: www.magnetsales.com Master Magnetics, Inc. - 747 South Gilbert Street, Castle Rock, CO 80104, Phone 1-800-525-3536, www.magnetsource.com . Forcefield Magnets - 2606 West Vine Drive, Fort Collins, CO 80521, Phone 1-877-944-6247, www.wondermagnet.com . Indigo Instruments - 169 Lexington Court, Waterloo, ON, Unit 1, N2J 4R9 Phone: (519) 746-4761 Fax: (519) 747-5636 Toll Free Phone: 1 (877) 746-4764 Computer Hardware Black Box Corp.- 1000 Park Drive, Lawrence, PA, 15241, Phone 1-412-746-5500, Fax 1-800-321-0746, www.blackbox.com Video Camera's Supercircuits- One Supercircuits Plaza, Leander, TX, 78641, Phone 1-800-335-9777, Fax 1-512-260-0444, www.supercircuits.com Videotapes, Videodiscs, Software Academic Information Systems, (IBM)- Tools for Learning Courseware Catalog IBM Corp., Dept. 8E9-ACIS, Tools for Learning, P.O. Box 2150, Atlanta, GA, 30301-9949 American Association of Physics Teachers- One Physics Ellipse, College Park, MD, 20740-3485, Phone 1-301-209-3340, Fax 1-301-209-0845, www.aapt.org The Astronomical Society of the Pacific- 390 Ashton Ave., San Francisco, CA, 94112, Phone 1-800-335-2624, Fax 1-415-337-5205, www.astrosociety.org Carolina Science Books and Multimedia, Carolina Biological Supply Co.- 2700 York Road, Burlington, NC, 27215, Phone 1-800-334-5551, Fax 1-800-222-7112, www.carolina.com CLEARVUE eav- 6465 North Avondale Ave., Chicago, IL, 60631-1996, Phone 1-800-253-2788, Fax 1-800-444-9855, www.clearvue.com The Education Group (The Video Encyclopedia of Physics Demos)- P.O. Box 1667-90069 Los. Angeles, CA, 90069. Telephone: (310)276-1122 Fax: (310)276-7330, www.physicsdemos.com Films for the Humanities and Sciences- P.O. Box 2053, Princeton, NJ, 08543-2053, Phone 1-800-257-5126, Fax 1-609-275-3767, www.films.com LOGAL- P.O. Box 1499, East Arlington, MA, 02174-0022, Phone 1-800-564-2587, Fax 1-617-648-2109, www.openhere.com shop1 software educational Merlan Scientific Ltd. - 247 Armstrong Ave., Georgetown, ON Canada, L7G 4X6, Phone 1-905-877-0171, Fax 1-905-877-0929, 1-800-387-2474, http: www.merlan.ca . MMI Corporation- 2950 Wyman Parkway, P.O. Box 19907, Baltimore, MD, 21211, Phone 1-410-366-1222, Fax. 1-410-366-6311, www.mmicorporation.com National Instruments, (Labview)- 6504 Bridge Point Parkway, Austin, TX, 78730, Phone 1-512-794-0100, www.natinst.com Physics Academic Software- P.O. Box 8202, North Carolina State University, Raleigh, NC, 27695-8202, Phone 1-800-955-8275, www.aip.org pas Physics Curriculum and Instruction- 22585 Woodhill Drive, Lakeville, MN, 55044, Phone 1-612-461-3470, Fax 1-612-461-3467 Pre-Engineering Software Corporation - 5800 One Perkins Place Drive, STE 10-D, Baton Rouge, LA, 70808, Phone 1-225-769-3728, Fax 1-225-769-3661, http: www.pre-engineering.com Sky Publishing Corp.- P.O. Box 9111, Belmont, MA, 02178-9111, Phone 1-800-253-0245, Fax 1-617-864-6117, www.skypub.com Teacher's Video Co.- P.O. Box SCF-4455, Scottsdale, AR, 85261, Phone 1-800-262-8837, Fax 1-602-860-8650 Team Labs- 6390B Gunpark Drive, Boulder, CO, 80301, Phone 1-800-775-4357, Fax 1-303-530-4071, www.teamlabs.com Vernier Software- 8565 S.W. Beaverton-Hillsdale Hwy., Portland, OR, 97225-2429, Phone 1-503-297-5317, Fax 1-503-297-1760, www.vernier.com Video Discovery - 1700 Westlake Ave. No. 600, Seattle, WA 984109-3012, Phone 1-206-285-5400, Fax 1-206-285-9245 www.videodiscovery.com . Ztek Co.- P.O. Box 11768, Lexington, KY, 40577-1768, Phone 1-800-247-1603, Fax 1-606-281-1521, www.ztek.com
Vacutec
Produces hemispherical energy analysers, electron, X ray, ion sources, and sample transfer. Includes list and description of products.
VACUTEC VSW ATOMTECHGROUP THE VACUTEC GROUP SEM TEM preparation, ion and atom sources ... ATOMTECH.CO.UK PLEASE SELECT: ABOUT VSW Analysers Systems Upgrades Excitation Sources X ray Monochromator UHV Components NEW CL50 VSW World-wide LINKS Opportunities Service Dept Catalogue HOME Components and systems for surface science ... For research and development plasma systems ... VACUTEC.CO.UK
Canberra Industries
Radiation monitoring and analysis instrumentation, serving industries engaged in nuclear power generation and decommisioning. Manufactures radiation detection and analysis instrumentation. Provides health physics services for industries engaged in nuclear power, decontamination and decommissioning, and safeguards. Headquarters are in Meriden, CT, USA.
CANBERRA, An AREVA Group Company: Analytical instruments, systems and services for radiation detection and radiation monitoring Regional Access: USA ---------------------- Belgium Canada France Germany Japan Russia United Kingdom CANBERRA is the world's leading supplier of analytical instruments, systems and services for radiation detection and radiation monitoring Homeland Security Website Tools to Fight Radiological Terrorism News: The CANBERRA 2006 Training Schedule is now available SP-502-4 "Introduction to Gamma Spectroscopy" scheduled for October 3rd - 6th in Aiken, SC Patch for the German version of the ISOCS Special Sphere Template New Training Catalog for Germany for Fall 2005 More News... Click here for info on the 2006 CANBERRA Users' Group Meeting Information Updated 11 10 2005 Home | Company | News | Products | Support | Training | Literature | Offices | Careers | Contact Us Privacy | Quality | Terms and Conditions | Contact Webmaster This site is best viewed with a 5.0+ browser. 1024x768 screen resolution is recommended Main companies AREVA group Nuclear Energy COGEMA FRAMATOME-ANP Transmission Distribution AREVA TD
SVT Associates - Complete MBE
Manufacturer of Ultra High Vacuum (UHV) and Molecular Beam Epitaxy (MBE) equipment. Also produces III-V epitaxial materials and devices, in-situ monitoring tools, and system deposition components.
SVT Associates : Complete MBE Welcome to SVT Associates SVT Associates is a leading Ultra High Vacuum (UHV) and Molecular Beam Epitaxy equipment development and manufacturing company. SVTA also produces state-of-the-art III-V epitaxial materials and devices, in-situ monitoring tools, and system deposition components. More Search SVTA.com: SVTA offers a turn-key system for real-time flux measurement and control in a thin film deposition process. ACCUFlux Process Controller is an advanced design utilizing atomic absorption spectroscopy to measure the atomic vapor flux density of solid and gas sources. The compact design provides closed loop control for high process repeatability. An advanced windows based software module allows monitoring, documentation and interfacing to process equipment. Copyright 2005 SVT ASSOCIATES, INC. All rights reserved. SVT Associates, Inc., 7620 Executive Drive, Eden Prairie, MN 55344 USA Phone: 952-934-2100 Fax: 952-934-2737 Email: sales@svta.com
Rare-Earth Magnets
Distributor and retailer of rare-earth (neodymium-iron-boron) magnets, ferrofluid, bismuth, magnetic viewing film, and other related products.
National Imports - Rare Earth Magnets Rare Earth Magnets - Arc-Segment Magnets - Block Magnets - Cube Magnets - Cylinder Magnets - Disc Magnets - Ring Magnets - Rod Magnets - Sphere Magnets - Technical Specifications - Pull Force Calculators Epoxy Adhesives - 3M Scotch-Weld Adhesives - National Imports Adhesives Division (Off-Site Link) Other Products - Bismuth - Ferrofluid - Gaussmeters - Magne-View Film - Safety Products - Steel Balls National Imports LLC - Magnetic Products Division National Imports is a distributor of MAGCRAFT permanent magnets, 3M adhesives, hardware products, and engineering supplies including rare earth magnetic materials. We specialize in providing high-quality neodymium-iron-boron (NdFeB) magnets at low prices with no minimum order size for our stock products. Our neodymium magnets are made with the world's most powerful permanent magnetic material. We only sell new neodymium magnets produced under license to the highest standards. All stock magnets that we carry have been manufactured under certified ISO 9002 quality management systems. We never sell unlicensed, used, or "surplus" magnets. Meeting All of Your Neodymium Magnet Requirements We carry a wide range of shapes, sizes, and grades of neodymium magnets. All of our stock magnets are sintered neodymium-iron-boron plated in nickel. All of our magnetic products carry a complete money back guarantee. If you are not completely satisfied, just return your purchase to us within thirty days in original condition and we will refund your money including our regular ground shipping charges.We are committed to providing our customers the best service and personal attention on every order. 2002-2005 - National Imports, LLC. All Rights Reserved.
LabSmith Innovative Laboratory Electronics
Manufacturer of laboratory electronics that control experiment timing, sequencing, coordination and integration.
LabSmith-Innovative Laboratory Electronics At LabSmith, we design and manufacture precision electronics that further the art of research. Our equipment is designed by seasoned researchers. We know that every hour of actual data-gathering represents one hundred late-night hours with loose wires, noisy signals, failed runs and aggravation. But we also believe it doesn't have to be this way, not even for the most cutting edge research. LabSmith creates functional building blocks that handle the exasperating aspects of experimentation: timing, sequencing, coordination and integration. Our goal is to craft rugged, innovative, affordable solutions to everyday lab chores, so that you can focus on science. Whether you work with gas dynamics, fluid mechanics, materials, MEMS, microfluidics, analytical chemistry or physical chemistry, LabSmith provides you with tools that are as essential and reliable as an oscilloscope or sturdy work bench. What's New at LabSmith: SVM340 Synchronized Video Microscope now available. 6000 Volt HVS448 High Voltage Sequencer now available. Updated (v1.2) LabView drivers for LC880 and HVS448 . Upgrade your HVS448 to V 1.127 Upgrade your LC880 to V 5.07 1159 Rebecca Drive Livermore,CA 94550 Phone (925) 292-5161 Fax (925) 454-9487 www.labsmith.com info@labsmith.com Copyright 2005 LabSmith Tools for Science
Partition Enterprises Pty Ltd
Manufacturer of density tracers. Density tracers are filled plastic particles which are used to determine partitioning characteristics of density separators and other units.
Partition Enterprises Pty Ltd - Home Pages Can you afford not to use Partition Enterprises Density Tracers? PARTITION ENTERPRISES PTY LTD ABN 28 010 473 542 Typically, Density Tracers are plastic particles which incorporate powders or other materials to impart suitable combinations of properties including density and colour. They are used to determine partitioning characteristics of density separators and other units accurately, rapidly and at low cost. Primitive forms of density tracers have probably been in use for many years, but they were developed for routine use in De Beers diamond mines around 1970, and by the Julius Kruttschnitt Mineral Research Centre for coal processing around 1980. Today, those industries remain the dominant users, but density tracers are also utilised in iron ore, gemstone and magnesite processing and in diverse research applications. In most Density Separation Plants regular Density Tracer Testing indicates adjustments which can Improve Yield by at least 0.5% Annual Cost (Large Plant) = approximately $25,000 Typical Payback (Any Plant) = 2 to 3 weeks This website is the copyright of Partition Enterprises Pty Ltd 2001. Rin did this.
PhysicsWeb - Business Directory
Directory of manufacturers and suppliers of physics-related products.
PhysicsWeb - Buyer's Guide Advanced site search business directory Search browse E-mail enquiries Add free listing Update your listing Featured companies advanced search Search for companies whose name contains Search terms and or whose description or keywords contain Search terms entire phrase any words that are located in Region All Regions Africa Asia Australia Oceania Caribbean Europe Middle East North America South America Country All Countries Australia Austria Bahrain Barbados Belarus Belgium Bosnia Herzegovina Botswana Brazil Bulgaria Canada China Congo Czech Republic Denmark Finland France Germany Greece Hong Kong Hungary Iceland India Iraq Ireland Israel Italy Japan Kazakhstan Korea, South Liechtenstein Lithuania Luxembourg Malaysia Mexico Netherlands New Zealand Norway Papua New Guinea Philippines Poland Portugal Russia Singapore Slovenia South Africa Spain Swaziland Sweden Switzerland Taiwan Thailand Turkey U.S. Virgin Islands Ukraine United Arab Emirates United Kingdom United States browse categories Choose a category below to browse sub-categories. Academic scientific publishing Beam equipment Computer hardware Computer software Consulting Cryogenics Education Courses Exhibitions Fibre optic products Imaging Intensified cameras Lab electronics Lasers Magnets Materials Microscopy Miscellaneous Optical components Power supplies Radiation equipment Recruitment Services Spectroscopy Test and measurement Test category temp Vacuum featured companies The European Physical Journal Hiden Analytical Creative Group Mclennan Servo Supplies World Scientific Publishing Applied Scintillation Technologies (UK) Varian, Inc. Vacuum Technologies More featured companies Become a featured company Home | News | Physics World | PhysicsJobs | Resources | Events | Best of PhysicsWeb Buyer's Guide | Contact us | Advertising | IoP members | Products press | Advanced site search Tel +44 (0)117 929 7481 | Fax +44 (0)117 925 1942 | E-mail info@physicsweb.org Copyright IOP Publishing Ltd 1996-2005. All rights reserved. Legal Notice
Oxford Scientific Ltd
Provides vacuum science and plasma instruments for HV, UHV, MBE and surface science applications. Instruments include plasma sources, atom sources, ion sources, e-beam evaporators, hydrogen sources.
Oxford Scientific. Plasma ion source, ion source, ECR source, atom source, plasma source, microwave ion source, RF plasma source, RF atom source, RF source, electron beam evaporator, e-beam evaporator, mini e-beam evaporator Oxford Scientific, plasma ion source, ion source, ECR source, atom source, plasma source, microwave ion source, RF, vacuum, electron beam evaporator, e-beam evaporator, mini e-beam evaporator, ultra high vacuum, UHV, molecular beam epitaxy, MBE, surface science, thermal gas cracker, hydrogen source, h-source, atomic hydrogen source, sputter gun, effusion cell, GaN, GaAlN, nitriding, thin films Manufacturers and Designers of Scientific Instruments for the HV, UHV, MBE and Surface Science Communities Products Contact Us News Oxford Scientific Location Links Home Welcome to the Internet Home of Oxford Scientific Limited Instruments for Innovators Products | Contact Us | News | Oxford Scientific | Location | Links | Home 2002 Oxford Scientific Limited | Legal
Integrated Design Tools
Produces particle image velocimetry systems, makers of proVISION and sharpVISION products and software.
IDT Cameras Plug and Play interface Multi-platform support TWAIN, Labview and Matlab drivers PIV Systems Reliable, portable and compatible solutions High Speed Cameras High res and super high res Systems Overview News: With the new X-Stream VISION Remote Control you may control the camera from a Windows Mobile Pocket PC. News: The new proVISION-XSTM Package has been released (Windows). News: The new X-StreamTM Timing Hub Application and SDK has been released (Windows and MAC). News: Our cameras are compatible with Mikromak's Winanalyze motion analysis software! News: IDT now provides rental equipment. Inquire today. News: X-Stream Cameras: Test the DEMO software [ Windows ] [ MAC OS X ]. News: sharpVISION Cameras: Test the DEMO software [ Windows ] Download: X-VISIONTM Ver. 1.13.05 (Cameras delivered after Nov 2004) Download: proVISION-XSTM Ver. 3.05.02 Update Download: X-VISIONTM Ver. 1.09.04 Update (Cameras delivered before Nov 2004) Download: X-StreamTM Timing Hub Ver. 1.01.01 Update Download: sharpVISIONTM Ver. 2.05.00 Update Download: proVISIONTM Ver. 2.02.03 Update
VME for Physics and Industrie
Provides process control, supervisory data acquisition systems and VME scalers and counters.
Welcome to drivesoft, your source for vme, scalers, counters and multi channel scalers Welcome to drivesoft Welcome Complete Systems to Maximize Productivity Since 1998, drivesoft has been a leading source of innovative process controls, motor drives and supervisory data acquisition systems in the Converting and Handling industries. drivesoft provides all the elements for a complete control system, including engineering, design, programming, panel fabrication, installation and commissioning. All of these disciplines are coordinated by our project management team to ensure a timely, smooth completion from small to extensive contracts. Our philosophy of providing our customers with a complete solution has enabled us to achieve strong growth and continued success. Cutting Edge Technology for New Equipment Customers who are investing in new machinery will benefit from the leading edge technology that a drivesoft control system provides, ensuring the line will be engineered to harness its fullest capabilities. Our expertise in process management affords our customers an unparalleled level of confidence that a drivesoft control system will perform to meet their production targets. Rebuilds: Enhancements for Existing Equipment Continued advances in drives, logic controllers and supervisory computer technology often warrant the rebuilding of control systems on existing machines to yield a quick return on investment. Machines that have become an overhead burden and a maintenance nightmare can now be transformed into competitive performers with advanced diagnostics. Physics, Industry and related fields: drivesoft has a partnership with SIS , a German based manufacturer for quality inspection systems, electronics for particle physics and industry as well as software engineering.(FASTBUS, VMEbus, VXIbus, etc.) Late breaking news SIS3150USB USB2.0 to VME interface shipping SIS3320 FADC shipping SIS3150USB USB2.0 to VME interface SIS3320 FADC with 32MBsamples per channel Business Home page | Quality Control | Physics | Industrial Controls | Contact Us This document maintained by webmaster@drivesoft.com . Material Copyright 1997-2005 drivesoft
The Rembar Company
Provides refractory metals and services to fabricate refractory metals.
Rembar.com Go to www.flash.com for plugin. Welcome to the Rembar web site! Here you will find a wealth of information related to refractory metals and their fabrication . See the history of our company and some brief information on what we offer. - See our New EDM Hole Master on our What's New page - Fabrication Parts Gallery Advanced Technology Contact Us : Refractory Metals Molybdenum TZM Niobium Rhenium Tantalum Titanium Tungsten Heavy Metal Porous Tungsten One of the Worlds Largest Inventories Of : SHEET TUBING WIRE ROD PLATE BAR RIBBON MORE... Your Complete Source For : ENGINEERING CAD CAM RD COMPLETE FABRICATION SERVICES CMM INSPECTION MATERIAL ANALYSES We can offer you almost any type of fabrication of a refractory metal that is possible to be made at the highest quality available. Inspection meets MIL I 45208 ISO 9000 specifications. Periodic Table of the Elements Size to Weight Calculator Refractory Metals Technical Data Material Safety Data Sheets | About | Fabrication | Technology | Contact Us | What's New | Quality | Calculator | Metal Specs | MSDS | * The Rembar Company specializes in refractory metals and their precision fabrication. Rembar can offer any type of fabrication of a refractory metal at the highest quality levels. We have one of the largest inventory of refractory metals such as, Sheet, Tubing, Wire, Rod, Plate, Ribbon... Site Map * Disclaimer : Rembar does not warrant or assume any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed. Rembar Co. Rembar is a registered trademarks. All other trademarks are the property of the companies referenced. 1995-2005 The Rembar Company, Inc. All Rights Reserved. Last Updated 01 05 Made in U.S.A. A wealth of information related to refractory metals and their fabrication.
iseg Spezialelectronic GmbH - USA
Provides high-voltage power supplies and related computer interfaces primarily for use in laboratories.
Welcome to iseg-usa iseg Welcome to iseg-usa Welcome to iseg-usa, your source for high voltage power supplies This side is currently under construction, please click on the link for information about contact for USA or contact: W-IE-NE-R, Plein Baus Ltd. 300 East Auburn Ave. Springfield, OH 45505 USA www.wiener-us.com Tel. : (937)324 2420 Fax : (937)324 2425 Email : sales@wiener-us.com Kontakt : Dr. Andreas Ruben We offer HV Power Supplies in NIM, CAMAC, VME, 3U Eurocassette, HV integrated on PMT-Basis, 8 16 32 Multichannel HV-Modules, Table Desk Instruments, 19" HV Power Supplies and an increasing number of DC DC converters and AC-Line driven units in a range of 0..15 kV and 0..3 kW. ISEG was founded in 1995 and has developed a series of multichannel modules for large applications, DC DC converters and AC-line driven PS. The units are of very high quality combined with reasonable pricing, and already in use at many laboratories throughout the world. The following features outline the quality of the modules: - Output voltages with very low ripple, noise, and high stability - High efficiency, very compact footprint - Low EMI - Analog or digital control via integrated interface such as RS 232, CAN, IEEE488.2, VME, CAMAC, etc. The particular strength of ISEG is in partnering with the end user to develop customized High Voltage Power Supplies. This includes either modifying existing units from our standard program or developing and manufacturing new power supplies to a specific customer need and specification. For further information please visit the iseg GmbH website in Germany by clicking on the link. Business Home page | Company Info Index | Products home This document maintained by info@iseg-usa.com . Material Copyright 2000-2005 iseg-usa
The Electro-Optics Foundry
Provides contract manufacturing services for electro-optic and vacuum microelectronic devices.
The Electro-Optics Foundry The Electro-Optics Foundry Foundry Properties Processes Frontend Backend Thin Films: Dielectrics Thin Films: Ferroelectrics Thin Films: Metals Thin Films: Organics Thin Films: Specials Micro-Fabrication Foundry Services Vacuum Micro-Electronics Facility Tour Gallery Product Areas Contact Us Home Hudson Research established the Electro-Optics Foundry in 1996 to provide manufacturers and researchers a secure contract manufacturing environment. The foundry is modeled on the classic foundries of the semiconductor industry. These companies offer complete semiconductor manufacturing facilities. A significant portion of the world semiconductor output comes from foundries. In that spirit, the Electro-Optics Foundry was established. But it was also recognized that the requirements of electro-optic fabrication, while similar to the semiconductor processes, are quite distinct. Thus, we adjusted our model to reflect that need. Where the semiconductor foundries have a fixed process that the customer design must conform to, the electro-optic foundry offers a more flexible approach. We offer a wide range of "a la carte'" processes which we tailor to your specific requirements. We also have standardized processes that conform to the standards set forth by the Stanford Nanofabrication Laboratory. If you have the expertise to define a process, we will run it for you. If you don't, we will define a process to meet your design goals. If you need a process developed and the associated technology transfer, we can help. The foundry is divided into two major sections: The Frontend and the Backend . The Frontend consists of the photolithography, metalizing, thin film, diffusion, etching and associated operations. The Backend operations are wafer dicing, polishing, packaging, wirebonding, optical testing, and other miscellaneous operations. There is now an extensive " Properties of Material " section where we present the complete properties of most materials of interest to our community. We can handle any aspect of product design , development and manufacturing. We are happy to be your second source as well. Or, take advantage of our high volume manufacturing capability. We can handle 200 wafer starts per day per shift in our 1100 square foot Class 100 clean room. Contact us to discuss your requirements at info@eofoundry.com Copyright 2004 Hudson Research Inc . New York
Silicon Sensing Systems Japan, Ltd
Provides a vibrating type gyroscope that uses micro-machined ring resonator for accurate and shock-resistent reading.
Gyroscope - Rate Gyro - Inertial Sensors SILICON SENSING SYSTEMS Japan Nihongo Home FAQ Catalog Company Contact Us Silicon VSG Rate Gyroscope "CRS-03"* CRS-03* View (29 x 18 x 29 mm) U.S. Sensors Expo Award Winning Product The rate gyroscope uses Coriolis effect of sensor element (vibrating resonator chip) to sense the speed of rotation ( rate of turn ). The new concept ring-shaped micro-machined resonator shows distinguished resistance against external shocks and vibrations over a wide range of temperature. Prefered by the customers of different applications due to its reliability compared to other gyros, about 5 million units have thus been produced here at Amagasaki-Japan as of November 2003. Ask other gyro manufacturers to submit the external-vibration resistance report! If they give you a vibration test-report upto 300Hz or less, that brand is likely to malfunction at slightly higher than 300Hz. You should assume normal mechanical vibration spreads out from a few hertz upto over 1000Hz. (Known among the industry: Brand-S dies at 338Hz, Brand-P dies at 400Hz or 700Hz) Our CRS03 CRS07 has been tested to 4000Hz at 4G. What does a self-vibrating resonator do? See what types of gyros exist Sensor ring resonator can be seen (the shiny ring).The center pillar is the magnet Click on photo for microscopic view of the MEMs product, the specialty of SSS Main production site in Amagasaki-Japan. Features Resistance against external shock vibrations. Wide range of operating temperature (-40 to +85 deg C) Low drift High reliability ASIC driven silicon micromachined resonator Applications Automotive Yaw Rate Sensor Global Positioning System ( GPS-INS, RTK ) Dead-reckoning Fluxgate Compass compensation In-Car Navigation Systems Mobile dish antenna stabilized platform Mobile camera platform stabilisation Robotics Simulators Telematics Fleet-management Remote Control Vehicles Inertial Dynamic measurement units Drive safety recorder (blackbox for car marine) AGV, wheelchair Marine Satellite Compasses Angle Wrench Agricultural Tractors Physiotherapy therapeutic Equipment 3-D input devices See Link Operating Principle A vibration is exerted to the silicon ring at ring's resonating frequency (Mode 1). ; Rotational motion produces Corioli's forces which couple vibration to a point 45 degrees relative to the driven axis (Mode 2). Monitoring the mode-1 null point (node) in the mode-2 gives a direct measure of applied angular rate. The above vibratory modes are unlikely to occur by external shock vibrations, hence the rate gyroscope can maintain consistent performance in harsh environments. Performance Output mode: Analog DC voltage centered at about 2.5VDC Gyro Version CRS03-02 CRS03-04 CRS03-11 CRS07-11 Rate Range + - 100 deg sec + -200 deg sec + -573 deg sec + -573 deg sec Operating temp -40 to +85 C -40 to +85 C -20 to +60 C -20 to +60 C Scale Factor (SF)* 20mV (deg sec) 10mV (deg sec) 3.49mV (deg sec) 3.49mV (deg sec) SF temp variation + - 3% + - 3% + -5% + -5% Bias (neutral)* 50% of Vdd 50% of Vdd 50% of Vdd 50% of Vdd Bias temp variation + - 60mV + -60mV + -100mV + -100mV Bias initial error + - 60mV + -60mV + -100mV + -100mV Number of Axis 1 1 1 1 Non-liniearity 0.5%FS 0.5%FS 0.5%FS 0.5%FS Bandwidth(-3dB, -90deg) 10 Hz 10 Hz 50 Hz 30 Hz Appearance Dimensions (exc. projections) Housing 29 x 18 x 29 mm Housing 29 x 18 x 29 mm PC board assembly 27 x 13 x 27 mm PC board assembly 21 x 13 x 22 mm Quiescent noise 1mVrms (3Hz to 10Hz) 1mVrms (3Hz to 10Hz) 1mVrms (3Hz to 10Hz) 1mVrms (3Hz to 10Hz) Power supply (Vdd) 5VDC + -250mV 5VDC + -250mV 5VDC + -250mV 5VDC + -250mV Current dissipation** not more than 50mA not more than 50mA not more than 50mA not more than 50mA *ratiometric, example given for Vdd=5.00Vdc **150mA at initializing, must raise to Vdd in less than 10mS Above are typical values. For guaranteed values see spec sheet prefixed by SST. Subject to change without notice or obligation. Do not use for equiipment with risk of life, environment, or properties. Option: CD-0026 Gyro Evaluation Board Frequently Asked Questions Download Gyro Catalog ! (pdf) Application Link ENQUIRY FORM You can also Telephone, Fax, or E-Mail us Tel Fax 1-800-596-4321 (Western and Mountain states only) SSSJ@ spp.co.jp Frequently Asked Questions Home Company Links (Interesting Applications) Silicon Sensing Systems Japan Ltd. exclusively covering the sales in Western USA Canada, Asia, and Pacific 1-10 Fuso-cho, SUMITOMO PRECISION Complex Amagasaki, Hyogo 660-0891 Japan Tel +81-6-6489-5868 Fax +81-6-6489-5910 (in U.S. Pacific and Mountain Time Zone, use voicemail 1-800-596-4321) sssj@ spp.co.jp Silicon Sensing Systems is a joint-venture company of Sumitomo Precision Products and BAES Specifications are subject to change without notice. Trademarks and brands are properties of their respective holders.Only browser visible contents are valid. Not desgined for life, environment, or property risk hazardous use. Prior to purchasing or using of the products of Silicon Sensing Systems Japan Limited (SSSJ) , the party (Customer) is reuired to indemnify and hold SSSJ, Silicon Sensing Systems Limited, and its affiliates, including its members, shareholders, managers, directors, officers, employees, agents and representatives, harmless from and against any and all liabilities, claims, demands, actions, costs, or expenses (including all reasonable legal or llitigation costs), by whomever asserted and regardless of nature or kind, including without limitation and or product liability claims arising from the use of any product supplied by SSSJ to Customer, claims for personal injuries (including death) and damage to property, whether in fort or under contract,directly or indirectly, in whole or in part, attributed to or arising fromthe use by Customer of any product supplied by SSSJ to Customer for any purpose including but without limitation, installing teh product on a product, equipment, or vehicle of any kind, or using the product for training or simulation purposes in relation to a product, equipment,or vehicle of any kind, or using the product for the support or maintenance of a product, equipment, or vehicle of any kind. SSSJ shall promptly notify Customer of any such claim for which indemnification will be sought. Customer shall have the right at its expense to assume and control the defence of such claims and SSSJ shall provide reasonable cooperation and information to Customer in order for Customer to defend the claims. Customermay not settle any such claim without the prior written consent of SSSJ which consent may not be unreasonably withheld. Limited warranty:SSSJ standard hardware products are warranted aggainst defects in materials and workmanship for a period of 2 weeks from the date SSSJ ships the products to Customer. This limited warranty is void if failure of the products has resulted from accident, abuse, misapplication, improper calibration by Customer, Customer supplied third party software not intended for use with the applicable SSSJ product or software, utilization of an improper hardware or software key, modifications to the product by Customer or a third party, or unauthorized maintenance or repair. Product and information not available for military or weapons usage. SNK NST6 JPV0001 JPV0002 JPV0003 micro gyro JPV0004 JPV0005 JPV0006 JPV0007 JPV0008 artificial horizon attitude indicator bae 9943 SSS_SGH-01 SSS SGH01-04 CRS03-01 flight G480 JR Propo G-480 panel carrier-based baes hobbies GPS-INS beeline GIS gyration gyromouse gyropoint mouse point memsic delphi phase-based hobby roll g-sensor delco gyrosensor ultragyro CRSO3-01 CRS 03-01 CRS O3-01 CRS03 real time kinematic century tower rollover -01 CRSO3 -01 CRS03-02 CRSO3-02 CRS koss neverlost agricultural tractor dynamic acceleration plymouth over trail crop real time kinematic allstar RTK geographical horizon mmq mmq50 mmq-50 qrs100 qrs-100 qrs-11 qrs-14 gyrochip systron-donner tracstar antenna survey micro strain xsense strategic inter-sense integrated intersense dqi UAV AHRS500CA AHRS500GA AHRS DMU antiskid AHRS400CC AHRS400CB AHRS400CA AHRS300CA microstrain bei unmanned anti guidestar gyrostar imu ins gps ins gps+ migit guidance guided skid precision c-migits furuno sc-60 sc-50 sc-120 jlr-10 m-migits measurement jupiter wage p y magnetometer trac star north-pointing vehicle jrc faa uav helicopter aero AHRS400CB HDX VG400CA VG400CB VG400CC SSS eureka jr-propo millenium award awareness gyrotrac code theodorite north-finding aerovironment situation hmd mount display head joystick control horizon stabilizer roll marine autopilot auto-pilot kvh horizontal stabiliser horizon motionpak scope soap random walk allen variance stabilised camera platform stabilized king dome puma siimu raymarine ins motosat heli sts cruise slip boat cruiser oversteer 03-02 CRS O3-02 CRS03 -02 CRSO3 inertial electronic-stability-control crs07 crso7 crs07-11 crso7-11 -02 CRS03-11 CRSO3-11 CRS 03-11 CRS O3-11 rotational CRS03 -11 CRSO3 -11 navigation sperry raven furuno kvh servo CRS03-05 CRSO3-05 CRS 03-05 CRS O3-05 CRS03 -05 turn rate of CRSO3 -05 ins system situation marine autohelm eye CRS03-04 CRSO3-04 CRS 03-04 CRS O3-04 aeroantenna CRS03 -04 CRSO3 -04 crs03 artificial horizon garmin vironment dragon crso3 siliconVSG silicon-vsg Silicon-VSG Silicon tactical VSG SILICON VSG SILICON-VSG vertical gyro gps ahrs efis pfd pointer skygate pointer micro Angular Rate Sensor Gyro for every application CRSO4 novatel imu gps futaba gps-imu gy601 gps-ins piezo gn-1000 magellan omnipless honda engineering dynamics CRS04 04 CRSO4 CRS02 CRSO2 02 O2 02-01 O2-01 avionics quartz gyro gy401 piezogyro thales jrc jr propo CRS02-02 CRSO2-02 02-02 O2-02 VCS ssp SSP BAES RRSO1 RRS01 RRS SiIMU 01 attitude indicator gy240 applanix javad g7000t Si-IMU Si VSG Si-VSG SiVSG micromachined micromachining MEMS mechanical electromechanical SC60 SC120 SC30 SC-60 SC-120 SC-30 GY240 GY401 GY502 GY501 GY601 GYA350 GYA351 GY-240 GY-401 GY-502 GY-501 GY-601 GYA-350 GYA-351 SSS_SGH01-03.06 SSS_SGH01-02.06 SSS_SGH01-03.07 SSS_SGH01-02.07 A2C52004767_F_ JRC A2C52101155_F_ Bosch A2C52004767_G_ A2C52101155_G_ A2C52004767_H_ A2C52101155_H_ SSS_SGH01-04.06 SSS_SGH01-04.06 SSS_SGH01-04.07 SSS_SGH01-04. 07SSS_SGH01-03.08 SSS_SGH01-02.08 SSS_SGH01-04.08 Silicon VSG VSG SGN1-100-10 SGN1-100-20 VSG100 Siemens VDO controller electronics Coriolis earth rotation drift cancel Kalman filter anti alias ADXL202 datron transco dbs inmarsat dish mobile seatel in motion finding direction azimuth elevation avcs dtg roll pitch servo moto-sat inmarsat-F inmarsat-F1 dish macome modell propo bias stability global positioning tamagawa agv yokogawa Flugschule sumitomo model sumi detector detection seiwa piezoelectric tokin antenna systron piezo Donner CRS03-02 CRS03-01 CRSO3-02 CRSO3-01 CRSO3-O1 CRSO3-O2 VDC VSC ESP Silicon Sensing Systems Japan tractor bae systems flugzeuge British Aerospace agriculture l3 cruise cruising murata wheel chair heading hold HH wheelchair robbe independence gyrostar BEI Technology lazer tail lock laser FOG fiber optic ring dry tuned spinning tuning fork coriolis comnav chart plotter force acceleration 3 axis DOF G6000T G6000 G460T G410T G460T-810G G6000T-SX SMM degree of freedom 6 three six ailron aileron ailerons rudder vertical draper sssj inertial moment of inertia angular telebee angle rotation yaw attitude robotics robot Aibo Asimo stabilized quartz locked stabilised platform litton jr acrobat sperry PF ALK sextant asb honeywill gws segway sss ht grand sht wing csa commercial sensor assembly manchester balance honeywell JAE furuno car navigation GPS compass fluxgate helicopters aircrafts model remotely controlled control camera drilling flight system positioning dynamics joystick seismic heading lock hold helicopter ginger PG 1000 leveling guidance UAV seismic building sway swing cable wire tower marine japangyro graupner japan-gyro act silicon-gyro heave surge sway nascar NMEA automotive ABS brake acro dead reckoning lucas testing geomechanical location sensing stabilisation stabilization fork lift quartz gyrochip 2 pg-1000 pg1000 silicongyro silicon gyro teves varity continental sssj crs03-11 crs03 crso3 crso3-11 crs03-02 crs03-01 crso3-01 crso3-02 crso3-o2 crso3-o1 crs02-01 crso2-01 crso2-01 crso2-02 crs04 crso4 rrs01 sirrs01 sirrs si-rrs01 rrso1 sirrso1 si-rrso1 siimu si-imu willows si-imu01 draper lab si-imuo1 imu01 watsons imuo1 gyrosensor in-car computing windriver XM Satellite Sirius gyrocompass E911 stand alone ubiquitous infotaiment N-Star J-M-Sat AutoPC Car Wings DVB-T MACHMP3 Travel Pilot M-Sat IVMS7001 Quick Scout GSM GPRS QuoVadis Joyride Pure Vision DAB Navistant On Star Wingcast InterTrak Tegaron Altea JM-SAT gyroscopic inertial measurement my drive.com Monet G-BOOK Internavi Comworxx Infomove TravRoute Rand McNally Destinator Webraska Benefon Arbiquity MobileAria caa in-car computer compass link gedas odysline egery passo oncall unit dynamical position speed velocity of turn moment spin spiral bosch missiles laboratory rockets aerial vehicles safety recorder sensa coursemaster ag tokimec MDP-A3U7 3D Motion Sensor unit CG -16D CG - L33 CG-16D CG-L33 CG16D CGL33 samplingengineering signalling signal 3dof 6dof 2dof 3-axis 6-axis 2-axis 1-axis axis axes round design gyros mechanics resonant systron forces x-axis y-axis z-axis wheels gyrowheels watson's marine voyage travel trail locus gmdss glonass gronass single axis dual axis log doppler radar trajectory reference systron-donner programme program anti skid helimax moment of robbe flying arcamax automotive automobile motorcycle tilt willow gyro-scope microelectromechanical senseur rollover over traverses mechanisms axles horizontal steer course steering traces automatic autopilot pilot auto guided rotor element chip rate on systron board on-board fuselage locus sensor piezoelectric angular rates transitional ceramic vehicles env 05d 52 enc 03j sensor sensa sensar env05d catalog specifications datasheet data sheet catalogue car beam moving object ITS ABS TRC chassis brakes suspension accident black watson systron-donner box blackbox recorder impact rocking rock spin shock ITS csm R C remote control plane ikarus airplanes rc aircrafts jr scale models sky hobby crafts stability remotelly radio aerobatic rudder ailerons elevators flights servo propo motor rotors tail propo landings takeoffs acrobatics beginners techinics technology technologies map matching techniques technicals automated rate sensor automatically positioned satellite pointing devices location fleet systron-donner qrs-11 qth horizon despatch trunking trunked radio transmitter receiver packet research transceiver institute ahrs vg vertical gyro horizontal artificial horizon reference flyer referential unit vessel stand vehicle systron-donner rotation steering systems repeaters machinery machining flying machine military aerospace rate of turn bae systems baesystems base british aerospace sextant honeywell allied signal signals braking Silicon VSG system ABS systron anti skid antiskid anti-skid tail lock physics heading lock fly HHGyro csm robbe frech model herr norvel sig realflight global ok model hobby ace aeroloft aerospace designs foil airborne factory athena institute bomber sgn1-100-10 sgn1-100-20 aeronautical nautical combat qrz dubois aqrs Flugzeug axe qrp krebs base Dumoulin-Froment marin avionique avion avions qrs Ortung ratiometric acc adaptive c3ap-15-21 cruise incident recording rotational gyrochip asv ers-110 ers-111 accelerometer drift accelerometers tractor ndk helico systron-donner denso helicos heading flight yaw Kreiselgerat revolutionary new directv kvh robocon crossbow parabola ?? ??? SPP vsg ion flux gate fluxgate magnetic rate sensor ratesensor strapdown strap down alps - ? , ? - ?? ??? GPS ?? Gyroscopy and Navigation ?? ??? ???????????????? ????? ?? ??????????? ?? ???? ???? ????????????? ??????? ???? ? ????? ? ???????? ???? ????GPS ??????? ????? ?????????????? ?? ?? ???? ???????? ?? ??????????????????????? ?? ?? ??????, ????? ? ??? ?, ???????????????? font ??????????? ???????? ???? ?????????? ?? GLONASS, Gallileo, GPS ????? font brand names belong to their respective owners. acceleration inertia guidance systems inertial gyros gyroscopes tilt angle magnetic aerial surveying micro agricultural navigation AHRS mining Avcs equipment antennae pointing assembly line process control automated excavating automotive testing automobile miniature brake testing bridge vibration monitoring camera stabilization low cost stabilisation crash testing dead reckoning directional drilling shock measurements drag bat rasing G meters dynamic positioning of marine vessels radar sonar fish unmanned finders earthquake detection experimental aircraft fall detections fleet underwater vehicle monitoring flight and data analysis flight control systems geomechanical goodrich leveling glide slope indicators rate sensing GPS INS positionings batting graders heave surge sway heavy high speed human biodynamics dynamics dynamicals intelligent joystick input devices lab laboratory instrumentation land survey mine detection laser leveling lift location sensing machine mapping medical sensors guidance nascar suspension package platform stabiliziing stabilising preventime heave maintenance pumping unit position remotely operated controlled vehicle seismic semi active seismometers snowcat boat racing structural geosurvey testing survey underwater guided unmanned air vibration virtual reality diver aiming Yokomo Hirobo ABC Piccolo Keyence SC Engine Model Tech Kalt Funkey club Aeroplane NHP Cmt-Rotor Hobbistar GWS PG-01N PG-01NP PG-02 PG-03 weather diving buoy dmu imu stability accelerometer compasses radars crane aerial excavator elevator escalator vertical reference attitude heading helicopter compensated compensation orientation axis angle angular moment momentum rotation elevation azimuth dish parabola cockpit dashboard yaw roll pitch rate its esp programme quartz piezo MEMS sensor mouse 3D 3-dimensional movement kinetic radome thales DBS direct broadcasting satellite inmarsat echostar tracking motion tuning golfclub fork dynamically tuned gyroscope spinning top fiber optic gyro ring laser ashtech gyro FOG RLG horizontal artificial horizon airplane helicopter glider cruise cruising autopilot maritime aerospace tractors mass tanks fuselage wings golf robot SILICONE robotics human behavior SPP Use the right gyro for telematics and fleet-managements for accurate dead reckoning detector multi-axis in-car navigation micromachined micromachining SILICON MEMS mechanical electromechanical. microgyro micro gyro seiko epson XV-3500CB You need a better gyro for traffic telematics fleet management on board EWTS4P011 model avionics ion SC60 SC120 Furuno SC30 SC-60 SC-120 SC-30 SC-10 experiments SC10 GY240 GY401 GY502 GY501 GY601 GYA350 JRC GYA351 GY-240 GY-401 GY-502 Silicone GY-501 GY-601 GYA-350 GYA-351 SSS_SGH01-03.06 SSS_SGH01-02.06 silicone EWT EWT2FNA001 SSS_SGH01-03.07 SSS_SGH01-02.07 gya352 gya-352 A2C52004767_F_ JRC A2C52101155_F_ gnss gps Bosch A2C52004767_G_ A2C52101155_G_ A2C52004767_H_ A2C52101155_H_ SSS_SGH01-04.06 SSS_SGH01-04.06 SSS_SGH01-04.07 SSS_SGH01-04. 07SSS_SGH01-03.08 SSS_SGH01-02.08 SSS_SGH01-04.08 Silicon VSG VSG SGN1-100-10 SGN1-100-20 VSG100 Siemens VDO controller electronics Coriolis earth rotation drift hsg-imit Kalman schwartz filter anti alias ADXL202 trainer datron dbs similator inmarsat dish mobile in motion north finding direction azimuth elevation dqi avcs dtg roll pitch servo propo litef migits meggitt bias stability global positioning tamagawa yokogawa sumitomo tele sumi motionpak mitsubishi motion datatech detector master CRS 03 CRS 03-02 CRS 03-01 CRS 03-04 CRS O3-02 CRS O3-01 CRS O3-04 SSS SGH01-02. 06 SSS SGH01-04. 06 SSS SGH01-05. 06 SSS_SGH01-05. 06 G480 G480T SNK NST6 JVP0001 JVP0002 JVP00-02 JVP00-03 JVP00-04 JVP00-05 JVP00-06 JVP00-07 0118 + 3401 ATS FO M ATSFOM 94V-0 leica BEI Technologies tilt sensor gyroview gimbal gyro-view MITE MICA view angular avionics UAVRPV RPV platform kalman filter kinematic correction continuous dynamic kinematics kinetic beeline lateral axes detection mannesmann piezoelectric tokin drive recorder blackbox black CRS O3 box fibersense teac remotely monitor black and decker sundstrand dyson angular rate vacuum cleaner autonomous alectrolux facom hazet hoover karacher devices movement outboards black decker silva simrad snapon blackdecker sunnen neverlost triaxis sextant gemini triana big boys toys robbe towerhobbies tower hobbies giro sssj motion sensing crossbow raytheon robot walking robots astronautics eagle airtronics technology century act jpl csem hobbico vte novatel kvh bae systems ring laser fiber optic hamlin dry dynamically tuned kearfott rotational condor asimo ginger antenna datatec sandia systron Donner CRS03-02 CRS03-01 CRSO3-02 CRSO3-01 CRSO3-O1 ibot CRSO3-O2 CRS03-05 FOG gyrostar gyroster i-bot tokin topre CG-L43 locus tuning fork litton E911 TCS phase slip sunday defence genesys cable sperry polysilicon marine maritime VDC VSC ESP Silicon Sensing Systems Japan BAE Systems British Aerospace Boeing cruise cruising murata wheel chair wheelchair wire vibratory element tests vibrating gis geographical independence lateral axis micro odometer gyrostar BEI Technology newcon itt steiner tasco r ship laser FOG solid state fiber optic ring dry tuned ship sense finder vessel find how to piezoelectric autopilot spinning tuning fork boat coriolis force acceleration 3 axis DOF degree auto pilot of freedom aviation vessel avia 6 three six aibo pino ritchie silva cockpit tokimec hozizon bow aircraft safety aviation avionics electronics jae tkk analogue imi mems comb ailron stern rudder vibrating nero env-05ea vibratory dead reckoning reckon vertical autohelm inertial moment analog of inertia angular angle rotation martin yaw attitude robotics robot Aibo Asimo piezo gyro stabilized stabilised platform litton tkk allied signal sperry wheel sextant solutions honeywill JAE furuno car navigation GPS compass fluxgate helicopters aircrafts model remotely controlled control azimuth tube camera self navigate flight system positioning vics dynamics joystick seismic tail heading lock hold helicopter ginger PG 1000 leveling guidance UAV seismic heave surge sway nascar NMEA automotive pg1000 ABS brake dead reckoning testing geomechanical location sensing stabilisation stabilization transom momentum trimble garmin speed magellan velocity fork lift quartz gyro comb gyrochip sphere gyrosensor wheel gyrocompass guided imi gyroscopics inertial measurement unit imar dynamical position speed rate sensor velocity of turn moment spin tedco spiral bosch missiles rockets chip aerial vehicle safety recorder sampling engineering 1 3 4 5 lawrance gimbal electric direction orientation 6 3dof 6dof 2dof 3-axis silicon gyroscopes jpl hughes 6-axis 2-axis 1-axis axis axes round design meso radar hsc ceramic gyro tokin video cameras camera binoculars gyros helimax mechanics resonant forces x-axis summers y-axis z-axis top wheels spheric gyrowheels marine icg540 voyage travel trail csm locus gmdss glonass gronass single axis murata manufacturing microgy litton mini-gyro micro-gyro microsensors reference adi dual axis log doppler radar irvine mems litef astrium chandler marshall cmt crossbow trajectory reference programme program anti vsg skid helimax sperry grain gmbh robbe flying arcamax automotive automobile motorcycle tilt microelectromechanical rollover over heli-max traverses nero mechanisms instrumental htm15 gold edition htm15a axles horizontal steer course steering traces heavy automatic autopilot intellisense pilot auto guided rotor element chip rate truck sensor spinning mass piezoelectric angular rates transitional quartz ceramic catalog tractor wesmar instrument raytheon specifications angle wrench precession datasheet century data sheet catalogue english british aerospace car beam moving object ngk ITS ABS TRC chassis brakes suspension accident black box blackbox recorder impact rocking rock spin slip slide G ?G- shock 2 csm angular speed tracking servo R C remote control plane airplanes aircrafts jr scale models sky hobby crafts stability aerobatic rudder ailerons elevators flights servo propo motor rotors tail spinning landings takeoffs acrobatics beginners techinics technology technologies techniques technicals automated automatically positioned satellite in-car navigation control urban sub-urban receiver blocked 12 channels chip-set offset gyro bias gyroscopes calibration mode DR system call center sperry centre alert tracking tracked vehicles flow driver awareness safety satellite based positioning intelligent road gyros networks mongkok wanchai manhattan freight passenger pointing devices location identifier fleet despatch trunking trunked radio systems gyros repeaters machinery machining machine military aerospace ratesensors scaled aeronautical nautical combat qrz aqrs qrs qsl ratiometric sensors gyration engines acc adaptive cruise lucas incident recording rotational asv ers-220 ers-110 gya352 gya-352 unmanned gyro system inertial navigation laser gyro attitude sensor, kraft heading sensor, horizon sensor, north finding horizon delphi data aquisition sundstrand aerial sensor gyro binocular gyro camera gyro horizon mechanical horizontally gyro scope gyroview fly sailplanes sailplane dinsmore dual servo trim throttle cut fpa flapperon pewatron flaperon mix elevon humphrey aileron rudder landing crow hovering gain sagem kearfott rlg selectable point curve thundertiger Adtran, Agere, Alcatel, BAE Systems, Cisco, ComDev, EADS, Ericsson, Hughes, L-3 Communications, Lockheed Martin, Lucent Technologies, Motorola, Northrop Grumman, Tektronix, Teradyne, Thales, curves throttles aveox age air sst astro cavazo mtm ems age dymondairplane gyro, inclinometer, angular tilt gravity rrs sirrs rrs01 torque wrench force measurements sirrs01 imu sensor, accerelation sensor, gyro trac nmea0183 nmea-0183 precision kinematics gyro track vehicle gyro tracking locus elevation fm l-3 communications fms ers-111 accelerometers ndk marine denso revolutionary new directv kvh robocon 3000 asimo ahrs vg ailrons crane tractor aibo imar inertia stick crossbow parabola SPP vsg , telematics telematiks pcb group triaxial piezotronics fleet management kearfott navtech momentum microring kvh inertial resonator micro ring microsensors fog gyroscope micro sensors telematics, , , physiotherapy , , , , aviation gyro-trac tracstar ASIC , gyrocompass compass gyrotrack gyrotrac gyro epson trackstar creation qualcomm akebono ep concept keyence qubik 356A13 silicon design shuttle imperio omnitech silicon sensing systems crs07-11 crs07-02 gy611 gy612 gy511 gy512 servo inertial mems gyro piezoelectric piezo ceramic ngk denso delphi japan colibrys silicongyro silicongyros angle mems gyro sssj sundance sss robotic sssj siemens teves vdo silicongyroscope bei systron creations koss sky mode tracstar silicondesigns skymode skyhopper hopper sports modelsports oritron bonanza g500t g550t g5000t ion g500 g550 g5000 g3000 jr brand pilot navtor icsensors movement dbs kvh summitt seatel bernardino platform dmu aerotech quartz helis great kinematics global blade propeller eurokit electro modelsports dumas desert commander clancy chief dynamics silicon gyro crs03 crs-03 xin hua models century velocity telebee aero model ogawa seiki oritron pioneer alpine panasonics xanavi denso in-car navigation top gun map matching gis angular gyroscopes rate ratesensors ratesensor glonass gmdss miller power master rcd fox erickson gyroscopes sundex racer racing boat lake rc gronass plane yellow propwash beijing precision stabilisation micro mach jk hobbies electronics knife edge rudder stick dauphin ergo windspeed heli myheli bme sirius chief castle vertical verticalgyro dynamically tuned dtg lanier ikarus zone hanger gws enya ace saito magnum engines world sig goldberg voyager eagle bell thunder tiger os o.s. engine kpg pni hpg jrg yog qrs okg qrp silky wind aqrs-11 trainer accurate accuracy single challenger imperio pcm1024za max-160fx-f1 g6000t-sx g460-810g fm7ch spcm8ch x-3810 x-378 max66II max66 max66-2 sqs shuttle sceady pcm1024zh airtronics rd6000 super ma-7 dumper airtronics-94557 air tronics vario uli streich location finder meister tsk f3c f3a f3b rc gradient inclination bank telecommande radio china model , GPS, DGPS,EWTS82, EWTS82XXXX, Panasonic, how gyroscopes work navigator piezo taxis amigo plane G5000T G550T G4000 G450 nej900 nej120s g460t PG-03 PG03 PG-01 PG01 MTF-1i CSM360 enya jr propo nea-120p g-400 g-5000-t g-5000-T , current position velocity stabilization speed status report trunked line traffic jam logistics ITS VDC VSC EPS ETS ETC EST ESC ESP BEI SGH01 BEI, BAE Systems BASE fgi gy hitec g5000t g-t5000T sanwa gws hirobo telebee panther arcamax ogawa remote control webra kyosho abc tamiya boat flight air supply taya engineering technologies, ENV05F, ENC03J, ENV-05F conexant piezogyro connexant gyrosensor sirf sextant ring honeywell boeing base nasa hovering nasda enc-03j env05C env05d vdo microsensors, vacuum cleaner dyson electrolux mayfair matsushita kionix strapdown strap down alps quartz gyroscope watson's flying knk watson base maxwell giroscope www.siliconsensing.com siliconsensing ? ? company and brand names belong to their respective owners. VDO SGH01-02
Laboratory Equipment
Manufacturers of Physics Laboratory Equipment for BS and MS students.
ses, techno, scientific equipment, scientific equipment services, techno instruments, roorkee, india In Brief Scientific Equipment Services and Techno Instruments are both ISO 9001: 2000 certified company engaged in manufacturing of complete laboratory experiments measuring instruments for BS and MS laboratories of Physics , Electronics Electrical Engineering . We are reputed for our quality products and excellent after sales support. PRODUCT QUICK SEARCH GENERAL LABORATORY INSTRUMENTS -- Digital Microvoltmeter, DMV-001 -- Digital Nanoammeter, DNM-121 -- Digital Picoammeter, DPM-111 -- True RMS AC Millivoltmeter, ACM-102 103 -- High Voltage Power Supply, EHT-11 -- Electromagnet Power Supply, EMU-75 DPS-175 -- Electromagnet Power Supply, EMU-50 DPS-75 -- Digital Gaussmeter, DGM-102 -- Digital Gaussmeter, DGM-202 -- Digital Gaussmeter, DGM-103 -- Digital Gaussmeter, DGM-204 -- PID Controlled Oven, PID-200 -- Travelling Microscope, TVM-02 -- Travelling Microscope, TVM-03 -- Regulated Power Supply, PS-12 -- Function Generator, FG-01 PHYSICS AND MATERIAL SCIENCE LAB EXPERIMENTS -- Planck's Constant Experiment (By Photoelectric Effect) -- Planck's Constant Experiment (By LED) -- Frank Hertz Experiment -- Four Probe Experiment, DFP-02 (Basic Model) -- Four Probe Experiment, DFP-03 (Advance Model) -- Four Probe Setup - Research Model -- Four Probe Setup, FP-01 (For Resistivity Mapping) -- Measurement of Magnetoresistance -- Two Probe Method (High Resistivity Measurement) -- Electron Spin Resonance Spectrometer -- Study of Thermoluminescence of F-centers -- Hall Effect Experiment -- Dependance of Hall Coefficient on Temperature -- Quinck's Tube Method -- Magnetic Hysteresis Loop Tracer -- Study of PN Junctions -- Study of Diode Characteristics -- Study of Dielectric Constant PHYSICS ELECTRONICS LAB EXPERIMENTAL SETUPS -- Study of Transistor Coupled Amplifier -- Study of Multivibrators -- Study of Semiconductor Diode Characteristics -- Study of h-Parameter of a Transistor -- Study of Power Supply (Solid State) -- Study of Modulation and Demodulation -- Study of Basic Operational Amplifier, Type-741 -- Study of Application of Basic Op. Amp., Type-741 -- Study of Astable Monostable Multivibrator, Type-555 -- Study of Integrated Circuit Regulator, Type-723 CONTROL LABORATORY EXPERIMENTS -- Digital Control System, DC-01 -- D.C. Motor Study, DCM-01 -- D.C. Position Control System, DCP-01 -- D.C. Speed Control System, DCS-01 -- Temperature Controller System, TCS-01 -- PID Controller, PID-01 -- Linear Variable Differential Transformer, LVDT -- Stepper Motor Study, SM-03 -- Relay Control System, RCS-01 -- Compensation Design, CD-02 -- Linear System Simulator, LSS-01 -- Potentiometeric Error Detector, PED-01 -- Light Intensity Control, LIC-01 -- Microprocessor Device Controller, MDC-01 -- Study of Temperature Transducers, STT-01 -- Stroboscope, STB-01 16, CIVIL LINES, ROORKEE-247 667, U.A. (INDIA) Phone : +91-1332-272852, Fax: +91-1332-274831, Email: info@sestechno.com 2003 SES. All rights reserved. Website designed by Krishnadasan Design
Bioscan, Inc.
Manufacturer of instrumentation, including HPLC, DNA RNA spectrophotometer, plate reader, counters with distribution from Washington, DC.
BIOSCAN - Welcome Your browser does not support script SEARCH Check out HiSPECT Setting new sensitivity and resolution standards for small animal SPECT imaging. PET NUCLEAR MEDICINE Bioscan provides breakthrough technology for one of the fastest growing medical imaging technologies on the market - PET. Click here for more information on the products and services Bioscan offers. LIFE SCIENCES Bioscan provides a wide range of radiochromatography detection equipment used in the production of radiopharmaceuticals and in the development of radiolabeled compounds for life science and pharmaceutical research. Click here for more information. MOLECULAR IMAGING Bioscan introduces HiSPECT, a small animal SPECT system which sets new standards for resolution and sensitivity. Click here for more information. Home | P.E.T. Chemistry Nuclear Medicine | Life Sciences | Services and Support | About Bioscan | Technical Application Notes | Contact Bioscan Terms - Conditions of Use | Privacy Policy | Copyright 1985 - 2005 Bioscan, Inc. All rights reserved
Scienglass
Supplier of glass and glass metal instruments and accessories for scientific applications.
Scienglass - Scientific Research glass blowing - Manufacturers and Consultants Index Page Scientific Research Glass Blowing - Manufacturers and Consultants Home Page AnalyticalInstruments Surface Tension Environmental Glassblowing Glass toMetal Seals More Information Optical Windows Contact Us Welcome to the Scienglass Web Site. Scienglass was established over thirty years ago by Ken Calkin. Ken was trained in Scientific Glassblowing, Glass Technology and Glass Engineering. He was in charge of a Research Glass Department in one of our largest defence industry organisations and then for many years employed in a senior position supplying this expertise to a large chemistry research department at Oxford University. Scienglass endeavours to keep up-to-date with the latest technology and supplies a broad range of glass and glass metal instruments and accessories worldwide. Scienglass Instruments can be made to customers' requirements or we can design, or assist in the design, to meet specific requirements. Whether this is a one-off design or small production runs we will be happy to quote. Here is a list of what we do and the type of establishments we cover: * ANALYTICAL INSTRUMENTS * DEFENCE INDUSTRY * DU NOUY RINGS * ENVIRONMENTAL SCIENCE * EXPORTS * GLASSBLOWING LABORATORY GLASSWARE * GLASS TO METAL SEALS * OPTICAL CELLS OPTICAL WINDOWS RING DISC ELECTRODES * SURFACE TENSION MEASUREMENT ACCESSORIES * TELEVISION AND FILM * TENSIOMETERS * UNIVERSITY SCIENCE DEPARTMENTS * WILLHELMY PLATES Copyright Scienglass 2002- All Rights Reserved
Mesytec GBR
Develops, produces and distributes detector electronics and readout systems for particle and photon detectors. Single and multi channel systems are available for SSDs, PMTs, and PSDs.
mesytec - innovative measurement systems innovative measurement systems instrumentation, development and consulting for scientific measurement needs especially for particle and photon detector systems contact products services Overviews: readout and data acquisition systems for: neutron detectors - silicon detector systems News: MPR-1 single channel charge integrating preamplifier for silicon detectors MHV-4 4 channel bias voltage supply for silicon detectors impressum mesytec gbr - wernher-von-braun-str. 1 - 85640 putzbrunn - germany tel: +49-89-456007-30 fax: +49-89-456007-39 info@mesytec.com
ORTEC Products
Supplier of radiation measurement systems, electronic instruments and modules, high resolution radiation detectors, and data analysis software for general nuclear research and related fields. Leading supplier of measurement systems, electronic instruments and modules, high-resolution radiation detectors, and data analysis software for high-resolution nuclear spectroscopy, fast-timing and pulse-height analysis. For general research in the nuclear industry and related fields.
ORTEC is a leading supplier of radiation detection and measurement systems, electronic instruments and modules, high resolution radiation detectors, and data analysis software for both OEM and end-user applications of high resolution nuclear spectroscopy, E-commerce Site Financing Options New on this Site Applications Products Contact Us Application Notes Training Courses News Releases Technical Papers Conf. Meeting Schedule Service Center Alliance Partners Electronic Newsletter About ORTEC Site Map Don't be fooled by the familiar face. Click the picture and find out about the worlds most advanced Ge spectrometer, the NEW DSPEC Pro. HPGe Detector Stocklist Charged-Particle Detector Stocklist NEW. . . more Charged-Particle Detector Stocklist now available DHS Contracts for Prototypes of Advanced Portal Monitor ORTEC is a provider of detectors, pulse-processing electronics, software, and spectrometers for measuring and quantifying the energy and time distributions of optical photons, X rays, gamma rays, charged particles, and radioactive nuclides... in the laboratory or the natural environment.
Vorg Electronics
Manufacturer of electronic transformers for halogen lamps, photomultiplier tube bases, cables, electronic transformers, PMT bases, PMT Arrays, transformers, and custom built electronics
Vorg Electronics
Colutron Research Corporation Home Page
Manufactures ion sources, ion guns and components. Also, high resolution beam imaging systems for ion, electron, and neutral beams as well as x-rays.
Colutron Research Corporation Home Page COLUTRON RESEARCH CORPORATION HOME PAGE Catalog and Information Request Form Free Download of Colutron Research Text Books Tiltles: (Atmospheric Electrostatics, The Deadbeat Universe) Products and Services Information . High Voltage Power Supply Modules Home Office: Colutron Research Corporation 2321 Yarmouth Ave. Boulder, CO 80301 USA Phone:(303) 443-5211 , FAX: (303) 449-5050 Email Addresses: Sales: saleshelpNOSPAM@colutron.com Technical help: technicalhelpNOSPAM@colutron.com Customers, please remove the NOSPAM part of the email address above when sending emails. This will allow us to answer you quicker by removing potential spam from our email server. Thanks! Sales Offices: JAPAN: APACE Science http: www.apace-science.com e-mail:Hiro Nishimura, hiro.nishimura@apace-science.com Daini-Mitomo Building 6F., 2 - 8, Ebisu-Nishi 2-Chome, Shibuya-Ku, Tokyo 150-0021 Japan Tel: 81-(0)3-3463-3204 , Fax: 81-(0)3-3463-3205, Contact: Hiro Nishimura KOREA: Soltech CO. Email:Hung Soon Chung, soltech1@chollian.net Room 202, Songchun Bldg., 503, Shinsa-Dong, Kangnam-Ku, Seoul, 135-120, South Korea Tel : 82 (02) 3444-8232, FAX:+82 (02) 3444-8234 Contact: Hung Soon Chung Copyright Colutron Research Corporation 1995, 1996, 1997, 1998, 1999, 2000. All rights reserved. Last modified 10 05 05
Tectra Plasma Sources
Provides the Tectra Plasma Source, a multi-purpose source producing either atoms or ions and finds uses in a range of HV and UHV applications.
Plasma Source as atom source, ion source and atom ion hybrid source (microwave plasma source) plasma source, plasma ion source, ion source, ECR source, atom source, atom beam source, microwave plasma source, plasma, source, microwave ion source, broad beam ion source, RF plasma source, RF source, kaufman ion source, kaufmann ion source, kaufman source, kaufmann source, microwave, ECR, RF Plasma Source: introducing the second generation of Atom Sources, Ion Sources and Atom Ion Hybrid Sources. tectra Gen2 Plasma Source Since 1997 tectra has produced more than 50 Plasma Sources as Atom Source, Ion Source and Atom Ion Hybrid Source. Based on this experience we now present the second generation sources, the Gen2. New Features of Gen2 Plasma Source: high performance direct microwave coupling (without need of tuning) improved microwave guide with minimised attenuation higher plasma density resulting in higher ion current bakeable magnets, still on air side, with closed cooling loop more compact, space saving air side setup Al2O3 plasma cup now standard with higher yield of secondary electrons and better resistance against aggressive gases additional display of extraction current to optimise the beam shape improved stability of microwave generation new grid supply for more versatile, wide range ion energies of 20eV - 2keV with same grid set LED to show if plasma is on or off pdf version of data sheet (206kB) Plasma Source Atom Source, Ion Source and Atom Ion Hybrid Source The tectra Plasma Source* is a multi-purpose source which can easily be user configured to produce either atoms or ions and finds uses in a wide range of HV and UHV applications. By easy exchange of the beam optics the source can be configured to operate in several distinct modes. The main modes are Atom Source, Ion Source and Atom Ion Hybrid Source. Besides delivering different species (atoms, ions, radicals) the Plasma Source covers the complete energy range from neutral thermal atoms to above 1.500eV. The shape of the beam and current densities can be altered by using different beam optics. A plasma is created in a coaxial waveguide by evanescent wave coupling of microwave energy at 2.45GHz. The plasma is further enhanced by the ECR action of a quadrupole magnetic field producing an extensive surface in the plasma on which electron cyclotron resonance at the given microwave frequency takes place. tectra Plasma Source + Power Supplies (new pictures coming soon) Key Features: Filamentless Suitable for use with most gases including reactive gases such as oxygen, chlorine, hydrogen, nitrogen etc. No microwave tuning Factory set. Simply turn the plasma on and off. User configurable The extraction optics are designed to be quickly and easily exchanged allowing users to customise their source to suit a particular combination of sample size, working pressure and current density. Easily exchanged apertures enable beam diameter, gas load and atom flux to be optimised. simple bakeout preparation new bakeable ECR magnets allow simple bekeout preparation by just undoing 4 screws. The magnets are still on the air side on a closed cooling loop. Hence no sintered material is in-vacuum. Al2O3 plasma region Alumina plasma cup as standard with higher yield of secondary electrons and better resistance against aggressive gases such as Oxygen compact the air side envilope sizes are brought to a minimum of just 258mm from flange (knife edge side) to case end (see schematic ) Integration of the robust microwave generator and the ion source, mean that no tuning of the source is required and there is no waveguide to construct or install. Due to the evanescent wave coupling, no electrodes are present in the plasma i.e. no filaments or other metal. The plasma is entirely surrounded by alumina or other dielectric materials e.g. BN. Therefore the source is also suitable for use with reactive gases such as oxygen and hydrogen. A selection of apertures and conductances allows the optimum balance between gas flow, working pressure and beam current to be achieved. The source is designed as a true UHV source making it suitable for use in UHV applications such as MBE as well as sputtering and other HV processes. Stainless steel, OFHC copper, BN, alumina and Kapton are the only materials exposed to the vacuum. All joints are welded. The magnets and all microwave parts are easily removed for bakeout at temperatures in excess of 200C. Modes of operation: Four distinct modes of operation are possible with this source depending principally on the beam optics which are fitted. The beam optics are constructed as one piece and may easily be exchanged by the user to allow the source to be used in another mode. The parts necessary to convert the source from one mode to another are all retrofittable by the user and can be added at any time in the future as research needs change. (1) Atom source The specially designed aperture plate inhibits ions from escaping from the plasma, yet allows reactive neutrals to escape and form the dominant beam fraction. The emitted particles are largely thermalised through multiple collisions on passing through the aperture. These neutrals have proven to be very effective in low damage surface treatments such as nitridation and oxidation(1,2). The further addition of an ion-trap option can completely remove the residual ion content from the beam where this may be of concern. (2) Downstream plasma source With this aperture plate a larger proportion of the charged particles in the plasma are allowed to escape. There is no active extraction or acceleration of the charged particles but a considerably higher ion current reaches the sample in this mode as compared with the atom source above. Samples mounted a few centimetres from the source are said to be downstream of the ion source and away from the most energetic species. Ion energies are defined by the intrinsic plasma potential and are around 25eV. (3) Hybrid source The beam optics in this mode combine the atom source aperture plate with electrodes providing active extraction of ions from the plasma. With no voltage applied to the electrodes the source functions like the atom source at (1) above. With voltage applied to the electrodes, ions with controllable energy can be added to the atom beam. Total beam current is in the ~50A range. Using this mode the advantages of both a low kinetic energy, chemically reactive, atom beam and a much higher kinetic energy, highly anisotropic ion beam may be explored. (4) Broad Beam Ion Source Dual or triple high conductance grid electrodes are used to produce the broad beam ion source mode. For sputtering applications, current densities at ~120mm of 2mA cm (focused optics) with ion energies of 1.3keV can be obtained while for deposition assistance (Ion Assisted Deposition or Dual Ion Beam Sputtering) the beam energy can be reduced to less than 100eV with current densities still in the 0.05mA cm range. Atom Source Mode Applications: Nitriding e.g. GaN, AlN, GaAsN, SiN etc. Hydrogen cleaning, hydrogen assisted MBE. Oxidation e.g. ZnO, Superconductors, Optical coatings, Dielectrics. Doping e.g. ZnSe Ion Beam Mode Applications: Ion beam assisted deposition (IBAD) for both UHV and HV processes Sputter deposition and dual ion beam sputtering Sputter cleaning surface preparation in surface science, MBE and HV sputter processes. In-situ etching e.g. Chlorine Specifications a) General Vacuum compatibility: Fully UHV compatible Bakeable: 200C Microwave power: 250W max at 2.45GHz Magnet type: Permanent rare-earth. Removeable for bakeout without breaking vacuum Mounting: NW63CF (4.5"OD) In vacuum length: 300mm (custom lengths possible): In vacuum diameter max = 57mm Beam diameter: ~25mm at source (narrower beams also easily produced) Plasma cup: Alumina Aperture: Alumina or Boron Nitride Gas flow rate: 0.01-100sccm depending on aperture selected Working pressure: ~10-7 Torr to 5x10-3 Torr depending on aperture, pump and application - please contact tectra to discuss your application. Differential pumping option available Working Distance: 50mm-300mm. 150mm typical Cooling: Fully water-cooled (including magnetron) Power supplies: Microwave Grid supply* * Ion and Hybrid Source only 19 rack mount. 3U height. 230VAC, 50Hz or 115VAC, 60Hz 19 rack mount. 3U height. 230VAC, 50Hz or 115VAC, 60Hz b) Atom source Atom flux 2x1016 atoms cm2 s at 10cm Beam divergence: ~ 15 half-angle typical Gases Nitrogen, Oxygen, Hydrogen (any most other non-condensible gases) Working pressure: 1x10-8 mabr to 1x10-1 mbar typical (using 500l s pump) and depending on selected grids, pump, optional differential pumping and gases. Working distance: 50mm to 300mm (150mm typical) Options: (1) Residual Ion Trap (2) Differential pumping (3) Ion source retrofit kit (4) Plasma igniter c) Ion source Ion current: 0 - 20mA (max.). Total beam current measured at 15cm Ion current density: 2mA cm2 at 1.3keV and 0.05mA cm2 at 100eV at 120mm distance. Ion energy: 25eV - 2000eV Beam diameter: ~25mm at source (narrower beams down to 1mm also easily produced) Extraction grids: Molybdenum (Graphite optionally) Focused and collimated beam grid sets available Gas flow rate: 5-10sccm typical (lower and higher flow ratespossible) Working pressure: 1x10-8 mabr to 1x10-1 mbar typical (using 500l s pump) and depending on selected grids, pump, optional differential pumping and gases. Working distance: 50mm to 300mm (150mm typical) Options: (1) Immersed filament beam neutralisation (2) Plane, focused and divergent grid sets made from molybdenum or pyrolytic graphite (3) Differential pumping (4) Shutter (5) Faraday Cup integrated in shutter Options Plasma Source with differential pumping for low pressure operation and with shutter Plasma Source with differential pumping for high pressure operation special Atom aperture for reduced flux small samples Atom aperture with quartz collimator tube special Atom aperture for reduced flux small samples Elongated version with second gas inlet References: The role of neutral oxygen radicals in the oxidation of Ag films. A. A. Schmidt, J. Offermann and R. Anton. Thin Solid Films 281-282 (1996) 105-107. Design and performance of a versatile cost-effective microwave ECR plasma source for surface and thin film processing. R.Anton, T. Wiegner, W. Naumann, M. Liebmann, C. Klein, C. Bradley. Rev.Sci.Instr. Feb 2000 tectra GmbH reserves the right to alter specifications without notice. Application Note *developed in collaboration with Prof. Dr. Anton, University of Hamburg, Inst. fuer Angewandte Physik contact: tectra GmbH Reuterweg 65 D-60323 Frankfurt M. Tel: Germany (+49) (0) 69 - 72 00 40 Fax: Germany (+49) (0) 69 - 72 04 00 email: info@tectra.de Contact Home Products last modified 15.11.03
Solar Energy Photovoltaics Tutorial Package
Provides an interactive tutorial package comprising of a comprehensive tutorial and laboratory grade photovoltaic module for "hands on" experiments and calculations.
Company Home Page PHOTOVOLTAICS Please click on any of the following links to the site you require: Educational Tutorial Packages Solar Pow ered Street Bus-stop Lighting Solar Powered Aviation Landing Lights
Edmund Optics
Manufacturing and integration of optical components. Includes lenses, prisms and filters. Custom and off the shelf optics.
The World's Largest Inventory of Optical Components Edmund Optics has sales offices around the world. Please select your country: Albania Algeria Andorra Angola Antigua and Barbuda Argentina Armenia Australia Austria Azerbaijan Bahamas Bahrain Bangladesh Barbados Belarus Belgium Belize Benin Bermuda Bhutan Bolivia Bosnia and Herzegovina Botswana Brazil Brunei Darussalam Bulgaria Burkina Faso Burma Burundi Cambodia Cameroon Canada Cape Verde Cayman Islands Central African Republic Chad Chile China Colombia Comoros Costa Rica Cote d'Ivoire Croatia Cyprus Czech Republic Democratic Rep of Congo Denmark Djibouti Dominica Dominican Republic East Timor Ecuador Egypt El Salvador Eritrea Estonia Ethiopia Falkland Islands Faroe Islands Fiji Finland France French Guiana French Polynesia Gabon Gambia Georgia Germany Ghana Gibraltar Greece Greenland Grenada Guadeloupe Guatemala Guinea Guinea-Bissau Guyana Haiti Honduras Hong Kong Hungary Iceland India Indonesia Ireland Israel Italy Jamaica Japan Jordan Kazakhstan Kenya Kiribati Kuwait Kyrgyzstan Laos Latvia Lebanon Lesotho Liberia Liechtenstein Lithuania Luxembourg Macau Macedonia Madagascar Malawi Malaysia Maldives Mali Malta Mauritania Mauritius Mexico Micronesia Moldova Monaco Mongolia Morocco Mozambique Namibia Nauru Nepal Netherland Antilles Netherlands New Caledonia New Zealand Nicaragua Niger Nigeria Norfolk Island Norway Oman Pakistan Palau Panama Papua New Guinea Paraguay Peru Philippines Poland Portugal Qatar Republic of the Congo Reunion Romania Russia Rwanda Saint Kitts and Nevis Saint Lucia Saint Vincent and the Grenadines Samoa San Marino Sao Tome and Principe Saudi Arabia Senegal Serbia and Montenegro Seychelles Sierra Leone Singapore Slovakia Slovenia Solomon Islands Somalia South Africa South Korea Spain Sri Lanka Suriname Swaziland Sweden Switzerland Taiwan Tajikistan Tanzania Thailand Togo Tonga Trinidad Tunisia Turkey Turkmenistan Turks and Caicos Islands Tuvalu Uganda Ukraine United Arab Emirates United Kingdom United States Uruguay Uzbekistan Vanuatu Vatican City Venezuela Vietnam Yemen Yugoslavia, Federal Rep Zambia Zimbabwe Remember my selection Copyright 2003, Edmund Optics Inc. 101 East Gloucester Pike, Barrington, NJ USA 08007-1380 Phone: (800)363-1992, Fax: (856) 573-6295 Site co-developed by InterActive Network Systems P.O. Box 1429, Blackwood, NJ 08012 USA Phone: (856)227-4428
AJA International Inc.
Manufactures thin film technology (sputtering). Also produces microwave power supplies, substrate heaters, sputtering systems and targets, ion sources, and RF DC power supplies.
Sputtering Systems with AJA International Inc. 809 Country Way North Scituate, MA 02066 Phone: (781) 545 - 7365; Fax: (781) 545 - 4105 topgun@ajaint.com Sputtering Equipment Substrate Heaters Microwave Equipment Ion Sources Company Info. E-mail AJA Representation Hot News New From AJA New ATC1500-F con-focal UHV sputtering system with load-lock delivers + - 1.5% uniformity over 4" substrate. System is fitted with an 850C rotating, RF biasable heater and (3) or (4) 2" target magnetrons with in-situ source head tilting to allow uniformity optimization at different working distances. AJA introduces the ZERO FOOTPRINT ATC3400-H batch coater. This 34" diameter chamber processes up to (6) 8" wafers, (9) 6" wafers or hundreds of small substrates with up to 4 different materials. The system shown is fitted with 400C backside quartz lamp heating, mag-lev turbo and a dry pump. AJA now offers 800C, rotating substrate heaters with RF bias for 3", 4", 6" and 8" substrates. These units can be ordered with a rotating, transverse magnetic field assembly with less than 2 degree skew. AJA uses special quartz lamp technology with 4000 hour lamp lifetime and low replacement cost. AJA International, Inc. is pleased to offer the following products: SPUTTER SOURCES SPUTTERING SYSTEMS PVD EQUIPMENT AJA manufactures ATC and Rapier Series magnetron sputtering systems; PVDX e-beam thermal sputter multi-technique deposition systems; A300-XP, A3CV, Stiletto and Nautilus magnetron sputter sources; peripheral equipment for substrate heating, cooling, RF biasing and motion. Sputtering systems are configured primarily for RD and pilot production with either UHV or HV construction. AJA International, Inc. also manufactures a wide range of magnetron sputter sources for RD and production applications ranging in target size from 1 to 40 and up to 12 ID cylindrical. Nautilus Series rotating magnetron sputtering sources are designed for production coating tools. AJA also offers sputter targets, PVD materials, and RF DC power supplies and switchboxes for sputter deposition. MICROWAVE AJA International, Inc. is the exclusive US distributor for Sairem microwave generators, power supplies, tuners, circulators, dummy loads, waveguide components, power splitters and microwave detectors. With extensive experience, the AJA Sairem combination will find a cost effective solution to your microwave application requirement. ION PLASMA SOURCES AJA is the exclusive US distributor for the unique COPRA plasma ion source manufactured by CCR. These sources can be used for many applications including ion assisted sputtering, ion beam sputtering, etching with almost any gas, 80% reactive gas dissociation, MTJ thin film oxidation, amorphous carbon deposition, and many more. This patented, RF powered source can deliver high currents even at low energies. AJA INTERNATIONAL, Inc. 809 Country Way North Scituate, MA 02066 Phone: (781) 545 - 7365; Fax: (781) 545 - 4105 topgun@ajaint.com Established in 1989, AJA International, Inc. is headquartered in North Scituate, Massachusetts, USA, with representation around the world. AJA International home page Sputtering Equipment Sputtering Targets PVD Materials Hot News Company History Philosophy E-mail AJA for quote or info Substrate Heaters Ion Plasma Sources Microwave Equipment Worldwide Representation
Desert Cryogenics
A manufacturer of cryogenic systems for use in device testing and physics, electronics, and materials research.
Probe Stations Home Systems Probe Stations Probe Stations Model Max of probe arms Temperature range Max sample size Magnet field HFTTP4 4 2 K to 400 K 25 mm (1 in) diamater 1 T horizontal field VFTTP4 4 2 K to 400 K 51 mm (2 in) diamater 2.5 T vertical field FWP6 6 4.5 K to 475 K 102 mm (4 in) diameter Not applicable TTP6 6 3 K to 475 K 51 mm (2 in) diameter Not applicable TTP4-1.5K 4 1.5 K to 475 K 25 mm (1 in) diamater Not applicable TTP4 4 3 K to 475 K 51 mm (2 in) diameter Not applicable *The above specs include equipmet options. Model HFTTP4 Features 10 kOe (1 T) horizontal field Operation from 2 K to 400 K Measurements from DC to 67 GHz Up to four micro-manipulated probe arms Up to 25 cm (1 in) diameter wafers More on HFTTP4 Probe Station Model VFTTP4 Features 25 kOe (2.5 T) vertical field Operation from 2 K to 400 K Measurements from DC to 67 GHz Up to four micro-manipulated probe arms Up to 51 mm (2 in) diameter wafers More on VFTTP4 Probe Station Model FWP6 Features Operation from 4.5 K to 475 K Measurements from DC to 67 GHz Up to six micro-manipulated probe arms Up to 102 mm (4 in) diameter wafers Sample stage with in-plane translation and in-plane rotation More on FWP6 Probe Station Model TTP6 Features Operation from 3 K to 475 K Measurements from DC to 67 GHz Up to six micro-manipulated probe arms Up to 51 mm (2 in) diameter wafers In-plane sample stage rotation More on TTP6 Probe Station Model TTP4-1.5K Features Operation from 1.5 K to 475 K Measurements from DC to 67 GHz Up to four micro-manipulated probe arms Up to 25 mm (1 in) diameter wafers More on TTP4-1.5K Probe Station Model TTP4 Features Operation from 3 K to 475 K Measurements from DC to 67 GHz Up to four micro-manipulated probe arms Up to 51 mm (2 in) diameter wafers More on TTP4 Probe Station Home | Temperature | Magnetics | Systems | Order Now Pricing | Service | Contact Us | What's New | Search | Site Map Copyright 2005 Lake Shore Cryotronics, Inc.
Pacific Nanotechnology, Inc.
Provides scanning probe products and services that facilitate advances in nanotechnology and nanoscience.
Advancing Nanotechnology Seminar on September 22, 2005... Standards References... September 2005 Image of the Month... Home About Us Products Our Customers News Events Application Gallery Technology Contact Careers Newsletter search of web-site " Buy Probes Online Click here to buy probes... home inquire newsletter search site map Advancing Nanotechnology Pacific Nanotechnology, Inc. provides products and services that facilitate advances in nanotechnology and nanoscience. Our atomic force microscope (AFM) products are optimized for research development and process control applications when visualization and measurement of nanometer sized surface structure is critical. View from a video microscope of a cantilever scanning over a sample on the Nano-R AFM. More information... New... Crystal Scanner With the new crystal scanner option and Point Scan technology for the Pacific Nanotechnology probe microscopes, everyone can get the highest quality nanoscale topographic images. More information... Sales Offices: United States Europe Israel Japan Asia Australia New Zealand 3350 Scott Blvd. 29, Santa Clara, CA 95054 Phone: 1-800-246-3704 Direct: 408-982-9492 Fax: 408-982-9151 Design development WDS Design Group Copyright 2002 Pacific Nanotechnology, Inc. All Rights Reserved. No part of this site can be copied without prior agreement with Pacific Nanotechnology.
Oxford Applied Research
Provides ion sources, atom sources, gas crackers, evaporation sources, as well as other specialized UHV components for MBE and surface science requirements.
Oxford Applied Research Home About us News Contacts Products ........... Valved RF crackers Valved Organic evaporators Nanocluster solutions Mini e-beam evaporators Thermal gas crackers RF atom sources RF ion sources DC ion sources Low energy ion source Ion milling systems Ionised beam K-cells Compound Dissociation K-Cell Mini Ion Guns Gas dosers Hydrice TM Oxford Applied Research Crawley Mill Witney, Oxon OX29 9SP, UK Tel: +44 1993 773575 Fax: +44 1993 702326 Oxford Applied Research is a supplier of UHV and HV components and systems for the deposition and characterisation of thin films. Our speciality lies in providing unique solutions to common deposition challenges. Nanotechnology and Surface Science Nanocluster Solutions Mini e-Beam Evaporators Thermal Gas Crackers Piezo-electric Gas Doser Ion Sources RF Ion Sources DC Ion Sources Mini Ion Guns Low Energy Ion Source MBE Components RF Atom Sources Valved RF Solids Crackers Valved Organic evaporators Compound Dissociation K-Cell Last updated:15 11 2005 Home About us News Contacts Site map
SPECS GmbH
Manufacturer of surface analysis components and systems.
nano, SPECS XPS, instrument, system, STM, LT-STM, MBE, LEED, EELS, Auger, ESCA, UPS, SIMS, PEEM, LEEM, Kelvin Probe, VT-STM Competence in Surface Analysis Surface Analysis Instruments and Materials Deposition Equipment for XPS, STM, LT-STM, MBE, LEED, EELS, UPS, Auger, ESCA, SNMS, RHEED, E-Beam Evaporators, Effusion Cells, Plasma Atom Ion Sources Product Guide Surface Analysis STM LT-STM LEEM MBE-Products Techniques Lists of publications N E W S About SPECS Contact SPECS How to find us Conferences International Support Surface Science Links Evaporation Guide Site Map SPECS GmbH Voltastrae 5 13355 Berlin Phone: +49 30 4678240 Fax: +49 30 4642083 support@specs.de
Atomic Hydrogen Source
Produces a thermal hydrogen cracker with uses such as damage free cleaning of surfaces.
Atomic Hydrogen Source H-flux Atomic Hydrogen Source In cooperation with Prof. Dr. E. Bertel of the University of Innsbruck we developed the new H-flux Atomic Hydrogen Source. The source works by thermally dissociating hydrogen in an electron bombardment heated tungsten capillary. H-flux Atomic Hydrogen Source with optional shutter Atomic Hydrogen can be used in surface science and thin film technolgy (MBE, GSMBE) mainly for the following applications: damage free in situ cleaning e.g GaAs, InP, Ge and Si. Removal of residual oxygen and carbon. Low temperature cleaning Surfactant - improvement of layer properties during growth post growth surface treatment improvement chemical passivation and surface reconstruction annealing of amorphous silicon Key features of the H-flux Atomic Hydrogen Source are the zero residual ion current and almost 100% cracking efficiency, due to the superior and unique Bertel design. Integral watercooling is included as standard to minimise heat load in the system and outgassing. A manual shutter is available as option. Typical operating conditions: the flux of Hydrogen atoms at 10-9 mbar in a chamber with typical pumps at a distance of 10cm is ca. 5x1013 atoms cm. The H-flux Atomic Hydrogen Source is UHV compatible and mounted on a NW35CF (2.75"OD) flange, making the source an easy retrofit to existing vacuum systems. Atomic Hydrogen Source (front view) References: "Simple source of atomic hydrogen for ultrahigh vacuum applications". U. Bischler and E. Bertel. J. Vc. Sci. Technol. A 11(2), Mar Apr 1993 "Quantitative characterisation of a highly effective atomic hydrogen doser". C. Eibl, G. Lackner, and A. Winkler. J. Vac. Sci. Technol. A 16(5), Sep Oct 1998. contact: Dipl.-Phys. Markus Mayer tectra GmbH Reuterweg 65 D-60323 Frankfurt phone: Germany (0) 69 - 72 00 40 fax: Germany (0) 69 - 72 04 00 email: info@tectra.de Contact Home Products last update: 2.6.01
Walker LDJ Scientific, Inc.
Manufacturer of magnetic measurement and analysis equipment. In addition, the company manufactures power supplies, laboratory electromagnets, and helmholtz coils.
Home C O N T E N T S t ABOUT US About Walker LDJ Scientific, our people, jobs, etc. t PRODUCTS I nfo about our products, data sheets, RFQ. t CONTACT US Get technical or customer support including RMA's. t IN THE NEWS P ress releases Calendar of events. Walker-LDJ Scientific introduces its newest high-accuracy gaussmeter... the MG-10D. Walker Scientific, a world leader in the field of magnetics and LDJ Electronics, Inc., the industry leader in magnetizing systems have come together to offer your best magnetics solutions. (800) 962-4638 - Contact our Webmaster . Copyright 2002 Walker LDJ Scientific, Inc. All rights reserved.
Quantum Design, Inc.
Provides automated materials characterization instrumentation - SQUID magnetometry, heat capacity, cryogenics, thermal conductivity, resistivity, helium 3, superconducting magnetics, susceptometry, physics and chemistry research.
Quantum Design WORLD HEADQUARTERS: map 6325 Lusk Boulevard San Diego, CA 92121-3733, USA 1.858.481.4400 Tel 1.858.481.7410 Fax Info@qdusa.com COPYRIGHT 2000 QUANTUM DESIGN ALL RIGHTS RESERVED. SITE UPDATED:
Inficon Holdings AG
Provides thin film deposition controllers, high sensitivity helium leak detectors, digital and analog vacuum gauge controllers, valves and fittings, and mass spectrometers and partial pressure controllers for gas analyzers.
INFICON Search: Semiconductor Vacuum Coating Processes Air Conditioning Refrigeration Industrial On-Site Organic Chemical Identification Monitoring Service Tools for HVAC R Automotive TripleGauge - three technologies in one compact gauge reduces cost and complexity of process and base pressure measurement Integrated Process Monitoring - Harness the Power of Integrated Process Sensors Continuous Chemical Monitoring System for Water - lab quality water analyses- unattended, automatic and reliable HAPSITE SituProbe Purge and Trap GC MS System - on-site, decision quality data on VOCs in water RF Sensor with FabGuard - real-time plasma process analysis that significantly reduces process variability Semiconductor International Magazine Features INFICON - In Situ Particle Detection for Pre-Metal Sputter Etch INFICON Hosts 2005 Analyst Day - Technology Seminar and Management Round Table Protec P3000 Helium Leak Detector Produces Reliable Results Even for Inexperienced Operators INFICON Publishes Half-Year Report 2005 Hot Ion Combination Gauge Measures 13 Decades With One Vacuum Connection and Automatic Self-calibrating Replacement Sensor HAPSITE Smart Chemical Identification System - Get fast, lab-quality data on-site to make critical decisions affecting life, health and safety INFICON Corporate Headquarters: Syracuse, NY, USA. Email: reachus@inficon.com :: FabGuard Sensor Integration and Analysis Systems :: Gas Concentration Controllers :: In Situ Particle Detectors :: Integrated Process Monitoring :: Leak Detectors :: RF Sensor Technology with FabGuard :: Residual Gas Analyzers :: Thin Film Deposition Controllers :: Vacuum Components :: Vacuum Gauges :: Vacuum Valves and Gas Dosing Systems :: Helium Leak Detectors :: Refrigerant Leak Detectors :: Service Tools :: Chemical Identification Systems (GC MS) :: Chemical Monitoring Systems (GC) :: Chemical Warfare Detection Systems (GC MS) :: Carbon Monoxide Meters :: Combustible Gas Leak Detectors :: Manifold Gauge Sets :: Refrigerant Charging Scales :: Refrigerant Leak Detectors :: Refrigerant Recovery Systems :: Ultrasonic Leak Detectors :: Vacuum Gauges :: Vacuum Pumps Home : Corporate Info : Investors : Newsroom : Product Index : Support : Contact Us Copyright 2005 INFICON
British Optical Ltd
International designer and manufacturer of optical and non-optical glass and glass protection system.
International Optics Limited British Optical Limited British Optical International Design And Manufacturer of Optical and Non-Optical Glass Product and Protection System. Enter The British Optical WebSite
CSEM Nano Hardness Tester
Producer and distributor of nano-hardness testers, a high precision instrument for the determination of the nano mechanical properties of thin films, coatings and substrates
nanoindenter nano-indenter nano hardness tester Indentation Elastic Modulus Return results 10 25 50 100 Nano Hardness Tester Features of the Nano Hardness Tester Fastest Nano Hardness Tester available. Hardness Young's modulus for depths as low as 15 nm . Automatic operation under Windows XP 2000 Spherical, Vickers and Berkovitch nano-indentations. Dynamic Mechanical Analysis for visco-elastic properties Creep, fatigue fracture toughness tests Mapping Option up to 1000 indents. Optional High and Low Temperature Testing AFM objective for nanometer scale imaging of indents. Possibility to add nano-scratch (NST) , micro-scratch (MST) and micro-hardness (MHT) modules. Industrial Platform for large samples is also available. See our full range of hardness testers Call us for a demo! Laboratory services also available Introduction to the NHT Nano Hardness Tester The Nano Hardness Tester is a high precision instrument for the determination of the nano mechanical properties of thin films, coatings and substrates. With the NHT you can quickly determine properties such as hardness and Young's modulus on almost any type of material - soft, hard, brittle or ductile. The NHT works on the following principle. An indenter tip, normal to the sample surface, with a known geometry is driven into the sample by applying an increasing load up to some preset value. The load is then gradually decreased until partial or complete relaxation of the sample has occurred. The load and displacement are recorded continuously throughout this process to produce a load displacement curve from which the nano-mechanical properties such as hardness, Young's modulus, stress-strain studies, time dependant creep measurement, fracture toughness, plastic elastic energy of the sample material can be calculated. The NHT can be used in a mapping mode to take data automatically from a variety of locations on your sample. The instrument can also be equipped with various sample holder such as a 300mm wafer chuck to fit your specific needs. Dynamic Mechanical Analysis (DMA) The Dynamic Mechanical Analysis uses sine wave loading curves to obtain a more complete analysis of the mechanical properties of viscoelastic materials. Measurement of the shift in phase angle, and amplitude between the imposed force sine wave and the penetration depth, produces the storage and loss modulus of the material. Faster Measurement The NHT design overcomes one of the basic problems of nano indentation testing - that of quickly locating the tip at the sample surface in order to commence measurements. The measuring head of the NHT uses a small 'contact ring' which advances ahead of the indenter tip. Because the position of the reference ring with respect to the indenter is already known the position of the sample surface can be quickly determined within a precision of 2-3 microns. As a results it is only during the final approach, in this 2-3 microns range, that the tip needs to be moved slowly in order to accurately determine an exact contact point. This unique feature brings speed measurement without concern for crashing the tip. The approach time is 10 to 50 times faster than other methods. (surface detection is very time consuming with most other instruments). Higher Thermal Stability The NHT takes the sample surface as its reference for measuring the penetration depth of the tip. This reduces the length of the so called system frame (the distance from the sample surface to indenter tip) to only 10mm. This distance can easily reach from 500 to 1000mm on standard nano-indenters. As the thermal stability depends on the length of the system frame (1-10nm per degree C per mm of material involved) the NHT has intrinsically better stability than instruments referencing below the sample. The sapphire ring also acts as a local environmental enclosure protecting the measurement spot from air currents, sound waves and changes in humidity and temperature, thus elliminating the need for special environmental conditions in order to obtain perfect measurements. With the use of the reference ring there is no need for stabilization time before and after the test. A complete software package for Indentation studies The software (Microsoft Windows XP 2000) includes a complete set of features for setting up the NHT and handling the data. Real time display of load versus displacement curves. Automatic calculation of hardness and elastic modulus with the Oliver and Pharr Techniques. Automatic data averaging Multi-cycle indentation with increasing load or depth for hardness, Young's modulus and stiffness versus depth. Multi-cycle for fatigue test. High Frequency mode analysis. Creep measurement by holding a constant maximum load or depth over time. Mapping of indentation up to 1000 points. Oliver Pharr, Quadratic and Tangential Analysis techniques. Easy point of contact verification for surface abnormalities. Positioning of each indent with the microscope. Images from color camera and AFM Objective directly incorporated in the file. Program each indent to a max depth or load. Control of loading unloading rates and pause time. Precise relocation of each indent. Export in ASCII format. Automatic Statistical Analysis of results tabulated with standard deviation. Large sample holder accommodates different types of sample The sample holder will accommodate samples up to 100 mm thick, on a work table 105 x 135 mm. Special sample holders are available to accommodate other sample sizes such as vacuum wafer holder for 12inch wafers. AFM Objective extends the applications of the NHT The combination of optical and scanning probe techniques gives you access to a whole range of capabilities with your NHT. The AFM objective fits to the NHT microscope in place of a standard optical objective. The AFM produces nanometer scale images revealing the imprint of the indents and other surface features in astonishing detail. The precise repositioning (0.5 micron) capability of the X-Y motorized table of the NHT combine with the large x-y ranges (20x20microns or 40x40 microns) of the objective ensures that the indent will always be in the center of the field of view in both optical and AFM modes. Optical inspection of large sample areas combined with nanometer resolution of the indents and other interesting micro and nano structures. Study of pile up around the indent. Critical Dimension ( CD ) measurements. Investigate etched structures and roughness of semiconductor surfaces. Profilometry of coatings and thin films. Specifications of the Nano Hardness Tester Depth Resolution 0.03 nm Maximum indentation depth 20 um Load Maximum Load 300 mN Resolution + - 1 uN Indentation positioning Work table dimension 105 x 135 mm X-Y range 30x21 mm (45mm optional) Spatial Resolution 250 nm Microscope Magnification 50 X and 1000 X (200X, 500X and AFM Objectives Optional ) Atomic Force Microscope Objective Resolution x, y, z, 1 nm Scan range 20 X 20 microns, (40x 40microns optional) Vertical range 2 microns (4microns optional) Instrument Dimensions NHT 425x375 mm, 500mm height Control unit 435x465 mm, 265mm height Total Weight 90Kg Specific Applications 13) Hardness of DLC-coated tappets- Automotive Industry Special Issue 12) Measurement of hardness as a function of depth in nitrided 316L stainless steel 11) In-situ Integrated Circuit (IC) characterization with the Nano Hardness Tester (NHT) 10) Nanoindentation with spherical indenters for characterization of stress-strain properties 9) Characterization of IC bonded gold wires with the Nano Hardness Tester (NHT) 8) Combined NHT AFM for investigating the mechanical properties of Cr2O3thin films 7) Combined NHT AFM for investigating the tip defects of common indenters 6) Combined NHT AFM for characterization of Silicon materials 5) Combined NHT AFM for characterization of coated systems 4) Atomic force microscopy of low load indentations into aluminum 3) New Integrated AFM Objective for better characterization of NHT indentations 2) Quality Control of IC bonding pads with the Nano Hardness Tester (NHT) 1) Nano Hardness Tester (NHT) for characterization of MoS2 thin films General Applications Semiconductor Technology Passivation layers Metallization Bond pads Mass Storage Protective coating on magnetic disks Magnetic coatings on disk substrates Protective coatings on CD's Optical Components Contact lenses Eye glass lenses Fibre optics Optical scratch resistant coatings Wear Resistant Coatings TiN, TiC, DLC Cutting tools Decorative coatings Evaporated metal coatings Pharmacological Tablets and pills Implants Biological tissue Automotive Paints and polymers Varnishes and finishes Windows General Engineering Rubber resistance Touch screens infoca@microphotonics.com [Return to Micro Photonics home page] [Return to mechanical testing menu] For Further information fill out our on-line request form or contact us at 1-866-333-4674: Micro Photonics Inc. PO Box 50443 Irvine, CA 92619-0443 Micro Photonics Inc. PO Box 3129 Allentown, PA 18106-0129
Aurelia Microelettronica
Belongs to CAEN group, sells a variety of nuclear and biomedical electronics.
CAEN, power supplies and data acquisition for physics for direct site access use the following links: Nuclear | Aerospace | Microelectronics | RFID Company
Mad City Labs, Inc.
Produces nanopositioning systems with sub-nanometer precision.
Mad City Labs: Nanopositioning, Nanopositioiners Tel: (608) 298-0855 Fax (608) 298-9525 Home | Products | Technical Information | International Sales | News | Contact Mad City Labs Home Product Guide Technical Information International Sales News Contact Mad City Labs Email Us Nanopositioning Catalog Featured Nanopositioning Products Nano-View The complete nanopositioning system offering long range motion with sub-nanometer precision. Nano-LP Series Still the lowest profile 3-axis nanopositioner available. Now with 200 m range of motion. Nano-PDQ Series Ultra high speed multi-axis nanopositioners for Stokes fluid drag measurements and other high speed tracking applications. Nano-MTA Series High speed 2-axis tip tilt mirror actuator which can be driven up to 400 Hz in the closed loop mode. Mad City Labs, Inc is the leading American manufacturer of nanopositioning systems with sub-nanometer precision at an affordable price. We have the largest product line of nanopositioning systems available and specialize in custom nanopositioner applications.We deliver the tools for nanotechnology in 30 to 45 days, and provide the highest level of customer service and satisfaction in the industry. Applications for nanopositioners include AFM, NSOM, Scanning Probe Microscopy, fiber positioning, interferometry, single molecule spectroscopy and lithography. Copyright 2005 Mad City Labs Inc.
Neocera Inc.
Provides pulsed laser deposition systems, metal oxide thin films and thin film devices, cryogenic temperature controllers, cryogenic sensors, magnetic and microwave microscopes, and sensor research and development.
Neocera, Inc. - Welcome to Neocera.com your solution for Pulsed Laser Deposition and Semiconductor Metrology New --- Magma Scanning Service --- Neocera is now offering scanning services using Neocera's state-of-the-art Magma C20 Scanning SQUID Microscope (SSM) Imaging System Article in Solid State Technology
The LDS Vacuum Shopper
Manufacturer and distributor of all types of vacuum equipment and components.
Right-aligned Column THE LDS Vacuum Shopper SAVE-This Week's Sale Items-SAVE LDS Purchases Sparrell Engineering a leading manufacturer of Custom vacuum and pressure feedthroughs-for details, click here Shop Online for Over 3,000 Vacuum Related Items Calibrated Gas Leaks Conflat Flanges Gauges Calibration Services Gauges New Gauges - Surplus ISO (Large Flange) Leak Detectors Buy Leak Detectors Rent Leak Detectors Spare Parts NW Flanges Pumps New Pumps Surplus Pumps Kits Traps Valves Really CHEAP Stuff University Only Items LDS also designs and fabricates custom leak detection and vacuum systems, vacuum components and chambers. Quality Vacuum Products for over 30 years. Our Vacuum Products catalog includes Mechanical Pumps, Calibrated Gas Leaks, Gauges, Vacuum Fittings, Flanges, Tubing, custom fixturing, Vacuum Equipment, Components, Chambers, Oil Filtration Systems, Traps, Gas Leak Gauge Calibration Services, Mechanical Turbopump Rebuilding and Leak Detector Repairs. Consulting for all leak detection and vacuum applications. Leak Detector rentals and on-site leak testing are also available. Thousands of items updated daily at the LDS Vacuum Store. LDS Vacuum Products, Inc. 773 Big Tree Drive Longwood, FL 32750 Phone: (407) 862-4643 Fax: (407) 862-8723 E-Mail LDS - hivacuum@aol.com ALL TYPES OF LOW COST VACUUM COMPONENTS RENT ALL TYPES OF VACUUM EQUIPMENT
Tantec USA
Manufacturer of surface treatment and analysis equipment and static electricity control equipment.
Industry Leader for Static Control Products, Surface Treating Systems and Surface Analysis Equipment See Video Static Control Applications Surface Treating Applications Surface Treating Video Demonstrations Surface Analysis Applications Industry Leader for Static Control Products, Corona Treating Systems and Surface Analysis Equipment. Static Control Video Demonstrations Sales and Manufacturing Sites Surface Analysis Video Demonstrations
Isotope Products Laboratories
Manufactures radiation standards, radiation sources, medical sources, and radiation source devices for health physics, medical, industrial, research, and nuclear power industries.
Isotope Products Laboratories NEW! IPL now distributes "NeuroShield"! NeuroShield is a patented shielding device for brain studies done with whole-body PET Scanners ... more
Vatell Corporation
Produces a line of HFM heat flux microsensors and circular foil heat flux gages.
Heat flux sensor - Vatell.com heat flux specialist bf sensor. fire smoke thermal analysis faa fire test nist calibration firee test radiation conduction We want to talk to you about your heat flux application. Contact us. Phone: (540) 961-3576 Fax: (540) 953-3010 e-mail: mkt@vatell.com heat flux sensor, gage, transducer - vatell offers hfm, thermogage, episensor, and bf, schmidt boelter and other heat flux measuring transducers, our heat flux sensors Products and Services Contact Us Which Transducer is Right for You? Company Background Some Useful Heat Flux Information: Articles and Product Literature about heat flux, journal articles references, etc. Newsletter - Thermateq"-nology (pdf) Do you want information on current topics in heat transfer and or the latest information on heat flux measurement instrumentation? Then contact us for a free subscription to Thermateq"-nology Heat Flux Units Conversion table (pdf) Online Unit Conversion Calculator for heat flux and other units (courtesy Cleave Books) Material Properties Database for a wide variety of materials (courtesy MatWeb) Our consultations are free! Contact us today about your heat flux measurement needs 20 Copyright 2001 Vatell Corporation. All rights reserved.
Mass Properties Measurement Instruments
Provides equipment to measure center of gravity, moment of inertia, product of inertia, igniter circuit testers, space simulators and gimbal balance machines.
Space Electronics - World Leader in Mass Properties Measurement Instruments CONTACTS REQUEST A QUOTE HOME PRODUCTS SERVICES LITERATURE ABOUT -- ALL PRODUCTS -- Center of Gravity (CG) Moment of Inertia (MOI) Combined CG and MOI Spin Balance Machines Weight and Center of Gravity Precision Centrifuges Gimbal Balance Machines Moment Weight Scales Circuit Testers Custom Instruments -- COMPONENTS AND PARTS -- Air Bearings Software Test Fixtures -- NEW PRODUCTS -- High Speed KSR Scripting Software -- ALL SERVICES -- Maintenance Consulting Seminars Measurement Services Machine Rentals Machine Relocations Certification Calibration Equipment Performance Certification Technical Papers Online Literature Online Tools --SAWE - Boston Chapter-- SAWE Boston Chapter - Main Page About the Boston Chapter About Space Electronics History Customer Commitment Location Login Space Electronics is the world leader in high-precision mass properties measurement. More about us SPECIAL OFFER 25% OFF All Mass Properties Measurement Services performed before December 31, 2005 Request a Quote Now French version German version Japanese version Portuguese version Spanish version Mass Properties Instruments KSR and MP Series measure Moment of Inertia and Center of Gravity Spin Balance Machines POI Series measure Dynamic Unbalance, Product of Inertia, Moment of Inertia, and Center of Gravity Moment Weight Scales FEATURED PRODUCT Gimbal Balance Machines Center of Gravity Moment Of Inertia Weight and Center Of Gravity Circuit Testers Gas Bearings Centrifuges Space Electronics LLC - 81 Fuller Way - Berlin, CT 06037 (USA) - Phone: +1 860 829 0001 - Fax: +1 860 829 0005 - Email: sales@space-electronics.com
Micromeritics Instrument Corporation
Provides instruments for evaluation of particle size, surface area, pore size, material density, and chemisorption. Includes online catalog and list of applications.
Particle Size Evaluation and Analysis Instruments - Micromeritics Today is Thursday, November 17, 2005 INSTRUMENTS FOR PARTICLE SIZE, SURFACE AREA, POROSITY, AND DENSITY Welcome to Micromeritics.com - An Industry Leader in Particle Science and Particle Technology Particle size , surface area , pore size , material density , and active surface area are characteristics that are crucial to the understanding of a variety of materials. This knowledge is essential in the development of products, the efficient utilization of raw materials, and the understanding of many natural phenomena. Pharmacology, cosmetics, nanotechnology, paints, pigments, food science, ceramics, textiles, geological science, and polymer science are some of the areas of science and technology that rely on Micromeritics' instruments to determine the physical characteristics of powders and solid materials. Micromeritics provides a complete line of scientific instruments and laboratory equipment targeted exclusively for areas of application and research involving particle science and particle technology, including the expanding area of nanoscience. Particle size analyzers employ laser diffraction, sedimentation, and electrozone sensing. Physical adsorption and mercury porosimetry instruments determine surface area and porosity. Material density can be determined by gas pycnometry and solids displacement. Chemical adsorption techniques are used to determine the active area of catalysts, metal dispersion, and surface energy. Temperature-programmed chemisorption (TPD, TPR, TPO) techniques are utilized in the chemisorption product line. Latest Micromeritics and Small Particle Technology News 10 18 2005 Micromeritics New ASAP 2420 Accelerated Surface Area and Porosimetry System 10 5 2005 Focus - Micromeritics Software Engineering Support 9 13 2005 Update on BOC-Edwards Vacuum Pumps More News Press Home | About Micromeritics | Products | Applications | Online Catalog | News Press | Lab Services | Customer Service | Contact Copyright 1996-2005 Micromeritics Instrument Corporation Privacy Policy | Site Map | Alcott Chromatography Site
Density Calibration Laboratory
Physics calibration laboratory, accredited by UK Government (UKAS). Produces liquid and solid density standards and calibrates hydrometers.
index WORLD-CLASS DENSITY METROLOGISTS The UKAS accredited laboratory of H D Fitzgerald is recognised as a leading world authority on density metrology. HD Fitzgerald's premises are designed, built and equipped exclusively for density measurement and calibration. Our laboratories guarantee compliance with the stringent ISO 9001 and ISO17025 requirements. WE OFFER A UNIQUE SERVICE: Production of traceable liquid standards for calibrating density meters Traceable calibration of hydrometers Production of traceably calibrated glass floats for density gradient columns Traceable calibration of density meters Supply of automatic density gradient column filler Production of the Alcofloat spirit test kit, a device to detect the watering down of alcoholic drinks. Almost all our calibrations have UKAS accreditation, and are supplied with UKAS calibration certificates, recognised worldwide. This gives complete confidence in the reliability and accuracy of the calibration. Please look at our current UKAS accreditation schedule (26.3 KB PDF) . OTHER EXPERT SERVICES INCLUDE: Manufacture and calibration of portable pressure pyknometry systems for proving on-line density meters. Determination of the coefficient of thermal expansion ( t) and compressibility ( p) of liquids. Independent evaluation and assessment of density meters. Technical assessment of Anton Paar DMA5000. (286KB PDF file) Technical advice and consultancy on all aspects of density measurement. CONTACT US: Telephone: +44 (0)1352 720774 Fax: +44 (0)1352 720249 E-mail: sales@density.co.uk Address: Cefn Du, Tremeirchion, St. Asaph, LL17 0US, United Kingdom site updated 25 03 05
Voss Scientific
Provides data acquisition and analysis, PC-based satellite telemetry, high-power microwave (HPM) sources, and computational electromagnetic products.
Voss Scientific Search Last update: 17 Aug 2004 Home Products Services Research Development Company Site Map Voss Scientific Data acquisition Synchronized Trigger Generator Antenna design Custom Software Computational electromagnetics Sensors and probes Voss Scientific 418 Washington St., SE Albuquerque, NM 87108 (505) 255-4201 Phone (505) 255-4294 Fax info @ spam vosssci.com
Sypris Test Measurement
Provider of on-site and mobile calibration services, test and evaluation services and electronic products under the F.W. Bell name including magnetic measurement instruments, current sensors and hall generators.
Sypris TestMeasurement Calibration Services Test Services Magnetics F.W. Bell Sypris Test and Measurement is a leading provider of calibration services, testing and component sourcing services, and specialty products that include state-of-the-art magnetic measurement instruments, current sensors and hall generators. We serve customers in a variety of markets, including military, aerospace, avionics, telecommunications, automotive, semiconductor, medical, FDA-regulated and more. Major corporations and government agencies choose Sypris for our exceptional breadth of offerings, our national reach, and our unrelenting commitment to delivering the highest quality products and services in the marketplace. As a subsidiary of Sypris Solutions, Sypris Test Measurement also offers customers the financial strength and stability that are essential to providing exceptional value in todays marketplace. From our headquarters in Orlando, Florida, Sypris Test Measurement operates three businesses and oversees more than 20 field locations across North America. On-site engagements in our customers locations and our fleet of mobile calibration units further extend our market presence. Sypris strives to be The One You Choose for calibration, testing and specialty products. We invite you to browse our site to learn more about why more leading corporations and government agencies are choosing Sypris. What's New? Investor Information Employment Contact Us Risk Factors Legal Notices
Nanofactory Instruments
Develops and markets scanning probe microscopy instrumentation, such as a combination TEM holder and STM instrument.
TEM electron microscopes: a new accessory for in situ measurements TEM electron microscopes: a new accessory for in situ measurements. TEM holder holders transmission electron microscope Gatan FEI Jeol Hitachi Nion Fischione, TEMSTM TEMAFM TEM-STM TEM-AFM STM-TEM AFM-TEM in-situ STM AFM probing scanning probe miscroscopes tunnelling tunneling, RHK Digital Instruments DME Omicron Nanosurf Pacific nanotechnology Triple-O, STM-holder AFM-holder Indenter-holder, nano nanoscale nanotech Carbon nanotube Carbon nanotubes nanowire nanowires point contact SWNT MWNT single-walled nanotubes multi-walled nanotubes fullerene fullerenes nanomanipulation nano-manipulation electron transport quantum dots
Spectra Gases
Specialty gases for high technology markets. Our core business is pure gases and gas mixtures for excimer lasers and lamps. Isotopic en-richment of gases for research. Manufacturer of rare, excimer laser, stable isotopic and environmental gases and gas mixtures.
Spectra Gases -Welcome to Spectra Gases Spectra is the global leader in next generation fine chemicals and high purity gases for the research, medical, fiber optic, semiconductor, environmental, laser, lighting and high purity gas handling equipment markets. Electronics - Semiconductor Spectra develops and manufactures the most unique semiconductor materials available anywhere in the world. We accomplish this by continually developing the most advanced manufacturing processes in our industry. Our cylinder surface treatment technology is just one example of how we support our customers' strict requirements. Spectra is the world's leading producer of isotopic semiconductor products. Isotopic materials provide optimal performance for current and emerging wafer manufacturing, leading to increased yields, less waste, optimal efficiencies and more durable chips. Environmental Spectra's Environmental Division is recognized around the world as the pre-eminent manufacturer of calibration gas standards for the environmental monitoring community. Our proprietary cylinder passivation processes, combined with the most advanced manufacturing techniques and the latest analytical methods, provide customers with the standards they require. Whether our customers' needs are at the percent or part per billion level, or they are monitoring stack emissions, auto emissions, ambient air or the workplace environment, analysts know that they can rely on Spectra. Lasers - Medical and Industrial Applications Spectra was established on the belief that excimer lasers and related technologies would help change the world. After working for decades in close collaboration with the leading laser manufacturers, we have become the world's largest supplier of excimer laser gases and laser equipment. Through our excimer laser gases and gas handling equipment, we support medical applications including vision correction, angioplasty and micro surgeries as well as industrial applications including photolithography, annealing and other micro-machining applications. Stable Isotopes - for Medical, Fiber Optic and Research Applications Spectra Stable Isotopes is a major producer of stable isotope labeled biochemicals, synthons and stable isotope specialty gases. Spectra is the world's largest manufacturer of deuterium, helium-3 and stable isotope labeled biochemicals. We offer quality assured products that include growth media for bacterial, yeast, insect and mammalian cell culture, RNA and DNA derivatives for oligonucleotide synthesis and fatty acids for metabolic studies. Also available are amino acids, protected amino acids, carbohydrates, ammonium salts, labeled solvents and reagents and a full line of stable isotope gases. Equipment The Equipment Division designs and manufactures value-added, application specific products such as high purity pressure control, flow control, toxic abatement components and systems to support the markets we serve. Engineers experienced in all aspects of standard or customized equipment are available to consult on issues such as purity, process application, properties and product recommendations. Windows Spectra manufactures and supplies rare gases and mixtures to the worldwide fenestration industry which incorporates these products into windows and doors to enhance insulation value and increase energy efficiencies. To increase the "R" value or decrease the "U" value for window and door insulation, the industry requires krypton, xenon and various rare gas mixtures. We also provide krypton gas recover equipment to help the industry reduce costs and increase productivity. Lighting We are the world's largest supplier of halogen and rare gas mixtures for incandescent, fluorescent and high intensity discharge lamps. Today's technologies demand higher efficiency and Spectra meets this challenge by consistently providing the highest quality in every multi-component gas mixture delivered. Our products meet the needs of the lighting industry by providing carefully analyzed research lighting gases for more energy efficient, longer lasting and brighter lamps. **This site is under construction and an interim solution** Copyright 1998 - 2004 Spectra Gases, Inc. General Information Environmental Division Stable Isotopes Pure Gases Electronics Semiconductor Gas Handling Equipment Laser Gases Lighting Gases Window Division Special Application Gas Markets R-20 Gas Recovery Systems Terms and Technical Data Reference Material Contact Spectra Gases Sales and Service Career Opportunities
Herbach and Rademan
Provides surplus electro-mechanical and scientific equipment.
Herbach Rademan, electric motor, power supplies, timing motor, solar panels, fans, transformer Enter Keyword or Item Request A Catalog Order by Fax Limited Quantity New Arrivals Adapters, Wall DC Adapters, Wall AC Air Cylinders Audio Visual Equipment Balloons, Weather Batteries and Chargers Books Breadboards Workstations Cable, Cords, Wires Capacitors Cases and Enclosures Communication Equipment Computer Components Counters Data Aquisition Electronic Components Fans Blowers Grab Bags Heating and Cooling Devices Kits - Educational, Robotics Lab Equip. Glassware Laser Devices Lights Lamps Magnets Magnetic Devices Mechanical Components Meters Miscellaneous Items Motors Accessories Optics P C Boards and Supplies Power Components Power Supplies Pumps and Compressors Regulators and Gauges Relays Science Demonstrators Security Equipment Solar Devices Soldering Equipment Switches Test Equipment Tools Transformers Valves Video, Educational Close-outs $49.95 Super Electric Stepper 150 oz in Holding Torque $17.95 Synchron Timing Motor 10 RPM $9.95 5 VDC 15 Amps Switching Power Supply Reversible, 4-phase, permanent magnet motor features holding torque of 150 oz in @2.25 VDC and 4.6 amps per phase ... 110 120 VAC, 60Hz. Self-starting, long life operation, aluminum rotor cover, precision rotor shaft. Supported by double bearings ... Input 110 220 VAC @ 3.5 amps; 220 VAC @ 2 amps, 50 60Hz. Output 110 watts maximum. DC voltages available +5V, +12V, -12V, ... $3.95 Regulated DC to DC Selectable Converter $39.95 Powerful Gearhead Motor 24 VDC 30 in lbs Torque $11.00 Axial Fan 200 CFM 110 - 120 VAC 12 VDC Stepped down to 1.5 VDC @ 800mA. DC to DC voltage divider allows any 12 volt DC to achieve a reduction of output from 12 VDC ... 24 VDC, 35.8 RPM brush-type motor having a high torque, 250 mA, no load. Two 5" leads. The offset shaft is 3 64"L x 5 16"dia. with a 'C' ... . Axial fan is 110 - 120 VAC, 50 60Hz, 0.33 - 0.27 amps. Unit has seven blades and brass bushings. The black metal frame is 4-11 16"sq. x ... $69.95 DC Motor Speed Control $4.95 Amber Glass Storage Bottle $28.95 Compact, Brushless DC Gearhead Motor Input 115 - 230 volts AC. Output 6 to 9 Amps. DC motor control for smooth speed control of permanent magnet and shunt-wound motors. ... 500 milliliter. Amber glass lab storage bottle has a medium mouth and a white plastic screw cap. The bottle protects light-sensitive ... Unit can be operated between 12 and 24 volts, 110 to 220 RPM, 4 in lb torque. This motor is strong for its size. The motor has a steel ... 2002 HR Company, Inc. All Rights Reserved. "HR Company" is a trademark of HR Company, Inc.
UHV Design
Manufacturer or vacuum components for molecular beam epitaxy (MBE), UHV sputtering, vacuum thin films and other UHV vacuum deposition components.
UHV vacuum components from UHV Design UHV Design Vacuum Components Career Opportunities in.... Sales and Marketing Machining UHV Solutions......through UHV Design Innovate New Catalogue Add me to the Innovate mailing list VIEW PRODUCTS Click here to receive a copy Website best viewed in 1024 by 768 pixels About UHV Design UHV vacuum components products, MBE manipulators, MBE (molecular beam epitaxy), UHV sputtering, UHV Manipulators, UHV CVD, thin film deposition, epitaxial growth, HV deposition, semiconductors, vacuum products, thin film technology, vacuum deposition, UHV Vacuum Components UHV Vacuum products
Digital correlator manufacturer
Manufacturer of digital correlator for dynamic light scattering and fluorescence correlation spectroscopy.
Welcome to Correlator.com Please read The case for high resolution correlator . New Products Flex02 640 MHz multiple tau correlator: High bandwidth USB 2.0 high resolution multiple tau Flex02 digital correlator Model number Operating clock rate Sample time Price Lead time Comments Flex02-01D 640MHz 1.5625 ns $10,500 in stock 4x as high resolution Auto cross, option to save one or two channel photon series at a user defined sample time simultaneously Flex02-02D 405MHz 2.4691ns $10,200 in stock 4x as high resolution Auto cross, option to save one or two channel photon series at a user defined sample time simultaneously Flex02-03D 300 MHz 3.3333ns $10,000 in stock 4x as high resolution Auto cross, option to save one or two channel photon series at a user defined sample time simultaneously Flex02-08D 125MHz 8ns $9,500 in stock 4x as high resolution Auto cross, option to save one or two channel photon series at a user defined sample time simultaneously Flex02-12D 80MHz 12.5ns $9,000 in stock 4x as high resolution Auto cross, option to save one or two channel photon series at a user defined sample time simultaneously Multiple tau and single tau user defined delay Flex01LQ digital correlator Flex01LQ-05 Single MT-64 multiple tau 5ns $13,000 in stock AxA or AxB, 4x as high resolution Auto cross Dual MT-32 multiple tau 5ns Dual (AxA, BxB or AxB, BxA), 2x as high resolution Auto cross Quad MT-16 multiple tau 5ns Quad (AxA, BxB, AxB, BxA) standard resolution Quad auto MT-16 multiple tau 160ns Quad (AxA, BxB, CxC, DxD) standard resolution Photon history recorder 60MHz Intensity limit 910KHz Dual channel recorder 40MHz Intensity limit 450KHz Single tau 8 bit 1M Selectable from 0.4 to 102 microseconds Single sample time, arbitary delay (0 to 1M), 1024 data points Single tau 8 bit 2M Selectable from 0.4 to 102 microseconds Single sample time, arbitary delay (0 to 2M), 1024 data points Single tau 16 bit 1M Selectable from 12.4 to 1638 microseconds Single sample time, arbitary delay (0 to 1M), 1022 data points Single tau 32 bit 2M Selectable from 1 to 107000 milliseconds Single sample time, arbitary delay (0 to 2M), 1024 data points Flex01LQ-08 Single MT-64 multiple tau 8ns $12,000 in stock AxA or AxB, 4x as high resolution Auto cross Dual MT-32 multiple tau 8ns Dual (AxA, BxB or AxB, BxA), 2x as high resolution Auto cross Quad MT-16 multiple tau 8ns Quad (AxA, BxB, AxB, BxA) standard resolution Single tau 32 bit 2M Selectable from 1 to 107000 milliseconds Single sample time, arbitary delay (0 to 2M), 1024 data points Flex01LQ-12 Single MT-64 multiple tau 12.5ns $11,000 in stock AxA or AxB, 4x as high resolution Auto cross Dual MT-32 multiple tau 12.5ns Dual (AxA, BxB or AxB, BxA), 2x as high resolution Auto cross Quad MT-16 multiple tau 12.5ns Quad (AxA, BxB, AxB, BxA) standard resolution Quad auto MT-16 multiple tau 320ns Quad (AxA, BxB, CxC, DxD) standard resolution Photon history recorder 60MHz Intensity limit 910KHz Dual channel recorder 40MHz Intensity limit 450KHz Single tau 8 bit 1M Selectable from 0.4 to 102 microseconds Single sample time, arbitary delay (0 to 1M), 1024 data points Single tau 8 bit 2M Selectable from 0.4 to 102 microseconds Single sample time, arbitary delay (0 to 2M), 1024 data points Single tau 16 bit 1M Selectable from 12.4 to 1638 microseconds Single sample time, arbitary delay (0 to 1M), 1022 data points Single tau 32 bit 2M Selectable from 1 to 107000 milliseconds Single sample time, arbitary delay (0 to 2M), 1024 data points Contact Information Telephone 908-725-1244 FAX 1-831-536-1849 Postal address 15 Colmart Way, Bridgewater, NJ 08807 Electronic mail General Information: Info@correlator.com Sales: Info@correlator.com Customer Support: Info@correlator.com Webmaster: Info@correlator.com Send mail to Info@correlator.com with questions or comments about this web site. Copyright 1998 Correlator.com Last modified: January 20, 2005
Bunting Magnetics Co.
Distributor of permanent magnets and magnetic equipment for industrial use.
Bunting Magnetics Company Search: Products by Industry --------------- Material Handling Chemical Processing Food Processing Magnets Pharmaceuticals Plastics Processing Printing Industry Magnetic Rubber --------------- Products by Category --------------- Dry Solids Processing Liquid Processing Plastics Processing Recycling Magnets Maintenance Aids Magnetic Tools Material Handling Workholding Electromagnets Printing --------------- METAL DETECTORS Choose Industry --------------- Wood Textiles Chemicals Food Plastics Rubber Recycling Quarry Test Sticks View All --------------- 2005 Bunting Magnetics Last Updated 11 17 05 Hot Off The Press Bunting announces big savings for your Rotary Hot Stamping operation Click for information Metex Profi Line Flat Coil Detectors for the Textile Industry Click for information NEW Products! Neo 50 Cartridges and Plate Magnets Strongest available in the industry. Click for information Magslide Permanent Magnetic Chip and Parts Conveyors Click for information USDA Technical Articles
X-TRONIX Scientific and Industrial Technologies
Provides equipment for vacuum techniques, including consumables, thin films and surface science, gas flow control, helium cryogenics, and particle physics.
X-TRONIX LTD - Thin Films, Epitaxy, Gas Flow, Cryogenics, Surface Science, Particle Nuclear Physics This page uses frames, but your browser doesn't support them. Copyright 2002-05 X-TRONIX LTD Legal Notice Last update 14 Nov 2005 webmaster: Switzerland
Virtual Escalator
Virtual Escalator is an physics safety educational tool.
PRECISION Worldwide Escalator Parts and Elevator Parts 8002330838 9082599009 USA
Derivation of basic gyroscope formula
Web page contains intuitive and clear, simple and intuitive derivation of Gyroscope Effects formula.
Gyroscope Abstract This text is dedicated to people that do not have adequate university education and are not familiar with the formalism and abstractions exposed in the books about Mechanics that deal with gyroscopes. For adoption of such approach the certain introduction and training of Higher Mechanics are necessary. But, the effect can be described only by elementary equations of particle's motion. For understating of such approach only the high school knowledge of mechanics formulas, elementary geometry and the fundamentals of the vector and infinitesimal calculus are necessary. The explanation of the gyroscopic effect is based on the queue of the simple equations that finally bring us to the formula of the effect. Gyroscopic effect Lets imagine the tiny contour with the radius r0 that rotates around its axe - r axe and also around the axe normal to r axe of rotation - z axe. The circular velocities around axes r and z are denoted with the r and z respectively. Then the position of every particle is determined by the following equations: (1) (2) (3) The acceleration is obtained as the second time derivation of coordinates: (4) (5) (6) Hence it is: (7) And (8) Angles and describes angular shift of axes r and z from the plane in which the contour was at the beginning of observation. Consequently we have: (9) (10) (11) Every moment could be choose and the most suitable one is when contour is in position equal to the starting position and it is the position when the = 0 : (12) (13) (14) Vector can be written as: (15) The basic formula for the particle motion is given by: (16) And while the next connection between force and moment of force also matters: (17) Finally we have: (18) For the tiny contour the following formula is valid: (19) Where m' is the mass across the unity of length. Further we have: (20) (21) The definition of radian is: (22) (23) (24) Finally we have: (25) Whereas: (26) When the integral (25) is solved than is obtained: (27) Inertia of contour is calculating by the following formula: (28) Hence it is obtained: (29) While these are in validation: (30) And (31) (32) Thus we conclude that the following formula is valid: (33) By all these is demonstrated that dynamics of the material point is substantially enough for derivation of Gyroscopic effect formula and that the all energy that produce the effect is accumulated in kinetic energy of rotating mass and consequently the device is not able to produce constant force in one direction. The force could be produced only by process that incorporates derivatives with orders higher then the second. Author of this article is Andrija S. Radovic , Andrija Radovic , all rights reserved. The parts or whole article can not be published without author's prior agreement and without author's name below text. Press the following button to download the article in the PDF format: Author: Andrija S. Radovi E-mail: andrijar@andrijar.com
Classical Mechanics on About.com
Articles with practical advice and solutions for lots of topical problems.
Physics: Classical Mechanics : Newton's laws of motion, Hamiltonians, Formulations of mechanics, Motion You are here: About Homework Help Physics OtherFieldsofPhysics Mechanics Homework Help Physics Essentials Worked Physics Problems Student Guides Reference - Constants - Glossary Submit your own Content Physics FAQ Articles Resources References, Glossary Worked Problems, Examples Thermodynamics Quantum Physics Electromagnetism Experiments Other Fields of Physics Physics Classroom Resources Books, History, Philosophy Physics Fun Physics Jobs Learn Online Forums Help FREE Newsletter Sign Up Now for the Physics newsletter! See Online Courses Search Physics Classical Mechanics Although one of the oldest fields of physics, classical mechanics (the science of motion, dating back to Newton) is still proving to offer new surprises and complexity. Whether you are interested in Newton's Laws of Motion or using the Hamiltonian formulations of mechanics, these sites will offer what you need to learn more Articles Resources Sort By : Guide Picks | Alphabetical | Recent Energy - Definition - Mechanics Work Physics Energy - Definition - Mechanics Work Physics - from the physics glossary at physics.about.com Momentum - Definition - Mechanics Dynamics Collisions and Motion Momentum - Definition - Mechanics Dynamics Collisions and Motion from the physics glossary at physics.about.com Galilean Transformation - Classical Mechanics and Relativity Galilean Transformations (or Galilean Transforms) (classical mechanics and relativity) definition from the physics glossary at physics.about.com Acceleration - Equations of Motion If an object is subject to constant acceleration, the equations of motion are quite simple. This article shows how you can derive equations for velocity and displacement, without any calculus. Honda's "The Cog" Promoting the new Accord, Honda's Latest advertisment is set to become the stuff of advertising legend. Watch as a Domino like dance of balancing, tipping, forces, momentum, viscosity, sound and wind plays out using the components of the new Accord. 10 more Articles Resources below More Categories Up a category Chaos (26) Related Categories Mechanics Experiments More Classical Mechanics links in "Chaos" Subject Listing Worked Projectile Problems and Examples Worked Vector Problems and Examples Articles Resources more from your guide The Riddle of the Sphinx As you walk through a deep forest, you come upon a clearing. Crossing the clearing, you hear the sound of something landing lightly behind you. Knowing this wood is full of perils, you spin around ready for anything, to find yourself face to face with a Sphinx. Here is my riddle: Beside you are two balls. One is hollow, the other is solid. Tell me which is which. The Physics of Stone Throwing Physicist Lyderic Bocquet of the Universite Claude Bernard Lyon (France) has investigated the science behind stone skipping. Amusement Park Physics Explores various rides including the chance to build your own virtual rollercoaster and analyze the physics behind it. NASA - Beginners Guide to Aerodynamics A NASA introduction to the physics of flight. Foucault Pendulum Learn about the Focault Pendulum and how it proves the earth's rotation. Collision Processes in One Dimension Brief introduction to collisions. Your weight on other worlds. Find out how gravity on other planets will affect your weight. Free Body Diagrams Beginning physics undergraduates learn that they are to use free body diagrams to solve problems with forces. Here is some extra explanation of FBDs. Kepler's Laws In the 17th century, Kepler compiled the astronomical data of Tycho Brahe into these empirical rules, that were later explained in terms of gravity by Isaac Newton. Lagrangian and Hamiltonian mechanics -- A short introduction A short introduction to these very powerful formulations of mechanics. Topic Index | Email to a Friend Our Story | Be a Guide | Advertising Info | Work at About | Site Map | Icons | Help User Agreement | Ethics Policy | Patent Info. | Privacy Policy | Kids' Privacy Policy 2005 About, Inc., A part of the New York Times Company . All rights reserved. Around About Oprah's Story About Hugh Hefner Tips on Saving Energy VIDEO: Digital Cameras VIDEO: Fitness Gadgets What's Hot The Physics of Superheroes absolute zero - definition Potential Energy Work and Kinetic Energy Physics Quiz Hubble's Successor Buoyancy - Archimedes' Prin... Headlines NASA ready to check bizarre prediction of Einstein's relativity "Is Earth in a vortex of space-time? We'll soon know... Scientists Offer Hydrogen Fix "Two scientists say they have come up with a way... The Physics of Superheroes by James Kakalios Teaching physics to undergraduates, James Kakalios encountered a problem almost... Jupiter's massive winds likely generated from deep inside its interior "A new computer model indicates Jupiter's massive winds are generated...
Classical Mechanics on Wikipedia
Free online encyclopedia with description of the theory and history of classical mechanics.
Classical mechanics - Wikipedia, the free encyclopedia Classical mechanics From Wikipedia, the free encyclopedia. Jump to: navigation , search In physics , classical mechanics or Newtonian mechanics is one of the two major sub-fields of study in the science of mechanics , which is concerned with the motions of bodies . The other sub-field is quantum mechanics . Roughly speaking, classical mechanics was developed in the 400 years since the groundbreaking works of Brahe , Kepler , and Galileo , while quantum mechanics developed within the last 100 years, starting with similarly decisive discoveries by Planck , Einstein , and Bohr . The initial stage in the development of classical mechanics is often referred to as Newtonian mechanics , and is characterized by the mathematical methods invented by Newton himself, in parallel with Leibniz , and others. This is further described in the following sections. More abstract, and general methods include Lagrangian mechanics and Hamiltonian mechanics . Classical mechanics produces very accurate results within the domain of everyday experience. It is enhanced by special relativity for objects moving with high velocity , more than about a third the speed of light . Classical mechanics is used to describe the motion of macroscopic objects, from projectiles to parts of machinery , as well as astronomical objects, such as spacecraft , planets , stars , and galaxies , and even microscopic objects such as large molecules . Besides this, many specialties exist, dealing with gases , liquids , and solids , and so on. It is one of the largest subjects in science and technology. Contents 1 Description of the theory 1.1 Position and its derivatives 1.1.1 Velocity 1.1.2 Acceleration 1.1.3 Frames of reference 1.2 Forces; Newton's second law 1.3 Energy 1.4 Beyond Newton's Laws 1.5 Classical transformations 2 History 3 Limits of validity 3.1 The classical approximation to special relativity 3.2 The classical approximation to quantum mechanics 4 See also 5 Notes 6 References 7 External links [ edit ] Description of the theory The following introduces the basic concepts of classical mechanics. For simplicity, it uses point particles , objects with negligible size. The motion of a point particle is characterized by a small number of parameters : its position , mass , and the forces applied to it. Each of these parameters is discussed in turn. In reality, the kind of objects which classical mechanics can describe always have a non-zero size. True point particles, such as the electron , are normally better described by quantum mechanics . Objects with non-zero size have more complicated behavior than hypothetical point particles, because of the additional degrees of freedom for example, a baseball can spin while it is moving. However, the results for point particles can be used to study such objects by treating them as composite objects, made up of a large number of interacting point particles. The center of mass of a composite object behaves like a point particle. [ edit ] Position and its derivatives The position of a point particle is defined with respect to an arbitrary fixed point in space , which is sometimes called the origin, O. It is defined as the vector r from O to the particle. In general, the point particle need not be stationary, so r is a function of t, the time elapsed since an arbitrary initial time. In pre-Einstein relativity (known as Galilean relativity ), time is considered an absolute in all reference frames . [ edit ] Velocity The velocity , or the rate of change of position with time, is defined as the derivative of the position with respect to time or . In classical mechanics, velocities are directly additive and subtractive. For example, if one car traveling East at 60 km h passes another car traveling East at 50 km h, from the perspective of the car it passes it is traveling East at 6050 = 10 km h. From the perspective of the faster car, the slower car is moving 10 km h to the West. What if the car is traveling north? Velocities are directly additive as vector quantities; they must be dealt with using vector analysis. Mathematically, if the velocity of the first object in the previous discussion is denoted by the vector v = vd and the velocity of the second object by the vector u = ue where v is the speed of the first object, u is the speed of the second object, and d and e are unit vectors in the directions of motion of each particle respectively, then the velocity of the first object as seen by the second object is: v' = v - u Similarly: u' = u - v When both objects are moving in the same direction, this equation can be simplified to: v' = ( v - u ) d Or, by ignoring direction, the difference can be given in terms of speed only: v' = v - u [ edit ] Acceleration The acceleration , or rate of change of velocity, is the derivative of the velocity with respect to time or . The acceleration vector can be changed by changing its magnitude, changing its direction, or both. If the magnitude of v decreases, this is sometimes referred to as deceleration or retardation; but generally any change in the velocity, including deceleration, is simply referred to as acceleration. [ edit ] Frames of reference The following consequences can be derived about the perspective of an event in two reference frames, S and S, where S is traveling at a relative velocity of u to S. v'' = v - u (the velocity v' of a particle from the perspective of S is slower by u than its velocity v from the perspective of S) a' = a (the acceleration of a particle remains the same regardless of reference frame) F' = F (since F = ma) (the force on a particle remains the same regardless of reference frame; see Newton's law ) the speed of light is not a constant the form of Maxwell's equations is not preserved across reference frames [ edit ] Forces; Newton's second law Newton's second law relates the mass and velocity of a particle to a vector quantity known as the force . If m is the mass of a particle and F is the vector sum of all applied forces (i.e. the net applied force), Newton's second law states that . The quantity mv is called the momentum . Typically, the mass m is constant in time, and Newton's law can be written in the simplified form where is the acceleration. It is not always the case that m is independent of t. For example, the mass of a rocket decreases as its propellant is ejected. Under such circumstances, the above equation is incorrect and the full form of Newton's second law must be used. Newton's second law is insufficient to describe the motion of a particle. In addition, it requires a value for F, obtained by considering the particular physical entities with which the particle is interacting. For example, a typical resistive force may be modelled as a function of the velocity of the particle, for example: with a positive constant. Once independent relations for each force acting on a particle are available, they can be substituted into Newton's second law to obtain an ordinary differential equation , which is called the equation of motion. Continuing the example, assume that friction is the only force acting on the particle. Then the equation of motion is . This can be integrated to obtain where v0 is the initial velocity. This means that the velocity of this particle decays exponentially to zero as time progresses. This expression can be further integrated to obtain the position r of the particle as a function of time. Important forces include the gravitational force and the Lorentz force for electromagnetism . In addition, Newton's third law can sometimes be used to deduce the forces acting on a particle: if it is known that particle A exerts a force F on another particle B, it follows that B must exert an equal and opposite reaction force, -F, on A. The strong form of Newton's third law requires that F and -F act along the line connecting A and B, while the weak form does not. Illustrations of the weak form of Newton's third law are often found for magnetic forces. [ edit ] Energy If a force F is applied to a particle that achieves a displacement s, the work done by the force is the scalar quantity . If the mass of the particle is constant, and Wtotal is the total work done on the particle, obtained by summing the work done by each applied force, from Newton's second law: , where Ek is called the kinetic energy . For a point particle, it is defined as . For extended objects composed of many particles, the kinetic energy of the composite body is the sum of the kinetic energies of the particles. A particular class of forces, known as conservative forces, can be expressed as the gradient of a scalar function, known as the potential energy and denoted Ep: . If all the forces acting on a particle are conservative, and Ep is the total potential energy, obtained by summing the potential energies corresponding to each force . This result is known as conservation of energy and states that the total energy , is constant in time. It is often useful, because many commonly encountered forces are conservative. [ edit ] Beyond Newton's Laws Classical mechanics also includes descriptions of the complex motions of extended non-pointlike objects. The concepts of angular momentum rely on the same calculus used to describe one-dimensional motion. There are two important alternative formulations of classical mechanics: Lagrangian mechanics and Hamiltonian mechanics . They are equivalent to Newtonian mechanics, but are often more useful for solving problems. These, and other modern formulations, usually bypass the concept of "force", instead referring to other physical quantities, such as energy, for describing mechanical systems. [ edit ] Classical transformations Consider two reference frames S and S' . For observers in each of the reference frames an event has space-time coordinates of (x,y,z,t) in frame S and (x' ,y' ,z' ,t' ) in frame S' . Assuming time is measured the same in all reference frames, and if we require x = x' when t = 0, then the relation between the space-time coordinates of the same event observed from the reference frames S' and S, which are moving at a relative velocity of u in the x direction is: x' = x - ut y' = y z' = z t' = t This set of formulas defines a group transformation known as the Galilean transformation (informally, the Galilean transform). This type of transformation is a limiting case of Special Relativity when the velocity u is very small compared to c, the speed of light . [ edit ] History Main article: History of classical mechanics The Greeks , and Aristotle in particular, were the first to propose that there are abstract principles governing nature. One of the first scientists who suggested abstract laws was Galileo Galilei who may have performed the famous experiment of dropping two cannon balls from the tower of Pisa . (The theory and the practice showed that they both hit the ground at the same time.) Though the reality of this experiment is disputed, he did carry out quantitative experiments by rolling balls on an inclined plane ; his correct theory of accelerated motion was apparently derived from the results of the experiments. Sir Isaac Newton was the first to propose the three laws of motion (the law of inertia, his second law mentioned above, and the law of action and reaction), and to prove that these laws govern both everyday objects and celestial objects. Newton and most of his contemporaries, with the notable exception of Christiaan Huygens hoped that classical mechanics would be able to explain all entities, including (in the form of geometric optics) light. When he discovered Newton's rings , Newton's own explanation avoided wave principles and resembled more the explanation for the decay of the neutral Kaons , K0 and K0 bar. That is, he supposed that the light particles were altered or excited by the glass and resonated. Newton also developed the calculus which is necessary to perform the mathematical calculations involved in classical mechanics. However it was Gottfried Leibniz who developed the notation of the derivative and integral which are used to this day. After Newton the field became more mathematical and more abstract. Although classical mechanics is largely compatible with other " classical physics " theories such as classical electrodynamics and thermodynamics , some difficulties were discovered in the late 19th century that could only be resolved by more modern physics. When combined with classical thermodynamics, classical mechanics leads to the Gibbs paradox in which entropy is not a well-defined quantity. As experiments reached the atomic level, classical mechanics failed to explain, even approximately, such basic things as the energy levels and sizes of atoms. The effort at resolving these problems led to the development of quantum mechanics . Similarly, the different behaviour of classical electromagnetism and classical mechanics under velocity transformations led to the theory of relativity . By the end of the 20th century, the place of classical mechanics in physics is no longer that of an independent theory. Along with classical electromagnetism , it has become imbedded in relativistic quantum mechanics or quantum field theory [1] . It is the non-relativistic, non-quantum mechanical limit for massive particles. [ edit ] Limits of validity [ edit ] The classical approximation to special relativity Non-relativistic classical mechanics approximates the relativistic momentum with m0v , so it is only valid when the velocity is much less than the speed of light. For example, the relativistic cyclotron frequency of a cyclotron , gyrotron , or high voltage magnetron is given by , where fc is the classical frequency of an electron (or other charged particle) with kinetic energy T and (rest) mass m0 circling in a magnetic field. The (rest) mass of an electron is 511 KeV. So the frequency correction is 1% for a magnetic vacuum tube with a 5.11 KV. direct current accelerating voltage. [ edit ] The classical approximation to quantum mechanics The ray approximation of classical mechanics breaks down when the de Broglie wave length is not much smaller than other dimensions of the system. For non-relativistic particles, this wave length is where is Plank's constant divided by 2 and p is the momentum. Again, this happens with electrons before it happens with heavier particles. For example, the electrons used by Clinton Davisson and Lester Germer in 1927, accelerated by 54 volts, had a wave length of 0.167 nm, which was long enough to exhibit a single diffraction side lobe when reflecting from the face of a nickel crystal with atomic spacing of 0.215 nm. With a larger vacuum chamber , it would seem relatively easy to increase the angular resolution from around a radian to a milliradian and see quantum diffraction from the periodic patterns of integrated circuit computer memory. More practical examples of the failure of classical mechanics on an engineering scale are conduction by quantum_tunneling in tunnel diodes and very narrow transister gates in integrated circuits . Classical mechanics is the same extreme high frequency approximation as geometric optics . It is more often accurate because it describes particles and bodies with rest mass . These have more momentum and therefore shorter De Broglie wave lengths than massless particles, such as light, with the same kinetic energies. [ edit ] See also List of equations in classical mechanics important publications in classical mechanics [ edit ] Notes ^ - Page 2-10 of the Feynman Lectures on Physics says "For already in classical mechanics there was indeterminability from a practical point of view." The past tense here implies that classical physics is no longer fundamental. [ edit ] References Feynman, Richard (1996). Six Easy Pieces, Perseus Publishing. ISBN 0201408252 . Feynman, Richard; Phillips, Richard (1998). Six Easy Pieces, Perseus Publishing. ISBN 0201328410 . Feynman, Richard (1999). Lectures on Physics, Perseus Publishing. ISBN 0738200921 . Landau, L. D.; Lifshitz, E. M. (1972). Mechanics and Electrodynamics, Vol. 1, Franklin Book Company, Inc.. ISBN 008016739X . Kleppner, D. and Kolenkow, R. J., An Introduction to Mechanics, McGraw-Hill (1973). ISBN 0070350485 Gerald Jay Sussman and Jack Wisdom , Structure and Interpretation of Classical Mechanics ( SICM ), MIT Press (2001). ISBN 0-262-019455-4 Herbert Goldstein , Charles P. Poole, John L. Safko, Classical Mechanics (3rd Edition), Addison Wesley; ISBN 0201657023 Robert Martin Eisberg, Fundamentals of Modern Physics, John Wiley and Sons, 1961 [ edit ] External links Binney, Kames. Classical Mechanics (Lagrangian and Hamiltonian formalisms) Crowell, Benjamin. Newtonian Physics (an introductory text, uses algebra with optional sections involving calculus) Fitzpatrick, Richard. Classical Mechanics (uses calculus) Hoiland, Paul (2004). Preferred Frames of Reference Relativity Horbatsch, Marko, " Classical Mechanics Course Notes ". Rosu, Haret C., " Classical Mechanics ". Physics Education. 1999. [arxiv.org: physics 9909035] Schiller, Christoph. Motion Mountain (an introductory text, uses some calculus) Sussman, Gerald Jay Wisdom, Jack (2001). Structure and Interpretation of Classical Mechanics General subfields within physics Atomic, molecular, and optical physics | Classical mechanics | Condensed matter physics | Continuum mechanics | Electromagnetism | General relativity | Particle physics | Quantum field theory | Quantum mechanics | Special relativity | Statistical mechanics | Thermodynamics Retrieved from " http: en.wikipedia.org wiki Classical_mechanics " Category : Classical mechanics Views Article Discussion Edit this page History Personal tools Create account log in Navigation Main Page Community Portal Current events Recent changes Random article Help Contact us Donations Search Toolbox What links here Related changes Upload file Special pages Printable version Permanent link In other languages Dansk Deutsch Espaol Franais Galego Hrvatski Bahasa Indonesia slenska Italiano Latina Magyar Nederlands Norsk (bokml) Polski Portugus Romn Suomi Ting Vit This page was last modified 02:36, 16 November 2005. 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Oscillations
Gives a solution on a symmetric, linear, triatomic molecule problem.
Oscillations(1) Small Oscillations Most problems have moved to: http: electron9.phys.utk.edu phys513 Modules module_5.htm Additional Problems: Problem: Two masses, 1kg and 2kg, are fixed horizontally to fixed side supports with springs as shown below. The masses are constrained to move along the horizontal line. From their equilibrium position m1 is given a displacement L to the right, while m2 is held fixed. At t=0 they are released from rest. Give the equation for the positions of m1 and m2 as a function of time. Solution: Problem: A symmetric, linear, triatomic molecule can be represented as in the following figure: If only motion in the x-direction is allowed, the Hamiltonian is the sum of the kinetic energy T and the potential energy V, where V = (1 2)k(x2-x1-b)2 + (1 2)k(x3-x2-b)2, with k the spring constant and b the equilibrium separation. (a) Write Hamiltons equations of motion for the molecule. (b) Assume that displacements from equilibrium are proportional to exp(iwt). Express Hamiltons equations in matrix form (i.e., a 33 matrix multiplying a 3-component column vector), and solve for the normal mode frequencies w1 w2 w3. (c) Discuss the nature of the three normal modes, showing the motions of the three atoms for each mode. Solution: Problem: A linear system of N-1 spheres of mass M and two fixed end spheres (of infinite mass) are connected by springs of spring constant k as shown. The equilibrium positions are given by xn0 = na. Let xn = xn0+un. Note that u0 = uN = 0. (a) Write down the Hamiltonian of the system. (b) Determine the equations of motion for the nth sphere (1 n N-1). (c) Assume a solution of the form xn(t) = exp(iwt)[Aeikan + Be-ikan] and determine the values of k allowed by the boundary conditions. (d) How many independent values of k are there? (e) From the equation of motion, determine the frequency wk associated with the allowed k-values. (f) Introduce normal coordinates Pk and Qk and write the Hamiltonian in terms of them (without proof or derivation). Student solution:
Wave Equation
Mathematical description and derivation of wave equations.
The Wave equation The Wave equation The one dimensional wave equation The three dimensional problem Retarded Potentials Waves in one space dimension An alternative derivation of the 1D Green's function The two dimensional Green's function A few problems: Exercises Books on Waves and Classical Mechanic presented by Fred Gill geovisit();
Kepler's Laws
Article in the Platonic Realms. Gives an novice's overview of Kepler's laws.
Kepler's Laws (PRIME) BROWSE ALPHABETICALLY LEVEL: Elementary Advanced Both INCLUDE TOPICS: Basic Math Algebra Analysis Biography Calculus Comp Sci Discrete Economics Foundations Geometry Graph Thry History Number Thry Physics Statistics Topology Trigonometry Keplers Laws he German mathematician and astronomer Johannes Kepler (1571 1630) was an avowed Platonist, and set out early in his professional career to demonstrate that the motion of the planets was circular, in accordance with the established Aristotelian doctrine, and that they could be described in terms of the Platonic solids . However, he was also a friend and assistant to the great Danish astronomer Tycho Brahe, who was making precise and detailed observations of the planets and stars. When Tycho Brahe died, in 1601, Kepler inherited this enormous mountain of raw data. After studying this data for 20 years, Kepler came to understand that his earlier assumptions about planetary motion had been naive, and that if an earth-centered (Ptolemaic) understanding of the universe were abandoned for a sun-centered (Copernican) model, then the motion of the planets was clearly elliptical. From this basis, Kepler generated his three famous laws of planetary motion: The orbit of each planet is an ellipse with the sun at one focus. The line segment joining a planet to the sun sweeps out equal areas in equal time intervals. The square of the period of revolution of a planet about the sun is proportional to the cube of the semimajor axis of the planets elliptical orbit. These laws are illustrated in the following diagram: Keplers laws imply that the speed of revolution of a planet around the sun is not uniform, but changes throughout the planets year. It is fastest when the planet is nearest the sun (called the perihelion) and slowest when the planet is farthest away (aphelion). Of course, a circle is also an ellipse an ellipse with eccentricity 0 and in which the foci coincide in the center of the circle and indeed the orbits of most planets are far more nearly circular than the diagram would suggest. But they are not circles nonetheless; they are ellipses with non-zero eccentricity. The third law means that if Y is the length of a planet's year, that is, the time it takes the planet to make a complete revolution about the sun, and if we denote by a the length of the semimajor axis of the planets orbit, then the quantity Y2 a3 is the same for every planet (and comet, and other satellite) in the solar system. Thus, if a planets orbit is known, the length of its year can be immediately calculated, and vice versa. Keplers laws were empirical, that is, they were derived strictly from careful observation and had no purely theoretical foundation. However, about 30 years after Kepler died, the English mathematician and physicist Sir Isaac Newton derived his inverse square law of gravity, which says that the force acting on two gravitating bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. Keplers laws may be derived from this theoretical principle using calculus. HOME | ABOUT | CONTACT | AD INFO | PRIVACY Copyright 1997-2004, Math Academy Online Platonic Realms. Except where otherwise prohibited, material on this site may be printed for personal classroom use without permission by students and instructors for non-profit, educational purposes only. All other reproduction in whole or in part, including electronic reproduction or redistribution, for any purpose, except by express written agreement is strictly prohibited. Please send comments and corrections to webmaster@mathacademy.com .
The Controversy over Newton's Gravitational Constant
History of the gravitational constant.
The Controversy over Newton's Gravitational Constant The Controversy over Newton's Gravitational Constant In 1686 Isaac Newton realized that the motion of the planets and the moon as well as that of a falling apple could be explained by his Law of Universal Gravitation, which states that any two objects attract each other with a force equal to the product of their masses divided by the square of their separation times a constant of proportionality. Newton estimated this constant of proportionality, called G, perhaps from the gravitational acceleration of the falling apple and an inspired guess for the average density of the Earth. However, more than 100 years elapsed before G was first measured in the laboratory; in 1798 Cavendish and co-workers obtained a value accurate to about 1%. When asked why he was measuring G, Cavendish replied that he was "weighing the Earth"; once G is known the mass of the Earth can be obtained from the 9.8m s2 gravitational acceleration on the Earth surface and the Sun's mass can be obtained from the size and period of the Earth orbit around the sun. Early in this century Albert Einstein developed his theory of gravity called General Relativity in which the gravitational attraction is explained as a result of the curvature of space-time. This curvature is proportional to G. Naturally, the value of the fundamental constant G has interested physicists for over 300 years and, except for the the speed of light, it has the longest history of measurements. Almost all measurements of G have used variations of the torsion balance technique pioneered by Cavendish. The usual torsion balance consists of a 'dumbbell' (two masses connected by a horizontal rod) suspended by a very thin fiber. When two heavy attracting bodies are placed on opposite sides of the dumbbell, the dumbbell twists by a very small amount. The attracting bodies are then moved to the other side of the dumbbell and the dumbbell twists in the opposite direction. The magnitude of these twists is used to find G. In a variation of the technique, the dumbbell is set into an oscillatory motion and the frequency of the oscillation is measured. The gravitational interaction between the dumbbell and the attracting bodies causes the oscillation frequency to change slightly when the attractors are moved to a different position and this frequency change determines G. This frequency shift method was used in the most precise measurement of G to date (reported in 1982) by Gabe Luther and William Towler from the National Bureau of Standards and the University of Virginia. It was published in 1982. Based on their measurement, the Committee on Data For Science and Technology, which gathers and critically analyzes data on the fundamental constants, assigned an uncertainty of 0.0128% to G. Although this seems quite precise, the fractional uncertainty in G is thousands of times larger than those of other important fundamental constants, such as Planck's constant or the charge on the electron. As a result, the mass of the Earth is known far less precisely than, for instance, its diameter. In fact, if the Earth's diameter were known as poorly as its mass, it would be uncertain by one mile. This should be compared to the 3 cm uncertainty in the distance between the Earth and Moon, which is determined using laser ranging and the well-known speed of light! Recently the value of G has been called into question by new measurements from respected research teams in Germany, New Zealand, and Russia. The new values disagree wildly. For example, a team from the German Institute of Standards led by W. Michaelis obtained a value for G that is 0.6% larger than the accepted value; a group from the University of Wuppertal in Germany led by Hinrich Meyer found a value that is 0.06% lower, and Mark Fitzgerald and collaborators at Measurement Standards Laboratory of New Zealand measured a value that is 0.1% lower. The Russian group found a curious space and time variation of G of up to 0.7% The collection of these new results suggests that the uncertainty in G could be much larger than originally thought. This controversy has spurred several efforts to make a more reliable measurement of G. One of the greatest difficulties in any G measurement is determining with sufficient accuracy the dimensions and density distribution of the torsion pendulum body (the dumbbell). A second limitation is in knowing the properties of the suspension fiber with sufficient accuracy. The Japanese physicist Kazuaki Kuroda recently pointed out that internal friction in the torsion fiber, which had previously been neglected, may have caused some of the problems in the existing measurements. Jens Gundlach, Eric Adelberger, and Blayne Heckel from the University of Washington Et-Wash research group have pioneered a method that elegantly sidesteps these uncertainties. They noted that if the usual dumbbell is replaced by a thin, flat plate hung by its edge, neither the pendulum's dimensions nor its density distribution have to be known with very high precision. In principle, one can obtain G by measuring the angular acceleration of a flat pendulum without even knowing its mass or dimensions. This simple fact had not been recognized in 200 years of gravitational experiments! The Seattle researchers eliminate the problems with the torsion fiber by placing the torsion balance on a turntable that continuously rotates between a set of attracting bodies. The turntable is controlled by a feedback loop that speeds it up or slows it down so that the suspension fiber never has to twist; G can then be accurately inferred from the rotation rate of the turntable. This new method uses eight, rather than two, attracting bodies and these are strategically placed on a second turntable that rotates in the opposite sense from the first turntable. This novel technique is discussed in the July 15 issue of Physical Review D. At the University of California at Irvine, Riley Newman and graduate student Michael Bantel are refining the frequency shift method. They plan to operate their balance at a temperature only 4 degrees above absolute zero to reduce the internal friction in the suspension fiber and to make its properties more constant. Their apparatus will also use a flat pendulum. The fact that this famous fundamental constant is still so uncertain testifies to the difficulty of gravitational measurements. The recent flurry of new ideas for measuring G would surely have pleased Isaac Newton (quite a clever experimenter himself) who started this whole enterprise over 300 years ago. Fig. 1 Photograph of the big G apparatus. The spheres are 12.5 cm in diameter. (JPG image) Fig. 2 Photograph of the pendulum with several mirrors directing the light beam. A penny was placed in the foreground for scale. (JPG image) Fig. 3 Schematic cut-open drawing of the big G apparatus. The inner turntable rotates at about 1rev 20min, the outer turntable rotates at about 1rev 5min. (PDF image) Relevant literature C.C Speake and G.T. Gillies Z. Naturforsch., 42a 663 (1987). "Why is G the least precisely known physical constant?" E.R. Cohen and B.N. Taylor, Rev. Mod. Phys., 59 1121 (1987). [The Committee on Data for Science and Technology report] G.G. Luther and W.R. Towler, Phys. Rev. Lett., 48, 121 (1982).[The most reliable measurement] W. Michaelis, H. Haars, and R. Augustin, Metrologia 32, 267 (1995). [The result from the German Bureau of Standards] M. Fitzgerald and T. R. Armstrong, IEEE Trans. on Inst. and Meas. 44, 494 (1995). [The result from New Zealand] H. Walesch, H. Meyer, H. Piehl, and J. Schurr, IEEE Trans. on Inst. and Meas. 44, 491 (1995). [The result from Wuppertal] V.P. Izmailov, O.V. Karagioz, V.A. Kuznetsov, V.N. Mel'nikov, and A.E. Roslyakov, Measurement Techniques 36, 1065 (1993). [The Russian result] Kazuaki Kuroda, Phys. Rev. Lett. 75, 2796 (1995). J.H. Gundlach, E.G. Adelberger, B.R. Heckel, and H.E. Swanson , Phys. Rev. D 54, 1256R (1996). J.H. Gundlach , Measurement Sci. and Tech. 10 454 (1999). J.H. Gundlach and S.M. Merkowitz , Phys. Rev. Lett. 85 2869 (2000).
Gravity
If you want to learn about gravity come here.
Gravity Search: Lycos Angelfire Planet Share This Page Report Abuse Edit your Site Browse Sites Previous | Top 100 | Next Gravity is a force of attraction only between bodies that have mass. The word 'gravity' comes from the Latin word "gravitas", meaning 'weight'. The force of gravity that one body exerts on another can be expressed as: G * m1 * m2 Fgravity = ____________ (1) r2 F = Force of gravity experienced by bodies. m1 = mass of body. G = Gravitational constant , 6.6726 * 10-11 m3 kg-1 s-2. m2 = mass of second body. r = radius of body. From this an important equation for finding the force of gravity on an object e.g. planet. Newton's second law states that: F = m * a. (2) If you substitute the 'F' in equation 1 with 'm * a' in equation 2, you will get: G * m1 * m2 m * a = ____________ (3) r2 Divide both sides by m and you will get: G * m a = _________ (4) r2 At a 90 degree angle: a = g (5) So the new formula is: G * m g = _________ (6) r2 Knowing the gravitational constant, the mass of the Earth, and your distance from the centre of the Earth, you can work out the gravity of Earth. Please note: Gravity is measured in Newtons(N) or kg m s-1. If you want to find out the surface gravity of the different planets, please click here . Made by Kevin Murphy. . Sign My Guestbook View My Guestbook
Physics at Appleby College
A comprehensive collection of Java Applets on Waves, Sound and Light.
to Physics at Appleby College by Cliff Sampson email cliff Sign Guestbook View Guestbook WAVES SOUND , OPTICS AND LIGHT ELECTROMAGNETISM Physics resources - directory of Physics related websites. Pendulum Observe the period of pendulum while you change length, mass or angle.(kim jong heon, korea) Pendulum experiment java applet Do a pendulum experiment with mouse(click drag:to change its initial conditions-- length of the pendulum, initial position, gravitational field strength). Parameters (gravitational field and its components, kinetic energy, potential energy, velocity ...) are viewed graphically or displayed with text(length, angle, half period...). A period-initial angle plot is generated automatically, just click drag the mouse and wait. Try and play with it to find out more features. (Fu-Kwun Hwang) Transverse Wave and Longitudinal Wave An interactive activity on transverse and longitudinal waves. Visual representation of the motion of the particles in the transverse and longitudinal waves is shown. Superposition of Two Waves (Java applet) This applet visualizes the mixing of two one-dimensional waves. The user is able to vary velocity and frequency of the waves and the two individual wave as well as the superposition is viewed graphically. Longitudinal Wave A simulation of the reflection of longitudinal waves from a boundary. Wave Interference An animation on the interference pattern formed by two point sources. Wave Machine Gravitational Fields Kepler Motion, Astrophysics and Cosmology A simulation on the reflection of waves from a boundary. There is a choice of different types of representation. An applet describing interference through ripples in water This applet shows the time variation of an interference pattern through waves on a water surface. the positions of the two sources as well as the frequency of the ripples can be changed to demonstrate their effects on the interference pattern. written by santosh pisharody for PHYS 252 at the University of Virginia. Beat Frequency When two sounds are very similar in frequency, one hears pulses or beats due to the nature of waves. Try to determine the unknown frequencies provided in this simulation. Doppler Effect (Single Source) This simulation lets you adjust the speed of ths sound waves, the speed of the object that is making the sound ( a train whistle or a passing car or airplane are common noise sources) and the frequency of the sound. Doppler Effect (Two Sources) This simulation describes the interference pattern of two moving sound sources Propogation of Electromagnetic Wave This java applet shows the relations between electric field E, magnetic field B and wave vector k, when electromagnetic wave propogate through space.(Fu-Kwun Hwang) Reflection and Refraction of Wave When a beam of light impings at some angle on the smooth flat surface, the wave "sees" a vast array of very closely spaced atoms that will somehow scatter it. As the wavefront descends, it excites one scatterer after another. The wavelets advance together and add constructively in only one directions, and there is one well-defined reflected beam. This java applet try to let you visualize it for reflected and refracted wave. (Fu-Kwun Hwang) Physics of rainbow The most charming example of chromatic dispersion is a rainbow. When white sunlight is intercepted by a drop of water in the atmosphere. Some of the light refracts into the drop, reflects from the drop's inner surface, and then refracts out of the drop. As with the prism, the first refraction separates the sunlight into its component colors, and the second refraction increases the separation. And the rainbow is there in the sky. This applet shows the physics of rainbow.(Fu-Kwun Hwang) Simple Prism The prism can be used to make miniature rainbows in the classroom. This virtual prism let's you see why Snell's Law can make that pretty spectrum of colors we see in the sky. Additive Color An interactive activity on mixing of light colours. By varying the intensities of the various colours, the resultant colour will be shown. Additive Colors (RGB) As you look at this monitor all the colors you see are produced with just red, green, and blue light! Subtractive Colors The colors you see around you on cars, plants, etc., are due to color subtraction. Plane Mirror Gif's Image formation in Plane Mirrors Optics and Lenses (Java Applet) Java Applet by Fu-Kwun Hwang that demonstrates properties of lenses. An object or the lense can be dragged and dropped and the focus length of the lense can be varied. Real and virtual images, parameters and traces are viewed graphically. Convex Lens An interactive activity on the nature type of the image of an object formed by a convex lens. By changing the object distance, the image formed is shown clearly in the ray diagram. Concave Lens An interactive activity on the nature type of the image of an object formed by a concave lens. By changing the object distance, the image formed is shown clearly in the ray diagram. Thick Lens An interactive activity on the nature type of the image of an object formed by a thick lens. By changing the object distance, the image formed is shown clearly in the ray diagram. Lens from ExploreScience This experiment simulates a 'thin converging lens' and shows the 3 basic rays that you can 'trace' to find the image. You can drag the lens back and forth, measure distances with the ruler, change the object size, and change the focal length. DC Electric Motor This simulations demonstrates the motor principle. It allows you to vary the current strength as well as the direction of flow. AC DC Generator This Java applet simulates an AC or DC generator which is reduced to the most important parts for clarity. Instead of an armature with many windings and iron nucleus there is only a single rectangular conductor loop; the axis the loop rotates on is omitted. Ohm's Law This Java applet simulates an electrical circuit. The voltage and the current can be varied and the resistence recorded. geovisit();
The Lagrange Points
Overview of the Lagrange points of the sun-earth-system. Links to a detailed derivation.
Lagrange Points The Lagrange Points The Italian-French mathematician Josef Lagrange discovered five special points in the vicinity of two orbiting masses where a third, smaller mass can orbit at a fixed distance from the larger masses. More precisely, the Lagrange Points mark positions where the gravitational pull of the two large masses precisely cancels the centripetal acceleration required to rotate with them. Those with a mathematical flair can follow this link to a derivation of Lagrange's result. Of the five Lagrange points, three are unstable and two are stable. The unstable Lagrange points - labelled L1, L2 and L3 - lie along the line connecting the two large masses. The stable Lagrange points - labelled L4 and L5 - form the apex of two equilateral triangles that have the large masses at their vertices. Lagrange Points of the Earth-Sun system (not drawn to scale!). The L1 point of the Earth-Sun system affords an uninterrupted view of the sun and is currently home to the Solar and Heliospheric Observatory Satellite SOHO . The L2 point of the Earth-Sun system will soon be home to the MAP Satellite and (perhaps) the Next Generation Space Telescope . The L1 and L2 points are unstable on a time scale of approximately 23 days, which requiress satellites parked at these positions to undergo regular course and attitude corrections. NASA is unlikely to find any use for the L3 point since it remains hidden behind the Sun at all times. The idea of a hidden "Planet-X" at the L3 point has been a popular topic in science fiction writing. The instability of Planet X's orbit (on a timescale of 150 days) didn't stop Hollywood from turning out classics like The Man from Planet X . The L4 and L5 points are home to stable orbits so long as the mass ratio between the two large masses exceeds 24.96. This condition is satisfied for both the Earth-Sun and Earth-Moon systems, and for many other pairs of bodies in the solar system. Objects found orbiting at the L4 and L5 points are often called Trojans after the three large asteroids Agamemnon, Achilles and Hector that orbit in the L4 and L5 points of the Jupiter-Sun system. (According to Homer, Hector was the Trojan champion slain by Achilles during King Agamemnon's siege of Troy). There are hundreds of Trojan Asteroids in the solar system. Most orbit with Jupiter, but others orbit with Mars. In addition, several of Saturn's moons have Trojan companions. No large asteroids have been found at the Trojan points of the Earth-Moon or Earth-Sun systems. However, in 1956 the Polish astronomer Kordylewski discovered large concentrations of dust at the Trojan points of the Earth-Moon system. Recently, the DIRBE instrument on the COBE satellite confirmed earlier IRAS observations of a dust ring following the Earth's orbit around the Sun. The existence of this ring is closely related to the Trojan points, but the story is complicated by the effects of radiation pressure on the dust grains. Finding the Lagrange Points The easiest way to see how Lagrange made his discovery is to adopt a frame of reference that rotates with the system. The forces exerted on a body at rest in this frame can be derived from an effective potential in much the same way that wind speeds can be infered from a weather map. The forces are strongest when the contours of the effective potential are closest together and weakest when the contours are far apart. A contour plot of the effective potential. In the above contour plot highs are colored yellow and lows are colored purple. We see that L4 and L5 correspond to hilltops and L1, L2 and L3 correspond to saddles (i.e. points where the potential is curving up in one direction and down in the other). This suggests that satellites placed at the Lagrange points will have a tendency to wander off (try sitting a marble on top of a watermelon or on top of a real saddle and you get the idea). A detailed analyis confirms our expectations for L1, L2 and L3, but not for L4 and L5. When a satellite parked at L4 or L5 starts to roll off the hill it picks up speed. At this point the Coriolis force comes into play - the same force that causes hurricanes to spin up on the earth - and sends the satellite into a stable orbit around the Lagrange point. This page was written by Neil J. Cornish as part of MAP's education and outreach program. To the MAP Technical Information Page Back to the MAP Home Page Please help us make this web site more useful and enjoyable by telling us what you would like to see at this site: David N. Spergel dns@astro.princeton.edu Gary Hinshaw hinshaw@stars.gsfc.nasa.gov Charles L. Bennett bennett@stars.gsfc.nasa.gov NASA Privacy Statement NASA IT Security Banner Last updated: Friday, 05-21-1999
Chaotic Systems
A brief overview of chaos theory and applications in classical mechanics.
Chaotic Systems Back to Contents! Next: Completing the Circle Up: CONSERVING EQUATIONS Previous: Second-order diff Chaotic Systems The word chaos has both a general meaning and a scientific meaning. As is usually the case, the general meaning tends to convey little of the strict definition that scientists and mathematicians apply to the word. In the American Heritage Dictionary (Note: you can also access the Oxford English dictionary online if the "American Heritage Dictionary" above refuses you access), we find that chaos is described as noun. 1. A condition or place of total disorder or confusion: ``emotions in complete chaos.'' 2. Often [Chaos]. The disordered state of unformed matter and infinite space supposed by some religious cosmological views to have existed prior to the ordered universe. 3. (Obsolete). A vast abyss or chasm. What scientists and mathematicians mean by chaos is very much related to the spirit of the definitions given above. We state that systems are chaotic if they: are deterministic through description by mathematical rules. have mathematical descriptions which are nonlinear in some way. This may seem to be a strange definition before we've motivated it, but it becomes clearer as we consider examples. We can see many examples using Maple (you knew that was coming, didn't you.) What follows below is an animation of one of the curves generated by the PFP 1994 class. Begin by loading plot library with(plots): Animate the curve animate([sin(u*t*2)+cos(u*t*3),sin(u*t)-cos((u*t)^2), t=0..1], u=0..2*Pi, frames=60,numpoints=100); The path traced out by end of the line as the animation proceeds certainly looks chaotic (in the general meaning of that word) as shown below. However, the general meaning of chaos implies unpredictability of the path. Certainly as you trace the animation out frame-by-frame you would be hard put to guess the next move of the end of the line, but, since the curve is generated from a mathematical formula, you can in fact predict exactly what the curve will do next in the animation and what its final shape will be. So what might appear to the naked eye as infathomably complex is, in reality, governed by a relatively simple mathematical expression. In essence, there is no difference between the complex path shown above and, say, a path along a straight line or sinusoidal curve. Its simply that a straight line path leads the eye in an obvious way from the start point to the end point. The animation for a line is particularly simple if we use a parametric description. If the slope is 1, then animate([u*t, u*t, t=0..1], u=0..2, frames=20); produces a boring path traced out by the end of the line as the animation moves along The trick, in practice, of predicting the path of something or the future course of an evolving system described by a complex algorithm comes in the sensitivity of the algorithm to small changes in the initial point. Let's take the case of a straight line and the complex curve we looked at previously. If the line is described by y = m*x + b, then making a change in the starting x point amounts to shifting the origin, i.e. we make x - x + a where a is the small shift in the starting point. We know precisely what effect this has on the line mathematically. We also can see "by eye" what effect this would have in predicting where we would end up. There's no need to use Maple to know that the line ends up a distance a from the previous end point predicted before the shift. For the case of our complex curve, things get even more complicated than they were before. For example, let's consider what a small shift in the initial position does. Just add in the shift, in this case 0.1 animate([sin(0.1+u*t*2)+cos(0.1+u*t*3),sin(0.1+u*t)-cos((0.1+u*t)^2), t=0..1], u=0..2*Pi, frames=60,numpoints=100); Now we note that our animated curve generally follows the same loopy pattern we saw before, BUT it ends up considerably further from the previous endpoint than the 0.1 shift might have led us to believe (compare the figure below with our previous one if you didn't do the Maple animation) The essence of chaos in science is just that: a relatively complex behavior which is strictly governed by a mathematical algorithm, but, is nonetheless unpredictable due to sensitivity to initial conditions. So, although in principle we can predict how a system will behave to an arbitrary level of precision, in practice we can't find the initial starting point of the system accurately enough to be able to predict in detail what will happen beyond a short period of time. Small mismeasurements eventually add up to a big discrepancy between calculated and observed behavior. The surefire way to have a system described by an algorithm that exhibits chaotic behavior is to have it be nonlinear. The importance of studying chaotic behavior lies in the fact that most systems encountered in the real world are nonlinear to some extent and either exhibit chaotic behavior or can be made to exhibit it. Prime examples are weather prediction, population kinetics (i.e. fluctuations in populations from generation to generation), fluid flow, mechanical and electrical oscillatory phenomena (e.g. heart beats or the electrical activity of your brain), the tumbling motion of the moon Hyperion in its orbit around the planet Saturn, economic systems, and many, many other phenomena. In fact, chaos is observed in so many systems in the real world that some scientists rank the understanding of chaos as being as important as the theories of relativity and quantum mechanics in that its ramifications stretch into every aspect of scientific study. Nonetheless, how do you know nonlinear behavior when you see it? Let's start by looking at an example. A relatively simple one is shown in the diagram below. The picture depicts a pendulum with a magnet (blue) as the bob on the end of a rigid rod which is free to swing on a supporting bar. Two other magnets (red) are fixed in position on either side of the equilibrium position (in the absence of the red magnets) of the blue magnet. The red magnets must be placed so that pendulum can rest in equilibrium with the blue magnet directly above either of the fixed magnets. Hence we have a system with two possible equilibrium positions. If the pendulum is pulled aside along the y axis and released, it quickly begins to execute an extremely complicated motion. Since the magnetic force is a strong function of the relative distance between the magnets and the magnetic forces can provide acceleration, deceleration, and damping (the damping force comes about because of induced currents, a topic you will learn more about in Physics 2 or 151). There is also damping due to friction of the pendulum support on the supporting rod. The damping eventually causes the blue magnet to move to one of the equilibrium points, BUT which one? That depends very much on the initial condition. If the pendulum starts its motion ever so slightly closer to one magnet than the other, then its motion will eventually become highly perturbed. The complexity of the motion is high enough so as to make it nearly impossible to determine which equilibrium position the pendulum will choose given certain starting positions. Of course the motion of the pendulum is strictly governed by Newton's Laws so we have a mathematical description of the motion. Certainly the motion is complex and sensitive to initial conditions. Therefore, this is a perfect example of chaotic motion! The figures below show the path of the pendulum magnet as projected on the plane with the fixed magnets. The white dot represents the position of one fixed magnet while the blue dot marks the position of the other fixed magnet. The colored path shows that the pendulum follows a complicated path to its eventual equilibrium position around one of the fixed magnets. The next figure displays which equilibrium position the magnet winds up on according to its initial position as projected on the plane containing the fixed magnets. The blue and white regions show initial positions which correspond to the magnet coming to equilibrium around either the blue or white fixed magnet. If we could blow up the region around the boundaries between blue and white areas, we would find that they are not infinitely sharp. Instead, we would see a complex structure which is termed a fractal. Fractals have fractional dimensions and the unique property of self-similarity to all levels of magnification. If you magnify any part of a fractal, you see a minature recreation of the overall fractal structure repeated on the small scale. Magnify a small piece of any part of the small structure and you see the overall structure repeated again and again, ad infinitum. The coastlines of continents and the structure of snowflakes are just two of the many examples of fractals found in nature. The most famous shape among the fractals is the Mandelbrot set shown below. Click on the image and you will see a movie that zooms in on the figure. As you go to higher and higher magnification, you see the same shape repeated over and over, albeit with surprising variations on combinations of shapes. Fractals, as you can well imagine, are well-represented on the Net. You can find nifty pictures like the ones below in a repository in France. Click on the above and wait if you want to see more pictures. The differential equation describing the motion of a pendulum that is damped and driven (i.e. some outside force provides the energy to keep the pendulum in motion) can be described most conveniently in terms of angles rather than position. This convention is explained in next week's readings but we've already mentioned it in the discussion of trigonometric functions. We simply say for now that we define angles in terms of radians, where the connection between displacement and angle is where s is the arc-length or distance the pendulum swings along its arc and R is simply the length of the pendulum arm (i.e. the radius of its swinging motion). Given the angular displacement, we can, by analogy with straight line motion, define the angular velocity and angular acceleration Keeping these terms in mind, you will learn in Physics 150 that the equation of motion we want, in angular terms, can be written down as follows: with b and C being constants which characterize the amount of damping and the strength of the driving force, respectively. The cosine term multiplying C specifies the frequency of the driving force. This differential equation is clearly second order in the angular displacement since the angular acceleration on the left-hand side of the equation is the second derivative of the angular displacement. Since the angular velocity in the damping term (1st term on the right-hand side (which we will abbreviate as rhs) of the equation) is just the first derivative of the angular displacement and the driving force term is independent of the pendulum displacement, the differential equation is linear except for the sine in the middle term on the rhs of the equation. The sine term is what makes the differential equation nonlinear. Physically, this term simply relates the effect of the gravitational force on a pendulum bob. Mathematically, it provides the coupling with the other terms on the rhs of the equation to make the pendulum capable of chaotic motion for particular values of the damping and driving constants. One of the most intellectually appealing aspects of chaos is its intimate mathematical connection to other curious entities such as fractals, Penrose tilings, and quasi-crystals. You can interactively explore these on the Web. Try the U. of Minnesota Geometry Center site for an interactive quasi-tiler for example in generating interestingly complex and colorful pictures. Another game showing the complexity of seemingly simple equations is orbifold pinball , which shows how hard it would be to play pinball on a curved surface. We will come back to this interesting notion of motion in a curved space when we discuss Einstein's theory of gravity later. Next: Completing the Circle Up: CONSERVING EQUATIONS Previous: Second-order diff larryg@truth.hep.upenn.edu Fri Mar 4 09:58:36 EST 1994 subsection3_2_5.html
Freshman Problems in Mechanics
Links to various problem sets relating to 1 and 2 dimensional kinematics. Easy mechanics problems and solutions.
The U of O Physics Student Page 1 Dimensional Kinematics Multi Dimensional Kinematics Newton's Laws Collisions Circular Motion Work and Energy (Click on the topic you wish to study...) The U of O Physics Student Page last update: November 6, 1995 dmason@zebu.uoregon.edu
Physics for Beginners
This site covers motion and forces for individuals with no prior knowledge of the subject.
Physics For Beginners: An introduction to physics for the absolute beginner Physics For Beginners (An introduction to physics for the absolute beginner) Home | Physics | Equation Solver | Pokemon Episodes | Hamster Dance Table of Contents Preface Definitions Speed Velocity Acceleration (with a picture) Newton's Laws of Motion 1st Law 2nd Law 3rd Law Force and Acceleration (Is there a relationship?) Mass Additive Nature of Forces Direction Acceleration in Detail Figuring Out the Direction of the Acceleration Constant Acceleration Units: What are they good for? Basic Units Length Mass Time Derived Units Speed Acceleration Force Converting Units Kinematics: In One Dimension and Under Constant Acceleration Sign Convention Velocity Formula Solving for the velocity Solving for the time Solving for the acceleration Solving for the initial velocity Distance Formula Choice of the Origin Solving for time Example 1: Initial velocity and acceleration in the same direction Example 2: Initial velocity and acceleration in opposite directions Using the Distance and Velocity Formulae in Combination: Bet You Can't Just Use One Some Useful Examples Making contact with Newton's First Law of Motion Gravity Gravity Near the Surface of the Earth Gravity In Detail Gravity's Dependence on Mass Gravity's Dependence on Distance General Gravity Formula Revealed Dependence on Mass Dependence on Distance Summary of Important Points about the Gravity Formula Some Interesting Observations about Gravity Scientific Notation: A Necessary Evil and Another Detour Sliding to the Right Sliding to the Left Summary Return of Gravity in Detail: Armed with the Scientific Notation A "Little" Something about Big G, the Mysterious Gravitational Constant Some Examples Big G, Meet Little g Uniform Circular Motion: Round and Round I Go General Observations Summary Direction of Velocity Summary How Much Force Do I Really Need? Relationship between Force and Speed Relationship between Force and Radius Summary
Simulations with Java
Provides several interactive physics simulations such as springs and masses, pendulums, molecules. Objects, mass, gravity, spring stiffness can be modified.
MyPhysicsLab Physics Simulation with Java Home Springs Single Spring Double Spring 2D Spring Double 2D Spring Pendulums Pendulum Chaotic Pendulum Double Pendulum Combos Cart with Pendulum Dangling Stick Collisions Colliding Blocks Rigid Body Collisions Sumo Wrestling Game RollerCoasters Roller Coaster Roller Coaster with Spring Roller Coaster with 2 Balls Roller Coaster with Flight Molecules Molecule 2 Molecule 3 Molecule 4 Molecule 5 Molecule 6 Explanations Help and FAQ Differential Equations Numerical Solutions Runge Kutta Method Math Refresher Physics Links Next MyPhysicsLab Physics Simulation with Java Click on one of the physics simulations below... you'll see them animating in real time, and be able to interact with them by dragging objects or changing parameters like gravity. Get Java software if you don't already have it. single spring double spring pendulum chaotic pendulum double pendulum 2D spring double 2D spring colliding blocks cart with pendulum dangling stick rigid body collisions sumo wrestling game roller coaster roller coaster with spring roller coaster with 2 balls roller coaster with flight molecule 2 molecule 3 molecule 4 molecule 5 molecule 6 The next set of simulations are non-interactive movies. fluid dynamics reaction-diffusion How Does It Work? Explanations of the math and physics are provided in the simulation web pages. Free source code is provided for those wanting to experiment on their own. Here are some additional pages about the underlying math and software. Help and FAQ How to get the simulations to work, and other answers. Diff Eq Intro A gentle introduction to differential equations Classifying Diff Eqs A taxonomy of differential equations Numerical Solutions How to solve a differential equation without really trying Runge Kutta Method The best numerical diffeq solver Math Refresher For those whose trig and calculus are a wee bit rusty. Links to related math, physics, and simulation websites. Displaying Math on the Web Notes about how to display mathematics on the web. Why Physics Simulation? These physics simulations can be used to: play around with for fun... try dragging with your mouse, or changing parameter settings learn about physics and how to set up a model of a physical system learn about numerical methods for solving equations learn about differential equations and techniques for solving them learn computer programming ( free source code is available) enhance your next video game project Besides being fun to play with, I hope these simulations inspire you to learn about the underlying math and physics. Simulations are essential in many areas of science and technology. When problems become more complex, it is difficult to use pure math techniques to predict what will happen. Scientists and engineers then create a mathematical model and use numerical techniques to run the model on a computer. We'd Like To Hear From You Send comments to Erik Neumann . To be notified when new simulations are added to this site, enter your email address and click below. e-mail address: This website was selected as "cool math site of the week" by the Knot a Braid of Links project of the Canadian Mathematics Society. Erik Neumann , 2004 Home Top Next
Physics of Sound
Rigorous derivation of sound wave equations from a molecular model of an ideal diatomic gas. General solution of the wave equations. Point source radiating in a moving medium.
Kepler's Laws
Summary of Kepler's three laws.
Orbital Energy and Kepler's Laws Orbital Energies, Kepler's Laws and Other Relationships Kepler's Laws Kepler's Three Laws can be used to describe the motion of the Planets: Planets move in orbits that are ellipses The planets move such that the line between the Sun and the Planet sweeps out the same area in the same area in the same time no matter where in the orbit. The square of the period of the orbit of a planet is proportional to the mean distance from the Sun cubed. The above rules were deduced empirically from the motions of the planet in the early 17th century, before Newton deduced the law of gravity and his laws of motion. When Newton's laws are applied to the planets, Kepler's laws can be derived with certain refinements. Description of Orbits Movement of a planet or satellite in an orbit can be described with the above rules and some simple plane geometry. The parameters of the ellipse in terms of eccentricity will be used but it also helpful understand the simple method of drawing an ellipse. Drawing an Ellipse Two pins, a length of string, a sheet of paper and a pencil are used to draw ellipses. The eccentricity of the ellipse is set by the spacing of the pins relative to the length of string stretched between the pins. The eccentricity = (distance between the pins) (length of string between the pins) This basic property of the ellipse can be used to determine relationships between certain parameters of the elliptical orbit. The length of the string equals twice the semi-major axis and the distance between the pins is twice the distance, c = e a. When the pencil is at the semi-major axis, the right triangle formed by the axes and the string allows one to write: a2 = b2 + c2 So...b = a ( 1 - e2)1 2 You can specify the shape of the ellipse that you wish to draw by its eccentricity, e or by its semi-minor axis, b. The size is determined by the semi-major axis. The ellipse in the drawing has an eccentricity = 0.8 so the width of the ellipse (twice the semi-minor axis) is ( 1- 0.8x0.8)1 2 = 0.6 of the length. Energy of an Orbit The Total energy of an object in orbit is the sum of kinetic energy (KE) and gravitational potential energy (PE). KE = 1 2 mv2 PE = - GMm r r = the distance of the orbiting body from the central object and v = the velocity of the orbiting body E = 1 2 mv2 - GMm r The semi-major axis is directly related to the total energy of the orbit: E = - GM 2a Semi-major Axis and Total Energy The relationship between these two can easily be derived for a circular orbit and also works for elliptical and hyperbolic orbits. As we see in the diagram: a = F m = GM r2 = v2 r. In the case of a circle e = 0 and r = a. So v2 = GM a and thus: E = 1 2 m(GM a) - m(GM) a = m (GM) (2a) E m = GM (2a) Incidently, the concept of circular velocity is useful in describing elliptical orbits. vc2 = GM a The energy also provides an expression for the velocity in orbit E m = GM (2a) = 1 2 v2 - GM r and hence v2 = GM a[2 r - 1 a] but written in terms of the circular velocity v2 = vc2[2 r - 1 a] Keplers 2nd Law We have already discussed Kepler's 1st Law without giving it its name. Kepler discovered first that planets move in elliptical orbits about the Sun. The 2nd Law of Kepler describes the relative velocity of the objects in their elliptical orbits. He discovered that the line from the Sun to the planet swept out equal areas in equal times. At first this does not seem very helpful but if we use a little geometery then we can use it quantitatively. The diagram on the right illustrates the law. The area of the shaded segment from A to B equal the area from segment C to D. Any body in the orbit around the Sun (o) will travel from A to B in the same time that it travels from C to D. The rate of sweeping our area by the line between Sun and orbiting object is called the Areal Velocity, A . In one period, P, of the orbit the line sweeps out the area of the ellipse so we can calculate this velocity from A = (area of ellipse) (period of ellipse) = (p a b) P A = p(1 - e2)1 2 a2 P Look at the diagram again; as an orbiting object goes from a to b the area swept out is approximately the area of the triangle o-a-b. That area is equal to the isoceles triangle o-a'-b' . The area of the later triangle can be calculate easily; that area is one half the base (length a'-c-b') times the height (length o-c). The height of the triangle is just the radius, r, of the orbit at point c and the base of the triangle is the velocity perpendicular, v_, to the radius line at that same point times the time of transit from a to b. So the rate of sweeping out area in the triangle at c is: A = v_r 2 There are only two points in the orbit where the perpedicular velocity equals the orbit velocity and that is a perihelion and aphelion. As a result we can relate the speed in orbit at these two poins most easily. rp = a (1 - e) and ra = a (1 + e) So... vara 2 = vprp 2 = (p a b) P and va = vp( 1 + e) (1 - e) With a little more derivation (using Kepler's 3rd Law) we can show that va = vc[( 1 + e) ( 1 - e )]1 2 and va = vc[( 1 - e) ( 1 + e )]1 2 Kepler's 3rd Law - Relationship between Period and Semi-major Axis This law was derived empirically by Kepler. He found that if the period of the planet was given in years and the semi-major axis was given in Astronomical Units (AU) then P2 = a3 It is easily derived for a circular orbit and the result applies to elliptical orbits when the radius of the circle is replaced by the semi-major axis of the ellipse. The period of an object in a circular orbit where r = a is P = 2pa v and hence since v = (GM a)1 2 P = 2pa3 2 (GM)1 2 This relationship is in metric units. If we transform to AU and years then we get 2p (GM)1 2 = 1yr AU3 2 Newton refined Kepler's 3rd law using center of mass motion. When this is considered then the mass, M is not just the mass of the central body (the Sun for the planets) but the sum of the masses of both the 'central' and 'orbiting' object. In the case of the solar system, Kepler was not too far off because the mass of the Sun is more than a thousand times the masses of all the planets and their mass add only a small amount. So the correct relationship is: P = 2pa3 2 (G(M+m))1 2 Larry Bogan - Feb 2000
Primitive Potentials and Newton's Laws from Symmetry
Symmetry of function. Finding of primitive without integration-summation. Newton's laws of any order. Mechanics of third order.
index About article. The symmetry of function and symmetric differentiation. The general development of increment of primitive in a power series with degrees of increment of derivative. Finding of primitive without integration-summation. Mechanics as a pure mathematics. The potentials unique. Newton's laws of any order. The elements of mechanics of third order and motion of particle (electron ?) in space. About author. Mathematician on formation. The programmer from 1986. 1984-beginnings of paper.From 1997 papers is in sci.physics.research. Tanks to all Web-Sites for admit my Url. Resume (see further load discussion). Russian version Backup copy of paper Load article from Mach 2001 geovisit();
Block and Tackle
Colorful illustrated tutorial shows how a block and tackle (as well as levers and gears) works.
Howstuffworks "How a Block and Tackle Works" Auto Stuff Science Stuff Health Stuff Entertainment Stuff People Stuff Computer Stuff Electronics Stuff Home Stuff Money Stuff Travel Stuff Shop for Stuff Popular Searches Body Armor Hurricane Hypnosis Intelligent Design Military Technology Stem Cells UFOs Sponsored By: Subjects Earth Science Engineering Life Science Military Physical Science ShortStuff Space Supernatural Browse the Science Library Explore Stuff Lidrock.com Big List of Articles Get the Newsletter Shop for Top Products Shop or Compare Prices Search HSW and the Web Main Science Engineering How a Block and Tackle Works by Marshall Brain Table of Contents Introduction to How a Block and Tackle Works Other Force Distance Tradeoffs Shop or Compare Prices If you have ever looked at the end of a crane, or if you have ever used an engine hoist or a come-along, or if you have ever looked at the rigging on a sailboat, then you have seen a block and tackle at work. A block and tackle is an arrangement of rope and pulleys that allows you to trade force for distance. In this edition of How Stuff Works we will look at how a block and tackle works, and also examine several other force-multiplying devices! Understanding the Block and Tackle Imagine that you have the arrangement of a 100 pound (45.4 kilogram) weight suspended from a rope, as shown below: In the above figure, if you are going to suspend the weight in the air then you have to apply an upward force of 100 pounds to the rope. If the rope is 100 feet (30.5 meters) long and you want to lift the weight up 100 feet, you have to pull in 100 feet of rope to do it. This is simple and obvious. Now imagine that you add a pulley to the mix, as shown below: Does this change anything? Not really. The only thing that changes is the direction of the force you have to apply to lift the weight. You still have to apply 100 pounds of force to keep the weight suspended, and you still have to reel in 100 feet of rope in order to lift the weight 100 feet. The following figure shows the arrangement after adding a second pulley: This arrangement actually does change things in an important way. You can see that the weight is now suspended by two ropes rather than one. That means the weight is split equally between the two ropes, so each one holds only half the weight, or 50 pounds (22.7 kilograms). That means that if you want to hold the weight suspended in the air, you only have to apply 50 pounds of force (the ceiling exerts the other 50 pounds of force on the other end of the rope). If you want to lift the weight 100 feet higher, then you have to reel in twice as much rope - 200 feet of rope must be pulled in. This demonstrates a force-distance tradeoff. The force has been cut in half but the distance the rope must be pulled has doubled. The following diagram adds a third and fourth pulley to the arrangement: In this diagram, the pulley attached to the weight actually consists of two separate pulleys on the same shaft, as shown on the right. This arrangement cuts the force in half and doubles the distance again. To hold the weight in the air you must apply only 25 pounds of force, but to lift the weight 100 feet higher in the air you must now reel in 400 feet of rope. A block and tackle can contain as many pulleys as you like, although at some point the amount of friction in the pulley shafts begins to become a significant source of resistance. Next Page Next Page HSW Home Table of Contents: Introduction to How a Block and Tackle Works Other Force Distance Tradeoffs Shop or Compare Prices Rate this Article! Home Store Newsletter Search Advertising Privacy Contact About Help 1998 - 2005 HowStuffWorks, Inc.
Central Forces with Java
A JAVA applet to simulate orbits in four different central forces: gravity, Yukawa, 1 R^4 and Black Holes
Central Force with Java Central Force Motion with Java The applet below illustrates the orbits of particles in a variety of color-coded forces. (Your browser is not Java aware) Overview of this site Investigate the qualitative behaviour of orbits in different forces (gravity, Yukawa potential, Harmonic force (i.e. spring), 1 R3 force) See how effective potentials are used to find turning points of orbits in a central force and for black holes Use the OrbitApplet to try and change the orbit of a spaceship to intercept a target (your chance to "make it so") Learn something about Java by delving into the source code including Booch-like diagrams of the object heirarchy employed Central Force Central force refers to a force which always acts towards a fixed point (the center). As the above Applet demonstrates different central forces result in qualitativly different orbits. Some forces produce closed orbits, others a "spirograph" pattern. (The black hole is not described by a force per se see the black hole explanation). Any given orbit can be characterized by two constants of the motion the energy E and angular momentum L. The angular momentum is simply the vector cross product of the radius vector with the orbiting body's momentum vector. The energy is found from adding the kinetic energy to the potential energy due to the central force. If we wish to consider only the radial motion we can rewrite the energy equation as (4) where we have combined two terms into an effective potential energy. In the plot below you can see the gravitational effective potential Veff(r) and the two terms which added together to form it. The Veff(r) curve has a minimum which corresponds to the energy for stable circular orbits for the value of L plotted. For energies larger than this the orbit is not circular and has minimum and maximum radii which can be read off from the plot. The turning points are the radii at which a line of constant energy intersects Veff(r). Thus the effective potential energy allows us to determine the range of r values through which a body with given E and L moves. Plot of Veff(r) vs r What these plots don't indicate is whether the orbits are closed. An object in a closed orbit retraces it's path every time it orbits the center. If an orbit is not closed it often resembles a "spirograph" type pattern. Some forces (e.g. 1 R^4) have an effective potential energy curve which has a maximum and therefore there are no stable circular orbits in such forces. You can investigate these plots and the behavior of objects in various forces by using... the Orbit Applet or look at the source code This page created by Peter Musgrave musgrave@astro.queensu.ca
How a Helium Balloon Works
Explanation of lifting capabilities of helium, hydrogen and hot air balloons, from How Stuff Works.
Howstuffworks "How Helium Balloons Work" Auto Stuff Science Stuff Health Stuff Entertainment Stuff People Stuff Computer Stuff Electronics Stuff Home Stuff Money Stuff Travel Stuff Shop for Stuff Popular Searches Body Armor Hurricane Hypnosis Intelligent Design Military Technology Stem Cells UFOs Sponsored By: Subjects Earth Science Engineering Life Science Military Physical Science ShortStuff Space Supernatural Browse the Science Library Explore Stuff Lidrock.com Big List of Articles Get the Newsletter Shop for Top Products Shop or Compare Prices Search HSW and the Web Main Science Physical Science How Helium Balloons Work by Marshall Brain Table of Contents Introduction to How Helium Balloons Work Floating in General Helium Flotation Hot Air Where Helium Comes From Lots More Information Shop or Compare Prices There is something incredibly neat about helium balloons! If you buy one at the circus or fair, you can hold its string and it will ride along above you. If you let go of the string, it will fly away until you can't see it anymore. If you have ever wondered why it flies away, then read on. In this edition of HowStuffWorks , you'll find out all about helium! Next Page Next Page HSW Home Table of Contents: Introduction to How Helium Balloons Work Floating in General Helium Flotation Hot Air Where Helium Comes From Lots More Information Shop or Compare Prices Rate this Article! Home Store Newsletter Search Advertising Privacy Contact About Help 1998 - 2005 HowStuffWorks, Inc.
On a general Method of expressing the Paths of Light,and of the Planets, by the Coefficients of a Characteristic Function
An original paper by William Rowan Hamilton, dated 1833.
On a general Method of expressing the Paths of Light, and of the Planets, by the Coefficients of a Characteristic Function On a general Method of expressing the Paths of Light, and of the Planets, by the Coefficients of a Characteristic Function By William R. Hamilton, Royal Astronomer of Ireland [Dublin University Review and Quarterly Magazine, Vol.I, 1833, pp. 795-826.] The law of seeing in straight lines was known from the infancy of optics, being in a manner forced upon men's notice by the most familiar and constant experience. It could not fail to be observed that when a man looked at any object, he had it in his power to interrupt his vision of that object, and hide it at pleasure from his view, by interposing his hand between his eyes and it; and that then, by withdrawing his hand, he could see the object as before: and thus the notion of straight lines or rays of communication, between a visible object and a seeing eye, must very easily and early have arisen. This notion of straight lines of vision, was of of course confirmed by the obvious remark that objects can usually be seen on looking through a straight but not through a bent tube; and the most familiar facts of perspective supplied, we may suppose, new confirmations and new uses of the principle. A globe, for example, from whatever point it may be viewed, appears to have a circular outline; while a plate, or a round table, seems oval when viewed obliquely: and these facts may have been explained, and reduced to mathematical reasoning, by shewing that the straight rays or lines of vision, which touch any one given globe and pass through any one given point, are arranged in a hollow cone of a perfectly circular shape; but that the straight rays, which connect an eye with the round edge of a plate or table, compose, when they are oblique, an elliptical or oval cone. The same principle, of seeing in straight lines, must have been continually employed from the earliest times in the explanation of other familiar appearances, and in interpreting the testimony of sight respecting the places of visible bodies. It was, for example, an essential element in ancient as in modern astronomy. The shapes and sizes of shadows, again, could not fail to suggest the notion of straight illuminating rays: although opinions, now rejected, respecting the nature of light and vision, led some of the ancients to distinguish the lines of luminous from those of visual communication, and to regard the latter as a kind of feelers by which the eye became aware of the presence of visible objects. It appears, however, that many persons held, even in the infancy of Optics, the modern view of the subject, and attributed vision, as well as illumination, to an influence proceeding from the visible or luminous body. But what finally established this view, and along with it the belief of a finite velocity of progress of the luminous influence, was the discovery made by Roemer, of the gradual propagation of light from objects to the eye, in the instance of the satellites of Jupiter; of which we have good reason to believe, from astronomical observation, that the eclipses are never seen by us, till more than half an hour after they have happened; the interval, besides, being found to be so much the greater, as Jupiter is more distant from the Earth. Galileo had indeed proposed terrestrial experiments to measure the velocity of light, which he believed to be finite; and Des Cartes, who held that the communication of light was instantaneous, had perceived that astronomical consequences ought to follow, if the propagation of light were gradual: but experiments such as Galileo proposed, were not, and could not, be made on a scale sufficient for the purpose; and the state of astronomical observation in the time of Des Cartes did not permit him to verify the consequences which he perceived, and seemed rather to justify the use that he made of their non-verification, as an argument against the opinion with which he had shown them to be logically connected. But when astronomers had actually observed appearances, which seemed and still seem explicable only by this opinion of the gradual propagation of light from objects to the eye, the opinion itself became required, and was adopted, in the legitimate process of induction. By such steps, then, it has become an established theorem, fundamental in optical science, that the communication, whether between an illuminating body and a body illuminated, or between an object seen and a beholding eye, is effected by the gradual but very rapid passage of some thing, or influence, or state, called light, from the luminous or visible body, along mathematical or physical lines, usually called rays, and found to be, under the most common circumstances, exactly or nearly straight. Again, it was very early perceived that in appearances connected with mirrors, flat or curved, the luminous or visual communication is effected in bent lines. When we look into a flat mirror, and seem to see an object, such as a candle, behind it, we should err if we were to extend to this new case the rules of our more familiar experience. We should not now come to touch the candle by continuing the straight line from the eye to a hand or other obstacle, so placed between the eye and the mirror as to hide the candle; this line continued would meet the mirror in a certain place from which it would be necessary to draw a new and different straight line, if we wished to reach the real or tangible candle: and the whole bent line, made up of these two straight parts, is found to be now the line of visual communication, and is to be regarded now as the linear path of the light. An opaque obstacle, placed any where on either part of this bent line, is found to hide the reflected candle from the eye; but an obstacle, placed any where else, produces no such interruption. And the law was very early discovered, that for every such bent line of luminous or visual communication, the angle between any two successive straight parts is bisected by the normal, or perpendicular, to the mirror at the point of bending. Another early and important observation, was that of the broken or refracted lines of communication, between an object in water and an eye in air, and generally between a point in one ordinary medium and a point in another. A valuable series of experiments on such refraction was made and recorded by Ptolemy; but it was not till long afterwards that the law was discovered by Snellius. He found that if two lengths, in a certain ratio or proportion determined by the natures of the two media, be measured, from the point of breaking, or of bending, on the refracted ray and on the incident ray prolonged, these lengths have one common projection on the refracting surface, or on its tangent plane. This law of ordinary refraction has since been improved by Newton's discovery of the different refrangibility of the differently coloured rays; and has been applied to explain and to calculate the apparent elevation of the stars, produced by the atmosphere of the earth. The phenomena presented by the passage of light through crystals were not observed until more lately. Bartolinus seems to have been the first to notice the double refraction of Iceland spar; and Huygens first discovered the laws of this refraction. The more complicated double refraction produced by biaxial crystals was not observed until the present century; and the discovery of conical refraction in such crystals is still more recent, the experiments of Professor Lloyd on arragonite (undertaken at my request) having been only made last year. For the explanation of the laws of the linear propagation of light, two principal theories have been proposed, which still divide the suffrages of scientific men. The theory of Newton is well known. He compared the propagation of light to the motion of projectiles; and as, according to that First Law of Motion, of which he had himself established the truth by so extensive and beautiful an induction, an ordinary projectile continues in rectilinear and uniform progress, except so far as its course is retarded or disturbed by the influence of some foreign body; so, he thought, do luminous and visible objects shoot off little luminous or light-making projectiles, which then, until they are accelerated or retarded, or deflected one way or another, by the attractions or repulsions of some refracting or reflecting medium, continue to move uniformly in straight lines, either because they are not acted on at all by foreign bodies, or because the foreign actions are nearly equal on all sides, and thus destroy or neutralise each other. This theory was very generally received by mathematicians during the last century, and still has numerous supporters. Another theory however, proposed about the same time by another great philosopher, has appeared to derive some strong confirmations from modern inductive discoveries. This other is the theory of Huygens, who compared the gradual propagation of light, not to the motion of a projectile, but to the spreading of sound through air, or of waves through water. It was, according to him, no thing, in the ordinary sense, no body, which moved from the sun to the earth, or from a visible object to the eye; but a state, a motion, a disturbance, was first in one place, and afterwards in another. As, when we hear a cannon which has been fired at a distance, no bullet, no particle even of air, makes its way from the cannon to our ears; but only the aerial motion spreads, the air near the cannon is disturbed first, then that which is a little farther, and last of all the air that touches us. Or like the waves that spread and grow upon some peaceful lake, when a pebble has stirred its surface; the floating water-lilies rise and fall, but scarcely quit their place, while the enlarging wave passes on and moves them in succession. So that great ocean of ether which bathes the farthest stars, is ever newly stirred, by waves that spread and grow, from every source of light, till they move and agitate the whole with their minute vibrations: yet like sounds through air, or waves on water, these multitudinous disturbances make no confusion, but freely mix and cross, while each retains its identity, and keeps the impress of its proper origin. Such is the view of Light which Huygens adopted, and which justly bears his name; because, whatever kindred thoughts occurred to others before, he first shewed clearly how this view conducted to the laws of optics, by combining it with that essential principle of the undulatory theory which was first discovered by himself, the principle of accumulated disturbance. According to this principle, the minute vibrations of the elastic luminous ether cannot perceptibly affect our eyes, cannot produce any sensible light, unless they combine and concur in a great and, as it were, infinite multitude; and on the other hand, such combination is possible, because particular or secondary waves are supposed in this theory to spread from every vibrating particle, as from a separate centre, with a rapidity of propagation determined by the nature of the medium. And hence it comes, thought Huygens, that light in any one uniform medium diffuses itself only in straight lines, so as only to reach those parts of space to which a straight path lies open from its origin; because an opaque obstacle, obstructing such straight progress, though it does not hinder the spreading of weak particular waves into the space behind it, yet prevents their accumulation within that space into one grand general wave, of strength enough to generate light. This want of accumulation of separate vibrations behind an obstacle, was elegantly proved by Huygens: the mutual destruction of such vibrations by interference, is an important addition to the theory, which has been made by Young and by Fresnel. Analogous explanations have been offered for the laws of reflexion and refraction. Whether we adopt the Newtonian or the Huygenian, or any other physical theory, for the explanation of the laws that regulate the lines of luminous or visual communication, we may regard these laws themselves, and the properties and relations of these linear paths of light, as an important separate study, and as constituting a separate science, called often mathematical optics. This science of the laws and relations of luminous rays, is, however, itself a branch of another more general science, which may perhaps be called the Theory of Systems of Rays. I have published, in the XVth and XVIth volumes of the Transactions of the Royal Irish Academy, a series of investigations in that theory; and have attempted to introduce a new principle and method for the study of optical systems. Another supplementary memoir, which has been lately printed for the same Transactions, will appear in the XVIIth volume; but having been requested to resume the subject here, and to offer briefly some new illustrations of my view, I shall make some preliminary remarks on the state of deductive optics, and on the importance of a general method. The science of optics, like every other physical science, has two different directions of progress, which have been called the ascending and the descending scale, the inductive and the deductive method, the way of analysis and of synthesis. In every physical science, we must ascend from facts to laws, by the way of induction and analysis; and must descend from laws to consequences, by the deductive and synthetic way. We must gather and groupe appearances, until the scientific imagination discerns their hidden law, and unity arises from variety: and then from unity must re-deduce variety, and force the discovered law to utter its revelations of the future. It was with such convictions that Newton, when approaching to the close of his optical labours, and looking back on his own work, remarked, in the spirit of Bacon, that ``As in Mathematics, so in Natural Philosophy, the investigation of difficult things by the method of Analysis ought ever to precede the method of Composition. This analysis consists in making experiments and observations, and in drawing general conclusions from them by induction, and admitting of no objections against the conclusions but such as are drawn from experiments or other certain truths.'' ``And although the arguing from experiments and observations by induction be no demonstration of general conclusions; yet it is the best way of arguing which the nature of things admits of, and may be looked upon as so much the stronger, by how much the induction is more general. And if no exception occur from phenomena, the conclusion may be pronounced generally. But if at any time afterwards, any exception shall occur from experiments, it may then begin to be pronounced with such exceptions as occur. By this way of analysis, we may proceed from compounds to ingredients, and from motions to the forces producing them; and, in general, from effects to their causes, and from particular causes to more general ones, till the argument end in the most general. This is the method of analysis: and the synthesis consists in assuming the causes discovered, and established as principles, and by them explaining the phenomena proceeding from them, and proving the explanations.'' ``And if Natural Philosophy in all its parts, by pursuing this method, shall at length be perfected, the bounds of Moral Philosophy will also be enlarged. For, so far as we can know by Natural Philosophy, what is the First Cause, what power He has over us, and what benefits we receive from Him, so far our duty towards Him, as well as that towards one another, will appear to us by the light of nature.'' In the science of optics, which has engaged the attention of almost every mathematician for the last two thousand years, many great discoveries have been attained by both these ways. It is, however, remarkable that, while the laws of this science admit of being stated in at least as purely mathematical a form as any other physical results, their mathematical consequences have been far less fully traced than the consequences of many other laws; and that while modern experiments have added so much to the inductive progress of optics, the deductive has profited so little in proportion from the power of the modern algebra. It was known to Euclid and to Ptolemy, that the communication between visible objects and a beholding eye is usually effected in straight lines; and that when the line of communication is bent, by reflexion, at any point of a plane or of a spheric mirror, the angle of bending at this point, between the two straight parts of the bent line, is bisected by the normal to the mirror. It was known also that this law extends to successive reflexions. Optical induction was therefore sufficiently advanced two thousand years ago, to have enabled a mathematician to understand, and, so far as depended on the knowledge of physical laws, to resolve the following problem: to determine the arrangement of the final straight rays, or lines of vision, along which a shifting eye should look, in order to see a given luminous point, reflected by a combination of two given spherical mirrors. Yet, of two capital deductions respecting this arrangement, without which its theory must be regarded as very far from perfect--namely, that the final rays are in general tangents to a pair, and that they are perpendicular to a series of surfaces--the one is a theorem new and little known, and the other is still under dispute. For Malus, who first discovered that the rays of an ordinary reflected or refracted system are in general tangents to a pair of caustic surfaces, was led, by the complexity of his calculations, to deny the general existence (discovered by Huygens) of surfaces perpendicular to such rays; and the objection of Malus has been lately revived by an eminent analyst of Italy, in a valuable memoir on caustics, which was published last year in the correspondence of the observatory of Brussels. To multiply such instances of the existing imperfection of mathematical or deductive optics would be an unpleasant task, and might appear an attempt to depreciate the merit of living mathematicians. It is better to ascend to the source of the imperfection, the want of a general method, a presiding idea, to guide and assist the deduction. For although the deductive, as opposed to the inductive process, may be called itself a method, yet so wide and varied is its range, that it needs the guidance of some one central principle, to give it continuity and power. Those who have meditated on the beauty and utility, in theoretical mechanics, of the general method of Lagrange--who have felt the power and dignity of that central dynamical theorem which he deduced, in the Mchanique Analytique, from a combination of the principle of virtual velocities with the principle of D'Alembert--and who have appreciated the simplicity and harmony which he introduced into the research of the planetary perturbations, by the idea of the variation of parameters, and the differentials of the disturbing function, must feel that mathematical optics can only then attain a coordinate rank with mathematical mechanics, or with dynamical astronomy, in beauty, power, and harmony, when it shall possess an appropriate method, and become the unfolding of a central idea. This fundamental want forced itself long ago on my attention; and I have long been in possession of a method, by which it seems to me to be removed. But in thinking so, I am conscious of the danger of a bias. It may happen to me, as to others, that a meditation which has long been dwelt on shall assume an unreal importance; and that a method which has for a long time been practised shall acquire an only seeming facility. It must remain for others to judge how far my attempts have been successful, and how far they require to be completed, or set aside, in the future progress of the science. Meanwhile it appears that if a general method in deductive optics can be attained at all, it must flow from some law or principle, itself of the highest generality, and among the highest results of induction. What, then, may we consider as the highest and most general axiom, (in the Baconian sense,) to which optical induction has attained, respecting the rules and conditions of the lines of visual and luminous communication? The answer, I think, must be, the principle or law, called usually the Law of Least Action; suggested by questionable views, but established on the widest induction, and embracing every known combination of media, and every straight, or bent, or curved line, ordinary or extraordinary, along which light (whatever light may be) extends its influence successively in space and time: namely, that this linear path of light, from one point to another, is always found to be such, that if it be compared with the other infinitely various lines by which in thought and in geometry the same two points might be connected, a certain integral or sum, called often Action, and depending by fixed rules on the length, and shape, and position of the path, and on the media which are traversed by it, is less than all the similar integrals for the other neighbouring lines, or, at least, possesses, with respect to them, a certain stationary property. From this Law, then, which may, perhaps, be named the LAW OF STATIONARY ACTION, it seems that we may most fitly and with best hope set out, in the synthetic or deductive process, and in search of a mathematical method. Accordingly, from this known law of least or stationary action, I deduced (long since) another connected and coextensive principle, which may be called, by analogy, the LAW OF VARYING ACTION, and which seems to offer naturally a method such as we are seeking: the one law being as it were the last step in the ascending scale of induction, respecting linear paths of light, while the other law may usefully be made the first in the descending and deductive way. And my chief purpose, in the present paper, is to offer a few illustrations and consequences of these two coordinate laws. The former of these two laws was discovered in the following manner. The elementary principle of straight rays shewed that light, under the most simple and usual circumstances, employs the direct, and, therefore, the shortest course to pass from one point to another. Again, it was a very early discovery, (attributed by Laplace to Ptolemy,) that in the case of a plane mirror, the bent line formed by the incident and reflected rays is shorter than any other bent line, having the same extremities, and having its point of bending on the mirror. These facts were thought by some to be instances and results of the simplicity and economy of nature; and Fermat, whose researches on maxima and minima are claimed by the continental mathematicians as the germ of the differential calculus, sought anxiously to trace some similar economy in the more complex case of refraction. He believed that by a metaphysical or cosmological necessity, arising from the simplicity of the universe, light always takes the course which it can traverse in the shortest time. To reconcile this metaphysical opinion with the law of refraction, discovered experimentally by Snellius, Fermat was led to suppose that the two lengths, or indices, which Snellius had measured on the incident ray prolonged and on the refracted ray, and had observed to have one common projection on a refracting plane, are inversely proportional to the two successive velocities of the light before and after refraction, and therefore that the velocity of light is diminished on entering those denser media in which it is observed to approach the perpendicular: for Fermat believed that the time of propagation of light along a line bent by refraction was represented by the sum of the two products, of the incident portion multiplied by the index of the first medium, and of the refracted portion multiplied by the index of the second medium; because he found, by his mathematical method, that this sum was less, in the case of a plane refractor, than if light went by any other than its actual path from one given point to another; and because he perceived that the supposition of a velocity inversely as the index, reconciled his mathematical discovery of the minimum of the foregoing sum with his cosmological principle of least time. Des Cartes attacked Fermat's opinions respecting light, but Leibnitz zealously defended them; and Huygens was led, by reasonings of a very different kind, to adopt Fermat's conclusions of a velocity inversely as the index, and of a minimum time of propagation of light, in passing from one given point to another through an ordinary refracting plane. Newton, however, by his theory of emission and attraction, was led to conclude that the velocity of light was directly, not inversely, as the index, and that it was increased instead of being diminished on entering a denser medium; a result incompatible with the theorem of shortest time in refraction. The theorem of shortest time was accordingly abandoned by many, and among the rest by Maupertuis, who, however, proposed in its stead, as a new cosmological principle, that celebrated law of least action which has since acquired so high a rank in mathematical physics, by the improvements of Euler and Lagrange. Maupertuis gave the name of action to the product of space and velocity, or rather to the sum of all such products for the various elements of any motion; conceiving that the more space has been traversed and the less time it has been traversed in, the more action may be considered to have been expended: and by combining this idea of action with Newton's estimate of the velocity of light, as increased by a denser medium, and as proportional to the refracting index, and with Fermat's mathematical theorem of the minimum sum of the products of paths and indices in ordinary refraction at a plane, he concluded that the course chosen by light corresponded always to the least possible action, though not always to the least possible time. He proposed this view as reconciling physical and metaphysical principles, which the results of Newton had seemed to put in opposition to each other; and he soon proceeded to extend his law of least action to the phenomena of the shock of bodies. Euler, attached to Maupertuis, and pleased with these novel results, employed his own great mathematical powers to prove that the law of least action extends to all the curves described by points under the influence of central forces; or, to speak more precisely, that if any such curve be compared with any other curve between the same extremities, which differs from it indefinitely little in shape and in position, and may be imagined to be described by a neighbouring point with the same law of velocity, and if we give the name of action to the integral of the product of the velocity and an element of a curve, the difference of the two neighbouring values of this action will be indefinitely less than the greatest linear distance (itself indefinitely small) between the two near curves; a theorem which I think may be advantageously expressed by saying that the action is stationary. Lagrange extended this theorem of Euler to the motion of a system of points or bodies which act in any manner on each other; the action being in this case the sum of the masses by the foregoing integrals. Laplace has also extended the use of the principle in optics, by applying it to the refraction of crystals; and has pointed out an analogous principle in mechanics, for all imaginable connexions between force and velocity. But although the law of least action has thus attained a rank among the highest theorems of physics, yet its pretensions to a cosmological necessity, on the ground of economy in the universe, are now generally rejected. And the rejection appears just, for this, among other reasons, that the quantity pretended to be economised is in fact often lavishly expended. In optics, for example, though the sum of the incident and reflected portions of the path of light, in a single ordinary reflexion at a plane, is always the shortest of any, yet in reflexion at a curved mirror this economy is often violated. If an eye be placed in the interior but not at the centre of a reflecting hollow sphere, it may see itself reflected in two opposite points, of which one indeed is the nearest to it, but the other on the contrary is the furthest; so that of the two different paths of light, corresponding to these two opposite points, the one indeed is the shortest, but the other is the longest of any. In mathematical language, the integral called action, instead of being always a minimum, is often a maximum; and often it is neither the one nor the other: though it has always a certain stationary property, of a kind which has been already alluded to, and which will soon be more fully explained. We cannot, therefore, suppose the economy of this quantity to have been designed in the divine idea of the universe: though a simplicity of some high kind may be believed to be included in that idea. And though we may retain the name of action to denote the stationary integral to which it has become appropriated--which we may do without adopting either the metaphysical or (in optics) the physical opinions that first suggested the name--yet we ought not (I think) to retain the epithet least: but rather to adopt the alteration proposed above, and to speak, in mechanics and in optics, of the Law of Stationary Action. To illustrate this great law, and that other general law, of varying action, which I have deduced from it, we may conveniently consider first the simple case of rectilinear paths of light. For the rectilinear course, which is evidently the shortest of any, is also distinguished from all others by a certain stationary property, and law of variation, which, being included in the general laws of stationary and varying action, may serve as preparatory examples. The length V of any given line, straight or curved, may evidently be denoted by the following integral: If now we pass from this to another neighbouring line, having the same extremities, and suppose that the several points of the latter line are connected with those of the former, by equations between their co-ordinates, of the form being any small constant, and , , , being any arbitrary functions of x, y, z, which vanish for the extreme values of those variables, that is, for the extreme points of the given line, and do not become infinite for any of the intermediate points, nor for the value , though they may in general involve the arbitrary constant ; the length of the new line may be represented by the new integral, taken between the same extreme values of x, y, z, as the former; and this new length may be considered as a function of , which tends to the old length V, when tends to 0, the quotient tending in general at the same time to a finite limit, which may be thus expressed, the last of these forms being obtained from the preceding by integrating by parts, and by employing the condition already mentioned, that the functions , , , vanish at the extremities of the integral. When the original line is such that the limit ( 4 ) vanishes, independently of the forms of the functions , , , and therefore that the difference of the lengths bears ultimately an evanescent ratio to the small quantity , (which quantity determines the difference between the second line and the first, and bears itself a finite ratio to the greatest distance between these two lines,) we may say that the original line has a stationary length, V, as compared with all the lines between the same extremities, which differ from it infinitely little in shape and in position. And since it easily follows, from the last form of the limit ( 4 ), that this limit cannot vanish independently of the forms of , , , unless that is, unless the ratios are constant throughout the original line, but that the limit vanishes when this condition is satisfied, we see that the property of stationary length belongs (in free space) to straight lines and to such only. The foregoing proof of this property of the straight line may, perhaps, be useful to those who are not familiar with the Calculus of Variations. To illustrate, by examples, this stationary property of the length of a straight line, let us consider such a line as the common chord of a series of circular arcs, and compare its length with theirs, and theirs with one another. The length of the straight line being called V, let be the height or sagitta of the circular arch upon this chord; so that shall be the diameter of the circle, and the trigonometric tangent of the quarter of an arc having the same number of degrees, to a radius equal to unity: we shall then have the following expression for the length of the circular arch upon the given chord V, This expression may be put under the form, which shows not only that the ratio of the circular arch to its chord is always 1, but also, that since the arch increases continually with its height at an increasing rate; its differential coefficient being positive and increasing, when is positive and increases, but vanishing with , and showing, therefore, that in this series of circular arcs and chord the property of stationary length belongs to the straight line only. Again, we may imagine a series of semi-ellipses upon a given common axisV, the other axis conjugate to this being a variable quantity . The length of such a semi-elliptic arch is an expression which may be thus transformed, thus the ratio of the elliptic arch to its given base or axis V is not only greater than unity, and continually increases with the height, but increases at an increasing rate, which vanishes for an evanescent height; so that in this series of semi-elliptic arcs and axis, the latter alone has the property of stationary length. In more familiar words, if we construct on a base of a given length, suppose one hundred feet, a series of circular or of semi-elliptic arches, having that base for chord or for axis, the lengths of those arches will not only increase with their heights, but every additional foot or inch of height will augment the length more than the foregoing foot or inch had done; and the lower or flatter any two such arches are made, the less will be the difference of their lengths as compared with the difference of their heights, till the one difference becomes less than any fraction that can be named of the other. For example, if we construct, on the supposed base of one hundred feet, two circular arches, the first fifty feet high, the second fifty-one feet high, of which the first will thus be a semicircle, and the second greater than a semicircle, the difference of lengths of these two arches will be a little more than double the difference of their heights, that is, it will be about two feet; but if on the same base we construct one circular arch with only one foot of height, and another with only two feet, the difference of lengths of these two low arches will not be quite an inch, though the difference of their heights remains a foot as before; and if we imagine the two circular arches, on the same base or common chord of one hundred feet, to have their heights reduced to one and two inches respectively, the difference of their lengths will thereby be reduced to less than the hundred-and-fiftieth part of an inch. We see then that a straight ray, or rectilinear path of light, from one given point to another, has a stationary length, as compared with all the lines which differ little from it in shape and in position, and which are drawn between the same extremities. If, however, we suppose the extremities of the neighbouring line to differ from those of the ray, we shall then obtain in general a varying instead of stationary length. To investigate the law of this variation, which is the simplest case of the second general law above proposed to be illustrated, we may resume the foregoing comparison of the lengths V, , of any two neighbouring lines; supposing now that these two lines have different extremities, or in other words, that the functions , , , do not vanish at the limits of the integral. The integration by parts gives now, along with the last expression ( 4 ) for the limit of the following additional terms, which belong to the extremities of the given line, the accented being the initial quantities, and d' referring to the infinitesimal changes produced by a motion of the initial point along the initial element of the line, so that d'V is this initial element taken negatively, when, therefore, the last integral ( 4 ) vanishes, by the original line being straight, and when we compare this line with another infinitely near, the law of varying length is expressed by the following equation: it may also be thus expressed, and shows that the length of any other line which differs infinitely little from the straight ray in shape and in position, may be considered as equal to its own projection on the ray. It must be observed that in certain singular cases, the distance between two lines may be made less, throughout, than any quantity assigned, without causing thereby their lengths to tend to equality. For example, a given straight line may be subdivided into a great number of small parts, equal or unequal, and on each part a semicircle may be constructed; and then the waving line composed of the small but numerous semicircumferences will every where be little distant from the given straight line, and may be made as little distant as we please, to any degree short of perfect coincidence; while yet the length of the undulating line will not tend to become equal to the length of the straight line, but will bear to that length a constant ratio greater than unity, namely the ratio of to 2. But it is evident that such cases as these are excluded from the foregoing reasoning, which supposes an approach of the one line to the other in shape, as well as a diminution of the linear distance between them. From the law of varying length of a straight ray we may easily perceive (what is also otherwise evident) that the straight rays diverging from a given point x' y' z', or converging to a given point x y z, are cut perpendicularly by a series of concentric spheres, having for their common equation, and more generally, that if a set of straight rays be perpendicular to any one surface, they are also perpendicular to a series of surfaces, determined by the equation ( 14 ), that is, by the condition that the intercepted portion of a ray between any two given surfaces of the series shall have a constant length. Analogous consequences will be found to follow in general from the law of varying action. It may be useful to dwell a little longer on the case of rectilinear paths, and on the consequences of the mathematical conception of luminous or visual communication as a motion from point to point along a mathematical straight line or ray, before we pass to the properties of other less simple paths. It is an obvious consequence of this conception, that from any one point (A), considered as initial, we may imagine light, if unobstructed, as proceeding to any other point (B), considered as final, along one determined ray, or linear path; of which the shape, being straight, is the same whatever point its ends may be; but of which the length and the position depend on the places of those ends, and admit of infinite variety, corresponding to the infinite variety that can be imagined of pairs of points to be connected. So that if we express by one set of numbers the places of the initial and of the final points, and by another set the length and position of the ray, the latter set of numbers must, in mathematical language, be functions of the former; must admit of being deduced from them by some fixed mathematical rules. To make this deduction is an easy but a fundamental problem, which may be resolved in the following manner. Let each of the two points A, B, be referred to one common set of three rectangular semiaxes OX, OY, OZ, diverging from any assumed originO; let the positive or negative co-ordinates of the final point B, to which the light comes, be denoted by x, y, z, and let the corresponding co-ordinates of the initial point A, from which the light sets out, be denoted similarly by x', y' , z'; let V be the length of the straight ray, or line AB, and let , , , be the positive or negative cosines of the acute or obtuse angles which the direction of this ray makes with the positive semiaxes of co-ordinates: the problem is then to determine the laws of the functional dependence of the positive number V, and of the three positive or negative numbers , , , on the six positive or negative numbers x, y, z, x', y', z'; and this problem is resolved by the following evident formul; It is a simple but important corollary to this solution, that the laws of the three cosines of direction , , , expressed by the equations ( 16 ), are connected with the law of the lengthV, expressed by the formula ( 15 ), in a manner which may be stated thus; being here a characteristic of partial differentiation. We find, in like manner, differentiating the function V with respect to the initial co-ordinates. And since the three cosines of direction , , , are evidently connected by the relation we see that the functionV satisfies simultaneously the two following partial differential equations of the first order and second degree, The equations ( 17 ), ( 18 ), ( 20 ), will soon be greatly extended; but it seemed well to notice them here, because they contain the germ of my general method for the investigation of the paths of light and of the planets, by the partial differential coefficients of one characteristic function. For the equations ( 17 ) and ( 18 ), which involve the coefficients of the first order of the functionV, that is, in the present case, of the length, may be considered as equations of the straight ray which passes with a given direction through a given initial or a given final point: and I have found analogous equations for all other paths of light, and even for the planetary orbits under the influence of their mutual attractions. The equations ( 16 ) when put under the form give evidently by differentiation and therefore the symbold referring here to an infinitesimal change of the final pointB, by a motion along the ray prolonged at its extremity; in such a manner that the equations ( 22 ) may be regarded as differential equations of that ray. They give the expressions which may, by ( 23 ), be put under the form implying still a partial differentiation, and dV being treated here as a function of dx, dy, dz. And comparing the expressions ( 25 ) and ( 17 ), we obtain the following results, which we shall soon find to be very general, and to extend with analogous meanings to all linear paths of light, It must not be supposed that these equations are identical; for the quantities in the first members are the partial differential coefficients of one function, V, while those in the second members are the coefficients of another function dV. In like manner, if we employ (as before) the characteristic d' to denote the infinitesimal changes arising from a change of the initial point A, by a motion along the initial element of the ray, we have the differential equations d'V being as before the initial element taken negatively, so that we have therefore and consequently, by ( 18 ), The same remarks apply to these last results, as to the equations ( 26 ). The general law of stationary action, in optics, may now be thus stated. The optical quantity called action, for any luminous path having i points of sudden bending by reflexion or refraction, and having therefore i+1 separate branches, is the sum of i+1 separate integrals, of which each is determined by an equation of the form the coefficient of the element of the path, in the rth medium, depending, in the most general case, on the optical properties of that medium, and on the position, direction, and colour of the element, according to rules discovered by experience, and such, for example, that if the rth medium be ordinary, is the index of that medium; so that is always a homogeneous function of the first dimension of the differentials , , , which may also involve the undifferentiated co-ordinates themselves, and has in general a variation of the form if we put for abridgment and we have also, by the homogeneity of , If we now change the co-ordinates of the luminous path to any near connected co-ordinates being any small constant, and any functions of and of the co-ordinates , which do not become infinite for , nor for any point on the rth portion of the path, and which satisfy at the meeting of two such portions the equation of the corresponding reflecting or refracting surface, and vanish at the ends of the whole path; we shall pass hereby to a near line having the same extremities as the luminous path, and having its points of bending on the same reflecting or refracting surfaces; and the law of stationary action is, that if we compare the integral or sum, , for the luminous path, with the corresponding integral for this near line, the difference of these two integrals or actions bears an indefinitely small ratio to the quantity , (which makes the one line differ from the other,) when this quantity becomes itself indefinitely small: so that we have the limiting equation, that is or finally To develop this last equation, we have, by ( 33 ) and ( 37 ), and therefore, integrating by parts, and accenting the symbols which belong to the beginning of the rth portion of the path, And since the extreme values, and values for the points of juncture, of the otherwise arbitrary functions , are subject to the following conditions: and r varying from 1 to i; and finally, for every value of r within the same range, to the condition being either seminormal to the rth reflecting or refracting surface at the rth point of incidence, and being the cosines of the angles which makes with the three rectangular positive semiaxes of co-ordinates x y z; the law of stationary action ( 40 ) resolves itself into the following equations: and in which is an indeterminate multiplier. The three equations ( 46 ), which may by the condition ( 36 ) be shown to be consistent with each other, express the gradual changes, if any, of a ray, between its points of sudden bending; and the equations ( 47 ) contain the rules of ordinary and extraordinary reflexion and refraction. All these results of that known law, which I have called the law of stationary action, are fully confirmed by experience, when suitable forms are assigned to the functions denoted by . For example, in the case of an uniform medium, ordinary or extraordinary, the function is to be considered as independent of the undifferentiated co-ordinates , and the differential equations ( 46 ) of the rth portion of the luminous path become simply and give by integration they express, therefore, the known fact of the rectilinear propagation of light in a uniform medium, because in such a medium depend only on the colour and direction, but not on the co-ordinates of the path, and are functions of not including , if we put for abridgment so that , , , represent the cosines of the inclination (in this case constant) of any element of the rth portion of the path to the positive semiaxes of co-ordinates. The formul ( 46 ) give also the known differential equations for a ray in the earth's atmosphere. With respect to the rules of reflexion or refraction of light, expressed by the equations ( 47 ), they may in general be thus summed up; in which refers to the sudden changes produced by reflexion or refraction, and are the cosines of the inclinations to the positive semiaxes of co-ordinates, of any arbitrary line , which touches the rth reflecting or refracting surface, at the rth point of incidence, so that In the case of ordinary media, for example, we have and the equation ( 51 ) may be put under the form in which so that the unchanged quantity is the projection of the index on the arbitrary tangent , each index being measured from the point of incidence in the direction of the corresponding ray: which agrees with the law of Snellius. In general, if we put and we may consider as the projections, on the axes of co-ordinates, of a certain straight line , of which the length and direction depend (according to rules expressed by the foregoing equations) on the form of the function or , and on the direction and colour of the element of the luminous path, before or after incidence; and if we put the equation ( 51 ) will take the form which expresses that the projection of this straight line on any arbitrary tangent to the reflecting or refracting surface, at the point of incidence, is not changed by reflection or refraction, ordinary or extraordinary: which is a convenient general form for all the known rules of sudden change of direction of a path of light. In the undulatory theory, I have found that the line is the reciprocal of the normal velocity of propagation of the wave; and its projections may therefore be called components of normal slowness: so that the foregoing property of unchanged projection of the line , may be expressed, in the language of this theory, by saying that the component of normal slowness in the direction of any line which touches any ordinary or extraordinary reflecting or refracting surface at any point of incidence is not changed by reflection or refraction. It was, however, by a different method that I originally deduced this general enunciation of the rules of optical reflexion and refraction, namely, by employing my principle of the characteristic function, and that other general law, of which it is now time to speak. This other general law, the law of varying action, results from the known law above explained, by considering the extreme points of a luminous path as variable: that is, by not supposing the six extreme functions ( 43 ) to vanish. Denoting, for abridgment, the three final functions of this set by , and the three initial functions by , and writing similarly v, dV, c., instead of the final quantities , , c. and v', dV', c., instead of the initial quantities , , c., we find this new equation, which is a form of my general result. It may also be put conveniently under this other form, in which and the symbols representing the initial quantities which correspond to and d'V being, according to the same analogy of notation, the infinitesimal change of the whole integralV, arising from the infinitesimal changes d'x', d'y', d'z', of the initial co-ordinates, that is, from a motion of the initial point x' y' z' along the initial element of the luminous path; so that d'V is the initial element of the integral taken negatively, If then we consider the integral or actionV as a function (which I have called the characteristic function) of the six extreme co-ordinates, and if we differentiate this function with respect to these co-ordinates, we see that its six partial differential coefficients of the first order may be represented generally by the equations ( 26 ) and ( 30 ), which were already proved to be true for the simple case of rectilinear paths of light. And as, in that simple case, those equations, being then equivalent to the formulae ( 17 ) and ( 18 ), were seen to determine the course of the straight ray, which passed with a given direction through a given initial or a given final point; so, generally, when we know the initial co-ordinates, direction, and colour of a luminous path, and the optical properties of the initial medium, we can determine, or at least restrict (in general) to a finite variety, the values of the initial coefficients which form the second members of the equations ( 30 ); and therefore we may regard as known the first members of the same equations, namely the partial differential coefficients of the characteristic functionV, taken with respect to the known initial co-ordinates: so that if the form of the functionV be known, we have between the final co-ordinates x, y, z, considered as variable, the three following equations of the path, or at least of its final branch, These three equations are compatible with each other, and are equivalent only to two distinct relations between the variable co-ordinates x y z, because in general V must satisfy a partial differential equation of the form in which, by what has been shown, and which is therefore analogous to the second formula ( 20 ): this equation ( 66 ) being obtained by eliminating the ratios of d'x', d'y', d'z', between the general formul\ ( 30 ). In like manner the formul ( 26 ) give generally a partial differential equation of the form analogous to the first of those marked ( 20 ), and the three following compatible equations between the variable initial co-ordinates x', y', z', of a path of light which is obliged to pass with a given direction through a given final point, But for the integration and use of these partial differential equations, the limits of the present communication oblige me to refer to the volumes, already mentioned, of the Transactions of the Royal Irish Academy. I may, however, mention here, that my employment of the characteristic functionV, in all questions of reflexion and refraction, is founded on an equation in finite differences, which, by the integral nature of this functionV, is evidently satisfied, namely, referring, as before, to the sudden changes produced at any reflecting or refracting surface having for its equation and being an indeterminate multiplier, employed for the purpose of being able to treat the co-ordinates of incidence as three independent variables. For example, the formulae ( 47 ), for a sudden change of direction, result immediately from ( 70 ), under the form by differentiating with respect to the co-ordinates of incidence, as three independent variables, and then reducing by the equation ( 71 ) of the ordinary or extraordinary reflecting or refracting surface. These results respecting the change of direction of a luminous path may be put under the form or under the following, and in general, all theorems respecting the changes produced by reflexion or refraction in the properties of an optical system, may be expressed, by the help of the formula ( 70 ), as permanences of certain other properties. The remarkable permanence, already stated, of the components of normal slowness of propagation of a luminous wave, was suggested to me by observing that my function V is (in the undulatory theory) the time of propagation of light from the initial to the final point, and therefore that the waves (in the same theory) are represented by the general equation and the components of normal slowness by the partial differential coefficients of V of the first order. The properties of the functionV, on which my whole optical method depends, supplied me also, long since, with a simple proof of the contested theorem of Huygens already mentioned, namely, that the rays of any ordinary homogeneous system, which after issuing originally from any luminous point, or being (in an initial and ordinary state) perpendicular to any common surface, have undergone any number of reflexions or refractions ordinary or extraordinary, before arriving at their final state, are in that state perpendicular to a series of surfaces, namely, to the series ( 75 ), which are waves in the theory of Huygens: because, by the properties of my function, the differential equation of that series is , and being the cosines which determine the final direction of a ray. It was also by combining the properties of the same characteristic functionV with the physical principles of Fresnel, that I was first led, (from perceiving an indeterminateness in two particular cases in the relations between the coefficients and the ratios of dx, dy, dz,) to form that theoretical expectation of two kinds of conical refraction which I communicated in last October (1832) to the Royal Irish Academy and to Professor Lloyd, and which the latter has since verified experimentally. Mr. MacCullagh has lately informed me that the same two indeterminate cases in Fresnel's theory had occurred to him from geometrical considerations, some years ago, and that he had intended to try to what geometrical and physical consequences they would lead. The method of the characteristic function has conducted me to many other consequences, besides those which I have already published in the Transactions of the Royal Irish Academy: and I think that it will hereafter acquire, in the hands of other mathematicians, a rank in deductive optics, of the same kind as that which the method of co-ordinates has attained in algebraical geometry. For as, by the last-mentioned method, Des Cartes reduced the study of a plane curve, or of a curved surface, to the study of that one function which expresses the law of the ordinate, and made it possible thereby to discover general formul for the tangents, curvatures, and all other geometrical properties of the curve or surface, and to regard them as included all in that one law, that central algebraical relation: so I believe that mathematicians will find it possible to deduce all properties of optical systems from the study of that one central relation which connects, for each particular system, the optical functionV with the extreme co-ordinates and the colour, and which has its partial differential coefficients connected with the extreme directions of a ray, by the law of varying action, or by the formul ( 26 ) and ( 30 ). It only now remains, in order to conclude the present remarks, that I should briefly explain the allusions already made to my view of an analogous function and method in the research of the planetary and cometary orbits under the influence of their mutual perturbations. The view itself occurred to me many years ago, and I gave a short notice or announcement of it in the XVth volume (page 80) of the Transactions of the Royal Irish Academy; but I have only lately resumed the idea, and have not hitherto published any definite statement on the subject. To begin with a simple instance, let us attend first to the case of a comet, considered as sensibly devoid of mass, and as moving in an undisturbed parabola about the sun, which latter body we shall regard as fixed at the origin of co-ordinates, and as having an attracting mass equal to unity. Let r be the comet's radius vector at any momentt considered as final, and r' the radius vector of the same comet at any other moment t' considered as initial; let also r'' be the chord joining the ends of r and r', and let us put for abridgment then I find, that the final and initial components of velocity of the comet, parallel to any three rectangular semiaxes of co-ordinates, may be expressed as follows by the coefficients of the functionV, and that this functionV satisfies the two following partial differential equations, which reconcile the expressions ( 78 ) with the known law of a comet's velocity. I find also that all the other properties of a comet's parabolic motion agree with and are included in the formul ( 78 ), when the form ( 77 ) is assigned to the functionV. They give, for example, by an easy combination, the theorem discovered by Euler for the dependence of the time (t - t') on the parabolic chord (r'') and on the sum (r + r') of the radii drawn to its extremities. More generally, in any system of points or bodies which attract or repel one another according to any function of the distance, for example, in the solar system, I have found that the final and initial components of momentum may be expressed in a similar manner, by the partial differential coefficients of the first order of some one central or characteristic functionV of the final and initial co-ordinates; so that we have generally, by a suitable choice of V, and , , c., being the masses of the system, and the functionV being obliged to satisfy two partial differential equations of the first order and second degree, which are analogous to ( 79 ), and may be thus denoted the functionF involving the final co-ordinates, and the functionF' involving similarly the initial co-ordinates, and the common form of these two functions depending on the law of attraction or repulsion. In the solar system H being a certain constant; and in general the partial differential equations ( 82 ) contain the law of living forces, which the other known general laws or integrals of the equations of motion are expressed by other general and simple properties of the same characteristic functionV: the coefficients of which function, when combined with the relations ( 80 ) and ( 81 ), are sufficient to determine all circumstances of the motion of a system. By this view the research of the most complicated orbits, in lunar, planetary, and sidereal astronomy, is reduced to the study of the properties of a single functionV; which is analogous to my optical function, and represents the action of the system from one position to another. If we knew, for example, the form of this one functionV for a system of three bodies attracting according to Newton's law, (suppose the system of Sun, Earth, and Moon, or of the Sun, Jupiter and Saturn,) we should need no further integration in order to determine the separate paths and the successive configurations of these three bodies; the eight relations, independent of the time, between their nine variable co-ordinates, would be given at once by differentiating the one functionV, and employing the nine initial equations of the form ( 81 ), which in consequence of the second equation ( 82 ) are only equivalent to eight distinct relations, the positions and velocities being given for some one initial epoch; and the variable timet of arriving at any one of the subsequent states of the system would be given by a single integration of any combination of these relations with the equations ( 80 ). The development of this view, including its extension to other analogous questions, appears to me to open in mechanics and astronomy an entirely new field of research. I shall only add, that the view was suggested by a general law of varying action in dynamics, which I had deduced from the known dynamical law of least or stationary action, by a process analogous to that general reasoning in optics which I have already endeavoured to illustrate. Observatory of Trinity College, Dublin, September, 1833. Links: Sir William Rowan Hamilton (1805-1865) History of Mathematics D.R. Wilkins ( dwilkins@maths.tcd.ie ) School of Mathematics Trinity College, Dublin
Gyroscope
Graphics, related links and a video combine to show you how gyroscopes work.
Howstuffworks "How Gyroscopes Work" Auto Stuff Science Stuff Health Stuff Entertainment Stuff People Stuff Computer Stuff Electronics Stuff Home Stuff Money Stuff Travel Stuff Shop for Stuff Popular Searches Body Armor Hurricane Hypnosis Intelligent Design Military Technology Stem Cells UFOs Sponsored By: Subjects Earth Science Engineering Life Science Military Physical Science ShortStuff Space Supernatural Browse the Science Library Explore Stuff Lidrock.com Big List of Articles Get the Newsletter Shop for Top Products Shop or Compare Prices Search HSW and the Web Main Science Physical Science How Gyroscopes Work by Marshall Brain Table of Contents Introduction to How Gyroscopes Work Precession The Cause of Precession Uses of Gyroscopes Lots More Information Shop or Compare Prices Gyroscopes can be very perplexing objects because they move in peculiar ways and even seem to defy gravity. These special properties make gyroscopes extremely important in everything from your bicycle to the advanced navigation system on the space shuttle . A typical airplane uses about a dozen gyroscopes in everything from its compass to its autopilot. The Russian Mir space station used 11 gyroscopes to keep its orientation to the sun , and the Hubble Space Telescope has a batch of navigational gyros as well. Gyroscopic effects are also central to things like yo-yos and Frisbees! In this edition of HowStuffWorks , we will look at gyroscopes to understand why they are so useful in so many different places. You will also come to see the reason behind their very odd behavior! Eco-friendly Electric scooters are a great commuting alternative. Click here to browse both gas powered and electric models. Next Page Top Selling Gyroscopes Amazon: $19.99 Fat Brain Toys: Unearth the powers of our universe. Special ball-bearing technology gives our Gyroscope an incredibly long spinning time. $7.95 Vermont Country Store: A gyroscope awakens the scientist in every child. Set it to spinning and make it perform gravity-defying feats that will captivate young learners. Bal... $7.95 Next Page HSW Home Table of Contents: Introduction to How Gyroscopes Work Precession The Cause of Precession Uses of Gyroscopes Lots More Information Shop or Compare Prices Rate this Article! Home Store Newsletter Search Advertising Privacy Contact About Help 1998 - 2005 HowStuffWorks, Inc.
An introduction to physics - Mechanics
An introduction to classical mechanics. Suitable for students who are beginning the subject.
Introduction to Physics 1 - Mechanics Introduction to Physics 1 - Mechanics The beginning... Hello. My name is J. D. Jones . To find out more about me and my background just click on my name which should appear underlined and in a distinct color. That underlined and colored name is an example of a "link". I will use links throughout this on line textbook to let you jump to new topics. I assume that since you have arrived at this page you are somewhat familiar with navigating around web sites so I will not spend more time on that subject. If you need additional help, use the Help menu item on your browser. Some of the images you find scattered around this page are screen shots from the lessons that follow. Others evidently are not. Just pause your cursor over any image to see a description. Those of us who write online material including Java applets, and those of you who need to run those applets are caught in the crossfire of the Java war. Microsoft tried to take over the Java virtual machine business a few years ago and failed. Sun Microsystems, the original Java company, won that battle and Microsoft is giving up, abandoning their Java technology and their support for Java. All new computers will now be shipped with the Sun Java runtime environment(JRE). That means that when websites are updated, the authors must make a choice about whether or not to move up to the modern Java language, not constrained by the limitations of the Microsoft virtual machine. At M. Casco we have decided to move on, since the move will be have to be made sooner or later. Consequently if you have a computer shipped before 2004, you will probably need to download a free Java plugin from Sun and install it on your computer in order to use the applets included on this website. We apologize for any inconvenience. It seems that this is one of the prices we have to pay as customers for progress in the technology marketplace. This is probably a good place to talk a bit about the organization of this course and some of the symbols you will see. There is a main thread to this story which is carried by the series of pages of which this is the first. These pages are linked together so that when you are at the end of one you may click on "Next" to go to the next one or on "Previous" to go back to the previous one. You may also click on a link to "Other" which gives you access to the course outline from where you may jump to any page. The links within the main thread are marked by a green ball like this. Next Because there are people of various backgrounds taking this course, I may provide additional background material to fill in some of the details that you might need. The links to the underlying details will look like this example. Numbers, Functions and Graphs When new terms are introduced, they will be linked to a glossary entry so if you find underlined and highlighted words in the text, just click on them to get to the definition. At the end of each page will be a link like this to jump to the glossary so you can browse for any term in which you are interested. Some things are easier to understand than others. Probably we will not always agree on what the hard stuff is but I may mark things that I found confusing when I was learning, with a little devil like this to alert you to trouble. You might want to take extra time going over that section. Occasionally I will include a link to my email box that looks like this to make it easy for you to leave questions for me. Are there any questions? I may limit the number of people to whom I respond, to those registered for this course by filling in our registration form. In that way I can give each of you individualized attention. This email interaction is an important benefit of this online textbook over a printed book. From time to time I may have a tidbit of information which some folks might find interesting but which is not required to understand the material. I will use a symbol like this to indicate a link to that stuff. I am here as your coach and trainer as you try to become the modern day equivalent of the ancient wizards, a person who understands more than most about how the universe works. If you succeed, people will be coming to you for answers and depending on your advice. It is not magic but a deeper understanding from which you will draw your powers. You will be well paid for your services but the real payoff is the satisfaction that comes from understanding things. I am looking forward to working with you. As you read the material I have written and as we interact by email, we will come to know each other better. We are beginning a long journey together but I will only go part way with you. If I am successful as your coach, you will go on to heights that I cannot reach. Imagine for example Joe Paterno tackling a running back or Bela Karoli doing a tumbling pass in a floor exercise to see what I mean. My job is to work with you to help you in two ways. One of my goals is to teach you some fundamentals. In particular, to teach you some physics which is the foundation of many sciences. The other goal is to teach you how to learn. You would not be at this level in your education if you had not already demonstrated a capacity to learn. What we are talking about here is getting to another level of learning. Many of you will be using this coaching program at the same time you are taking a formal course in physics at college or perhaps even at high school. You will have a teacher and textbook which will give you much of the information you will need. It is not my intention to replace either the teacher or the book. I am available through this on line course to provide extra examples, a different point of view, some additional help where you need it and most of all encouragement that it is all worth it. For those of you who are not taking a physics course along with this coaching program I will try to provide enough detail so that you will be able to make sense of the subject as a stand-alone course. If this was easy, everybody would be doing it and its value would be low. You have wisely chosen the high effort high reward path. Perhaps the ideal use for a course like this if you are a student is to give you a competitive advantage over the other people against whom you will be measured. Whether we like it or not there is an element of competition in everything we do. Striking the right balance between cooperation and competition is a life skill that really successful people have mastered. If you can work through this material with me, I guarantee that you will do well in that freshman physics course which many institutions use to cut the numbers of people in their advanced science and engineering courses to a select few. Not only that but your classmates are going to be looking to you for help. Never pass up an opportunity to teach. It is not until you have to explain something to someone else that you really learn it. Your academic reputation is going to be established in those first few semesters and success breeds success. One of the secrets of successful learning is to get past the "Why do I have to know this?" issue. It is surprising how many otherwise very bright people will sabotage themselves by stewing about the payback for their learning effort rather than focusing on the material. We need to spend time fooling around with frictionless pulleys, weightless rods and other stuff made from the rare element, unobtainium, in order to get on with the business of predicting the future. That is the work of scientists and engineers and that is where we are going with this learning adventure. I know that we will need frequent booster shots to immunize ourselves from this "What is the use of it all?" question so I will try to provide reminders of where we are going from time to time. Everything has a beginning and the beginning for this journey is with a topic from physics called "Mechanics". Now here is an instance of where the language gets in the way. The word mechanics brings to mind people in matching pants and shirts with a name over the pocket and a box of tools. That is not the kind of mechanics we are talking about here. Physics, and all branches of science, must use words to convey information. The words used in the sciences come from the common language and have precise meanings, usually related to the common usage. Mechanics is the study of moving objects. For now we will deal with classical mechanics which deals with objects moving slowly relative to the velocity of light and objects large relative to the size of atoms and molecules. The reason for starting with mechanics is that many of the basic principles we will learn there apply to other topics. There is another aspect of the language of science which we are going to have to come to grips with. That is mathematics. We are going to assume for the most part that you took and understood the college prep high school math courses. I know that for some of you that assumption is wrong and for some of you the assumption is OK but it was decades ago. So here's the deal. I will include a review of some mathematics in the background material as we go along. In fact here is the first of the promised background pages. There we will review the ideas of numbers, functions and graphs, and cover the symbols we will use for the mathematical operations of addition, subtraction, multiplication, division and exponentiation . I also introduce the graph paper that will serve as the drawing area for many future displays. Do not be afraid to use the Are there any questions? link to fill in the gaps. In addition, we will be using the capability of the personal computer to avoid a lot of the mathematical complications. Back in the 17th century, Isaac Newton and some of his friends (and enemies) invented calculus to replace millions of trivial calculations with a few complex ones. In the 20th century we have a tool to reverse that. What computers do best is simple math very fast. We will be substituting millions of simple calculations, easily understood, for the few complex ones. Oh, you will still need to learn calculus, but not very much for this course. So let's get on with it. Next Other
The Physics and Math of Soccer
Discusses shape of a soccer ball, spin effects, motion of projectiles.
The Math Physics of Soccer "(one of the) Best Soccer Links Ever Witnessed By Mortal Eyes!" -- Richmond Hill Soccer "Featured Site - July 2002" -- The Soccer Patch "You can be schmart and play soccer, too. In fact, I played soccer ven I was your age... yah, it's true! I played a lot of soccer during English and History class. That's why I only did vell in Mathematics and Physics! I made a joke, yah??" WEBMASTER'S NOTE: I can tell this Math Physics of Soccer site has become quite popular so, if you don't mind, drop me an e-mail with your suggestions and comments. Thanx! ...and visit our other pages Soccer PONG! Soccer d'Art Soccer Magazine This site is listed in...
Intrinsic Localized Modes
Dynamics of defect-free periodic lattices in terms of plane wave phonons. Web text by Albert J. Sievers, Cornell.
Intrinsic Localized Modes Last Updated: November 28, 2000. 1997 FIR Group, LASSP, Cornell University
Inexplicable Secrets of Creation
Relationships between number theory and physics.
Inexplicable Secrets of Creation "Upon looking at these numbers, one has the feeling of being in the presence of one of the inexplicable secrets of creation ." [D. Zagier] mysterious occurrences on the interface of physics and number theory this set of pages was larely inspired by my number theory and physics archive introductory prime number theory resources number theory and Jungian archetypes number theory and Taoist aesthetics related curiosities home page e-mail
Klaus Brauer's Soliton Page
Presents a history of J.S.Russell's discovery of solitary waves, and animations of one-, two- and three-soliton solutions to the Korteweg-de Vries equation. Includes an article in PDF format on finding exact solutions to the KdV equation using the method of Backlund transform with the help of Mathematica.
USF+AppSysSc: Klaus Brauer's SOLITON Page http: www.usf.uni-osnabrueck.de ~kbrauer solitons.html | Welcome to Klaus Brauer's SOLITON Page One of the most exciting phenomena in dealing with non-linear Partial Differential Equations are the Solitons, i.e. solitary waves. The first person reporting these phenomena was the Scottish engineer John Scott Russel , who described the propagation of a wave in shallow water. Nowadays we have better knowledge of the underlying mathematical properties. Solitons are the solutions of the famous non-linear Korteweg - de Vries Equation. A solution to this PDE may be found in using the method of Bcklund transform. Korteweg - de Vries Equations The solution may be visualizied as a 3D Plot and as a Contour Plot (both generated with Mathematica 4.0). Finally it can be nicely observed by looking at the animated graph, produced as well with Mathematica 4.0. Analytical solution and graphical representation of the One Soliton solution . It is possible to construct solutions to the Korteweg - de Vries equation which are non-linear superpositions of regular and irregular single solutions. The interested reader is referred to the book: Vvedensky, Dimitri D. Partial Differential Equations with Mathematica - Chapter 9 Addison-Wesley Publishing Company, Reading, MA, ISBN 0-201-54409-1, 1993 The author of this Web page has written an article (16 pages as a PDF file). The contents points out to some history, presents Vvedensky's solutions, and shows some Mathematica code. Watch the paper here with Acrobat Reader , Size: 1031 KB Download a ZIP version of the PDF file here , Size: 920 KB This construction method has been performed for two and for three superpositioned solutions. Each of them have a parameter, say b1 and b2 for two waves and b1, b2 and b3 for three waves. The effect is that a wave travels the faster the greater that parameter is - thus overtaking a slower wave. The two or the three waves preserve their shapes even after the overtaking process. Analytical solution and graphical representation of the Two Solitons solution Analytical solution and graphical representation of the Three Solitons solution Further Information: A lot of information including the revival of John Scott Russel's experiments are given by Heriot-Watt University (Edinburgh Scotland) . The University of Kyoto Japan has prepared a Soliton-Lab Art Gallery . Further Information, especially on the Sine-Gordon-Equation, solved by using the Computer Algebra System Maple is coming from Tver State University in Russia (by the way: Tver is a partner city of Osnabrck), look at the page of Andrey E. Miroshnichenko . Lots of Links may be found from R. Victor Jones' Soliton Page . Concerning waves in general, please visit Waves, Waves, Waves . An easy introduction comes from the Technical University of Denmark Even a German TV channel has brought solitons to the public. Real solitons observed in the Strait of Gibraltar. Update: August 17th, 2004 Zurck zu Klaus Brauers Heimatseite Back to Klaus Brauer's Homepage
Differential Equations and Oscillations
Many problems in physics are described by differential equations. As a complete discussion of differential equations is beyond the scope of this chapter we will deal only with linear first and second order ordinary differential equations.
DIFFERENTIAL EQUATIONS AND OSCILLATIONS DIFFERENTIAL EQUATIONS AND OSCILLATIONS Many problems in physics are described by differential equations. This is due in part to the basic laws of nature (like Newton's second and Schrdinger equation) being differential in form, The differential nature of these physical laws in turn may be a reflection of our use of continuous variables like position and probability. (The use of differential equations may also reflect traditionally-trained physicists viewing problems in differential forms). As a complete discussion of differential equations is beyond the scope of this chapter we will deal only with linear first and second order ordinary differential equations. We start with deriving two methods to solve first order differential equations numerically ( Euler and Runge-Kutta ). These methods can be extended to solve second order differential equations which we will do using the harmonic oscillator and the realistic pendulum as examples. First Order Differential Equation Method Numeric, Euler's Algorithm Project Assessment Method Numeric, second order Runge-Kutta Method Method Numeric, fourth order Runge-Kutta Method Project Second Order Differential Equations Harmonic Oscillator With Viscous Friction Project The Realistic Pendulum Energy Project About this document ... Next: First Order Differential Equation Author: Rubin H. Landau rubin@physics.orst.edu WWW Implementation: Hans Kowallik, Manuel Paez kowallih@ucs.orst.edu
Journal on Applied Clifford Algebra
Journal devoted to the development of Geometric Analysis in particular through the use of Clifford Algebras, Quaternions, Hypercomplex Analysis and Multivector Techniques. Main emphasis en the applications to Physics.
Clifford Algebras, Advances in applied clifford algebras Esta pgina usa marcos, pero su explorador no los admite.
Twistor Theory
Description of Twistor Theory
RDEGRAAF.nl [Physics: Twistor Theory] Home Gallery Guestbook New Search RDEGRAAF.nl note: this page is meant as a link page to the various resources available on the internet (some are 'mirrored' locally). Twistor Theory Here a what-I-found on Twistor Theory; presentations, online lectures and literature. Presentation A presentation of twistor theory by Roger Penrose and Fedja Hadrovich can be found at users.ox.ac.uk (deep-link) and is mirrored locally. Images are taken from the twistor website . The Twistor Programme R. Penrose and M. A. H. MacCallum, Phys. Reports. 6C (1972) p. 241 ( pages ) An original copy can obtained at the partner site sciencedirect.com of the originating publisher Elsevier . Spinors and Space-Time A description of spinors is exhaustively explained in two books by R.Penrose and W.Rindler. Spinors and Space-Time (Volume 1, Two-Spinor Calculus and Relativistic Fields) Spinors and Space-Time (Volume 2, Spinor and Twistor Methods in Space-Time Geometry) ( Sample Chapter ) The originating publisher cambridge.org reprinted these two ( 1 , 2 ) books and can be bought through their website. Links Einstein's Equation and Twistor Theory: Recent Developments (more audio-streams are to be found in section Online Talks ). R. Penrose - On the Origins of Twistor Theory ( mirror ) R. Penrose - The Central Programme of Twistor Theory ( mirror ) R. Jozsa - Applications of Sheaf Cohomology in Twistor Theory ( mirror ) F. Hadrovich - Twistor Primer ( mirror ) R. Penrose, M. MacCallum - An Approach to Quantisation of Fields and Space-Time ( mirror ) R. Penrose, F. Hadrovich - Twistor Theory ( mirror ) F. Hadrovic - Twistors --- What Are They? ( mirror ) Andrew Hodges - Twistor Diagrams Books Introducing the Concept of Spinors Moshe Carmeli et al - An Introduction to the Theory of Spinors Elie Cartan - The Theory of Spinors Set Theory and Numbers State Reduction and Special Relativity Time-asymmetry
Geometry and Duality
Lecture notes from the ITP miniprogram on Geometry and Duality
ITP Miniprogram on Geometry and Duality home activities inside KITP directory talks visit info help other UCSB Nov 17, 2005 INSTITUTE FOR THEORETICAL PHYSICS Miniprogram on Geometry and Duality January 12 - 30, 1998 Coordinators: D. Morrison, I. Singer, E. Witten SCHEDULE (REVISED 1 13 98) All sessions for the week of 1 12 98 will be held in the ITP Main Seminar Room, Kohn Hall. [Week 1] [ Week 2 ] [ Week 3 ] Notes from talks in this program are presented below --- just click on the links. ITP intends to keep these talks posted on the Web indefinitely. Feedback? You can also hear audio recordings from some of the talks, if your computer is suitably equipped . Look for talks marked [Audio]. ITP is grateful to the Coordinators and the ITP staff who made this conference a success. See also: Notes from the IAS 1996-97 Program in Quantum Field Theory at http: www.math.ias.edu QFT . Search this conference by name or keyword: Monday, January 12, 1998 Time Speaker Title 10:30 Dan Freed (IAS and Univ. of Texas) Introduction to Supersymmetry I[Audio] 1:30 Greg Moore (Yale) D-branes 101a[Audio] 3:30 David Morrison (Duke) Mathematical Aspects of String Duality I[Audio] Tuesday, January 13, 1998 Time Speaker Title 9:00 am Dan Freed (IAS and Univ. of Texas) Introduction to Supersymmetry II[Audio] 11:00 Greg Moore (Yale) D-branes 101b[Audio] 2:00 Robbert Dijkgraaf (Univ. of Amsterdam) Matrix Theory Matrix Strings I[Audio] Wednesday, January 14, 1998 Time Speaker Title 9:00 am Dan Freed (IAS and Univ. of Texas) Introduction to Supersymmetry III[Audio] 11:00 Greg Moore (Yale) D-branes 101c[Audio] 2:00 Robbert Dijkgraaf (Univ. of Amsterdam) Matrix Theory Matrix Strings II[Audio] 4:00 David Morrison (Duke) Mathematical Aspects of String Duality II[Audio] Thursday, January 15, 1998 Time Speaker Title 9:00 am Dan Freed (IAS and Univ. of Texas) Introduction to Supersymmetry IV[Audio] 11:00 David Morrison (Duke) Mathematical Aspects of String Duality III[Audio] 2:00 Robbert Dijkgraaf (Univ. of Amsterdam) Matrix Theory Matrix Strings III[Audio] 4:00 David Morrison (Duke) Mathematical Aspects of String Duality IV[Audio] Friday, January 16, 1998 Time Speaker Title 9:00 am Dan Freed (IAS and Univ. of Texas) Introduction to Supersymmetry V[Audio] 11:00 Robbert Dijkgraaf (Univ. of Amsterdam) Matrix Theory Matrix Strings IV 2:00 David Morrison (Duke) Mathematical Aspects of String Duality V[Audio] last modified 4 27 99 ds
Doing Physics with Quaternions
A research effort to see how much of standard physics can be done using only quaternions, a 4-dimensional division algebra.
Doing Physics with Quaternions Promote this project! Buy buttons or a T shirt Doing Physics with Quaternions doug sweetser@alum.mit.edu (. pdf ) Get a HARD COPY of this site! (I prefer it :-) A one page summary of my unified field model for gravity and EM is available here: pdf A technically detailed Mathematica notebook starts from the Lagrange density for unifying gravity and EM, and gets to two experimental tests that can confirm or reject the proposal (available as html , pdf , or .nb ) Talk entitled "Realizing Einstein's Dreams: Unifying Gravity and Light, and Why Quantum Mechanics is Weird" for the Spring NE Section of the APS AAPT ( html or pdf ) Talk entitled "Why a Rank 1 Unified Field Theory is Compelling and Its Background Mathematical Structure" for the 8th Eastern Gravity Meeting ( html or pdf ) Talk entitled "Unifying Gravity and EM by Generalizing EM" for the 7th Eastern Gravity Meeting ( html or pdf ) Poster for Brookhaven National Lab meeting, "Unifying Gravity and EM by analogies to EM" ( pdf ). A more formal presentation of the unified field model is available here: pdf (v1.4, 18 pages). MIT IAP course: "Unifying gravity and EM by analogies with EM" Slides available. Day 1: Lagrange Densities ( html or pdf ) Day 2: Fields and Quantum Mechanics ( html or pdf ) Day 3: Forces, Metrics, and New Physics ( html or pdf ) The Cosmological Consequences of the Chain Rule ( pdf ), slides for a 15 minute talk at joint APS AAPT meeting, March., 2004. A Universe with zero dark matter is good :-) 4-potential Equations for Gravity and Electromagnetism ( pdf ), slides for a 15 minute talk at a joint APS AAPT meeting, Oct., 2003. Dynamic graphs , a way to visualize complex numbers and quaternions using animations. Uses gif, so all can see for the first time the cosine of a quaternion! This is hugely fun, honest. Figuring out stuff takes time (money) and money. If I can raise $0.3 K, that will cover a local meeting, $2 K would mean I could buy Mathematica (used a student version for a decade), $5.2k would go for a Mac with Final Cut Pro (making "Stand-Up Physicist" teaching videos) and $30 K would mean a year devoted to math and physics. This stuff may be important enough for me to ask so directly for funding. Intro , Mathematics , Classical , SR , EM , QM , G , Conclusions Introduction An overview A brief history of quaternions Mathematics (. pdf ) Multiplying quaternions the easy way Inner and outer products Scalars, vectors, tensors and all that Quaternion analysis (. pdf ) Topology Where quaternions fit in math , adapted from Max Tegmark, 1998. Tools for algebra, trig, logs... and a Quaternion calculator (in Java) An open source project QEMation to develop Quaternion Equation driven aniMation. The first result of this effort, Visualizing Constant Inertia , is more interesting from a math physics perspective than one might guess. (. pdf ) F = m a, in an inertial frame, in polar coordinates, and in a rotating reference frame The simple harmonic oscillator and wave equation 4 tests for a conservative force (. pdf ) Doing the work of the Lorentz group with rotations and dilations An alternative algebra for boosts Problem set questions and solutions from MIT's 8.033, Classical and Relativistic Mechanics Index and links to solved problems PS 1: Kinematic effects of relativity PS 2: More kinematic effects PS 3: The Lorentz transformation and the addition of velocities PS 4: The Doppler effect, 4- vector invariants, and the twin paradox PS 5: Energy, Mass and Momentum PS 6: The Compton effect and threshold collision problems (. pdf ) Classical electrodynamics Electromagnetic field gauges The Maxwell equations in the light gauge: QED? The Lorentz force The stress-energy-momentum 2-tensor of the electromagnetic field (. pdf ) Bracket notation quaternions: quaternions as a complete inner product space Multiplying polar representations (without Campbell-Hausdorff!) Commutators and the uncertainty principle Unifying the representations of spin and angular momentum The Schrdinger equation The Klein-Gordon equation Time reversal (. pdf ) Einstein's vision Einstein spent the last forty years of his life trying to unify gravity and electromagnetism in a way that also lead to a new subtle understand of quantum mechanics. Just like for special relativity and general relativity, he was looking for a new logical foundation that would not change any experimental tests much at all. For a general audience, there is a slide presentation for ways of thinking about events using quaternions. A draft paper ( pdf , v1.4) and notes for a talk ( pdf ) on unifying gravity and electromagnetism in a way that can be quantized are available. This method contains no quaternions, but the algebra is based on that earlier effort. To a degree that has really surprised me, the pair of papers (last updated September 2001) is a work in progress towards that goal: Einstein's Vision I: Classical unification of gravity and electromagnetism using Riemannian quaternions (. pdf ) [undergoing revision] Einstein's Vision II: Unified force with constant velocity profiles (. pdf ) Earlier versions are still accessible. Most of today's research on gravity involves quantum gravity theory. I have two ideas in this direction. In the paper on the unified force, to get the algebra correct, the 4-force was normalized to the potential, which in turn required hbar c by dimensional analysis. If that form of the force equation is correct, then if hbar goes to zero, then the unified force disappears. This is a basic characteristic of any quantum theory. What puzzled Einstein for decades was the why of quantum mechanics. I believe that quaternion analysis may answer that difficult question. I have a sketch of a third paper - Einstein's Vision III: Quantum unified field theory. This involves what I am calling the general correspondence principle. Quaternion analysis (see above) has a timelike automorphic quaternion derivative for classical physics and a spacelike automorphic quaternion derivative for quantum mechanics. The unified field equation in the first paper is classical if the automorphic quaternion derivative is timelike, and quantum if spacelike. The symmetry of this equation is none other than U(1)xSU(2)xSU(3) (I am certain about the electroweak symmetry, but not completely certain about the strong part). This may be a justification for the standard model. A paper was submitted to a peer review journal on the content of the second paper, with all references to quaternions deleted :-) You may read a summary of that process, along with a call for papers , the submission , and comments from the first referee , second referee , and editor . I learned, so it was good. Strings and Relativistic Quantum Gravity A slide presentation of string ideas, small movies, little math Answering prima facie questions in quantum gravity using quaternions (post to s.p.r) The length of a quaternion in curved spacetime: a close relative of the affine parameter of general relativity General metrics Gravitational redshift experiments A summary of physics equations written as quaternions Conclusions Stuff to get Check out the buttons! A bound Xerox copy of these web pages is available. cost: $30 for "Doing physics with quaternions", $40 for "Doing physics quaternions." + lecture notes on "Dynamic grpahs, quaternion analysis, and unified field theory" And $5 for shipping (actually costs $7). Includes the button, "A brief definition of spacetime" There are two ways to pay: US mail to: Douglas Sweetser, 1340 Comm Ave Apt 7, Allston, MA 02134 account: sweetser@world.std.com at PayPal.com Mathematica 3.0 notebooks used to create these pages, free to download print Attended the Second Meeting on Quaternionic Structures in Mathematics and Physics in Roma, Italy, September 1999. Presented a paper with Prof. Guido Sandi of BU entitled "Maxwell's vision: electromagnetism with Hamilton's quaternions" . 2003 Joint Fall Meeting of the New England Sections of APS and AAPT, Bates College, Maine, Oct 3-4. Delivered a 15 presentation titled: "4-Potential Equations for Gravity and Electromagnetism" (html, or as a pdf ). A few good papers: Sudbery's first paper (memo, 1977, 44 pages) on why quaternion analysis is no good. Sudbery's second paper (1979, 28 pages) on the topic. Please look to my work above on quaternion analysis for a much better alternative!. C. A. Deavours paper, "The Quaternion Calculus" . My critique is that using his definition of a quaternion derivative, if a function like f=q is analytic in q, f^2 is not. That indicates a better definition must be found before quaternion analysis can really begin. Salamin's paper (1979, 9 pages) on rotations. Howell and Lafon's paper (1975, 13 pages) on the efficiency of quaternion multiplication. Silberstein's paper (1912, 20 pages) on using biquaternions for quaternion special relativity. Biquaternions are NOT an algebraic field, and are not used in any operations on this web site. Let's talk... Join the newsgroup, quaternions@TheWorld.com. This is a low traffic newsgroup where I give updates sporadically on the status of the project. To subscribe, send email to majordomo@TheWorld.com. The body (not the subject!) should just contain this: subscribe quaternions If you ever want to leave this newsgroup, send a similar message, where the body reads "unsubscribe quaternions". Quaternion Question and Answer , a site for chatting about quaternions. Feedback welcome! (Would like to know why you visited, what could be added.) Other Stuff Doug's background in physics Thanks to... Intro , Mathematics , Classical , SR , EM , QM , G , Conclusions Home Page | Quaternion Physics | Pop Science Java | The Bike | Lindy Hop | Contact Doug Copyright 1997, doug sweetser@alum.mit.edu All rights reserved worldwide. Roughly translate this page into: French , German , Italian , Portuguese , or Spanish Web quaternions.com
Solitons
Resources at Heriot-Watt University. Meetings, local and other links.
Solitons Home Page Department of Mathematics Solitons Home Page Some brief soliton movies: KdV single soliton , KdV 2-soliton collision . moving sine-Gordon breather . A list of papers on experimental studies of solitons in water, kindly supplied by Jerry Bona. Future Soliton and soliton-related conferences Workshop Nonlinear Physics. Theory and Experiment. IV , Gallipoli (Lecce), Italy, June 22 to July 1, 2004. Algebraic Theory of Differential Equations (details not yet available, dates provisional) 7-12 August (preceded by a Summer School 30 July to 5 August 2006) Recreating Scott Russell's soliton. An account of the discovery of the Soliton by Scott Russell in 1834 and of our successful attempt to recreate it in 1995 The experimental apparatus The soliton BBC "Local Heroes" programme page on the soliton See NATURE, V376, No. 6539, 3rd August 1995, p373 for another picture and account of the recreated soliton, also Optics and Photonic News, October 1995, Vol. 6 No 10, pg 9. Other soliton-related pages Encyclopedia of Nonlinear Science . The Falaco Soliton . Nonlinear Dynamics Distance Education Project , Institute of Theoretical Physics, Sao Paulo, Brasil. Solitons and Soliton Collisions , Tver State University Algety - Optical soliton company. Soliton-Lab art gallery A good recent source (unfortunately not web based) for optical soliton technology is Scientific American, Dec 2001, pp20-21. Discrete Self-trapping Equation , for those interested in discrete nonlinear Schrdinger type equations. downloadable version of ed. A.P. Fordy and J.C. Wood, Harmonic maps and integrable systems Soliton machine at the Snibston Discovery Park Bell Labs researchers set new soliton transmission record , 5 lectures on soliton equations by Edward Frenkel. Light Bullet Home Page , research into 3-dimensional optical envelope solitons at Simon-Fraser University, Canada. Solitons Dynamics Group , Virginia Commonwealth University. Cornell page on Intrinsic Localized Modes (Discrete Breathers). Sergej Flach's Discrete Breather Homepage NHK Soliton homepage (in Japan, "Soliton" is the name of a popular TV show for the younger generation...) Recent Soliton and soliton-related conferences Selected Problems of Modern Mathematics , dedicated to the 200th anniversary of C.G. Jacobi, Kaliningrad, Russia, April 4-8, 2005. Symmetry in nonlinear mathematical physics June 20-26, 2005 in Kyiv, Ukaine. FPU+50 : Nonlinear waves 50 years after Fermi-Pasta-Ulam ... , Rouen (France) June 21-25, 2005. Symmetries and Integrability of Difference Equations , EuroConference on Analytic Difference Equations, Special Functions and Quantum Models on the Lattice Chair: Jarmo Hietarinta (University of Turku, Finland) Helsinki, Finland, 19-24 June 2004 Workshop NONLINEAR PHYSICS. THEORY AND EXPERIMENT.III , Gallipoli (Lecce), Italy, June 24 to July 3, 2004. Minisymposium "Nonlinear waves in complex systems" in the framework of the Summer School Advanced Problems in Mechanics 2004 (APM'2004) , 24June - 1 July, 2004, Saint-Petersburg (Russia) NEEDS 2002 June 10-16 2002, Cadiz, Spain. Localization and Energy Transfer in Nonlinear Systems June 17-21, 2002, San Lorenzo de El Escorial, Madrid, Spain. OSTE 2002 International Workshop on 'OPTICAL SOLITONS : Theory and Experiments' January 24 - 29, 2002 (Cochin University, India) Integrable Systems, July to December 2001, Isaac Newton Institute, Cambridge, UK. NEEDS 2001 July 24-31 2001, Isaac Newton Institute, Cambridge, UK. Nonlinear evolution equations and wave phenomena: computation and theory, April 9-12, 2001, Georgia USA Edinburgh Conference 1995 Electronic Proceedings. Chris Eilbeck Heriot-Watt University, Edinburgh chris@ma.hw.ac.uk
Clyde Davenport's Commutative Hypercomplex Mathematics
Summary and application as it relates to electromagnetic theory and special relativity.
Clyde Davenport's Home Page Clyde Davenport's Home Page If your browser does not log on automatically, Please click here for the frameless version of this Web site.
The Dirac Delta Function
A brief introduction to the properties and uses of the Dirac delta function.
Dirac delta function Next: 3 Construction of Green's function Up: Part I Theoretical Foundation Previous: 1 Self-adjoint operator 2 Dirac delta function In physics and engineering, we inevitably deal with the notion of "point actions", that is, actions which are highly localized in space and or time. These include point forces and couples in solid mechanics, impulsive forces in rigid body dynamics, point masses in gravitational field theory, point charges and multipoles in electrostatics, and point heat sources and pulses in the theory of heat conduction. In order to introduce the "point action", let us imagine that a sudden excitation administered to a system, the excitation can be denoted by which has a nonzero value over the short interval of ,but is otherwise zero. The total impulse imparts to the system is thus defined by The value of I is a measure of the strength of the sudden excitation. In order to provide a mathematical model of the function , it is convenient to think of it as having a constant value over the close interval . Furthermore, we wish to choose this constant value in such a way that the total impulse is unity. Hence, we write Mathematically, this definition of the above expression is nonsense because the limit is infinite for x = a. Now let us idealize the function by requiring it to act over shorter and shorter interval by allowing tends to zero. Although the interval about x = a is shrinking to zero, we still want I = 1, i.e. We can use the result of this limit process to define an "idealized" unit impulse function, , which has the property of imparting a unit impulse to the system at x = a but being zero for all other values of x. The defining properties of this function are therefore By a similar kind of limit process, it is possible to define the integral of a product of the unit impulse function and any continuous and bounded function f; that is Recalling that which is the mean value theorem of the integral calculus, we find that For some in the interval . Consequently, in the limit we can deduce that Having already discussed the one-dimensional delta function in some detail, we will extend the definition to two dimensions with a short discussion. As in the case of the one-dimensional delta function , we note that may be visualized as the formal limit of a sequence of ordinary functions. Symbolically, where For example, and are two-dimensional . And the same as one dimension, for every h which is continuous over the region , which contains the point and , we have Next: 3 Construction of Green's function Up: Part I Theoretical Foundation Previous: 1 Self-adjoint operator Cheung Sau Hung Wed Sep 15 10:03:39 HKT 1999
Solitons
An overview of the classical and quantum theory related to solitons
Physics Essays Contents Click to download Solitons as .pdf file Linked to at: The Net Advance of Physics Altair 7 Communications Universit Paris 7 Denis-Diderot
Local Quantum Physics Crossroads
An international forum for information exchange among scientists working on mathematical, conceptual, and constructive problems in local relativistic quantum physics (LQP).
Local Quantum Physics Crossroads Local Quantum Physics Crossroads "LQP Crossroads" is an international forum for information exchange among scientists working on mathematical, conceptual, and constructive problems in local relativistic quantum physics (LQP). Aims 30-Jan-04 People 24-Oct-05 Papers (submission simplified) 15-Nov-05 Bibliography 9-May-05 Events 14-Nov-05 Jobs 4-Aug-05 Links 6-Jul-05
Complex Geometry of Nature and General Relativity
A paper by Giampiero Esposito attempting to give a self-contained introduction to holomorphic ideas in general relativity. The main topics are complex manifolds, spinor and twistor methods, heaven spaces.
[gr-qc 9911051] Complex Geometry of Nature and General Relativity General Relativity and Quantum Cosmology, abstract gr-qc 9911051 From: Esposito Giampiero [ view email ] Date: Mon, 15 Nov 1999 11:06:50 GMT (124kb) Complex Geometry of Nature and General Relativity Authors: Giampiero Esposito Comments: 229 pages, plain Tex Report-no: DSF preprint 99 38 An attempt is made of giving a self-contained introduction to holomorphic ideas in general relativity, following work over the last thirty years by several authors. The main topics are complex manifolds, spinor and twistor methods, heaven spaces. Full-text: PostScript , PDF , or Other formats References and citations for this submission: SLAC-SPIRES HEP (refers to , cited by , arXiv reformatted); CiteBase (autonomous citation navigation and analysis) Which authors of this paper are endorsers? Links to: arXiv , gr-qc , find , abs ( - + ), 9911 , ?
Five Lectures on Soliton Equations
A self-contained review by Edward Frenkel of a new approach to soliton equations of KdV type.
[q-alg 9712005] Five Lectures on Soliton Equations Quantum Algebra and Topology, abstract q-alg 9712005 From: Edward Frenkel [ view email ] Date: Sun, 30 Nov 1997 23:55:01 GMT (39kb) Five Lectures on Soliton Equations Authors: Edward Frenkel Comments: 42 pages, Latex2e; Contribution to Surveys in Differential Geometry, Vol. 3, International Press Subj-class: Quantum Algebra; Algebraic Geometry This is a self-contained review of a new approach to soliton equations of KdV type developed by the author together with B. Feigin and B. Enriquez. Full-text: PostScript , PDF , or Other formats References and citations for this submission: CiteBase (autonomous citation navigation and analysis) Which authors of this paper are endorsers? Links to: arXiv , q-alg , find , abs ( - + ), 9712 , ?
Radial Symmetric Fourier Transforms
Fourier transforms of radially-symmetric functions can be performed efficiently using the Hankel transform of order zero. Illustrations of the method are presented, and of the Gibbs' phenomenon.
Radially Symmetric Fourier Transforms Astronomical Data Analysis Software and Systems III ASP Conference Series, Vol. 61, 1994 Book Editors: D.R. Crabtree, R.J. Hanisch, J. Barnes Electronic Editors: D. Durand, J. Barnes, D.R. Crabtree Radially Symmetric Fourier Transforms M. Birkinshaw Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138-1596 Abstract: Fourier transforms of radially-symmetric functions can be performed efficiently using the Hankel transform of order zero. Convolutions of radially-symmetric functions can also be performed simply. Illustrations of the method are presented, and the Gibbs' phenomenon associated with the ROSAT PSPC PRF is discussed. Introduction A model is often convolved with an instrument response at some stage in the analysis of astronomical data. Frequently both functions are radially symmetric, for example when fitting the X-ray surface brightness of a cluster of galaxies. At times there is a direct need for the Fourier transform of a radially-symmetric function, for example in calculating the response of an optical interferometer to a limb-darkened star. When convolutions or Fourier transforms of radially-symmetric functions are to be calculated, the one-dimensional Hankel transform of order zero (the radial Fourier transform, RFT) is a useful alternative to the two-dimensional Fourier transform. This paper demonstrates the use of the RFT and describes some of its properties. Mathematical development Fourier Transforms The Fourier transform of the two-dimensional function is which, if is radially symmetric, becomes where is the angle between and . The integral representation of the Bessel function is so that equation (2) can be rewritten in RFT form where is radially symmetric in Fourier space. The inverse relation, is easily proved, and demonstrates that the forward and back RFTs are identical operations on functions and . The relationships (4) and (5) are well known (e.g., Bracewell 1965) and are examples of the Hankel transform of order zero. Sample RFTs calculated using (4) are shown in Figure 1 and Figure 2 . Convolutions The convolution of two functions and is and it is well known that the Fourier transform of is related to the Fourier transforms of and by If both and are radially-symmetric functions, with Fourier transforms radially symmetric in Fourier space, then is radially symmetric in Fourier space, and is radially symmetric in real space with Thus to evaluate the convolution of two radially-symmetric functions, we need to evaluate two integrals like (4) and one like (8). This scheme requires only two evaluations of the Bessel function per -space value per -space value, because the calculations of and can be performed together. Accurate algorithms for are readily available. An example of a convolution performed using RFTs is given in Figure 3 . Gibbs' phenomenon As in other Fourier transform techniques it is important to be aware that jumps in the functions, or their derivatives, cause the appearance of the Gibbs' phenomenon. This is apparent in the fractional error panels of Figure 1 and Figure 2 , where truncation of the functions at large has caused low-amplitude oscillations. In Figure 1 , which shows the RFT of the point response function (PRF) of the ROSAT Position Sensitive Proportional Counter (PSPC), further oscillations are generated at small . The amplitude of these oscillations was intially large, but was reduced to the level seen in Figure 1 by making a small 1 per cent) alteration of the standard form of the PRF (Hasinger et al. 1992) to replace the cusp at (from the ``scattering term'') with a higher-order singularity at arcmin. In Figure 3 , which shows the convolution of the functions of Figure 1 and Figure 2 the Gibbs' phenomenon has little effect. Thus the RFT is useful for performing accurate convolutions of arbitrary-length and irregularly-sampled arrays quickly: the 8027-element convolution in Figure 3 used a 1395-point Fourier transform array and took under 10 min on a SPARCstation 2. This technique has been used to fit ROSAT images of elliptical galaxies (Worrall Birkinshaw 1994). This work was supported by NASA grant NAG5-2312 and contract NAS8-39073. References Bracewell, R. 1965, ``The Fourier Transform and its Applications'': McGraw-Hill, New York Hasinger, G., Turner, T.J., George, I.M., Boese, G. 1992, NASA GSFC Office of Guest Investigator Programs, Calibration Memo CAL ROS 92-001 Worrall, D.M., Birkinshaw, M. 1994 , this volume
Topology and Physics
An essay by C. Nash on the historical connection between topology and physics.
[hep-th 9709135] Topology and physics-a historical essay High Energy Physics - Theory, abstract hep-th 9709135 From: Cnash [ view email ] Date: Thu, 18 Sep 1997 17:17:44 GMT (140kb) Topology and physics-a historical essay Authors: C. Nash Comments: Plain TeX, 60 pages, postscript figures included. v2: Spelling of K\"onigsberg corrected, thank you to all those who told me of this infelicity. v3: Some extra material added. I am much obliged to the numerous people who sent me emails about this article. v4: Some final additions. I am again much obliged to the numerous people who sent me emails Subj-class: High Energy Physics - Theory; Algebraic Geometry; Differential Geometry; Quantum Algebra This is an article on the interaction between topology and physics which will appear in 1998 in a book called: A History of Topology, edited by Ioan James and published by Elsevier-North Holland. Full-text: PostScript , PDF , or Other formats References and citations for this submission: SLAC-SPIRES HEP (refers to , cited by , arXiv reformatted); CiteBase (autonomous citation navigation and analysis) 1 trackback ( What's this? ) (send trackbacks to http: arxiv.org trackback hep-th 9709135) Which authors of this paper are endorsers? Links to: arXiv , hep-th , find , abs ( - + ), 9709 , ?
Symplectic Geometries in Quantum Physics and Optics
A comparison of symplectic geometry with Euclidean or unitary geometries in quantum physics and optics
[quant-ph 9509002] The Real Symplectic Groups in Quantum Mechanics and Optics Quantum Physics, abstract quant-ph 9509002 From: Arvind [ view email ] Date: Tue, 5 Sep 1995 04:20:00 GMT (28kb) The Real Symplectic Groups in Quantum Mechanics and Optics Authors: Arvind , B. Dutta , N. Mukunda , R. Simon Comments: Review article 43 pages, revtex, no figures, replaced because somefonts were giving problem in autometic ps generation Journal-ref: Pramana 45 (1995) 471 text of abstract (We present a utilitarian review of the family of matrix groups $Sp(2n,\Re)$, in a form suited to various applications both in optics and quantum mechanics. We contrast these groups and their geometry with the much more familiar Euclidean and unitary geometries. Both the properties of finite group elements and of the Lie algebra are studied, and special attention is paid to the so-called unitary metaplectic representation of $Sp(2n,\Re)$. Global decomposition theorems, interesting subgroups and their generators are described. Turning to $n$-mode quantum systems, we define and study their variance matrices in general states, the implications of the Heisenberg uncertainty principles, and develop a U(n)-invariant squeezing criterion. The particular properties of Wigner distributions and Gaussian pure state wavefunctions under $Sp(2n,\Re)$ action are delineated.) Full-text: PostScript , PDF , or Other formats References and citations for this submission: SLAC-SPIRES HEP (refers to , cited by , arXiv reformatted); CiteBase (autonomous citation navigation and analysis) Which authors of this paper are endorsers? Links to: arXiv , quant-ph , find , abs ( - + ), 9509 , ?
Non Commutative Geometry
Preprints of Alejandro Rivero about Connes's NCG and the Standard Model. Also some historical articles on related topics.
Alejandro Rivero - Research Articles Articulos y Preprints The numbers refer mostly to www.arxiv.org , from where you can get .dvi, .ps or .tex versions. If you want to do some private comment, or to request information, please send first a blank message to rivero@dftuz.unizar.es . Also, using javascript, you can leave directly a public comment . Note that some articles have separated "Comment" sections. (Ah, by the way: "Weblog Commenting and Trackback by HaloScan.com" . Blog enthusiasts can Trackback the whole page or also separate article groups) 92-07p353 Experience in RTN , a reconfigurable network of transputers. 9210014 and 9302007 : old, unrelated, lattice calculations DFTUZ 93-03 , on a trick of SUSY Q.M. 9411081 Dirac Delta and Renormalization [gzip] in 1D Quantum Mechanics. This was a section of my PhD Thesis. In following years, the issue was widely studied; you can peruse the references in P L Christiansen et al (2003) for instance. Tunneling via instantons (last. mod 1994). (note added 27-9-2002: This is, up to this date, the only paper I sent individually to publish. The referee considered it "not urgent", which now I know it is true, see Phys. Rev. D 46, 46854690 (1992) . But instead giving this reference-surely unknown to him too-, he argued that the letter was "just calculations" and that he "did not understand formula number (1) in the paper", and so he asked for rewritting. Which I did not) . It seems it has been useful to someone (quant-ph 0406200) 9605006 (gzip) was a wrong paper trying to fit the Z' boson in the framework of Connes Standard Model. (www) Backlinks . If Gore invented Internet, I invented self-trackback ( C ) C | T | 9710026 Introduction to the Tangent Groupoid gzip and an unfinished revisit in 2002. C | 9802102 Tangent Groupoid and quantization gzip . See also section 6 of Varilly's C | T | 9803035 Feynman formula (zero dim derivation) gzip C | T | 9804169 Conjectures looking for a NCG (*) C | T | 9904021 Section of a Cone (history) In some sense it forms a "trilogy" with 0006065(v2) and 0309104, below C | 9905021 On Generations and quantization ambiguity C | T | 0001033 On Barrow (fantasy history. Thanks marcus@physicsforums by John Aubrey' reference). Also, according Mordechai Feingold, Late in 1655 John Worthington wrote to Samuel Hartlib that Barrow "hath undertake to doe something upon Archimedes which shall awaken all the world". Worthington did not elaborate, and Barrow had already left England. Did he found The Method ? C | 0006065v2, Rhythmos, Diathige, Trope (jpg tar.gz), see greek online at xxx C | 0006065 on Democritus, v1 (philology for atoms) C | 0007027 The ambiguity (again, on NCG and generations) C | T | 0108136 Lessons From Numerical Analysis (the Brouder's clue) C | T | 0203024 Discrete spectral triples converging to Dirac operators C | 0204238 around Poincare duality C | T | 0208180 Lecture on Divergences . (It was quoted here . I wonder how) C | T | 0302285 Flashes of Noncommutativity going back to Newton. 0308 Alquimia , a divulgative article for the magazine Liceus. Spanish. 0308 referee report for a letter of Maurice de Gosson, the main evangelist of the Symplectic Camel Principle . C | 0309104 Democritus as taoist and a footnote . Collected as Interesting Reading by Neutrino Unbound 0311 referee report for a letter of JM Isidro. C | T | 0312003 Relates nuclei shells to the masses of Higgs , Top, and W Z. It is so strange that I will try to publish version 2 ( * ) in order to get some readers :-) See the original note here , and also mesones.pdf if you are asking for the usual massive mesons (but then you could prefer the pretty plots of Mac Gregor ). 0404086 On Planck area, Planck time and Planck mass. ( * ) [Comment ] | 0405076 The 115 GeV signal from nuclear physics. ( * ) See also draft of new version C | LS9530 ( EXT-2004-048 ) The Lamb's Balance. It could be fused with 0405076, as the ArXiV moderator suggested, but by the moment I prefer to keep it separately. The figure above shows the histogram of beta decays known to the NUDAT database, counted in bins of nuclear mass number A. Do not buy it straightly, it has a lot of mixed input. A contour plot of the two peaks in the NZ plane is available here . Left, you can see a plot of relevant standard model masses (diagonal lines) and magic numbers (vert, horiz) compared against the drip lines predicted by some popular nuclear models. We show 68 GeV, W, Z, 115 Gev, 175 Gev and 246 GeV. Please click in the figure to see all the auxiliary lines. Note that the simple existence of the diagonals shows that the distance from stability line downwards to neutron drip line and leftwards to proton dripline is approximately equal. This fact is independent of if you buy or not the particle balance theory; it is already noticeable in the old liquid drop model, and becomes exact when microscopic corrections are included. Perhaps a trilogy on experimental inputs concludes here; a fourth work, trying to extract more info from all the database of beta (W-) decays, needs a previous separation according allowedness of each decay before to try to balance them against nuclear masses. On the other side, theoretical work on the LBC is hard to pursue alone :-| 0407118 On distance to the drip lines. Alternatively, we could be in presence of a persistent systematic error ( * ) 08 2004...Well, simply a very short note on gravity along the lines of 0404086 . Why 3+1 compactification? Kepler laws, simply. 0409022 on spectral triples for D=26. ( * ) 0503104 A collaboration with Hans de Vries trying to decipher some mass relationships between leptons and electroweak bosons. ( * ) 0505220 : the very puzzling formula of Yoshio Koide for charged leptons. A splash of modesty. 0507144 , a spotting of the triangle anomaly in J Psi (and Z0?!)( * ) 0507... , on the GUT value 3 8. The result is probably uninteresting, because the ArXiV moderators rejected the first version of this note. A knowledge person tells me that my comment is "just a curiousity, but it is sort of amusing", another that "find it very interesting" and both informs that it has not been seen in the literature. That is a consolation; sort of. ( * ) As a consequence of one of the email exchanges above, I did a new try of publication, sending out the articles marked with ( * ) above. 0508... is an spin-off of the previous article, where we have accidentally tripped over the Ab Forward Backward anomaly. Actually, the calculation of cross sections for the channel 11 of ZFITTER has some problem with EPS round-offs, but I am not sure if we can attach it to this effect. Memorandum on SUSY, to work on it after summer. Email welcome. 0511165 is a fusion of previous 0507... and 0508... done to upload it towards the ArXiV (which was slightly reorganised during Summer 2005) for communication and quotability purposes. What I keep doing in the theory field A basic motivation I hold is that to solve any differential equation you really need to discretize the evolution variables and then to define the infinitesimal limit. Here our conjecture is that in physical (say General Relativity) world, this leaves behind a residual action. In the formulation of noncommutative geometry it should coincide with the Standard Model. IE, 4-dim differential volume form should induce the four elementary fermionic fields. It seems that motivation keeps me jumping between three layers: Ancient: Studiyng how the atomists understood the calculation of volume, as well as their objections to a dynamical theory. Modern:By looking the work of Newton and Barrow, and also how they could get inspiration from the previous layer. The controversy regarding proposition I in the Principia is inspiring, too. Contemporary: Mainly in the field of non commutative geometry, renormalisation and all. that. Lately, to my own surprise, I have found myself on phenomenology rooms. Looking for more empirical input, so to say, and an excuse for extra reading on practical QFT. The trip seems to go round tro NCG and to try SUSY there. References With some scripting , it is easy to query spires to build a global list of eprints refereced in our papers. Here you can see the First and Second levels of iterated references. C | T | A draft of an author chronology table covering the first decade of Non Commutative Geometry is here . Also I am trying to keep a bibliography here and its first and second iterations, the latter usable only for searches IMHO. Also, Sitarz maintained a page on books and reviews You could also to try some graphical tool as the CiteSeer Relator ( here pictured as an example in Jan 2003). Proyectos de Fin de Carrera . 2003. A student is doing an XML version of the "Anales de la Corona de Aragon". Comment | Trackback | 2003. Two students are working on a QuickCam Mouse , middle way between Tom Cruise and Playstation II. 2004. The camera trick is being ported to a Zaurus PDA attached to the USB port of a PC Mensajes Electronicos 1989 HD para Mac II 1992 KdV en Mathematica 1992 scanner 1993 Sheaves 1993 Pen Input 1993 NCG 1993 Linux and its damm'd GUI 1994 www Imagemap Alternative , FigA (see also this example ) 1996 A LINK tag for documents pointing to ours? 1996 Overproduction -- 1997 Photosynthesis CPL (Circularly Polarized Light, perhaps from an ice block or other byrrefringent material? Fue en algun momento Una ventaja evolutiva? ) 1997 Historia 1998 Memoria (mitos, cantos...) 1999 Grail Search also in Arthuriana , this message 1999 infinitesimal -- 2000 Geom Renormalizaton 2000 Inverse over Z HM 2002 Tao coincidences and a chinese quest for names HM 2002 Frustrum -- 2002 Prehistory of the atom 2002 Pascal calls to X11 Ph 2002 thread on numerical calculus Ph 2002 space-time coordinates as SUSY partners Ph 2002... Some reading on history of alchemy drove to try calculations for the possibility of induced alpha emission of Hg201, which has a near threshold Gamow pseudostate stabilised with a huge barrier. Left unpublished, I am afraid, but surely some traces can be found in the web. (the point being that Hg201- Pt197+He4 is exotermic but can not be done via usual alpha disintegration. Pt197 decays to Au197; some coldfusioners in Texas reported this kind of beta radiation) 2003... Keeping the alchem quest I entered to study the masive standard model bosons . 2003 Solving the IFRAME onload riddle in Mozilla. 2003 Getting the quantum from quantum gravity. See also here 2004. And the inverse square law from De Broglie lengths and times? Thus 3+1 compactification... is it compulsory from Quantum Mechanics? 2004. This is not mine , but it could be of some importance , specially if combined with Smirnov's identities. For instance one gets ln(sin(cabibbo)=-sinh(ln(pi)). Amazing, even if only a memotecnic resource Bases de datos Hep-Spires: a y ea , as well as name XXX: Physics and Mathematics En Google Otros Ver la pagina sobre politica Ver el blog
Open Problems in Mathematics and Physics
Links to open problems in mathematics, physics and other subjects.
Links to open problems in mathematics, physics and financial econometrics RESEARCH OPEN QUESTIONS October 10th, 2005 GENERAL Lists of unsolved problems Science magazine 125 big questions MATHEMATICS (PHYSICIST'S PERSPECTIVE) Sir Michael Atiyah's Fields Lecture (.ps) Areas long to learn: quantum groups , motivic cohomology , local and micro local analysis of large finite groups Exotic areas: infinite Banach spaces , large and inaccessible cardinals Some recent links between mathematics and physics Number theory and physics Conjectured links between the Riemann zeta function and chaotic quantum-mechanical systems Deep and relatively recent ideas in mathematics and physics Standard model and mathematics: Gauge field or connection Dirac operators or fundamental classes in K-theory ( Atiyah-Singer index theorem ) String theory and mathematics: Mirror symmetry Conformal field theory Mathematics behind supersymmetry Mathematics of M-Theory Chern-Simons theory Unified theory: Langlands Program , Witten on Langlands , Theory of "motives" Lists of unsolved problems Long standing open problems PRICE P versus NP The Hodge Conjecture The Poincar Conjecture The Riemann Hypothesis Yang-Mills Existence and Mass Gap Navier-Stokes Existence and Smoothness The Birch and Swinnerton-Dyer Conjecture Mathworld list Mathematical challenges of the 21st century including moduli spaces and borderland physics Goldbach conjecture Normality of pi digits in an integer base Unsolved problems and difficult to understand areas PRICES Fields Medal and Rolf Nevanlinna Prize Abel Prize PHYSICS Important unsolved problems in physics Quantum gravity Explaining high-Tc superconductors Complete theory of the nucleus Realizing the potential of fusion energy Climate prediction Turbulence Glass physics Solar magnetic field Complexity, catastrophe and physics Consciousness Required mathematics Peter Woit's list Riemannian geometry More general geometry of principal and vector bundles: connection, curvature, etc. Spinor geometry Lie groups and representation theory deRham cohomology Required physics Another list from the European Journal of Physics Learn it all in one fell swoop Physics Today (NRC) Learn it all on the web John Baez's list David Gross list Nature's greatest puzzles at SLAC PRICES Nobel Prize for physics Wolff COSMOLOGY AND ASTROPHYSICS Eleven key questions about the universe Inflation Survey Of The Universe Linde-Vilenkin, inflation (horizon, flatness, density-fluctuation) Photons, ordinary visible matter, ordinary nonluminous matter, MACHOs, exotic dark matter WIMPs, dark energy, Standard model, supersymmetry, technicolor, string theory, M-theory, Multiverses (eternal inflation, Smolin, ekpyrosis) Brane cosmology Ekpyrotic Universe Randall-Sudrum QUANTUM GRAVITY What they look like: Schrodinger's equation Dirac's equation Einstein's equation Superstring action Connes-Chamseddine spectral action Area eigenvalues Survey of quantum gravity Problem of continuous approaches: parametrization of the dynamical degrees of freedom in a diffeomorphism invariant way M-theory Problem of infinity of vacua Top questions in M-theory Review article Top ten string theory questions String theory Ten physics problems for the next millenium from the Strings 2000 Conference Are all the (measurable) dimensionless paramters that characterize the physical universe calculable in principle or are some merely determined by historical or quantum mechanical accident and uncalculable? How can quantum gravity help explain the origin of the universe? What is the lifetime of the proton and how do we understand it? Is nature supersymmetric and if so, how is supersymmetry broken? Why does the universe appear to have one time and three space dimensions? Why does the cosmological constant have the value that it has, is it zero and is it really constant? What are the fundamental degrees of freedom of M-theory (the theory whose low-energy limit is eleven-dimensional supergravity and which subsumes the five consistent superstring theories) and does the theory describe nature? What is the resolution of the black hole information paradox? What physics explains the disparity between the gravitational scale and the typical mass scale of the elementary particles? Can we quantitatively understand quark and gluon confinement in quantum chromodynamics and the existence of a mass gap? Timeline Holographic principle AdS CFT Supergravity Twistor correspondence What are twistors? Twistor theory Witten's article Problems: construct a quantum theory of gravity from some basic principles assuming noncommutative geometry (John Madore, ...) or express some sector or limit of an underlying theory in terms of the language of noncommutative geometry Noncommutative geometry Euclidean quantum gravity Stephen Hawking Problem: show the classical limit of smooth space-time can be recovered Discrete approaches Lorentzian Regge calculus a variant: causal dynamical calculations Causal sets (Rafael Sorkin, ...) Problem: cannot mimic general relativity at large scales Loop quantum gravity Hamiltonian or spin network approach Lagrgangian approach or spin foam models Topos theory Emerging properties (Sakharov induced gravity, ...) CONDENSED MATTER List of open questions including condensed matter problems PARTICLE PHYSICS Standard model open questions Areas of research Technicolour: the unifying symmetry is a scaled-up version of the strong force Unnaturalness problem: original calculation in which the introduction of the Higgs boson in the standard model gives it and the Z and two W infinite mass Supersymmetry: for every fermion in the standard model, there is a corresponding supersymmetric boson, and vice versa Failure to account for gravity Theories of extra dimensions: there are at least five dimensions and a single new particle, a gravitational boson called a graviton Flavour problem: why are they three and only three generations of fermions and why do the particles in each generation have the masses that they do? Neutrino oscillation Hierarchy problem: why do the different forces operate at such different energies, are they all manifestations of the same underlying phenomenon, and if they are, can they be united mathematically? COMPLEX AND CHAOTIC SYSTEMS Non-linear dynamics Evolutionary dynamics Cellular automata Self-organising systems Networks PHYSICS OF FINANCE Future of econometrics Evolutionary finance Nonparametric estimation Forecasting Economic and Financial Time Series Using Nonlinear Methods Scientific study of financial data UNSOLVED PROBLEMS IN BIOLOGY SEVENTY OPEN QUESTIONS IN ARCHEOLOGY NINE UNDECIPHERED LANGUAGES geovisit();
Kinetic Theory and its Applications.
This resource is devoted to mathematical aspects of kinetic theory and its applications in physics and chemistry. .
Kinetic Equations - | | | | | | | | | | | | | english | . , , , . , , . . , . , , . , . , - . . . , , , , . , , . . , , , , . | | | | | | | | | | Copyright Kinetix, 2000-2005
Euclidean Geometric Transforms for Physics
A new method of correlating physics formulas to derive one formula from a related formula using Euclidean geometry to represent the inter-relationship of physics formulas.
Physics with Transforms by Rodolfo Padilla Search: Lycos Tripod Aeon Flux Share This Page Report Abuse Edit your Site Browse Sites Previous | Top 100 | Next Physics with Transforms by Rodolfo Padilla Home Table of Contents Explanation the Transform Physics with Transforms side 1 Physics with Transforms side 2 Math Chart side 1 Math Chart side 2 Index of Geometry of Physics with Transforms Glossary Algebra Ratios Similitude Euclid About Me go to Book by Rodolfo Padilla in Spanish vea libro de Rodolfo Padilla en Espanol
An Introduction to Noncommutative Geometry
A set of lecture notes by Joseph C. Varilly on noncommutative geometry and its applications in physics.
[physics 9709045] An Introduction to Noncommutative Geometry Physics, abstract physics 9709045 From: Joseph C. Varilly [ view email ] Date: Tue, 30 Sep 1997 22:38:08 GMT (91kb) An Introduction to Noncommutative Geometry Authors: Joseph C. Varilly Comments: 85 pages, Plain TeX, lectures at EMS Summer School on NCG and Applications, Sept 1997 Report-no: UCR-FM-12-97 Subj-class: Mathematical Physics; Differential Geometry; Quantum Algebra These are lecture notes for a course given at the Summer School on Noncommutative Geometry and Applications, sponsored by the European Mathematical Society, at Monsaraz and Lisboa, Portugal, September 1-10, 1997. 1. Commutative geometry from the noncommutative point of view. 2. Spectral triples on the Riemann sphere. 3. Real spectral triples, the axiomatic foundation. 4. Geometries on the noncommutative torus. 5. The noncommutative integral. 6. Quantization and the tangent groupoid. 7. Equivalence of geometries. 8. Action functionals. Full-text: PostScript , PDF , or Other formats References and citations for this submission: CiteBase (autonomous citation navigation and analysis) Which authors of this paper are endorsers? Links to: arXiv , physics , find , abs ( - + ), 9709 , ?
Recent Developments in Skyrme Models
An introduction by T. Gisiger and M.B. Paranjape to recent, more mathematical developments in the Skyrme model. The aim is to render these advances accessible to mainstream nuclear and particle physicists.
[hep-th 9812148] Recent mathematical developments in the Skyrme model High Energy Physics - Theory, abstract hep-th 9812148 From: M. B. Paranjape [ view email ] Date: Thu, 17 Dec 1998 16:38:25 GMT (598kb) Recent mathematical developments in the Skyrme model Authors: T. Gisiger , M.B. Paranjape Comments: 129 pages, about 30 figures, original manuscript of published Physics Reports Report-no: UdeM-GPP-TH-98-57 Journal-ref: Phys.Rept. 306 (1998) 109-211 In this review we present a pedagogical introduction to recent, more mathematical developments in the Skyrme model. Our aim is to render these advances accessible to mainstream nuclear and particle physicists. We start with the static sector and elaborate on geometrical aspects of the definition of the model. Then we review the instanton method which yields an analytical approximation to the minimum energy configuration in any sector of fixed baryon number, as well as an approximation to the surfaces which join together all the low energy critical points. We present some explicit results for B=2. We then describe the work done on the multibaryon minima using rational maps, on the topology of the configuration space and the possible implications of Morse theory. Next we turn to recent work on the dynamics of Skyrmions. We focus exclusively on the low energy interaction, specifically the gradient flow method put forward by Manton. We illustrate the method with some expository toy models. We end this review with a presentation of our own work on the semi-classical quantization of nucleon states and low energy nucleon-nucleon scattering. Full-text: PostScript , PDF , or Other formats References and citations for this submission: SLAC-SPIRES HEP (refers to , cited by , arXiv reformatted); CiteBase (autonomous citation navigation and analysis) Which authors of this paper are endorsers? Links to: arXiv , hep-th , find , abs ( - + ), 9812 , ?
Homological Methods in Mathematical Physics
These lecture notes by Joseph Krasil'shchik and Alexander Verbovetsky are a systematic and self-contained exposition of the cohomological theories naturally related to partial differential equations.
[math 9808130] Homological Methods in Equations of Mathematical Physics Mathematics, abstract math.DG 9808130 From: Alexander Verbovetsky [ view email ] Date ( v1 ): Mon, 31 Aug 1998 09:57:31 GMT (107kb) Date (revised v2): Mon, 21 Dec 1998 17:07:11 GMT (107kb) Homological Methods in Equations of Mathematical Physics Authors: Joseph Krasil'shchik , Alexander Verbovetsky Comments: 150 pages, AmS-LaTeX 1.2 (based on LaTeX 2e), needs to run through LaTeX four times, no figures, Lectures given in August 1998 at the International Summer School in Levoca, Slovakia. Revised version 2 (Mon, 21 Dec 1998): misprints corrected, Definition 4.3 on page 70 changed Report-no: DIPS 7 98 Subj-class: Differential Geometry; Analysis of PDEs; Mathematical Physics; Exactly Solvable and Integrable Systems These lecture notes are a systematic and self-contained exposition of the cohomological theories naturally related to partial differential equations: the Vinogradov C-spectral sequence and the C-cohomology, including the formulation in terms of the horizontal (characteristic) cohomology. Applications to computing invariants of differential equations are discussed. The lectures contain necessary introductory material on the geometric theory of differential equations and homological algebra. Full-text: PostScript , PDF , or Other formats References and citations for this submission: CiteBase (autonomous citation navigation and analysis) Which authors of this paper are endorsers? Links to: arXiv , math , find , abs ( - + ), 9808 , ?
Lectures on Orientifolds and Duality
Notes by Atish Dabholkar on orientifolds emphasizing applications to duality.
[hep-th 9804208] Lectures on Orientifolds and Duality High Energy Physics - Theory, abstract hep-th 9804208 From: Atish Dabholkar [ view email ] Date: Thu, 30 Apr 1998 17:36:23 GMT (70kb) Lectures on Orientifolds and Duality Authors: Atish Dabholkar Comments: 64 pages, LaTeX, 13 epsf figures Report-no: TIFR TH 98-13 This is an introduction to orientifolds with emphasis on applications to duality. Based on lectures given at the 1997 Trieste Summer School on Particle Physics and Cosmology, Italy. Full-text: PostScript , PDF , or Other formats References and citations for this submission: SLAC-SPIRES HEP (refers to , cited by , arXiv reformatted); CiteBase (autonomous citation navigation and analysis) 1 trackback ( What's this? ) (send trackbacks to http: arxiv.org trackback hep-th 9804208) Which authors of this paper are endorsers? Links to: arXiv , hep-th , find , abs ( - + ), 9804 , ?
Holomorphic Methods in Mathematical Physics
This set of lecture notes by Brian C. Hall gives an introduction to holomorphic function spaces as used in mathematical physics. The emphasis is on the Segal-Bargmann space and the canonical commutation relations.
[quant-ph 9912054] Holomorphic Methods in Mathematical Physics Quantum Physics, abstract quant-ph 9912054 From: Brian C. Hall [ view email ] Date ( v1 ): Sat, 11 Dec 1999 20:51:37 GMT (55kb) Date (revised v2): Thu, 14 Sep 2000 23:07:02 GMT (56kb) Holomorphic Methods in Mathematical Physics Authors: Brian C. Hall Comments: Final version Subj-class: Quantum Physics; Mathematical Physics Journal-ref: Contemporary Mathematics, Volume 260, pp. 1-59 This set of lecture notes gives an introduction to holomorphic function spaces as used in mathematical physics. The emphasis is on the Segal-Bargmann space and the canonical commutation relations. Later sections describe more advanced topics such as the Segal-Bargmann transform for compact Lie groups and the infinite-dimensional theory. Full-text: PostScript , PDF , or Other formats References and citations for this submission: SLAC-SPIRES HEP (refers to , cited by , arXiv reformatted); CiteBase (autonomous citation navigation and analysis) Which authors of this paper are endorsers? Links to: arXiv , quant-ph , find , abs ( - + ), 9912 , ?
This Week's Finds in Mathematical Physics
This is a column written about modern topics in mathematical physics.
TWF This Week's Finds in Mathematical Physics John Baez This is a column on mathematical physics where I describe papers and books that I happen to find enjoyable. It appears on sci.physics.research , sci.math.research, sci.physics, and sci.math - but I put it on this website to make it permanently accessible. I don't write a new issue every week, but when I do, it is always this week. Warning: the things I include are not necessarily more important or better than things I don't! Mostly I try to write about subjects I actually understand, which limits the selection tremendously. Also, my comments are not intended as "reviews" evaluating the papers. They are simply aimed at getting you interested. To see the latest edition, click here . To get to all the old issues, click here. For a table of contents of all the old issues, click here . To search all the issues for a given word or phrase, click here . The search feature above was kindly provided by Laurent Bartholdi. I really love it! You can also get the original ASCII versions of This Week's Finds if you want. But if you want these.... Information survives by people copying it. So, please download a tar file containing all of weeks 1-214 in ASCII or HTML ! I often update old issues of This Week's Finds to correct errors or add extra information, so please beware that the material in these tar files is only up-to-date as of May 8, 2005. The readme files explain that I am maintaining all rights to This Week's Finds, but letting you have a copy for personal use. Think deeply of simple things. - motto of the Ross Summer Mathematics Program 1992 - 2005 John Baez baez@math.removethis.ucr.andthis.edu home
Celestial Mechanics Research
Links, animations, references, and a brief description of research into n-body problems.
Marshall Hampton Research Page This page is still under construction. My research: Central configurations in the n-body problem My primary areas of mathematics are, broadly speaking, dynamical systems and geometry. My thesis is in the field of celestial mechanics. It is on the concave central configurations of the 4-body problem. Central configurations can be thought of as generating self-similar solutions of the n-body problem, which is (classically, at least) the study of the dynamics of n point masses interacting according to Newtonian gravity. The three-body case was solved by Euler and Lagrange . Euler found that for any ordering of three collinear point masses there was a spacing of the masses making them a central configuration. Lagrange found that the only non-collinear three-body central configuration is the equilateral triangle, which is a central configuration for any three (positive) masses. Here's an animation of one of the solutions of Lagrange. Here's an animation of a concave 4-body central configuration . Its a typical example of the sort of central configuration that I have shown exists for any four (positive) masses. Papers and books related to my research: A good place to start is the book Celestial Encounters, by Florin Diacu and Philip Holmes. Newton's Clock: Chaos in the Solar System, by Ivars Peterson, is also a very good nontechnical book about celestial mechanics, although not as closely related to what I am working on. At the other extreme, for the mathematical diehards there is nothing better than Siegel and Moser's classic book, Lectures on Celestial Mechanics. A really excellent recent introduction to celestial mechanics, with a focus the solar system, is Murray and Dermott's book Solar System Dynamics. There is an excellent article by J. Wisdom, in the journal Icarus, vol.72, 1987, no.2, p.241-275, which is a more technical introduction to chaotic dynamics in the solar system. The work of R. Moeckel is largely responsible for my interest in low-n body problems; particularly his overview in the 1988 Proc. Hamiltonian Dynamical Systems, AMS Contemporary Math. vol. 81, edited by K. Meyer and C. Saari, and his paper Chaotic Dynamics Near Triple Collision, Arch. Rational Mech. Anal., 107, 1989, no.1, 37-69. Another nice article connecting the three body problem with gauge theory and geometric phases is The Geometric Phase of the Three-Body Problem, by R. Montgomery, in Nonlinearity, 9, 1996, p.1341-1360. For the insatiably curious, you can peruse my research bibliography (in postscript format), (or in dvi format). Recently Montgomery (with A. Checiner) has also found some exciting new orbits of the equal mass three-body problem using variational techniques (Chenciner, A., and Montgomery, R. "A remarkable periodic solution of the three-body problem in the case of equal masses", Ann. of Math. (2) 152 (2000), no. 3, 881--901). Central configurations play an important part of this work. Montgomery wrote a nice follow-up article on this as well - "A new solution to the three-body problem", Notices Amer. Math. Soc. 48 (2001), no. 5, 471--481). Web sites related to my research These include links to some other researchers in the field and some very cool animations of n-body orbits (done by other people). The background image is the chaotically spinning moon Hyperion.
Discrete Self-trapping Equation
A bibliography in BibTeX format for those interested in discrete nonlinear Schrdinger type equations.
The Discrete Self-Trapping Equation The Discrete Self-Trapping Equation The equation where is a complex n-vector, and M is a real symmetric matrix, is known as the Discrete Self-Trapping (DST) Equation. See J. C. Eilbeck, P. S. Lomdahl, and A. C. Scott, Physica D, 16, 318-338, 1985, for details. In the cases where M is tri-diagonal with constant coefficients, this reduces to a discrete form of the Nonlinear Schrdinger (DNLS) equation. A survey concentrating on the quantized version of the DST equation will be found in A. C. Scott, J. C. Eilbeck and H. Gilhoj, Quantum lattice solitons, Physica D 78, 194-213, 1994. A bibliography file dst.pdf on this equation, is available. Alternatively, download the file dst.tex and the accompanying .bib file dst.bib and process these using LaTeX and BibTeX. Chris Eilbeck Heriot-Watt University chris@ma.hw.ac.uk tel. +44 (0)131 451 3220
Hyperreal World
Nonstandard analysis and its applications to quantum physics, by H.Yamashita. Mixed English Japanese.
Hideyasu YAMASHITA's Page for Mathematics and Physics HYPERREAL WORLD H. YAMASHITA's Page for Mathematics and Physics mirror1 mirror2 Last modified: In this site, I often use PDF files, so please install Acrobat Reader on your computer. If your browser is IE, Active X must be set executable to use Acrobat as a helper application of your browser. "Hyperreal" is one of main notions in a field of mathematics, called Nonstandard Analysis.(NSA) Contents 1. NSA Informal and intuitive introduction to nonstandard analysis Formal introduction to nonstandard analysis Toward the mathematical foundation of path integrals Nonstandard introduction of quantum physics Invitation to Nonstandard Analysis (links) H. Yamashita's Articles Nonstandard Links NSA Bibliography 2. Miscellaneous Introduction to geometry (selected topics) Home Email: leibniz@sun-inet.or.jp or yamasita@dpc.aichi-gakuin.ac.jp
Mathematical Methods I
This site contains the complete lecture notes and homework sets for PHYCS498MMA, a course of mathematical methods for physics given to entering graduate students, and senior undergraduates, at the University of Illinois at Urbana-Champaign.
MATHEMATICAL METHODS I MATHEMATICAL METHODS I Course Page PHYS 598MMA, Fall 2005 10:30 to 11:50 Monday, Wednesday, Room 144 Loomis Laboratory. This web-page contains links to documents such as handouts and other useful stuff. These files are mostly in postscript (.ps) format or in PDF (.pdf) so make sure that your browser is configured to automatically process such files. If it is not, and you use Unix Netscape, go to "edit preferences - Navigator - Applications" and include "ghostview %s" under application Postscript Document. Similarly use "xpdf %s" for PDF. If you use some other O S and browser you will have to figure this out on your own. Syllabus Outline The course covers four related areas: Calculus of Variations. Equations of mathematical physics as variational problems, conservation laws, Lagrange multipliers, origin of eigenproblems, variational approximation schemes. Ordinary differential equations. Linear equations: Solution space, linear independence, Wronskians, normal forms. Eigenvalue problems: importance of boundary conditions, formal and true self-adjointness, completeness of eigenfunctions, Fourier series, continuous spectra and Fourier integrals. Green Functions: Range-nullspace theorem, Fredholm alternative, constructing Green functions via jump conditions. Partial Differential equations. Classification of PDE's. Hyperbolic equations: wave equation, method of characteristics, shocks and weak solutions. Heat equation: solution by integral transforms. Elliptic equations: Dirichlet and Neumann problems, Poisson's equation, Legendre functions, spherical harmonics, Bessel and spherical Bessel functions, examples from electrostatics. Integral Equations. Type I and type II Fredholm and Volterra equations, solution via Fourier and Laplace transforms, Abel's equation. Separable Kernels: compact and Hilbert-Schmidt operators, Fredholm alternative again. Perturbation methods: Neumann and Fredholm series. A more detailed, but approximate, week-by-week syllabus can be found here. Homework Sets There are weekly homework sets. Your solutions must be deposited in the 498mma box before 4pm on the due date, which will always be a Thursday. This time has been chosen to encourage you to go to the Physics Department Colloquia which are at 4pm each Thursday. Homework number 0, due Thursday Sept 01st. (for a PDF version click here ),( solutions , pdf ) Homework number 1, due Thursday Sept 08th. - (PDF) ,( solutions , pdf ) Homework number 2, due Thursday Sept 15th. - (PDF) ,( solutions , pdf ) Homework number 3, due Thursday Sept 22th. - (PDF) ,( solutions , pdf ) Homework number 4, due Thursday Oct 6th. - (PDF) ,( solutions , pdf ) Homework number 5, due Thursday Oct 13th. - (PDF) ,( solutions , pdf ) Homework number 6, due Thursday Oct 20th. - (PDF) ,( solutions , pdf ) No homework this week. Midterm exam monday 31st Oct Homework number 7, due Thursday Nov 3rd - (PDF) ,( solutions , pdf ) Homework number 8, due Thursday Nov 17th. - (PDF) ,( solutions , pdf ) Homework number 9, due Thursday Dec 01st. - (PDF) ,( solutions , pdf ) Homework number 10, due Thursday Dec 08th. - (PDF) ,( solutions , pdf ) Homework number 11, optional problems. --- (PDF) Homework will be graded on the "alpha", "beta", "gamma", system with an "alpha" (essentially correct) worth 5 points, a "beta" (a major error) worth 2 points, and a "gamma"(a feeble attempt) worth 1 point. Exams The midterm exam will be held in class on Monday October 31st. The final exam will be in 144 LLP Sat dec 17th, 8-11am Old Exams: Midterm Exam, Fall 2002 - (PDF) Midterm Exam, Fall 2003 - (PDF) Final Exam, Fall 2003 - (PDF) Lecture notes The lecture notes are a fairly accurate representation of the course as given in the classroom. They are no longer password protected, and so are available to the general public. The notes are also available as a PDF file . This, as with the PDF versions of the homework sets, has been created so as to avoid type 3 fonts as far as possible. There are still some type 3 fonts in the figures, however, and ghostview and xpdf do not display the resulting PDF quite as prettily as the PostScript version. Printed versions of the PDF seem fine, though. Acknowledgement The structure of this course, and hence of the notes, owes a lot to Paul Goldbart who taught it very successfully for several years. Many of the examples (particularly in chapter 1) and some of the homework problems are lifted directly from his notes. Textbook Although the lecture notes should be self contained, I recommend Mathematics for Physicists by Phillipe Dennery and Andre Krzywicki (Dover Pulications, $12.95) as a textbook. This text covers much of the material in this course, and also the complex variable part of MMB. Grades and Gradebook Registered students may access the on-line gradebook by using your university username and password. You will need to accept cookies, and have JavaScript turned on for the gradebook to work. Your grade in the course will be determined as from your total scores weighted as follows: Homework 60%, Midterm exam 10%, Final Exam 30%. Cultural Enrichment Links Some of the material in the course is supposed to introduce you to the wider culture of mathematical physics and its applications in the real world. Here are links relating to some of the topics discussed: People A Short Biography of George Green can be found here . This site also contains the biographies of many other mathematicians and mathematical physicists. Wave Phenomena Images of Hydraulic Jumps and Bores can be found here . Images and description of the Kelvin ship wake can be found here and here Solitons A nonlinear pulse obeying the KdV equation does not form a shock, but instead decays into solitions. Here is a movie of this phenomenon. It is taken from the ``soliton lab'' created by Kanehisa Takasaki at the univerity of Kyoto. Staff Finding me: Office: 2117 ESB. Phone: 3-2891. e-mail: m-stone5@uiuc.edu My office hour is Thursday 10:30-11:30am, in 2117 ESB. Graders and TAs: Suk-Bum Chung Office: 4110 ESB Phone: 4-8065 E-mail: sukchung@uiuc.edu Office Hour: Monday 5-6pm, 3rd floor ESB MRL interpass. Shiying Dong 496 Loomis Lab Phone: 4-6687 E-mail: Sdong2@uiuc.edu Office hour: Tuesday 4-5pm, 3rd floor ESB MRL interpass. Back to Mike's Home Page Last updated 18 08 05
Dimensional Analysis
A simple review of the powerful technique of dimensional analysis.
dimensional analysis DIMENSIONAL ANALYSIS Department of Physics, University of Guelph When doing physics problems, you'll often be required to determine the numerical value and the units of a variable in an equation. The numerical value usually isn't too difficult to get, but for a novice, the same can't be said for the units. This self-instruction unit deals with dimensional analysis, which is a useful method for determining the units of a variable in an equation. Another use of dimensional analysis is in checking the correctness of an equation which you have derived after some algebraic manipulation. Even a minor error in algebra can be detected because it will often result in an equation which is dimensionally incorrect. The first panel lists the objectives of this unit. Read these objectives carefully. 1. Given the definition of a physical quantity, or an equation involving a physical quantity, you will be able to determine the dimensions and SI units of the quantity. 2. Given an equation, you will be able to determine if the equation is dimensionally correct or incorrect. Panel 1 Most physical quantities can be expressed in terms of combinations of five basic dimensions. These are mass (M), length (L), time (T), electrical current (I), and temperature, represented by the Greek letter theta (q). These five dimensions have been chosen as being basic because they are easy to measure in experiments. Dimensions aren't the same as units. For example, the physical quantity, speed, may be measured in units of metres per second, miles per hour etc.; but regardless of the units used, speed is always a length divided a time, so we say that the dimensions of speed are length divided by time, or simply L T. Similarly, the dimensions of area are L2 since area can always be calculated as a length times a length. For example, although the area of a circle is conventionally written as pr2, we could write it as p r (which is a length) r (another length). Now try the questions in Quiz 1 . Now that you can determine the dimensions of physical quantities, it'll be useful to write the SI units for the quantities. SI stands for International System (Systme Internationale). The SI unit for mass is the kilogram, for length the metre, for time the second, for current the ampere, and for temperature the kelvin. Notice that kelvin is abbreviated as just K. The degree symbol,, and the word "degree" are not used with kelvin. As a quick example, let's look at speed, which has dimensions of length divided by time or L T. Its SI units are then metres divided by seconds, represented as m s or ms-1. Now try Quiz 2 . Some combinations of SI units are given special names. For example, the unit of energy, kgm2 s , is given the special name joule, which is abbreviated as J. Study the information presented below. a) energy joule (J) kgm2 s2 b) force newton (N) kgm s2 c) frequency hertz (Hz) (cycles)s-1 d) power watt (W) J s = kgm2 s3 e) charge coulomb (C) As You might be wondering when to write joule, J, or kgm2 s2 as the energy unit. The SI convention is that if there is no number in front of the unit, then the unit is written as a full word. For example, you would write "energy is expressed in joules," with "joules" written out in full, since there is no number associated with it in the sentence. If there is a number, then "J" ( or less commonly, "kgm2 s2") is used. Thus, you would write "the energy is 6.4 J". Panel 7 Now test yourself on the SI special names. Do Quiz 3 . Panel 9 Some quantities have no dimensions. For example, the sine of an angle is defined as the ratio of the lengths of two particular sides of a triangle. Thus, the dimensions of the sine are L L, or 1. Therefore, the sine function is said to be "dimensionless". There are many other examples of "dimensionless" quantities listed in the following table. all trigonometric functions exponential functions logarithms angles (but notice the discussion in the next paragraph) quantities which are simply counted, such as the number of people in the room plain old numbers (like 2, p, etc.) Notice that some quantities which are "dimensionless" have units. For example, angles can be measured in units of radians or degrees, but angles are "dimensionless". Another familiar example is a frequency unit, (cycles) per second. The second, of course, is a time unit but the cycles are "dimensionless". That's the reason for cycles being written in parentheses above. Take a few moments and learn the "dimensionless" quantities above. Now try Quiz 4 . Try NOT to look at the table while you do it. We've now done all the basics so let's get into some fine points. There are two special cases of quantities which are "dimensionless". First, the argument of a trigonometric function, and second, the exponent in any exponential function. The argument of a trig function is an angle, of course, so it's "dimensionless"; and an exponent of an exponential function is the same thing as a logarithm so it's "dimensionless". These facts often are useful in helping to determine the dimensions of a quantity. For example, if we're given that y = ekt, where t is the time, we can state that k must have dimensions of time-1 in order that the exponent be "dimensionless". Now let's see how well you can use this information in Quiz 5 . A common notation, which means "the dimensions of a quantity", is simply the quantity written inside square brackets []; thus, [area] = L2. Now you should be able to try Quiz 6 . In an algebraic expression, all terms which are added or subtracted must have the same dimensions. This implies that each term on the left-hand side of an equation must have the same dimensions as each term on the right-hand side. For example, in the equation a = bc + (1 2)xy, "a" must have the same dimensions as the product "bc", and the product "(1 2)xy" must also have the same dimensions as "a" or "bc". Remember that the "1 2" in "(1 2)xy" is just a plain old number and so it has no dimensions. An equation in which each term has the same dimensions is said to be dimensionally correct. All equations used in any science should be dimensionally correct. The only time you'll encounter one which isn't is if there is an error in the equation. So dimensional analysis is a valuable tool in helping you to detect an equation in which you made an error in algebra, for example. Let's try this out on some equations. Try Quiz 7 . where F is force r is radius is length v is speed R is distance What are the dimensions and SI unit of h (viscosity)? We're just about finished now. Let's do a sample question. This is a typical question which is fairly difficult. We're given an equation (shown on the left) involving force, radius, length, speed, and distance, and are asked for the dimensions and SI units of eta, (h), which is a viscosity. First, we rearrange the equation to solve for h and then convert it to an equation involving dimensions. Note that the negative sign is interpreted as "-1". Okay, you finish it off. When you've worked out the answer, move on to see if you're right or not. Well, the correct answer for the dimensions is ML-1T-1. The corresponding SI unit is kgm-1s-1. If you didn't get this answer, try the question again. You've probably just made a simple error with your exponents. The final panel consists of a post-test for you to try, now that you know the basics of dimensional analysis. If you can do these questions, you're in good shape. Good luck. This is the end of the tutorial on DIMENSIONAL ANALYSIS. Return to: Physics Tutorials Menu
Twistors- What are they?
A set of notes introducing spinors and twistors.
Twistors --- What Are They? Next: Contents Twistors --- What Are They? Fedja Hadrovic November 9, 1997 Contents Introduction Spinors Electromagnetism in spinor notation Twistors Quantisation Klein Correspondence Classical fields About this document ... Fedja Hadrovic Sat Jan 3 17:20:50 GMT 1998
6th European Conference on Luminescent Detectors and Transformers of Ionizing Radiation
The Ivan Franko National University of Lviv invites you to the International scientific conference The 6th European Conference on Luminescence Detectors and Transformers of Ionizing Radiation in Lviv, Ukraine, June 19 23, 2006.
Lumdetr 2006
6th Symposium SiO2, advanced dielectrics, and related devices"
6th international conference on the physics of silicon dioxide and other dielectrics of scientific and applicative interest. To be held in Mondello, Palermo, Italy, 25-28 June 2006
Symposium SiO2006 - Advanced Dielectrics and Related devices 6th symposium "SiO2 , advanced dielectrics and related devices" Hotel la Torre , Mondello (Palermo) 25-28 June 2006 Please fill the pre-registration form and receive updated news about the symposium Pre-registration deadline: 31 October 2005 Download here the first announcement Symposium Committees Proceedings Deadlines Venue Sponsors and Links News: Page updated on 9 16 2005. Deadlines added Contact us at sio2006@fisica.unipa.it Design and realization: Fabrizio Messina PHP programming: Eugenio Vitrano Powered by counter.bloke.com
Bianisotropics 2004
Bianisotropics 2004 10th Conference on Complex Media and Metamaterials. Ghent, Belgium, 22-24 September 2004
BIAN04 This page uses frames, but your browser doesn't support them.
Zakopane Conference on Nuclear Physics
The aim of the conference is to increase the mutual communication of physicists representing various areas of nuclear physics. The selection of topics to be discussed is directed to cover new developments in research of all nuclear physics rather than of few narrow subjects. Zakopane, Poland, 4-10 September 2006
Zakopane Conference on Nuclear Physics
14th International Conference on Photoacoustic and Photothermal Phenomena
The biennial International Conferences on Photoacoustic and Photothermal Phenomena (ICPPP) is concerned with the science, applications and technologies of acoustic, thermal, and general diffusion-wave fields,14th ICPPP. Cairo, Egypt, January 2007
14 ICPPP - International Conference on Photoacoustic and Photothermal Phenomena, Cairo, Egypt, 25-31 August, 2006 14th INTERNATIONAL CONFERENCE ON PHOTOACOUSTIC AND PHOTOTHERMAL PHENOMENA Cairo, Egypt, January 6 - 9, 2007 Conference web site still under construction [Home] [ Feedback ] [ Contents ] [ Search ] Copyright 2005 14th INTERNATIONAL CONFERENCE ON PHOTOACOUSTIC AND PHOTOTHERMAL PHENOMENA
14th International Conference on Positron Annihilation
ICPA-14: McMaster University, Canada, July 23-28 2006. Highlights progress in fundamental aspects of positron and positronium physics and chemistry, applications to materials science and industry, and developments in experimental techniques.
ICPA-14, Hamilton, Canada: International Conference on Positron Annihilation The XIVth International Conference on Positron Annihilation Welcome Proceedings Important Dates List of Topics Registration Committees Submit Abstract McMaster Accommodation How to Get Here Things to Do Restaurants Contact Us Welcome ICPA-14 will be held at McMaster University, Hamilton, Ontario, Canada, between July 23rd and July 28th 2006. The conference will highlight progress made in fundamental aspects of positron and positronium physics and chemistry, applications of positron annihilation techniques to materials science and industry, and new developments in experimental techniques. The official language of the conference will be English. For information on using this site please see below. This site provides information on the conference and its surroundings. The first set of links on the sidebar provides factual information regarding the conference. Important: The conference website will be updated regularly with information regarding registration, abstract submission, scientific and social programs etc. Please check the site regularly for the latest information on ICPA 14. To find out about McMaster University or the City of Hamilton use the second set of links. You will also find instructions on how to get to here from the two main airports nearby. There is information on things to do, places to eat, and ways to enjoy your stay while attending the conference. If you are unable to find the information you need on this website please feel free to Contact Us . Copyright Info
International Conference for Physics Students 2002 Budapest
XVII International Conference for Physics Students ICPS2002. 20-28 Aug 2002, Budapest, Hungary.
International Conference for Physics Students in 2002 --- ICPS2002
Frontier Science Research Conference: Laser-Matter Interaction-2005
Scientific understanding in laser-matter interaction research
FRONTIER SCIENCE RESEARCH CONFERENCE--F S R C - LASER-MATTER-INTERACTION-2005
4th International Conference on Physics Teaching in Engineering Education PTEE 2005
Focus: European Dimension of Physics in Engineering Education; June 29-July 1, 2005; Brno, Czech Republic.
PTEE 2005 - Invitation Anonymous user News Main Invitation Scope Chairman Details Important Deadlines Contact Topics Committees Programme and Organizing Local Organizing EPS Abstracts List of EPS Abstracts Workshops Abstracts of Workshops Programme Time Schedule Conference Programme Photo Conference Open Welcome Party Workshops Lednice Venuse 1 Venuse 2 Video Registration Conference Open Concert Welcome Party Workshops and Poster Beer Exposition Brno Participants Area Login DPHYS FEEC BUT SEFI Invitation Allow us to invite you to: 4th International Conference on Physics Teaching in Engineering Education PTEE 2005 Focus European Dimension of Physics in Engineering Education June 29-July 1, 2005 Brno, Czech Republic For SEFI PWG organised by: Brno University of Technology Department of Physics FEEC BUT Under the auspices of: Prof. Jan Vrbka , Rector of the Brno University of Technology Petr Duchon , Member of the European Parliament Invitation Under the auspices of: Organized by: Sponzored by: The scope of International Conference on Physics Teaching in Engineering Education (PTEE) includes all aspects of physics teaching in engineering education. The aim of the conference is to bring together people working in this field to provide them with a forum for the exchange of ideas and experience. Conference PTEE is arranged by Working Group Physics and Engineering Education (PWG) of Societ Europenne pour la Formation des Ingnieurs (SEFI) as a periodic event. The previous conferences in this series were organised in Copenhagen (1997) , Budapest (2000) and Leuven (2002) . Webmaster
Unifying Concepts in Glass Physics III
Conference and School. Bangalore, India. School: 25 - 26 June; Conference: 28 June - 1 July 2004.
CDSAGENDA V.5 Conference and School on Unifying Concepts in Glass Physics (Bangalore, India)Sch: 25 - 26 June, Conf: 28 June - 1 July [ Go To ] " [ Scientific Calendar ] " [ Downloads ] " [ Help ] " User Login | Event Admin Login Category: List of Bases 2004 ICTPactivitiesoutsideTrieste Go To CDSAgenda Home Agenda Map Agenda Search What's on at ICTP ICTP Home Page Scientific Calendar Next year Calendar This year Calendar Previous year Calendar 2003 2002 2001 Downloads Excel Activity Programme Template ICTP Agenda Manual Help User Guide About AM 5.0 Bugs Comments Database Stats Access Stats Conference and School on Unifying Concepts in Glass Physics (Bangalore, India)Sch: 25 - 26 June, Conf: 28 June - 1 July Cosponsor(s): Jawaharlal Nehru Centre for Advanced Scientific Research (JNCASR) Start Time: 25 June 2004 Ends On: 1 July 2004 Location: Bangalore - India Organizer(s): S. Franz, S. Sastry Material: no notes available List Of Participants (HTML) List Of Participants (PDF ) announcement application_form programme This Agenda is incomplete If you want to make a direct link from your Web page to this agenda, please use this URL: http: cdsagenda5.ictp.trieste.it full_display.php?ida=a0372 Maintained by: The CDS Support Team ( Bugs and reports ) This page is loaded in 0.24446105957 seconds.
Institute of Physics: Conferences
Listings on future meetings and conferences organised by the Conference Department of the Institute of Physics, as well as information on self-service meetings organised by the Institute Groups.
Institute of Physics: Conferences Home Page Home Page | Text Menu Phase Transitions in Polymeric Systems 17 November 2005 Institute of Physics, London Registration Deadline: 10 Nov '05 Bio-Dielectrics: Theories, Mechanisms and Applications, 10-12 April 2006 Abstract Deadline: 6 Jan '06 Photon06 4-7 September 2006 University of Manchester, UK Request Further Information Welcome to the Conferences Home Page! On this page you will be able to find listings on future meetings and conferences organised by the Conference Department of the Institute of Physics, as well as information on self-service meetings organised by the Institute Groups. You will also be able to find out more about our Conference team and what it does, as well as to obtain information specifically aimed at Groups or Divisions wishing to organise a conference by using the Institute service. The Conference Organising team works free of charge to the Institute's Groups and Divisions. For full details see submenu "Our Services". OUR MISSION To increase the status, reputation and membership of the Institute by providing the best professional conference organising service to encourage and facilitate the dissemination of knowledge of the science of physics The Institute is a well established member of the INTERNATIONAL ASSOCIATION OF PROFESSIONAL CONGRESS ORGANISERS. All members on our conference team are trained to meet the internationally established professional standards for conference organisation. Copyright Institute of Physics and IOP Publishing Ltd. 2000 - 2003. The Institute of Physics is a registered charity, No. 293851. Home Page | About Us | Info For Organisers | Our Services | Forthcoming Institute Conferences | How To Reach Us | Hotels | What's On In Physics | Contact Details The AA-Standard refers to all pages within the domain for which this is the home page
ARENA Workshop
International ARENA Workshop on "Acoustic and Radio EeV Neutrino Detection Activities", May 17-19 2005, DESY Zeuthen, Germany
ARENA Workshop, May 17-19, DESY Zeuthen Diese Seite verwendet Frames. Frames werden von Ihrem Browser aber nicht untersttzt. Bitte verwenden Sie einen anderen Browser. This page is using frames. Frames are not supported by your current browser. Please use another browser.
Breaking frontiers.
Breaking frontiers: submicron structures in Physics and Biology. Conference - Zakopane 2005, Poland.
Zakopane 2005 - School of Physics To enter the site, please, click the photo.
ErasmusIntensive Program on Ion Beam, proton and hyperfine techniques - Madrid 2005
This ERASMUS IP aims to bring together young physicists for a series of lectures and tutorials. Topics are: CEMS thin layer, optics, nano-magnetism, Muon spin rotation, channelling blocking, software and practical applications. Madrid, 8-18 May 2005
Erasmus School 2005 Erasmus School 2005 - Madrid Erasmus Intensive Programme 2005 Ion Beam, photon and hyperfine methods in nano-structured materials MADRID 8-18th May 2005 ENTER:
The XXV Conference on Solid State Physics and Materials (E-MRS)
The XXV Conference on Solid State Physics and Materials Science Workshop on Photonic Materials and Optoelectronic Devices (II), The Egyptian Materials Research Society (Eg-MRS), 6 - 10 Mar 2005 Luxor, Egypt
The Egyptian Materials Research Society (Eg-MRS) The Egyptian Materials Research Society (Eg-MRS) Egyptian Journal of Solids Free full text electronic edition on our new web site 8 2005 Copyright 2005 The Egyptian Materials Research Society (Eg-MRS) Maher Ahmed
Optics of Biological Particles
Fluorescence and Other Optical Properties of Biological Particles, 3-6 Oct 2005.
Optics of Biological Particles
SPIE Web Conferences
Calendar of SPIE Events. SPIE promotes further innovation in optics and photonics through conferences across the globe, in topics such as nanotechnology, defense and security, biomedical optics, and remote sensing.
Content-type: text html Page-Completion-Status: Normal Calendar - Conferences - SPIE Web home contact product search join SPIE view cart Furthering Innovation in Optics and Photonics Nanotechnology Defense Security Aerospace, Remote Sensing, Astronomy Automation, Inspection, Product Engineering Biomedical Optics Communications Fiber Optics Electronic Imaging, Displays, Medical Imaging Lasers Applications Microelectronics, Optoelectronics, Micromachining Optical Physics, Chemistry, Biology Optical Science Engineering Signal Image Processing Conferences CALENDAR Welcome to SPIE Conferences Below, you will find the entire calendar of SPIE Events. Here are other ways to search for SPIE Events: Browse for Calls for Papers or Advance Programs Browse for Events by Region Browse for Events by technology areas (follow the links to the left) EPIC SPIE Workshop on Laser Applications in Europe 23-24November2005 Dresden, Germany Co-Sponsored by SPIE and EPIC Program Exhibition Optics Japan 2005 23-25November2005 Tokyo, Japan SPIE is a cooperating organization Program Optical Technologies for Communications 2005 28-30November2005 Ufa, Bashortostan Republic, Russia Sponsored by SPIE Russia Chapter. SPIE will publish proceedings. Optomechatronic Technologies: ISOT 5-7December2005 Sapporo, Japan Program AdvanceRegistrationEnds21November2005 Microelectronics, MEMS, and Nanotechnology An SPIE Event 11-14December2005 Brisbane, Australia Program AdvanceRegistrationEnds25November2005 International Conference on Optics Optoelectronics-ICOL 2005 12-15December2005 Dehradun, India SPIE is a cooperating organization Fourth International Conference on Optical Communications and Networks 14-16December2005 Bangkok, Thailand Sponsored by SPIE Thailand Chapter. University of Arizona College of Optical Sciences Workshop-Computer Generated Holography and Diffractive Optical Elements 14-16December2005 Tucson, Arizona USA SPIE is a co-sponsor Program IST SPIE's Electronic Imaging 2006 15-19January2006 San Jose, California USA Program AdvanceRegistrationEnds15December2005 Photonics West An SPIE Event 21-26January2006 San Jose, California USA Program AdvanceRegistrationEnds6January2006 Exhibition Biomedical Optics 2006 An SPIE Event 21-26January2006 San Jose, CA USA Part of Photonics West Program AdvanceRegistrationEnds6January2006 Exhibition 22nd European Mask Lithography Conference (EMLC2006) 23-26January2006 Dresden, Germany SPIE is a cooperating organization Program Winter College on Quantum and Classical Aspects of Information Optics 30January-10February2006 Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste Italy Applications are due 30 September 2005. In collaboration with the International Commission for Optics, SPIE--The International Society for Optical Engineering, the Optical Society of America, and the International Society on Optics Within Life Sciences Program Medical Imaging An SPIE Event 11-16February2006 San Diego, California USA Program AdvanceRegistrationEnds31January2006 Exhibition Microlithography An SPIE Event 19-24February2006 San Jose, California USA Program AdvanceRegistrationEnds3March2006 Exhibition Smart Structures Materials NDE An SPIE Event 26February-2March2006 San Diego, California USA Call for Papers AbstractsDue15August2005 Exhibition Photonics Europe An SPIE Europe Event 3-7April2006 Strasbourg, France Call for Papers AbstractsDue19September2005 SPIE Defense and Security Symposium 17-21April2006 Orlando (Kissimmee), Florida USA Call for Papers AbstractsDue3October2005 Photomask Japan 2006 18-20April2006 Yokohama, Japan Abstracts will be accepted beginning on 20 October Announcement Optical Data Storage 23-26April2006 Montreal, Canada SPIE is a co-sponsor and is publishing proceedings Program High-Power Laser Ablation An SPIE Event 7-11May2006 Taos, NM USA Call for Papers AbstractsDue24October2005 Astronomical Telescopes and Instrumentation An SPIE Event 24-31May2006 Orlando, Florida USA Call for Papers AbstractsDue7November2005 Exhibition International Optical Design Conference 4-8June2006 Vancouver, British Columbia Canada SPIE is a co-sponsor and will publish Proceedings Call for Papers Fifth International Workshop on Information Optics (WIO-06) 5-7June2006 Toledo, Spain SPIE is a cooperating organization Program Photonics North 2006 5-8June2006 Quebec City, Canada SPIE is a technical co-sponsor Program Great Lakes Photonics Symposium An SPIE Event 12-16June2006 Dayton, Ohio USA Call for Papers AbstractsDue28November2005 Exhibition XII Conference on Laser Optics 26-30June2006 St. Petersburg, Russia Sponsored by SPIE Russia Chapter. SPIE will publish proceedings. 7th National Symposium on Display Holography 10-14July2006 St. Asaph, United Kingdom SPIE Europe is a technical co-sponsor Program 5th World Congress of Biomechanics 29July-4August2006 Munich, Germany SPIE is a cooperating organization Optics Photonics An SPIE Event 13-17August2006 San Diego, California USA co-located with SPIE's 51st Annual Meeting Call for Papers AbstractsDue30January2006 Exhibition APOC 2006Asia-Pacific Optical Communications 5-8September2006 Gwangju, South Korea Speckle 2006 International Conference 13-15September2006 Nimes, France SPIE is a cooperating organization and is publishing proceedings Program Photomask Technology An SPIE Event 17-22September2006 Monterey, California USA Boulder Damage Symposium An SPIE Event 25-27September2006 Boulder, Colorado USA Optics East An SPIE Event 1-4October2006 Boston, Massachusetts USA International Optical Fiber Sensors Conference (OFS 18) 23-27October2006 Cancun, Mexico SPIE is a technical co-sponsor Program 50 Years of SPIE Author Guidelines Technical Groups Scholarships Grants | SPIE Home | Publications | Conferences | Exhibitions | Membership | Education | Telephone: +1 360 676-3290 | Fax +1 360 647-1445 | Email: spie@spie.org 1994 2005 SPIEThe International Society for Optical Engineering | Privacy Policy | SPIE is a not-for-profit international society dedicated to advancing optics and photonics.
ONW-2005 - Current Problems in Optics of Natural Waters - International Conference
Topics: Fundamental problems of radiative transfer theory; Optical properties of natural waters; Light propagation in water media and underwater imaging; Remote sensing, including satellite sensors and lidars;Optics of maritime atmosphere and the sea surface. St. Petersburg, 12-16 Sep 2005
ONW'2005 Current Problems in Optics of Natural Waters. International Conference ONW'2001 | ONW'2003 | ONW'2005 | ONW'2001 | ONW'2003 | ONW'2005 |
Listing of Conferencess, Symposia, Summer Schools and Workshops
Listings of academic events worldwide.
Specialized Listings - Welcome to Conferences Symposia, Summer Schools, and Workshops This entire page will be displayed in browsers that do not support frames. Edit in this mode to customize this page for non-frame-supporting browsers. For browsers that do support frames, design your page in the Edit Frames mode.
From Solid State to Biophysics II
Conference aims to understande living matter which, given its enormous complexity, may require some of the techniques at least partly elaborated in solid state physics. Croatia 26 June - 2 July 2004
From Solid State to BioPhysics III Home Advisory Committee Future conferences International Conference From Solid State To BioPhysics III June 24 - July 1, 2006 Hotel 'Croatia' , Cavtat, Dubrovnik, Croatia Sponsored by: Croatian Ministry of Science and Technology Organization (co-)supported by: Rudjer Boskovic Institute, Zagreb, Croatia cole Polytchnique Fdrale de Lausanne, Switzerland Faculty of Science, Zagreb, Croatia Institute of Physics, Zagreb, Croatia University of Dubrovnik, Croatia Co-chairs: Lszl Forr and Davor Pavuna cole Polytchnique Fdrale de Lausanne (EPFL) Switzerland Conference Scientific Secretary: Sylvia Jeney, EPFL International Advisory Committee: D. Andelman (Israel) N. W. Ashcroft (USA) S. Barisic (Croatia) A. Bishop (USA) N. Ban (Switzerland) I. Bozovic (USA) C.W. Paul Chu (USA China) I. Dikic (Germany) A. Fersht (U.K.) P.G. de Gennes (France) I. Giaver (USA) A. Heeger (USA) A. Jnossy (Hungary) D. Juretic (Croatia) R. Laughlin (S.Korea USA) P.-A. Lindgard (Denmark) S. Marcelja (Australia Croatia) G. Margaritondo (Switzerland) M. Milun (Croatia) K.A. Mller (Switzerland) P. Perfetti (Italy) J.C. Phillips (USA) Y.W. Park (S.Korea) D. Pines (USA) R. Podgornik (Slovenia) J. Prost (France) M. Radman (France) T. Rizzo (Switzerland) E. Sackmann (Germany) A. Sienkiewicz (Poland) S. Takada (Japan) M. Thorpe (USA) F.Vidal (Spain) G. Whitesides* (USA) M. K. Wu (Taiwan) M. Zinic (Croatia) * did not confirm yet The Scope of the 3rd Conference Following the success of our first two conference in this series , the 3rd conference will continue the cross-disciplinary approach toward the emerging understanding of the living matter, which given its enormous complexity may require some of the techniques and approaches elaborated in solid state physics or contemporary bio-sciences. The interdisciplinary discussion of carefully selected leading experts in solid state, soft-matter and bio-sciences will take place in a relaxed yet rigorous, stimulating setting. Deadlines 2nd announcement: 1st December 2005 Abstracts: 15th April 2006 Registration : 15th May 2006 Further information: Sylvia.Jeney _{AT}_ epfl.ch Webmaster: Branimir Lukic (Lausanne)
6th International Conference on Nitride Semiconductors (ICNS-6)
The conference will cover all aspects of group-III nitride semiconductors. Bremen, Germany, 28 Aug - 2 Sep 2005
ICNS-6 Home Login Home Topics Contact Program Downloads Accomodation Registration Photo Gallery Social Events Important Dates Conference site Invited Speakers Late News Papers Create user account Abstract Submission Chairs Committees Commercial Exhibition Presentation Guidelines Young Researchers Award Publication Manuscript submission Bremen, Germany August 28 - September 2, 2005 The venue continues a series of conferences formerly held in Nagoya Japan (1995), Tokushima Japan (1997), Montpellier France (1999), Denver USA (2001) and Nara Japan (2003). Latest news Photos uploaded 2005-09-19 A selection of photos taken during the conference are available now and can be downloaded here . Manuscript submission deadline postponed 2005-07-30 The new deadline for manuscript submission is set to August 15, 2005. Program for posters is online 2005-07-17 The program can be downloaded here . Program is online 2005-07-01 The program can be downloaded here . Notification of acceptance sent by e-mail 2005-06-03 The notification of abstract acceptance has been sent by e-mail. Hotel reservation form available 2005-06-01 The Hotel reservation form is now available here . Abstract deadline postponed 2005-04-01 The new Abstract Deadline is set to April 5, 2005 12:00 CEST. Abstract submission opened 2005-03-14 Abstract submission Abstract submission 2005-03-09 Abstract submission will be opened on March 14. Second announcement released 2005-02-11 The second announcement is sent out. Abstract Deadline changed 2005-01-24 The new Abstract Deadline is set to April 1, 2005. First announcement released 2004-07-12 The first announcement is sent out via e-mail. Abstract Deadline set 2003-10-29 The Abstract Deadline is set to March 11, 2005. Sponsored by Deutsche Forschungsgemeinschaft Messe Bremen GmbH University of Bremen Nolting-Hauff-Stiftung AIXTRON Avis Coherent Cree EMF FEI LayTec Lumilog Nichia Osram PANalytical Sony Toyoda Gosei Veeco
III Wandlitz Days On Magnetism
Local-Moment Ferromagnets: Unique Properties for Modern Applications. Berlin, Germany; 15-18 March 2004.
III. Wandlitz Days On Magnetism, HU-Berlin, Theoretical Solid State Physics III. Wandlitz Days On Magnetism, HU-Berlin, Theoretical Solid State Physics Frame ALERT! This document is designed to be viewed using Netscape 3.0's Frame features. If you are seeing this message, you are using a frame challenged browser. A Frame-capable browser can be downloaded from Netscape Communications . III. Wandlitz Days On Magnetism: Local-Moment Ferromagnets: Unique Properties for Modern Applications Berlin, 15-18 March 2004 This international workshop brings together experimentalists and theoreticians working in the field of local moment ferromagnets. It is focused on classes of materials which are considered to have high potential for modern applications. It is the scope of the workshop to present the present state of affairs and to pinpoint trends for future research towards a deeper understanding of the magnetism in these materials. Organizers Program Participants Oral and Poster Presentations Abstracts Proceedings Deadlines Location Dates Travel Information Registration Payment
CNFT-2004
2nd National Conference on Theoretical Physics. Constanta, Romania; 26--29 August 2004.
IFIN-HH-DTP-2nd National Conference on Theoretical Physics It seems your browser cannot display frames. To view this site properly please use a browser capable of displaying frames!
Mathematical Ideas in Nonlinear Optics
Workshop on Mathematical Ideas in Nonlinear Optics: Guided Waves in Inhomogenous Nonlinear Media. ICMS, Edinburgh, Scotland, UK; 19--23 July 2004.
Workshop on Mathematical Ideas in Nonlinear Optics Home Page Workshop on Mathematical Ideas in Nonlinear Optics: Guided Waves in Inhomogenous Nonlinear Media 19-23 July 2004, Edinburgh Workshop Home Page | Scientific Programme Participants | Workshop Arrangements Scientific Organising Committee: David Parker, Edinburgh ( d.f.parker@ed.ac.uk ) Charles Stuart, EPFL ( charles.stuart@epfl.ch ) Michael Weinstein, Columbia University Bell Labs ( miw2103@columbia.edu ) The major aims of this interdisciplinary Workshop are: to survey recent analytical and numerical advances for optical systems far from the NLS regime to identify phenomena and theory likely to be important to developments in the near future to provide opportunity for interaction and discussion of problems of practical and mathematical importance. Lectures, which will be held in Ewing House at Pollock Halls, will run for five full days, starting first thing on Monday 19 July and finishing in the afternoon on 23 July. Attendance is by invitation only. There may be a few spare places; anyone interested should contact one of the Organisers. The meeting is supported by the Engineering and Physical Sciences Research Council Updated 21 June 2004 Workshop Home Page | Scientific Programme Participants | Workshop Arrangements MAIN ICMS PAGES Future Events | Travel Information | Call for Proposals | Publications Previous Events | Useful Links | About ICMS | Front Page
SCELL-2004 International Conference on the Physics, Chemistry and Engineering of Solar Cells
SCELL-2004 is intended as a vehicle for the dissemination of research results on materials science and technology related to photovoltaic, photothermal and photoelectrochemical solar energy conversion. Badajoz, Spain, 13-15 May 2004
SCELL-2004 Basic and Applied Research on Solar Cells Pre-registration If you want to keep informed, please pre-register or email us at scell-2004@formatex.org Satellite Conference of the 1st International Meeting on Applied Physics ( APHYS-2003 ) INFO FOR SPEAKERS [ ] ACCEPTED ABSTRACTS (being updated) [ ] How to reach Badajoz - Transportation Information (Coaches provided to Madrid and Lisbon airports) Discover our region: Extremadura Last-minute abstracts will be accepted until April 30th, but inclusion in the ordinary abstracts book can not be guaranteed. SPONSORS SCELL2004 Proceedings - Special Issues Full papers of oral and poster accepted presentations will make up a special issue of two International Journals: Solar Energy Materials and Solar Cells published by Elsevier and availbale through ScienceDirect Journal of Materials Science published by Kluwer and availble through Kluwer Online Instructions for authors... SCELL-2004: Groups seeking partners EU PV Documents - Fundamental PV Science and applications Title: Development of High Efficiency Low Cost Thin Films CdTe Solar Cells From: Centre for Thin Film Chalcogenide Photovoltaic Materials Research, Tallinn Technical University, ESTONIA Details here Title: Photovoltaic Cell and Module Characterisation From: Photovoltaics Research Group in the Department of Physics at the University of Port Elisabeth (UPE), SOUTH AFRICA Details here Title: Concentration of Solar Energy with Fresnel Lenses From: Department of Corrosion and Protection, CENIM-CSIC, SPAIN Details here Title: Photovoltaic modules characterisation and simulation of their outdoor performance From: Department of Physicochemical Research, University of Opole. POLAND Details here Photovoltaic Barometer 2003 Catalogue of photovoltaic projects - FP5 (1999-2002) Size:1,7Mb Photovoltaic Solar Energy - Best Practice Stories Publication Size:745Kb Solar Grade Silicon - A Global Assessment A Task Force for the Creation of a Consortium to Set-up a Solar Grade Silicon Production plant 225 Kb"SAHARA" Fifth Framework Programme - Successful projects Best Practice Projects Yearbook 1997-2000 Size:22Mb PV faade at railroad station Lehrter Berlin Final Technical report - Thermie 4FP Size:4,5Mb Solar City Guide Publication Size:1,2Mb Technology Implementation Plan (TIP) - Project results Examples of Good Practice PLENARY SPEAKERS Dr. Rolf Brendel, Head of the Division for Thermosensorics and Photovoltaics at the Bavarian Center for Applied Energy Research (ZAE Bayern), Germany [ www ] Lecture: Thin-film crystalline Si solar cells from layer transfer using the porous Si (PSI) process Author of Thin-Film Crystalline Silicon Solar Cells: Physics and Technology, published by Wiley (2003) Prof. Gehan Amaratunga, Head of Electronics, Power and Energy Conversion, Electrical Engineering Division, Engineering Dept. Cambridge University UK [ www ] Lecture: Polymer- nanotube solar cells with dye sensitisation Dr Jenny Nelson, Organic photovoltaics group, Blackett Laboratory, Imperial College, UK. [ www ] Lecture: Charge transport and recombination in molecular solar cells Author of The Physics of Solar Cells, published by World Scientific Publishers, May 2003. SCELL-2004
2nd International Conference on Materials Science and Condensed Matter Physics
2nd International Conference on Materials Science and Condensed Matter Physics,21 Sep - 26 Sep 2004, Chisinau, Moldova, registration deadline: 07 Jun 2004.
INTERNATIONAL CONFERENCE on MATERIALS SCIENCE and CONDENSED MATTER PHYSICS To view this page, your browser must support frames. s
CLEO IQEC 2004
The Conference on Lasers and Electro-Optics International Quantum Electronics Conference are the most highly regarded conferences in the fields of lasers, electro-optics and quantum electronics. California 16-21 May 2004
CLEO QELS 2006 Home Page CLEO QELS are the most highly regarded conferences in the fields of lasers and electro-optics. Researchers, Educators, Engineers, Students and Business Leaders from around the world are drawn to the technical conference to discuss the latest findings in the scientific community. An equal number of end-users from growing industries including Biomed, Nanotechnology, Displays and Defense visit the Exhibit to see innovative applications in optics technology, learn about new products and find technical and business solutions. We encourage you to bookmark this site and check back often to learn about programming announcements, company and product listings and exhibitor updates. See you in Long Beach! Submissions for CLEO QELS 2006 are now open! 2005 Conference Statistics and Archive 2005 Exhibitor List Sign up for Email Updates Sponsored by: CLEO QELS2006 is managed by the Optical Society of America 2010 Massachusetts Avenue NW Washington, DC 20036, USA Tel: 202.416.1907 Fax: 202.416.6140 E-mail: cleo.info@osa.org
International Conference For Physics Students (ICPS)
A conference run by the International Association of Physics Students (IAPS). Reports on past and future conferences, including photographs, message board, and Powerpoint presentations used. 7-13 Aug 2003.
ICPS2003 - INTRO The 18th International Conference for Physics Students - ICPS 2003 - was held in Odense in the period 8th-13th of August 2003 The next IAPS conference - ICPS 2005 - will be held in Coimbra in the period 11th-18th of August 2005.
RIKEN Symposium
Soft dipole mode, coherent mode and molecular structure in drip line nuclei. Change of shell structure and new magicity in nuclei far from the stability line. Effects of halo and skin vs. deformation on radii, magnetic and quadrupole moments. ...
================================= RIKEN Symposium Physics at Drip Lines 13 to 15 of February, 2001 (special session 16 February) ================================= Final Circular The international symposium "Physics at Drip Lines" will be held from the 13 to the 15 of February, 2001 in RIKEN, Japan. Main topics of the symposium are 1. Soft dipole mode, coherent mode and molecular structure in drip line nuclei. 2. Change of shell structure and new magicity in nuclei far from the stability line. 3. Effects of halo and skin vs. deformation on radii, magnetic and quadrupole moments. 4. Continuum, clustering and resonance effects in halo nuclei. 5. Effective interactions in nuclei near drip lines. 6. Other related topics. The updated program can be seen on the conference web site : http: tkynt2.phys.s.u-tokyo.ac.jp drip The conference will start in the morning of February 13 and end in the late afternoon of February 15 and will take place in the Okochi Memorial Hall of RIKEN. ****** Special Session ********* We have a special session in the morning of February 16 because of overwhelming response to the symposium. The special session is devoted on the discusions on "Radii and densities at drip lines and related topics". The participants are encouraged to stay in the conference site until the morning of February 16. ********************************** Detailed information about the conference site and transportation can be seen also in the website: http: tkynt2.phys.s.u-tokyo.ac.jp drip The registration fee is 3000 yen which should be paid upon arrival in Japanese currency. The registration fee will include a copy of the proceedings, a booklet of abstracts, costs of coffee and the conference banquet. The conference banquet will be held on Feb. 13 at Hirosawa club on RIKEN campus. The accomodation has been announced to those who had requested. If you requested but got no message on it, please let us know immediately. The conference proceedings will be published. The deadline and the maximum number of pages will be announced later. We are all looking forward to having you in RIKEN soon. Organizing Committee: H. Sagawa (co-chairman, Aizu), T. Otsuka (co-chairman, Tokyo RIKEN), I Tanihata (RIKEN), T. Suzuki (RIKEN Fukui), K. Ikeda (RIKEN), K. Kato (Hokkaido), T. Suzuki (Nihon University), A. Ozawa (RIKEN), N. Itagaki (Tokyo) Correspondence: E-mail: sagawa@u-aizu.ac.jp Fax: +81-242-37-2752 Regular mail: Physics at Drip Lines conference c o H. Sagawa Professor of Physics Center for Mathematical Sciences University of Aizu Aizu-Wakamatsu, Fukushima 965-8580 Japan tel: +81-242-37-2725 ***************************************************************************** T e n t a t i v e P r o g r a m ****************************************************************************** =============== February 13th =============== 9:30- Registration 10:00-12:10 H. Sagawa (Univ. of Aizu) (10) "Opening address" Aksel Jensen (Arhus) (40) "Survey of halos: Structure, occurrence conditions and high energy breakup reaction mechanisms" M. Ploszajczak(Caen) (40) "DESCRIPTION OF EXOTIC NUCLEI USING THE SHELL MODEL EMBEDDED IN THE CONTINUUM" P.F. Bortignon (Milano) (40) "BEYOND MEAN FIELD THEORY IN NUCLEI AT THE DRIP LINES" L U N C H 13:15-15:25 M. Lewitowicz (Ganil) (50) "Present status and perspectives of the study of drip-line nuclei at GANIL" K. Hagino (Kyoto) (40) "QRPA in the coordinate space representation" T. Otsuka (Tokyo RIKEN) (40) "Effective interactions and magic numbers" C O F F E E B R E A K 16:00-18:00 D. Vretenar (Zagreb) (40) "RELATIVISTIC MEAN-FIELD DESCRIPTION OF EXOTIC NUCLEAR STRUCTURE" H. Iwasaki (Tokyo RIKEN)(30) "Experimental studies of E1 and E2 transitions in 12Be" T. Suzuki(Nihon University) (30)"Pigmy and soft dipole states in nuclei far from the stability line" M. Tohyama (Kyorin Univ.) (20) "Soft dipole mode in time-dependent density-matrix theory" ******************************************************************************* 18:15-20:00 Symposium Banquet at Hirosawa Club ******************************************************************************* =============== February 14th =============== 9:15-10:35 Nguyen Van Giai(Orsay) (40) "Continuum Hartree-Fock-Bogoliubov calculations in Carbon and Oxygen regions." K. Kato (Hokkaido) (40) "Study of halo nuclei by Complex scaling method" C O F F E E B R E A K 11:00-12:30 M. Thoennessen (MSU) (50) "Structure of Nuclei Beyond the Dripline" Ramon Wyss (Stockholm) (40) "Fundamental excitations in N=Z nuclei" L U N C H 13:30-15:20 H. Horiuchi (Kyoto) (40) "AMD study of cluster structures in light nuclei" K. Matsuta(Osaka) (30) "Electromagnetic moments and effective operators in nuclei near and far from the stability line" M. Yamagami(Kyoto) (20) "Exotic Shapes and Shape Coexistence in N=Z Nuclei from 64Ge to 84Mo suggested by Symmetry-Unrestricted Skyrme-HFB Calculations" T. Nakamura (TIT) (20) "Low-lying structure of 6He studied by the 6Li(t,3He)6He Reaction" C O F F E E B R E A K 15:50-17:50 I. Tanihata (RIKEN) (40) " Past and Future of RIB experiments in RIKEN I" A. Ozawa (RIKEN) (30) "Past and Future of RIB experiments in RIKEN II" Gianluca Colo (Milano) (30) "Effects of Collective Modes on Shell Structure in 10Be and 24O" T. Nakatsukasa(RIKEN) (20) "3D real space calculations of the continuum response" =============== February 15th =============== 9:15-10:35 P. Descouvemont(Brussels) (40) "Exotic nuclei in a microscopic cluster model" M. Freer(Birmingham) (40) "Nuclear Molecules" C O F F E E B R E A K 11:00-12:30 N. Itagaki (Tokyo) (30) "Molecular-orbital structure in Be and C isotopes" Carmen Angulo(Louvain-la-Neuve) (30) $B!I(BRecent experiments using the 6He radioactive beam at Louvain-la-Neuve$B!I(B M. Ito (Hokkaido) (30) "6He+6He Molecular Resonances in Highly-Excited States in 12Be" L U N C H 13:30-15:10 I. Hamamoto (Lund) (40) "New Structure Problems in Drip Line Nuclei" S. Shimoura (CNS Tokyo)(40) "Present status and perspectives of the study of drip-line nuclei at CNS" Nguyen Ding Dang (RIKEN Hannoi)(20) "Pygmy and Giant Dipole Resonances in Neutron-Rich Nuclei within Quasiparticle Representation of Phonon Damping Model" C O F F E E B R E A K 15:40-17:00 K. Asahi(TIT RIKEN) (40) "Q-moment and magnetic moments in exotic nuclei". K. Ikeda (RIKEN) (40) "Summary" =============== February 16th =============== 9:30-12:15 "Special Session: Radii and densities at drip lines and related topics" S. Yoshida (Hosei Univ.) (30) "New spin-orbit interactions and isotope shifts" A. Kohama (RIKEN) (30) "Feasibility to Determine the Surface of the Matter Distribution of Nuclei at RIBF" K. Oyamatsu (Aichi Shukutoku Univ.) (30) "Structure of neutron rich nuclei in neutron star crusts" ************* break 15minutes ****************** H. Nakada (Chiba Univ.) (30) "Many-body effects around proton-drip line and mirror asymmetry" H. Sato (RIKEN) (30) "Effective Interactions and interaction radii of extremely neutron rich nuclei."
4th International Conference on B Physics and CP Violation - BCP4
B factories offer various opportunities to look for new physics at presently accessible energies. Belle, Babar, and CLEO are taking data and the next few years represent very exciting period for B physics.
BCP4
ICPS 2000 Zadar
International Conference for Physics Students in Zadar, Croatia (August 4-11, 2000).
Iskon portal etvrtak,17.11.2005. chat forumi freemail web imenik registracija korisnika iskon portal | infocentar | webcafe | klik magazin | internet usluge | pomo i podrka Internet web imenik arhiva naslovnica vijesti sport film tv glazba crna kronika novac kultura znanost tehnoklik fotografija auti lijepi i zdravi bebe web kuhinja iz drugih medija webcafe infocentar ticket shop arhiva Preferences- Navigator- HomePage- Use Current Page\n\nOpera:\nNavigation- Set home page- Set current page as home page' ); }" neka ovo bude vaa poetna stranica EUR 7,353653 USD 6,287323 GBP 10,865327 CHF 4,757183 opirnije Zagreb 6 8C Pula 13 14C Split 13 14C Osijek 7 7C opirnije Djelatnica ik u telemarketingu u Puli Elektroinstalater - elektriar Tajnica k generalnog direktora Broker s licencom (m ) Service coordinator (m f) Samostalni knjigovoa (m ) david m. friedman GLAVA ZA SEBE - KULTURNA POVIJEST PENISA m.robert pirsig ZEN I UMJETNOST ODRAVANJA MOTOCIKLA elizabeth kostova POVJESNIARKA f. william engdahl SJEME UNITENJA - GEOPOLITIKA GENETSKI ... malcolm gladwell TREPTAJ - MO MILJENJA BEZ MILJENJA vijesti Rambo iz Popovae Nakon to je iz puke pucao oko kue, susjedi su pozvali policiju. Kad mu je policija uspjela oduzeti puku, poeo je po njima pucati iz pitolja, a kad su se sklonili, na njihov je automobil bacio bombu. tenis Poraz u meu karijere Najvaniji ispit u dosadanjoj karijeri, prema vlastitim rijeima, Ljubo je odradio izrazito loe. U borbi za ulazak u polufinale Masters Cupa glatko je izgubio od Davida Nalbandiana sa 6:2, 6:2. svijet Kovanica u ast propalom ustavu Italija u povodu godinjice potpisivanja ustava EU u Rimu izdaje kovanicu od dva eura. To to ustav nee zaivjeti, jer su ga Francuska i Nizozemska odbile, nije ih uope omelo. vijesti 'CRKVA GRIJEI' Etika i krizma ne idu zajedno Jo dvije ljudske rtve ptije gripe Vlada: Potvrditi granicu s BiH 'TO PRIJE MOGUE' HR529 za Hrvatsku u NATO-u Francuska: Nasilje na normalnoj razini LORA Oevid u vojnoistranom centru sport TUKLA IH TURSKA MURIJA 'Zaklat emo vas' U Njemakoj dva hrvatska izbornika Uhien pijani srpski novinar PASJE POPODNE 'Sudac je mahao srpskom zastavom' Vojska trai Divca Turci zabili etiri i ispali BUCKSI OSVOJILI ZAPAD Kuko ispred Boguta znanost i tehnologija U TUNISU NITA NOVO SAD zadrava kontrolu nad internetom Otvoren portal za mrtve Koje su posljedice pornografije? STVAR JE U OEKIVANJIMA enama je smjenije Stiu nadljudski jaki roboti Izgubljen u svemiru OPASNOST IZ DUBINA... SVEMIRA Kako protiv asteroida? ivot NIJE SVE ZA SVAKOGA Oblici lica i frizure Najbolje za trbune miie Kupci oprezno! FATALNI FU Posljednji piercing minkanje - sve po redu Mlijeko, ali ne i okolada RADIONICE Zapleite trbuni i afro ples iz drugih medija Veernji list Sruit emo hrvatski prijelaz na Plovaniji Vjesnik Tajni letovi ugrozili odnose SAD-a i panjolske Slobodna Dalmacija Konvoji su nam nosili smrt Glas Amerike Hoe li 22. 11. biti potpisan Dayton 2? Goliavi sport - Talijanke Victoria's Secret Fashion Show Osvajanje prostora, Kolekcija Generali Foundation arhiva Australski ragbijai 50 najboljih filmskih plakata 25 najveih svjetskih megalopolisa Najbolje naslovnice naega doba Ulini rat u predgraima Pariza Mali je gol! - Luka Nieti Miss Playboy TV 2005. MTV European Music Awards 2005 Exposed - Sve grudi Playboya Francuski ragbijai Let 3 - Rado ide Srbin u vojnike (Pika) Nokia Cro-a-Porter Osijek Fashion Incubator Goliavi sport - Grkinje Hundertwasser - grafike Potres u Pakistanu i Indiji Mini Bol Fashion Week 10 naj ispada slavnih sisa Bikini-party! Kate Moss - pad jednog anela Dan poslije Katrine MTV Summer Tour Modna guterica Zadar Teroristiki napad na London Utrka s bikovima Pamplona 2005 Bijelo dugme u Zagrebu 51. bijenale u Veneciji Jacko na slobodi Hrvatski svjetionici Miss Universe 2005. - bikini Helmut Newton 1920-2004 Nije li Brad Pitt zasluio Oskara? World Press Photo 2005 Norijada diljem Hrvatske Cannes 2005 Najljepa lica showbiza Park Ribnjak nedjeljom 25 godina bez Tita Kupai kostimi Arhitektonska rasko Dubaija 50 najseksipilnijih ena Benedikt XVI. Slavne, bogate i gojazne Vjenanje Charlesa i Camille Sprovod Ivana Pavla Drugog Ivan Pavao Drugi Svi Gotovinini plakati Veernje haljine! Star Wars: Osveta Sitha Najbolje europske guze Najbolje noge showbiza Veliki petak na Filipinima Goliavi sport - Brazilke Goliavi sport - Rumunjke Goliavi sport - Njemice II. Goliavi sport - Njemice I. Goliavi sport - Ruskinje Kapaljka - Babe of the month Noni ivot Zagreba 13 Noni ivot Zagreba XII Noni ivot Zagreba 11 Noni ivot Zagreba 10 Noni ivot Zagreba 9 Noni ivot Zagreba 8 Noni ivot Zagreba 7 Noni ivot Zagreba 6 Noni ivot Zagreba 5 Noni ivot Zagreba 4 Noni ivot Zagreba 3 Noni ivot Zagreba 2 Noni ivot Zagreba 1 Noni ivot Paga 8 Noni ivot Paga 7 Noni ivot Paga 6 Noni ivot Paga 5 Noni ivot Paga 4 Noni ivot Paga 3 Noni ivot Paga 2 Noni ivot Paga 1 Izbor za Klik djevojku II Izbor za Klik djevojku I MTV-sise Anne Nicole Smith 77. dodjela Oskara Retro Oskari SAG Awards 2005. Peugeot - Auto snova 2020. 2005 North American Auto Show 62. dodjela Zlatnog globusa Zlatni medvjed, Sljeme 2005. Tijelo Gen duhovnosti? Smisao ivota? Supermodeli Nakit Oluja nad Hrvatskom Arafatov ivot u slici Hrvatski svjetionici minkeri Ameriki izbori Lijepa Afrika Emocionalna inteligencija Paris Motor Show - noviteti Paris Motor Show - koncepti Big Brother - Goli u jacuzziju Oboavana ivot London Fashion Week 2 London Fashion Week 1 MTV Video Music Awards 2004 Sustav koordinata Ruska talaka kriza Povratak olimpijaca Zatvaranje Olimpijskih igara Odbojkaice na pijesku Otvorenje Olimpijskih igara Mars Express Streetparade04 Zrich Ljetna pria Starsky Hutch Piknik na malom irokom Brijegu Tko je bri u Pamploni? Batman Begins Movie Stills Marlon Brando (1924. - 2004.) Hrvatski navijai u Portugalu Pendrek po turskim leima Hrvatske navijaice u Portugalu Zagreb Gay Pride 2004 Eurokaz 2004. Ciconia Ciconia Celebrity Fair by Hoyka Vatreni ispraaj prema Portugalu MTV Movie Awards Harry Potter Madonna Re-Invention tour World Press Photo 2004 Norijada Modne ikone Klovievi dvori: Pod istim nebom Zagreb auto show 2004. izdvajamo Dobitnici ulaznica za premijeru Severinine predstave Osvojite ulaznice za Severininu predstavu Vodimo vas na Dokumaniju! Osvojite ulaznice za Famous! anketa Koliko zimskih guma imate na autu? nijednu jednu dvije tri etiri scena DVD KRITIKA Gradonaelnik Sunset...; Palindromi; Rat svjetova Plakat za 690.000 dolara Quaid dobio zvijezdu DOBRO JE INITI DOBRO Jamie Cullum je mladi Samaritanac Snoop Dogg ide u zatvor Jo jedan ubojica pronaao Isusa Intervju: Nura Bazdulj Hubijar SA(N)JAM KNJIGE U ISTRI Nominacije za Kiklopa zabava ERA RAZVODA U HRVATA Kad vie nema ljubavi... Mathew McConaughey je najseksipilniji Nazovi umorstvo radi izlazaka REKLI, NE POREKLI Bubnu i ostanu slavni To je samo prijateljski poljubac! anamari se skinula za Playboy POSRAMLJENA BOGATAICA Paris dobila nogu iskon666@iskon.org top news 15:29 - 17.11.2005. NATO: Samo tako Hrvatska 14:43 - 17.11.2005. Sony povlai 'zatiene' CD-e 14:13 - 17.11.2005. Ne piti vodu u ibensko-kninskoj upaniji 14:08 - 17.11.2005. Vlada: Potvrditi granicu s BiH 13:34 - 17.11.2005. Izuzetna suradnja Hrvatske i OESS-a kolumne Sandi Blagoni: BLOGOS Koliki kukuruz raste u Izraelu Pavle Kalini: KONTRAS Europa je i islamska Lucijan Cari Tko to tamo pliva e-mail korisniko ime: lozinka: pop server: net inet otvori besplatni e-mail webc@fe IGRICA TJEDNA Snowy: Space Trip STRANICA TJEDNA Ivan Hrvatska VIC DANA Uiteljica HOROSKOP | spremi stranicu u favorites | piite nam (c) 2000-2005 Sva prava pridrana. Uvjeti koritenja . Impresum .
Non Linear Dynamics Conference
The Conference is a cross disciplinary meeting for all scientists interested in theoretical and experimental aspects of the applied non-linear dynamics, covering the whole spectrum from semiconductors to information technologies.
The Subject of the Conferece Last Update: Aug-2001 With the support of the E.U. LATEST NEWS : Thessaloniki, Greece - 27-30 8 2001 Aristotle University of Thessaloniki - Greece Physics Department Informatics Department The Organizing Committee wishes to thank the following sponsors of the Conference: - The Greek Ministry of Education - The Aristotle Univeristy of Thessaloniki (AUTh) The Conference is a cross disciplinary meeting for all scientists interested in theoretical and experimental aspects of the applied non-linear dynamics, covering the whole spectrum from semiconductors to information technologies. Emphasis will be given on the following underlying aspects, which are common to the most of the recent developments in this field : - The Research Committee of AUTh - Singular International SA - Intracom SA - Microsoft SA 1. Non-linear Phenomena in Semiconductors and Semiconductor Devices 2. Non-linear Phenomena in Laser-Systems 3. Non-linear Dynamics based Communications 4. Patterning in Complex Media 5. Low-Dimensional Systems 6. Applied Chaos Theory 7. Biological Systems The participants are kindly requested to proceed with their payments and hotel reservations
Intermag Europe 2002
An annual conference organised by the IEEE magnetics society on fundamental and applied magnetism. In 2002 the conference will be held in Amsterdam, The Netherlands.
Intermag_2002
The Calorimetry Conference
Calcon2002: the 57th annual Calorimetry Conference. This year's symposia include: biothermodynamics, thermodynamic databases, nanotechnology, pharmaceutical research, and solution thermodynamics. Held August 11-16, 2002 at Rutgers University, NJ, USA.
CalCon 2005 The following material originates with an organization not subject to the Official Languages Act and is available on this site in the language in which it was written. Les informations suivantes proviennent d'un organisme qui n'est pas assujetti la Loi sur les langues officielles et elles sont mises votre disposition dans la langue d'origine seulement. Home Officers and Board of Directors Symposia Huffman Honorary Symposium Registration Abstract Submission Call for Award Nominations Schedule Program Accomodations Travel Social Program Welcome to CalCon 2005 The 60th Calorimetry Conference hosted by the National Institute of Standards and Technology U.S. Department of Commerce Gaithersburg, MD, USA June 26 July 1 2005 The deadline for abstracts submission is extended to May 17. In the tradition of the Calorimetry Conference, the decennial anniversary of the Calorimetry Conference will be held at the National Institute of Standards and Technology in Gaithersburg, Maryland. Topics of research that cover thermodynamics and calorimetry measurements will be presented at the conference. The conference will take place in the Conference Facilities in the Administration Building of the National Institute of Standards and Technology from June 26 to July 1, 2005. For information on the scientific program please contact: Mirek Gruszkiewicz, Program Chair Oak Ridge National Laboratory Chemical Sciences Division P.O. Box 2008, MS 6110 Oak Ridge, TN 37831-6110 gruszkiewicz@ornl.gov (865) 574-4965 fax: (865) 574-4961 For information on Conference venue and accommodations please contact: Professor Fred Schwarz, Local Arrangements Chair Center for Advanced Research in Biotechnology National Institute of Standards and Technology 9600 Gudelsky Drive Rockville, MD 20850 frederick.schwarz@nist.gov (301) 738-6219 fax: (301) 738-6255 photo used with permission; thanks to the Washington, DC Convention Tourism corporation
Third European Quantum Information Processing and Communication Workshop
The purpose of the workshop is to promote interaction across the broad subject area of Quantum Information Processing and Communication. Trinity College, Dublin, Ireland; 15--18 September 2002.
QIPC Workshop Agenda REGISTRATION DEADLINE: Monday 5th August 2002 LIMITED SPACES AVAILABLE (Places will be allocated on a first come first served basis) The 2002 Quantum Information Processing Communication Workshop will be held at The University of Dublin, Trinity College, Ireland The purpose of the workshop is to promote interaction across the broad subject area of QIPC. Session chairs will begin with a short introductory review of their session's area to put in context the session contributions within the wider arena of QIPC. Talks from invited speakers will be accessible to a wide multi-disciplinary QIPC audience, which will include both theorists and experimentalists. Workshop Contact: Sarah Hulbert - QUIPROCONE Administrator Email: Sarah_Hulbert@hp.com Telephone: +44 117 312 8079 Fax: +44 117 312 9870 Please note that there will be no financial aid for participants other than speakers. This has taken the form of a ZERO WORKSHOP FEE. Workshop Planning Committee: J. Twamley (Workshop Chair), T. Spiller (QUIPROCONE), P. Malinverni (EC), S. Hulbert (QUIPROCONE administrator), P. Knight, F. De Martini, P. Lindelof, N. Luetkenhaus, H.Roehrig, M. Roetteler, T. Felbinger, , R. Dum (EC), G. Kalbe (EC).
European Conference on Organic Electronics and Related Phenomena 2003
European Conference on Organic Electronics and Related Phenomena 2003 ECOER
Microresonators as building blocks for VLSI photonics - Summer school - Erice (Italy) October 2003
The scope of the course is to provide state of the art information in the field of advanced devices for photonics and optical communication. The course focuses on the theory and application of optical microresonators for wavelength selection and routing, for switching and for high-speed modulation.
Erice summer School - 39th Course - Microresonators as building blocks for VLSI Photonics Ettore Majorana Centre for Scientific Culture International School of Quantum Electronics 39th Course co-sponsored and organized by Universit degli Studi di Roma "La Sapienza" and Dipartimento di Energetica MICRORESONATORS AS BUILDING BLOCKS FOR VLSI PHOTONICS Erice, Sicily, Italy 18th-25th October 2003 co-sponsored by Italian Society of Optics and Photonics (SIOF) European Commission European Research Office (ERO) Directors of the Course Mario Bertolotti Alfred Driessen Francesco Michelotti Universit di Roma "La Sapienza" University of Twente Universit di Roma "La Sapienza" Lecturers R.Baets, Ghent University - IMEC, Belgium N.Baker, Nortel Networks, London, UK M.Bertolotti, Universit degli studi di Roma "La Sapienza", Italy J.Ctyroky, Academy of Sciences, Prague, Czech Republic L.Dalton, Washington University , Seattle, WA, USA R.De La Rue, University of Glasgow, UK M.Diemeer, MESA+ Research Institute, Twente, The Netherlands A.Driessen, MESA+ Research Institute, Twente, The Netherlands A.Fiore, Ecole Polytechnique Federale de Lausanne, Lausanne, Switzerland R.Grover, University of Maryland, College Park, MD, USA P.Guenter, ETH Zurich, Switzerland M.Hammer, University of Twente, The Netherlands P.Mataloni, Universit di Roma "La Sapienza", Italy F.Michelotti, Universit degli studi di Roma "La Sapienza"Italy J.Mueller, Technical University of Hamburg, Harburg, Germany A.Rousseau, Ecole Nationale Superieure de Chimie de Montpellier, France Ch.Wachter,Fraunhofer-Institut Angewandte Optik, Jena, Germany J.Zyss, Ecole Normale Superiure de Cachan, France Topics Analytical approach to the description of ring microresonator devices Characterisation of organic materials for integrated devices Classical theory of resonating structures Electronic and optical confinement in semiconductors Fabrication tolerances and performance of microresonator based devices Inorganic materials for active microresonator based integrated devices Introduction to PBG structures: theory and bulk effects Microresonators as building blocks for VLSI photonics Nanophotonics in silicon on insulator: the potential and the challenges Numerical approaches to microresonator devices Organic active ring microresonator based devices and new device concepts Polymers and organic crystals for passive microresonator based integrated devices Quantum dots and microcavities Semiconductor micro-ring resonators for signal processing Synthesis of organic materials for integrated devices Theory and application of entangled pairs generation 2-D Polymer microcavity lasers: from whispering gallery modes to chaos Programme Transparencies of the Lectures Abstracts of the Lectures The Cultural Centre Short Seminars Useful Information Poster Sessions Transportation Conference Proceedings Accomodation and Facilities Registration fee Social Events Deadline for Applications More Info
High Energy Density Plasma Physics-2003
High Energy Density Plasma Physics 2003. Conference Details, General Info on the FSRC, Info on the FSRC Publications, and Tourist Info, California, 10-12 Feb 2003
FRONTIER SCIENCE RESEARCH CONFERENCE--F S R C-HIGH-ENERGY-DENSITY-PLASMA-PHYSICS-2003
2nd Russian Conference on Gallium, Aluminum and Indium Nitrides
2nd Russian conference "Gallium, Aluminum and Indium Nitrides". Ioffe Institute of RAS, St Petersburg, February 3-4, 2003
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Photonics-2004: 7th International Conference on Optoelectronics, Fiber Optics and Photonics
"Photonics" is a series of international conferences organized biennially within India. Cochin, 8-11 Dec 2004
| Photonics2004 | Photonics 2004 Redirect | 08-11 December 2004, Kochi (Cochin), India This is an auto redirect page!! You will be automatically linked to Photonics 2004 home page in 5 seconds. Sorry for the inconvenience caused. If not working, please try http: www.photonics2004.com Web Management Team - International School of Photonics-
2nd East European Symposium on statistical physics and biological information
organized by East European Biology Society will be held in Bratislava, Slovakia within June 19th-23rd 2004. Limited number of participiants.
EEBSOC Conference 2004 POSTPONED! This event will be postponed to summer 2005 due to organizational issues. We apologize for any inconvenience it might have caused. New date will be announced soon Welcome! After succesful beta symposium in 2002 we are back with another challenge. Main aim of 2nd East European Sympozium in Bratislava, Slovakia in declared areas is to bring together physicists, biologists, and also matematicians and chemists who are looking for challenges in the biological sciences in the post-genomic era. Today is November 17, 2005 Web site partially sponsored by:
ElectroWeak Interactions and Unified Theories 2001
The 36th Rencontres de Moriond session devoted to Electroweak Interactions and unified Theories will be held in Les Arcs 1800.
ElectroWeak Interactions and Unified Theories, 2001. ElectroWeak Interactions and Unified Theories, 2001 Clickez sur le drapeau pour avoir la version Francaise The XXXVIth Rencontres de Moriond session devoted to ELECTROWEAK INTERACTIONS AND UNIFIED THEORIES will be held in Les Arcs 1800 from Saturday, March 10th to Saturday, March 17th, 2001. Les Arcs 1800 is a pleasant winter sport resort located in the French Alpes, at 1800 m alt., about 120 km from Geneva and 12 km from Bourg-Saint-Maurice. The nearest railway station is Bourg-Saint-Maurice, trains (TGV) from Paris to Bourg-Saint- Maurice are quite convenient. The nearest international airport is Geneva. Click here to locate Bourg-Saint-Maurice in Europe, here to locate Bourg-Saint-Maurice in the french Alp mountains, and here for a local map. PROCEEDINGS (preliminary) TRANSPARENCIES PREPARING CONTRIBUTIONS TO THE PROCEEDINGS (DEAD LINE: Mai 15th) Manuscript for the proceedings of the Conference : To be sent before May 15th, 2001 : 1) hardcopy to Claude Barthlemy Rencontres de Moriond LPT - Bt. 210 91405 Orsay cedex France 2) electronic form to Los Alamos preprint repository. Instructions and help for submition here . Remember to inform us of the submission number on Los Alamos Typing instructions : Instructions (in english) (fichier word) Instructions (in english) (fichier PDF) LaTex instructions(PDF) Template LaTex file Template LaTex file Conference Program First Bulletin (2001 session) Second Bulletin Program Committee Conference secretariat Registration Form (2001 session) Application for an European grant (2001 session) Moriond EW 2000 page Others "Rencontres de Moriond"
EPS2003 Meeting in Aachen
The International Europhysics Conference on High Energy Physics, EPS 2003, will be held in Aachen, Germany. The conference will consist of poster sessions, parallel sessions and plenary sessions. Germany, 17-2 July 2003
EPS 2003 Meeting in Aachen European Physical Society International Europhysics Conference onHighEnergyPhysics EPS (July 17th-23rd 2003) in Aachen,Germany LINKS: Home News Deadlines Bulletin Schedule Programme Talks Transperencies Registration List Participants Reserve a Hotel Social Events Tickets Proceedings Travel Advice Maps Karman Auditorium About Aachen Technical Conference Coordinators Local Contact Persons Additional Links Photos Submit Abstract Submit Papers List Abstracts List Papers HEP2003 Europhysics Conference in Aachen, Germany Location: RWTH - Aachen Karman Forum Eilfschornsteinstr. 15 D-52062 Aachen, Germany The EPS 2003 conference papers are now available at Topical Volume in The European Physical JournalC . The Pentaquark Talk is now available. This is the first HEP conference without using national quotas. Webmaster: Achim Burdziak Last modified: Thu May 27 12:28:30 2004 Legal Disclaimer
The Society of Rheology 74th Annual Meeting
Minneapolis, Minnesota, USA; 13--17 October 2002. On-line registration and submission process.
The Society of Rheology: 74th Annual Meeting, Oct 2002 74th Annual Meeting October 13 - 17, 2002 Minneapolis, Minnesota General Information Meeting Organizers Technical Program Organizers Short Course Registration and Lodging Exhibitor Information Submit and Update Abstracts Browse Program and Abstracts Program Updates Book Download Social Program and Sponsors Student-Member Travel Grants Student Poster Competition Guidelines Please e-mail suggestions and comments to albertco@umche.maine.edu . Updated 25 January 2004
Bianisotropics 2002
9th International conference on Electromagnetics of Complex Media. Marrakech, Morocco; 8--11 May 2002.
bianisotropics 2002 conference
EPS-12
The 12th General Conference of the European Physical Society, "Trends in Physics". Budapest, Hungary; 26--30 August 2002.
EPS-12: Trends in Physics
ETOPIM 6
Sixth International Conference on the Electrical Transport and Optical Properties of Inhomogeneous Media. Geophysicists, physicists, mathematicians, and electrical engineers will participate. Snowbird, Utah, USA; 15--19 July 2002.
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15th Workshops in Particle Physics, Italy
The Rencontres will bring together about 120 active experimentalists and theorists to review the status and the future prospects in elementary particle physics.
new 2001 La Thuile , Aosta Valley March 4-10, 2001 This is the fifteenth of Workshops in Particle Physics being held yearly at the Planibel Hotel of La Thuile, Aosta Valley. La Thuile is a beautiful mountain village located 1450 m a.sl., about 40 km north of the city of Aosta, on the road to the Mont Blanc. The hotel is at the bottom of a vast skiing area connected with the French ski resort La Rosiere and it is an outstanding complex for winter sports and congresses. The Rencontres will bring together about 120 active experimentalists and theorists to review the status and the future prospects in elementary particle physics. As a special event this year, a session will be devoted to celebrate the 65th birthday of J. Tran Thanh Van, founder of the Rencontres de Moriond which were the first in a series of winter conferences in Particle Physics. CONFERENCE ORGANIZERS Giorgio Bellettini Giorgio Chiarelli Dip. di Fisica, Univ. di Pisa I.N.F.N., Sezione di Pisa Mario Greco Dip. di Fisica "Edoardo Amaldi" Universita' di Roma III I.N.F.N., Sezione di Roma III Deadline to submit written contribution: May 30, 2001 Talks Online: Sessions Author Index Bulletin 1 Bulletin 2 Programme Proceedings: Instructions to Authors ( postscript , tex , style ) For more information contact us at: La Thuile Secretariat Last Change on March 21, 2001 by Giorgio Chiarelli
34th Annual Modern Infrared Detectors and Systems Application 5-day short course in Santa Barbara
For 34 years the University of California in Santa Barbara has hosted an internationally recognized symposium on the newest advances in infrared thermography. June 16 - 20, 2003
Modern Infrared Detectors | UC Santa Barbara Extension Enroll Now | Information Request | Site Map | Contact Us University of California, Santa Barbara Course Catalog Certificate Programs Special Programs International Programs Concurrent Enrollment Customized Training Student Services About Us 39th Annual Modern Infrared Detectors and System Applications June 19 - 23, 2006 - A Five-Day Short Course with Hands-On Lab Activities at the University of California, Santa Barbara Infrared (IR) applications have increased dramatically over the last decade as arrays of infrared detectors have increased in size, performance, and availability. For over 30 years, this internationally renowned course covering the field of infrared technology has served as an ideal primer for individuals wishing an intensive exposure to current thinking as well as an update for those seeking to review and refresh their knowledge. From a review of basic infrared detection methods, to an introduction to advanced focal planes and systems, instruction is geared to allow participants to immediately apply what they have learned. The course features infrared devices for military and commercial useincluding both cooled and uncooled detectors. Course Approach Since learning is enhanced by hands-on experience, this course offers a rare balance between classroom learning and laboratory experiments with infrared devices. There are three laboratory sessions that coordinate with lecture discussion sessions: infrared detectors, focal plane electronics, and infrared systems. After an introduction to infrared radiation, device evaluation, and detectors, participants put theory into practice in a unique infrared laboratory where they measure fundamental properties of infrared detectors. Focal plane electronics are likewise introduced in the classroom before the lab experience of building simple circuits. Finally, the theory of infrared systems is coupled with a hands-on demonstration of modern infrared cameras representing a broad spectrum of commercial systems. TOP Who Attends In recent years, participants have included: Government personnel active in using or developing infrared devices Managers of IR projects Users and potential users of IR equipment Technical personnel broadening their knowledge of IR Anyone getting started in the field of Infrared Course Satisfaction Here is how the participants rated this course in the past: 97% rated the program good or excellent 94% believe this course will be useful in their current position 94% would recommend this course to co-workers and colleagues TOP Course Organization Each day of the five-day course introduces new concepts while reviewing and reinforcing previous material. The first day covers the basics of infrared, from terminology to phenomenology. The second day is Detectors and leads off with a morning lecture that describes how infrared radiation is converted into electronic signals and includes the latest developments in the field. The afternoon is a hands-on laboratory session that demonstrates the detector concepts. The third day, Focal Plane Electronics, covers readout circuits and multiplexers. A combination of lecture and hands-on laboratory is again used to connect theory with practice. Day four covers testing of infrared focal planes and systems with a special discussion on remote sensing. The lab activity on this day is test driving thermal imaging systems and other infrared equipment. Local infrared detector manufacturers offer tours of their facilities as an off-campus activity. The fifth and last day is Systems Day when the components discussed during the previous days are brought together into infrared systems and sensors. TOP UCSB Extension | International Programs | Office of Academic Programs | Off Campus Studies | UCSB Ph: 805.893.4200Email: main@els.ucsb.edu This is official University of California, Santa Barbara information. Please read the Policies and Procedures regarding this server. webmaster@els.ucsb.edu .
The XXIII Conference on Solid State Science (ESSSA) Egypt
The XXIII Conference on Solid State Science Workshop on Physics and Application Potential of Functional Ceramic Thin Films Sharm Al-Shiekh - Sinai - Egypt 28 Sept. - 2 Oct. 2002
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Spanish Relativity Meeting ERE 2001
This is the site for the Spanish Relativity Meeting 2001 which will be held in Madrid at the Polytechnical University from 18-21 September 2001. The main topic will be Relativistic Astrophysics.
E.R.E. 2001
NanoteC2001 Conference
The third international conference with the aim of promoting carbon science in the nano scale as, for example, fullerenes, nanotubes, nanowires, and sp3 forms. Brighton, Sussex.
NanoteC2005 The British Carbon Group presents NanoteC'05 Nanotechnology in Carbon and Related Materials 31st August - 3rd September 2005 University of Sussex at Brighton, U.K. Starting and finishing at lunchtime This is the seventh international conference sponsored by the British Carbon Group with the aim of promoting carbon science in the nano scale: fullerenes, nanotubes, nanowires, sp3 forms, etc. Enter main site To see lecture programmes, speaker lists etc of previous years, you can visit: NanoteC'01 , NanoteC'02 NanoteC'03 , and NanoteC'04 .
Lake Louise Winter Institute 2001: Fundamental Interactions
The purpose of the Lake Louise Winter Institute is to explore recent trends in physics in an informal setting. The Winter Institute has been in existence since 1986.
Lake Louise Winter Institute, University of Alberta 2006 Lake Louise Winter Institute 2006 17th-23rd February 2006 Alberta, Canada Main page Registration and Program How to get there Accommodation Proceedings Invited Speakers David E. Kaplan, John Hopkins University, "Physics Beyond the Standard model" H. J. Frisch, U Chicago, "Collider Physics Experiments" J. Harris, Yale, "Experimental Evidence on the Quark-Gluon Plasma at RHIC" J.Kluge, U Darmstadt, "Fundamental Experiments at Low Energy" S. Oser, U.B.C., "Neutrino Physics:Present and Future" M. Pospelov, U Victoria, "Low Energy Tests of Standard Model" The Lake Louise Winter Institute is an annual event organized by the University of Alberta to explore recent trends in subatomic physics. The institute consists of series of pedagogical lectures given by invited speakers as well as participant talks covering the latest experimental and theoretical results in the field. The institute is held in the Chateau Lake Louise , a four star hotel in the heart of the Canadian Rockies. Lectures are held in the morning and evening to allow the afternoon free for hiking, sighseeing, skiing and other activities. Packed lunches are available for those wishing to spend the entire afternoon out. Accommodation is available in the Chateau Lake Louise at a cost of $302.76 day for single occupancy or $213.72 day for double occupancy which includes all meals and taxes. A subsidy of $60 day is available for students attending the conference. In addition there is a conference fee of $350 for non-students and $150 for students ($450 and $200 respectively after 15th January 2006). Registration, Abstract Submission, Talk Download and Program Details Details on how to book accomodation Details on how to get to the conference Proceedings style files and instructions The Lake Louise Winter Institute is sponsored in part by the Institute of Particle Physics, the TRIUMF Laboratory, the University of Alberta and the Theoretical Physics Institute at the University of Alberta. This page maintained by: RWM .
Frontiers In Contemporary Physics - II
Topics : Search for the Quark-Gluon Plasma CP Violation and B Decays Cosmology: Cosmological Constant, CMB Spectrum, Early Universe Field Theory Developments in Neutrino Physics Highest Energy Cosmic Rays Tests of the Standard Model, and Beyond, With High Energy or High Statistics Data Prospects for Future Accelerator and Non Accelerator Programs
Johns Sheldon Webster Elementary Particle Physics JSWHEP Menu Home What Is EP Physics? Group Members Recent Publications FOCUS Activities CI Development Related Links CMS Home US CMS Home FOCUS Home Register Article ACCRE RTES Open Science Grid iVDGL Grid Skim Portal Physics Department Vanderbilt NSF JSWHEP Internal Dark Matter? Extra Dimensions? This elementary particle physics (EPP) research group is investigating fundamental questions about the structure and behaviour of the universe. Our work provides information about the weak and strong forces (counterparts to gravity and electromagnetism) and offers sensitive probes for new fundamental phenomena. There is growing evidence that discoveries in the next decade may bring to light new physical phenomena that will shed light on important mysteries. For example, the matter asymmetry of the universe tells us two things: there must be large sources of CP violation we have not yet found and there must be baryon number violating processes, which are also not yet observed. Also, the amount of dark matter in the universe is about ten times larger than the amount of baryonic matter, but no dark matter candidates have been observed. An unknown force, often called ``dark energy,'' is forcing the universe apart. These are only three examples. CMS and FOCUS Experiments in this field are long lived (5-15 years). We are major contributors to two: the FOCUS experiment at the Fermi National Accelerator Laboratory (Fermilab), near Chicago, Illinois, and the CMS experiment at CERN in Geneva, Switzerland. Cutting Edge Technology Particle physics experiments present significant technical challenges, which require us to collaborate with colleagues in other disciplines to develop new cutting-edge technologies. Our activities in this area are described here . JSWHEP in the Vanderbilt Register The activities of our group have recently been described in the Vanderbilt Register. This research is supported by the National Science Foundation under Grants SCI-0121658, PHY-0243614 and PHY-0456724.
9th Vienna Conference on Instrumentation
Topics : Instrumentation in High Energy and Nuclear Physics, Synchrotron Radiation and Neutron Experiments, Astrophysics, Biology, Medicine; associated Electronics Satellite Workshop on Applications, February 24, 2001 (W. Bartl, B. Sitar)
Vienna Conference on Instrumentation Registration Accommodation for all participants except those of the Academy Exchange Program only for participants by the Academy Exchange Program Submissionof Abstract Beamer File Paper HOME CONFERENCE PROGRAM (with presentation and draft paper files!) PROGRAM booklet (pdf) BOOK OF ABSTRACTS ECTS credits for Students Circular Venue (map) Social Events Information for companies VCI Talks 2001 VIENNA Culture Fun Vienna Guide Public Transport LIST OF PARTICIPANTS 10th Vienna Conference on Instrumentation Vienna, Austria - February 16 - 21, 2004 Dear colleagues, The first Wire Chamber Conference (WCC) took place in January 1978. From 1980 to 1998 it was hosted every three years. Soon the Wire Chamber Conference expanded thematically to the field of alternative technologies, which is accounted for in the change in 2001 of the title to Vienna Conference on Instrumentation (VCI). Yours, Meinhard Regler (Chairman) Click here to view the poster of VCI 2004 1st Vienna Wire Chamber Conference, February 1978 (click to enlarge) Chairman of the OC: Meinhard Regler Last update 20 01 2004 mailto webmaster: wimmer@hephy.oeaw.ac.at
Cosmion-2001
21 May of 2001 we commemorate the 80th Anniversary of Andrei Dmitrievich Sakharov. The foundation of CosmoParticle Physics, with which the progress in our fundamental knowledge is related, stands among the most important results of his scientific activity.
Cosmion-2001 V International Conference on COSMOPARTICLE PHYSICS (Cosmion-2001) Dedicated to 80-th Anniversary of Andrei D. Sakharov (21-30 May 2001, Moscow-St.Peterburg, Russia) Center for Cosmoparticle Physics "Cosmion", Miusskaya Pl. 4, 125047, Moscow, Russia Tel. (7)-095-972 37 82; Fax. (7)-095-973 03 60; E-mail: mkhlopov@orc.ru , after March 27, 2001: khlopov@ihes.fr . 1-st Circular (last update March 26, 2001)fg Dear Colleagues, 21 May of 2001 we commemorate the 80th Anniversary of Andrei Dmitrievich Sakharov. The foundation of CosmoParticle Physics, with which the progress in our fundamental knowledge is related, stands among the most important results of his scientific activity. Many significant principles of this science were formulated first in the works of Zeldovich and Sakharov. Under Sakharov's charge the ideas of the Programme of Cosmoparticle research, initiated with active support of Zeldovich, were put forward. The last scientific work of A.Sakharov "On CosmoParticle Physics", (Vestnik Acad. Nauk SSSR, 1989, N-4, 39) may be viewed as his Scientific Testament in this field. The development of cosmoparticle physics was widely discussed at the now being traditional International Conferences on CosmoParticle Physics "Cosmion-94", "Cosmion-96", "Cosmion-97" and "Cosmion-99" held in Moscow. The 5th International Conference on CosmoParticle Physics (Cosmion-2001) dedicated to 80th Anniversary of Andrei D. Sakharov is to be held in Moscow and St.Peterburg during May 21-30, 2001. This meeting will discuss the present stage of studies in CosmoParticle Physics in a number of Scientific Meetings and Workshops covering various aspects of this actively developing scientific area. The main topics of the 5th International Conference on CosmoParticle Physics (Cosmion-2001) include fundamental relationship between macro- and micro-worlds, quantum gravity and quantum cosmology, relativistic astrophysics, physics of inflation and the early Universe, baryogenesis, cosmological nucleosynthesis, new particles and symmetries in the Universe, the physics of dark matter and of a cosmological term, large scale structure of the Universe and the cosmic background radiation (its spectrum, anisotropy, Sakharov oscillations etc.), cosmoarcheology and cosmochronology, high energy physics in astrophysics, exotic and compact objects, etc. It is the tradition of the Cosmion conferences to consider these topics in their fundamental unity, following the basic strategy of CosmoParticle physics to elaborate the system of complex cross-disciplinary links between foundations of micro- and macro-worlds. We hope that participants and invited speakers will present new ideas and results of National studies and International cooperation in the field of CosmoParticle Physics, making the first steps on the the way to fundamental physics of XXIth Century and III Millenium. The official language of the Conference will be English. The programme includes St-Peterburg Sessions (28-30 May). The Conference Proceedings will be published as the Supplement to "Gravitation and Cosmology". Some limited financial support will be available. On behalf of the Organizing Committee. Yours sincerely Prof. Maxim Yu. Khlopov Preliminary Scientific Programm National Scientific Organizing Committee International Advisory Committee Local Organizing Committee Russian Visa Application Fee, Accomodation and Financial Support Location in Moscow
2001 A Spacetime Odyssey
Two theories revolutionized the 20th century view of space and time: Einstein's General Theory of Relativity and Quantum Mechanics. Their union has spawned elementary particle theories with extra spacetime dimensions, the inflationary model of big-bang cosmology, dark matter in the universe, radiation from quantum black holes and the fuzzy spacetime geometry of superstrings and M-theory.
2001: A Spacetime Odyssey Conference Home Scientific Program Schedule of Talks Students Registration Travel Information Accomodations Arts MCTP Inaugural Conference of the Michigan Center for Theoretical Physics May 21-25, 2001 University of Michigan, Ann Arbor Two theories revolutionized the 20th century view of space and time: Einstein's General Theory of Relativity and Quantum Mechanics. Their union has spawned elementary particle theories with extra spacetime dimensions, the inflationary model of big-bang cosmology, dark matter in the universe, radiation from quantum black holes and the fuzzy spacetime geometry of superstrings and M-theory. These developments, derived from the 19th century mathematics of Riemannian geometry and Lie groups, have in their turn inspired new directions in the pure mathematics of topology and knot theory. In view of the mission of the Michigan Center for Theoretical Physics to provide a venue for interdisciplinary studies in the mathematical sciences, this Inaugural Conference will bring together Astronomers, Cosmologists, Particle Physicists and Mathematicians to share their different perspectives on the 21st century view of spacetime. Invited speakers include: John Bahcall (IAS) Jacob Bekenstein (Jerusalem) Stanley Deser (Brandeis) Paul Frampton (UNC, Chapel Hill) Wendy Freedman (Carnegie Observatories) Mary K. Gaillard (Berkeley) Sheldon Glashow (Boston) Alan Guth (MIT) James Hartle (UC Santa Barbara) Peter Higgs (Edinburgh) Arthur Jaffe (Harvard) Robert Kirshner (Harvard-Smithsonian Center for Astrophysics) Andrei Linde (Stanford) Lev Okun (ITEP) Alexander Polyakov (Princeton) Helen Quinn (SLAC) John Schwarz (Caltech) Joseph Silk (Oxford) Isadore Singer (MIT) Paul Steinhardt (Princeton) Michael Turner (Chicago) Martinus Veltman (Michigan) Shing-Tung Yau (Harvard) Bruno Zumino (Berkeley) Organizing Committee Fred Adams Ratindranath Akhoury Dan Burns Michael Duff Katherine Freese Gordon Kane James T. Liu Conference Secretaries Tina Wells Angie Milliken Scientific program Public Lecture by prof. Veltman, 1999 Nobel Prize for Physics - Thursday, May 24, 8:00pm Conference Banquet - in the Michigan League, Wednesday, May 23, 6:30pm-10:30pm. Schedule of Talks - including links to the online proceedings Guide to the Conference Site Conference Proceedings Press coverage of 2001: A Spacetime Odyssey Financial Assistance for Students Registration Information Online Registration Travel Information (including information on discounted airfare from Northwest Airlines) Accommodations Spacetime Art For further information contact Angie Milliken ( amillik@umich.edu ) Conference Home Scientific Program Schedule of Talks Students Registration Travel Information Accomodations Arts MCTP Webmaster
4th Sigrav Graduate School on Contemporary Relativity and Gravitational Physics
The SIGRAV Graduate School in Contemporary Relativity and Gravitational Physics is held annually at the Centre for Scientific Culture "Alessandro Volta", Villa Olmo, Como. It is primarily addressed to PhD students and young researchers in Physics and Mathematics who are interested in general relativity, astrophysics, experimental gravity and the quantum theories of gravitation.
GEOMETRY AND PHYSICS OF BRANES 4th SIGRAV GRADUATE SCHOOL ON CONTEMPORARY RELATIVITY AND GRAVITATIONAL PHYSICS and 2001 SCHOOL ON ALGEBRAIC GEOMETRY AND PHYSICS (SAGP2001) VILLA OLMO (COMO), 7-11 MAY 2001 GEOMETRY AND PHYSICS OF BRANES Supported by: SIGRAV (Italian Society for Gravitational Physics), National Research Project "Singularities, Integrability, Symmetries", SISSA (Trieste), University of Insubria (Como-Varese), Departmente of Chemistry, Physics and Mathematics of the University of Insubria at Como, Physics Department of the University of Milan, Physics Department of the University of Turin, Physics Department of the University of Rome "La Sapienza", Physics Department of the University of Rome "Tor Vergata", Physics Department of the University of Pavia. Download the first circular (Latex file) See the programme (PDF) The SIGRAV Graduate School in Contemporary Relativity and Gravitational Physics is held annually at the Centre for Scientific Culture "Alessandro Volta", Villa Olmo, Como. It is primarily addressed to PhD students and young researchers in Physics and Mathematics who are interested in general relativity, astrophysics, experimental gravity and the quantum theories of gravitation. In 2001 the School will be a joint venture with the School on Algebraic Geometry and Physics organized by the Mathematical Physics Group of the International School for Advanced Studies (SISSA) in Trieste. The School on Algebraic Geometry and Physics is part of a series of events that SISSA is organizing since 1996 aiming at fostering the interaction between mathematicians working in pure algebraic geometry and researchers who are interested in applications of algebraic geometry to physics, especially string theory and integrable systems. Information on the "Algebraic Geometry and Physics'' series is available from the web page http: www.sissa.it fm workshops.html, while information on the SIGRAV schools may be obtained from the page http: www.sigrav.unige.it como. Programme. The lectures will start in the morning of May 7 and will end in the afternoon of May 11. The theme of the school will be GEOMETRY AND PHYSICS OF BRANES. Lecturers: Kenji Fukaya (Kyoto), Deformation theory, homotopical algebra, Floer homology and mirror symmetry Cesar Gomez (Madrid), Geometry of tachyons in string theory Antonella Grassi (Philadelphia), Large N dualities and transitions in geometry Alberto Lerda (Piemonte Orientale), Introduction to branes Yassen Stanev (Rome Tor Vergata), Two-dimensional conformal field theory on open and unoriented surfaces. In addition there will by a lecture by Masa-Hiko Saito (Kyoto) and a few shorter contributions. Accommodation. Participants will be accommodated in hotels nearby Villa Olmo and will be requested to pay an all-inclusive conference fee, also covering bed and breakfast, of ITL 900,000 (EURO 465). Those wishing to forgo this possibility are requested to pay a registration fee of ITL 250,000 (EURO 130). Some support to cover local expenses will be available; if you need support please mention that in your application. Please note that no support to cover travel expenses will be available. Participation is limited to 60, and applications will be accepted on a first-come-first-served basis. Registration and accommodation forms may be downloaded from here or may be requested by e-mail at grschool@fis.unico.it. Applications should be sent to this address NOT LATER THAN MARCH 29, 2001, and a copy should be sent to sagp2001@fm.sissa.it. For information please write to sagp2001@fm.sissa.it, or to moschell@fis.unico.it, or contact directly the Organizing Secretariat at Centro"A.Volta'' : tel. +39 031 579812 13, fax +39 031 573395. Advisory Committee: E. Arbarello (Rome La Sapienza), R. Dijkgraaf (Amsterdam), B. Dubrovin (SISSA Trieste), Yu. Manin (MPI Bonn), M.S. Narasimhan (SISSA Trieste), C. Viallet (LPTHE Paris). Scientific and Organizing Committee: U. Bruzzo (SISSA, co-chairman), M. Carfora (Pavia), P. Fre' (Turin), V. Gorini (Como, co-chairman), A. Lerda, (Piemonte Orientale), U. Moschella (Como), A. Sagnotti (Rome Tor Vergata). SIGRAV Council: U. Bruzzo (SISSA), R. Cianci (Genoa), I. Ciufolini (Lecce), E. Coccia (Rome Tor Vergata), M. Colpi (Milan Bicocca), V. Ferrari (Rome La Sapienza), M. Francaviglia (Turin), P. Fre' (Turin), A. Giazotto (Pisa), V. Gorini (Como), L. Lusanna (Florence), A. Masiero (SISSA), U. Moschella (Como), T. Regge (Turin), A. Sagnotti (Rome Tor Vergata). SAGP2001 is the fifth event of a series of workshops and schools on algebraic geometry and physics. The previous events took place in 1996 in Trieste (WAGP96), in 1997 in Medina del Campo, Spain (WAGP97) in 1999 in Marseille Luminy (SAGP99), and in the year 2000 in Trieste again (WAGP2000). Information about these activities may be gathered from the web links here under. WAGP96 SISSA Home Page WAGP97 WAGP2000 SAGP99 Updated on 2 Jan 2001 (ub)
5th Topical Workshop at the Gran Sasso Laboratory
The last round of solar neutrino experiments has not obtained a convincing proof ("smoking gun") of the oscillations: Distortion of the boron neutrino spectrum, day night effect or seasonal variation of neutrino flux. The purpose of the workshop is to discuss how such proofs can be found in the future experiments.
5th Topical Workshop at the Gran Sasso Laboratory 5th Topical Workshop at the Gran Sasso Laboratory Solar Neutrinos: Where are the Oscillations? March 12-14, 2001 Organizers: Venya Berezinsky and Francesco Vissani Scientific Secretary: Vincenzo Fantozzi The last round of solar neutrino experiments has not obtained a convincing proof ("smoking gun") of the oscillations: Distortion of the boron neutrino spectrum, day night effect or seasonal variation of neutrino flux. The purpose of the workshop is to discuss how such proofs can be found in the future experiments (Borexino, LENS, Kamland) or data (GNO, SNO, SuperKamiokande). Are neutrino oscillations the only explanation of the solar neutrino and atmospheric neutrino data? What is the status of the exotic solutions? What is the status of sterile neutrino, and why do we need it in the light of the recent SuperKamiokande data? Is the astrophysical solution still alive? We intend to discuss these and other problems. The workshop will include brief presentations and sessions of discussion, each led by a discussion leader. Announcement [ html , ps or pdf ] Program Poster Session List of Participants Travel Instructions
16th Annual Workshop on Nonlinear Astronomy and Physics
The objective of the workshop is to bring together for three days experts from galactic dynamics, solar system dynamics, and applied mathematics to discuss problems and recent progress which has been made in applying the technology of nonlinear dynamics to problems relevant to galactic astronomy and exo-solar planetary systems.
NONLINEAR DYNAMICS IN GALAXIES AND EXO-SOLAR PLANETARY SYSTEMS The Sixteenth Annual Workshop on Nonlinear Astronomy and Physics is scheduled to take place on the University of Florida campus in Gainesville, Florida on Thursday 15 February through Saturday 17 February 2001. The objective of the workshop is to bring together for three days experts from galactic dynamics, solar system dynamics, and applied mathematics to discuss problems and recent progress which has been made in applying the technology of nonlinear dynamics to problems relevant to galactic astronomy and exo-solar planetary systems. The principal focus is on interdisciplinary interactions between astronomers in different areas who are, in many respects, addressing problems that require similar tools and methodologies. We aim typically for a small workshop, with a total of some fifteen to twenty speakers, each giving talks of order 30 - 40 minutes in length, thereby providing an environment conducive for extensive one-on-one exchanges. Our particular hope is to stimulate interactions between individuals in diverse fields addressing problems which, despite obvious differences, share significant commonalities. The workshop is supported in part by the Department of Astronomy, Department of Physics, and College of Liberal Arts and Sciences at the University of Florida. We have also received a modest grant from the National Science Foundation to help support the participation of graduate students and young postdocs from other institutions. Students and or postdocs interested in such support should contact: kandrup@astro.ufl.edu. There will be six regular sessions, two each on Thursday, Friday, and Saturday, in the mornings and afternoons. There will also be an informal reception poster session where students and postdocs can present their work. The following material is extracted from our successful NSF grant proposal: Motivation The objective of the workshop is to bring together for three days selected experts from galactic dynamics, solar system dynamics, and applied mathematics to discuss problems and recent progress which has been made in applying the technology of nonlinear dynamics to problems relevant to galactic astronomy and exo-solar planetary systems. The principal focus is on interdisciplinary interactions between astronomers in different areas who are, in many respects, addressing problems that require similar tools and methodologies. The workshop is funded primarily by the Departments of Astronomy and of Physics, the College of Liberal Arts and Sciences, and the Office of Research, Technology, and Graduate Education at the University of Florida. Introduction Cross-disciplinary research in Astronomy and Physics has become increasingly intense and productive over the past decade. It is evident from numerous examples that developments in one field can proceed more quickly when infomation is made available about parallel developments in other fields. This occurs not only by exchange of methods and techniques but also from conceptual refinement resulting from different perspectives applied to similar problems. One of the most effective means for stimulating such exchanges is to assemble expert representatives from several different fields for discussions of broadly defined topics in which there have been recent developments. The 2001 Florida Workshop in Nonlinear Astronomy and Physics, to be held on 15 - 17 February at the University of Florida, will assemble a collection of theorists from the fields of galactic dyanmics, solar system dynamics, and applied mathematics to discuss various topics involving applications of nonlinear dynamics to problems in galactic astronomy and exo-solar planetary systems. Now is a particularly appropriate time for such a workshop. Over the past several years, observations provided both by the Hubble Space Telescope and ground-based telescopes have provided compelling evidence that many galaxies are genuinely three-dimensional, i.e., neither spherical nor axisymmetric, that they typically have a central density cusp, and that the center of the galaxy often contains a supermassive black hole. However, succesfully modeling cuspy triaxial galaxies requires new techniques which necessitate a more sophisticated understanding of nonlinear dynamics than is the case for axisymmetric systems without a central cusp. The past several years have also witnessed the discovery of numerous planets around other stars as well as increasingly detailed images of protoplanetary discs. Synthesising these observations with an improved understanding of planetesimals and other debris from the formation of our own Solar System could lead to the first clear picture of how planetary systems form and evolve. Until recently, much of the theoretical work in both these areas has been almost completely numerical, with the aim of modeling specific astronomical objects. However, the success of these efforts would suggest that the time has come to assess this work so as to better understand the specific dynamical features which are responsible for what is actually observed. Although protoplanetary systems and galaxies are very different sorts of objects, the dynamical issues that arise exhibit striking similarities. In both cases, one is concerned with resonance phenomena and tidal interactions in a complex phase space associated with a system which is nearly, but not completely, Hamiltonian. The Workshop The main purpose of this workshop, the sixteenth in a series of annual Workshops in Nonlinear Astronomy and Physics held at the University of Florida, is to acquaint the participants with developments in neighbouring areas. Our past experience is that the Florida Workshops are very conducive to such cross-fertilization: in particular, many collaborations have developed from interactions during the first fifteen workshops. The Workshop will focus on four basic themes: New theoretical tools and techniques Some of these are primarily computational, e.g., the development of improved, more efficient integration schemes which, combined with recent advances in hardware, allow one to perform computations that were almost inconceivable a decade ago. In particular, it is now possible to solve both the N-body problem and partial differential equation using symplectic integration schemes similar to those which have been developed by accelerator dynamicists over the past decade. However, the past few years have also seen significant advances in the tools available to dynamicists interested in understanding and quantifying transport phenomena in a complex phase space, including, e.g., spectral techniques and short time Lyapunov exponents Resonance Phenomena Resonance phenomena clearly play a major role in both galaxies and protplanetary systems. In the context of galactic astronomy, it has been recognised recently that resonances can play a crucial role in phenomena as different as the origins of spiral structure and warps in galactic discs; the dynamical evolution of globular clusters and satellite objects in and near our Galaxy; and tidal interactions between different galaxies situated in a dense cluster environment. It also appears likely that resonance overlap will trigger large amounts of chaos in the centers of realistic triaxial galaxies which may preclude the possibility of their achieving a true equilibrium. Resonance overlap clearly accounts for the origin of the Kirkwood gaps in the asteroid belt and is the driving mechanism that results in the transfer of meteorites from the asteroid belt to the Earth. Resonance overlap also has a pivotal role in the orbital evolution of comets in the Kuiper belt, although this is less well understood. Transport Theory in Chaotic Phase Spaces Phase space transport undoubtedly plays an important role in both galaxies and planetary systems. Planetary systems exhibit a systematic secular evolution as planetesimals and other smaller objects drift through a complex phase space. A correct interpretation of the asteroid belt and the Kuiper belt as fossil relics of the early Solar System requires that one account for this evolution, so that one can translate what is currently observed into useful information about what the Solar System was like more than four billion years ago. Our own Solar System is the best example of a well-observed, dynamically evolved disk system and may be our best guide to understanding the dynamical evolution of protoplanetary disks in general. Phase space transport is likely to prove a crucial ingredient in the formation and dissipation of bars and other transitory structures in galaxies, particularly near corotation and the Lindblad resonances and, in cuspy triaxial galaxies, could be associated with systematic changes in shape that can in principle be inferred from the Sloan Digital Sky Survey and other similar projects. Low Level Perturbations Comparatively low amplitude perturbations, often associated with dissipation, can play an important role in the evolution of both galaxies and protoplanetary systems. For example, comparatively weak forces associated with Poynting-Robertson light drag and even the Yarkovsky effect may have had a profound effect on the dynamical evolution of dust and other small bodies in our own Solar System and in other, exo-solar systems. Galaxies situated in a dense cluster are continually subjected to near-random forces and torques associated with neighbouring objects which imply that they are never in a true equilibrium; and, at least for cuspy triaxial galaxies, it is likely that the existence of discrete substructures like globular clusters and giant molecular clouds can have a significant effect. The workshop will explore the themes described above, but the meeting will be defined by the participants and will follow directions generated by their presentations and discussions. Confirmed Speakers Courtlandt Bohn, Fermilab: Chaotic-Mixing Time Scales in Charged-Particle Beams and Galaxies Philip Boyland, University of Florida: How does topology influence Hamiltonian dynamics? Robert Buchler, University of Florida George Contopoulos, University of Athens: Order and Chaos in Self-Consistent Galactic Models Chris Hunter, Florida State University: Spectral analysis of orbits via discrete Fourier transforms Henry Kandrup, University of Florida: Noise, graininess, and phase space diffusion in the N-body problem Richard Lovelace, Cornell University: Hamiltonians for Accretion Disk Modes Poynting Outflows and Jets from Accretion Disks Daniel Pfenniger, Observatoire de Geneve: The highly non-linear dynamics of interstellar matter Renu Malhotra, University of Arizona: Resonance sweeping phenomena in the solar system Andrea Milani, University of Pisa: Stable chaos and diffusion in the asteroid main belt Ji Qiang, Los Alamos National Laboratory: Self-Consistent Modeling of Coulomb Collisions Edward Spiegel, Columbia University: Glen Stewart, University of Colorado: Negative Energy Modes and the Nonlinear Evolution of Planetary Rings ORGANISERS: Henry E. Kandrup: kandrup@astro.ufl.edu Stanley D. Dermott: dermott@astro.ufl.edu J. Robert Buchler: buchler@phys.ufl.edu
Particle Astrophysics Winter School
The main goal of the school is to review major experimental efforts in the particle astrophysics field, their underlying theoretical motivation and implications.
Winter School: 2nd bulletin
MULTIMETOX TEM'2002
International Workshop on microstructural characterisation of oxide films and multilayers by TEM and HREM. Polish Academy of Sciences, Warsaw, Poland; 26--27 September 2002.
TEM MULTIMETOX TEM'2002 Submit registration form (Deadline: 6 September 2002) International Workshop on Microstructural characterisation of oxide films and multilayers by TEM and HREM 26-27 September 2002, Warsaw, Poland Organised by: Institute of Physics of the Polish Academy of Sciences Promoted by European Thematic Network MULTIMETOX Place Institute of Physics of the Polish Academy of Sciences, Al. Lotnikw 32 46, Warsaw, Poland Scope: Overview of actual stage of transmission electron microscopy methods for microstructure characterisation of thin films and heterostructure Presentation of useful computer programs Demonstration of experimental techniques Information on research activities of the Institute of Physics, PAS. Subjects: TEM and HREM measurements of thin layers and heterostructures (lectures and demonstrations), Computer techniques of image interpretation (lectures and practice at computer lab), TEM characterisation of thin layers in comparison with the complementary methods, Preparation of cross-section and planar-view samples (lecture and demonstration). List of invited speakers: Prof. T.Dietl (IP PAS, Poland) Prof. G.Van Tendeloo (RUCA, Belgium) Prof. J.Kossut (IP PAS, Poland) Prof. P.A.Stadelmann (CIME-EPFL, Switzerland) Dr. P.Ruterana (ESCTM-CRISMAT, France) Program Location and Travel Accommodation: Guest house at the Institute of Physics and at a hotel about 5 minutes walk from the Institute. Social events: The sight-seeing tour around Warsaw is planed on Saturday (28th September).
1st International Conference on Physics in Culture
This Conference deals with the development, adaptation and application of solid state physics methods for the study and treatment of cultural materials.
PinC Physics in Culture Welcome to the 1st International Conference on Physics in Culture 1o
Euroconference: Spin and Charge Transport in Nanostructures
A multidisciplinary conference with reviews by leading experts intended for young researchers. Grants available for young researchers from EC and associated states. Braga, Portugal, September 1 to 5, 2003
ISTAS
XXVI ICPIG 2003
XXVI-th International Conference on Phenomena of Ionized Gases. Greifswald, Germany; 15--20 July 2003.
XVI ICPIG Greifswald 2003
Eurocvd 13
International conference on Chemical Vapor Deposition. Glyfada, Greece.
Eurocvd 13 Conference - alt="Your browser understands the APPLET tag but isn't running the applet, for some reason." Your browser is completely ignoring the APPLET tag! Eurocvd 14 Conference You are visitor since 19th April of 2000 Send mail to webm@imel.demokritos.gr with questions or comments about this Web Site.Last modified: April 19, 2000
International Conference on Magnetism ICM 2003
The International Conference on Magnetism (ICM) belongs to a series of Conferences, held triennially under the auspices of the International Union of Pure and Applied Physics (IUPAP), with the purpose of providing a forum to the international magnetism community.
International Conference on Magnetism
The Megagauss Institute
US sponsor of the Megagauss Conferences on high magnetic field science and applications - Information on Megagauss.
Megagauss Institute US Sponsor of the Megagauss Conferences On High Magnetic Field Science and Applications The IEEE Nuclear and Plasma Sciences Society along with The Megagauss Institute hosts the "2006 International Conference on Megagauss Magnetic Field Generation and Related Topics" including "The International Workshop on High Energy Liners and High Energy Density Applications." November 5-10, 2006 Santa Fe, New Mexico USA Dr. Robert Reinovsky, Chair Dr. Peter Turchi, Technical Chair Janet Neff-Shampine, Conference Administrator Click here to download the Megagauss 2006 Poster in Adobe pdf format. Megagauss II 1979 Washington, DC, USA Dr. Peter J. Turchi, Chair Megagauss III 1983 Novosibirsk, Russia Prof. V. Titov , Chair Megagauss IV* 1986 Santa Fe, NM, USA Dr. Max Fowler, Chair Megagauss V* 1989 Novosibirsk, Russia Dr. Genady Shvetsov, Chair Megagauss VI* 1993 Albuquerque, NM, USA Dr. Bill Cowan, Chair Megagauss VII* 1996 Sarov, Russia Dr. Victor Selemir, Chair Megagauss VIII* 1998 Tallahassee, FL, USA Dr. Hans Schneider-Muntau, Chair Megagauss IX* 2002 Moscow - St. Petersburg, Russia Dr. Victor Selemir, Chair Megagauss X** 2004 Berlin, Germany Prof. M. von Ortenberg, Chair * Limited number of Proceedings available. ** Proceedings in preparation. Email Contact: contact@megagauss.org The Megagauss Institute is a not-for-profit scientific and educational activity incorporated in the State of New Mexico.
100 Years of Quantum Theory
A symposium and celebration held in Berlin, Germany in December 2000 celebrating the 100th anniversary of Max Planck's famous lecture on the theory of black body radiation.
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MAMOA Workshop
National Workshop and International Symposium on the Mathematical Aspects of Modern Optics and Its Applications (WS-MAMOA), Physics Department, Bandung Institute of Technology (ITB), Bandung, Indonesia, from 29 January to 9 February, 2001.
MAMOA 2001 National Workshop and International Symposium Mathematical Aspects of Modern Optics Physics Department Institut Teknologi Bandung, Bandung, Indonesia 29 January - 9 February, 2004 Invitation Background Program Committee The Workshop Participants FAQ The International Symposium Fees Registration Procedure Invitation The organizing committee cordially invites you to take part in the National Workshop and International Symposium on the Mathematical Aspects of Modern Optics and Its Applications (WS-MAMOA), which will be held at the Physics Department, Bandung Institute of Technology (ITB), Bandung, Indonesia, from 29 January to 9 February, 2001. Background Modern Optics (MO) including Nonlinear Optics (NLO) is one of the scientific backbones for integrated optics and photonic technology in general, which support among others, the important developments of optical communica-tion as well as optical information processing systems. In an era of increasing demand for higher speed in data communication and pro-cessing, the roles of modern optics devices are becoming more important and even indispens-able. The acquaintance with these technologies, and hence its underlying fundamentals of modern optics, will most certainly benefit the overall performance of a society in the global competition. There are therefore compelling needs for the universities and RD organizations in Indonesia and neighboring regions to make a serious entrance into this particular field of study. It is for the purpose of meeting those needs that this event is organized. Program Committee M.O. Tjia (ITB) E. van Groesen (U. Twente) H.J.W.M. Hoekstra (U. Twente) The Workshop The activity planned for The Workshop consists of intensive lectures and tutorials given by senior scientists from ITB and the University of Twente (U. Twente). The lectures are designed to cater for participants with diverse backgrounds in physics and mathematics. This is followed by independent group projects to be carried out by the participant under the guidance of experienced staffs. This activity will be held over a period of 10 days from 29 1 to 7 2. The Workshop covers the following topics: Basic theory and mathematical tools Wave propagations in uniform structures Orthogonality of waveguide modes Coupled mode theory Scattering matrix theory Examples of applications Numerical methods Unidirectional methods (Finite difference (FD), and Fast Fourier transform (FFT) Beam Propagation Method (BPM)) Pandirectional methods (Time domain BPM, Perfectly matched layer (PML)) Gratings mode solving photonic band gaps Nonlinear Optics 2nd order effects 3rd order effects Participants University students, graduates, graduate students as well as working scientists and engineers interested in modern optics and it applications are all eligible to participate in the Workshop and Symposium. Lecturers, Group Project supervisors and Tutors for the Workshop Prof. Dr. E. van Groesen (U. Twente) Prof. Dr. H.J.W.M Hoekstra (U. Twente) Prof. Dr. T. P. Valkering (U. Twente) Prof. Dr. M.O. Tjia (ITB) Prof. Dr. R.E. Siregar (UNPAD) Dr. F. P Zen (ITB) Dr. A. Soehianie (ITB) Ir. R. Stoffer (U. Twente) Language The official language adopted during the activities is English. The Indonesian language may be used occasionally as considered appropriate. Facilities and Rewards Handouts, necessary tools and rooms for the activities will be provided by the organizers. Lunches and refreshments will also be offered to all participants. Student participants with outstanding performance will be recommended for some research awards to continue their projects or as potential recipients of scholarship for further studies at the University of Twente, the Netherlands. The International Symposium The International Symposium on Modern Optics and Its Application will be held on 8th and 9th February, right after the workshop. Presentation of both invited and contributed papers are expected at the symposium. For the Symposium, topics on various aspects of Modern Optics and its applications are welcome. Submission of Abstract A prospective contributor is expected to submit an abstract of approximately 100-150 words in length, typed single spaced in 12 point Times New Roman. The abstract should be submitted to the Secretariat, before 20 November 2000. Acceptance of Abstract Acceptance of abstract will be informed via e-mail by the organizing committee on the 20th of December 2000 along with detailed instruction on writing format. Authors of accepted abstracts are expected to prepare and submit the full papers to the secretariat on the opening day of the Symposium (8th February). Proceedings of the Symposium will be issued within six months after the event. Papers to be published in the Proceeding are subject to reviews by referees. An order placed for the proceeding during the Symposium requires a prepayment of Rp. 100.000,- per copy. Fees A registration fee will be imposed according to the following rates Rp. 750.000, for participants from universities and research institutes. Rp. 250.000, for students. Rp. 2.000.000, for participants from industries and abroad. The amounts stated above cover the fees for Workshop and Symposium. For those who are interested in The Symposium only, the registration fee will be Rp. 500,000,-. Financial Support Limited funds are available for partial supports of land and sea travels for participants from Indonesian Universities outside Jawa. Application for registration fee discount will also be considered. Registration Procedure How to register - you can register now by email but it only works when using Microsoft Internet Explorer and Outlook Express as your default email application. You may switch your browser to I.E. if your are not using it now, or view the Registration Form , print and copy it and then send it manually, by your email, fax or post. Registration Filled-out registration form should be sent to the Secretariat by mail, e-mail or fax, preferably before the 20th of December 2000. Important dates: Pre-registration before 20 December 2000 will be enjoyed 10% discount. Payment should be transferred to the following account: Darminto Fitrilawati, BNI Bank, ITB Branch Office, Acc. No.: 236.783 018 429. 901 On Site Registration : 08.00-09.00 AM Western Indonesia Time, Monday, 29 January 2001 for Workshop, and the same time on Thursday, 8 February 2004 for the Symposium. Created 7 8 04
SESAPS 2003
The 70th annual meeting of the Southeastern Section of the American Physical Society. Holiday Sunspree Resort, Wrightsville Beach, Wilmington, NC, USA; 6--8 November 2003.
SESAPS 2003 Attention The deadline for submission of contributed abstracts has been extended to 5 pm on August 13. Note that there will also be an SPS undergraduate poster session, which requires an abstract submitted to Dr. Tim Black. Contacts Registration Agenda Abstract Submission SPS Poster Session and Activities Local Weather Local Attractions Accommodations Directions The 70TH annual meeting of the Southeastern Section of the American Physical Society will be held at the Holiday Inn SunSpree Resort at Wrightsville Beach, NC on November 6-8, 2003. SESAPS UNCW Physics UNCW APS Web Author : Dave Hughes
APHYS-2003
First International Meeting on Applied Physics. Badajoz, Spain; 15--18 October 2003.
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PhysicsWeb - Events
Find information on physics conferences, workshops and summer schools.
PhysicsWeb - Events - Current events (1-10 of 48) Advanced site search events Type of event All types Conferences Courses Exhibitions Lectures talks Schools Workshops Event dates Entire year January February March April May June July August September October November December 2005 2006 2007 Current events Approaching deadlines New events All events Add an event Change events password quick search Search for events Current events (1-10 of 48) [1] 2 3 4 5 Next NDT Roadshow 12 Various locations across UK, United Kingdom 25 Oct 2005 to 30 Jun 2006 Regine Parsons Second International Conference on Flow Dynamics Sendai, Miyagi, Japan 16 Nov 2005 to 18 Nov 2005 Introduction to Confocal Raman Microscopy Ulm, Germany 17 Nov 2005 to 18 Nov 2005 Harald Fischer International Symposium on Scientific Imaging: Seeing the Invisible Madrid, Spain 17 Nov 2005 to 18 Nov 2005 Pablo Artal 4th WSEAS Int.Conf. on E-ACTIVITIES (E-Learning, E-Communities, E-Commerce, E-Management, E-Marketing, E-Governance, Tele-Working) (E-ACTIVITIES '05) Miami, Florida, United States 17 Nov 2005 to 19 Nov 2005 4th WSEAS Int.Conf. on ELECTRONICS, CONTROL SIGNAL PROCESSING (ICECS '05) Miami, Florida, United States 17 Nov 2005 to 19 Nov 2005 4th WSEAS Int.Conf. on COMPUTATIONAL INTELLIGENCE, MAN-MACHINE SYSTEMS and CYBERNETICS (CIMMACS '05) Miami, Florida, United States 17 Nov 2005 to 19 Nov 2005 2005 WSEAS IASME Int.Conf. on ELECTROSCIENCE AND TECHNOLOGY FOR NAVAL ENGINEERING and ALL-ELECTRIC SHIP(NAVAL'05) Miami, Florida, United States 17 Nov 2005 to 19 Nov 2005 HSDPA HSUPA (High speed downlink uplink packet access) course at Oxford University Oxford, United Kingdom 18 Nov 2005 Peter Holland 5th Conference on Nuclear and Particle Physics Egypt 19 Nov 2005 to 23 Nov 2005 Registration deadline: 31 Jul 2005 MNH Comsan [1] 2 3 4 5 Next e-mail alerts Sign up to our FREE events alerting service E-mail address Subscribe Unsubscribe Home | News | Physics World | PhysicsJobs | Resources | Events | Best of PhysicsWeb Buyer's Guide | Contact us | Advertising | IoP members | Products press | Advanced site search Tel +44 (0)117 929 7481 | Fax +44 (0)117 925 1942 | E-mail info@physicsweb.org Copyright IOP Publishing Ltd 1996-2005. All rights reserved. Legal Notice
EP2DS-14 Prague
14th International Conference on the Electronic Properties of Two-Dimensional Systems, Prague, Czech Republic : July 30 - August 3, 2001
EP2DS -- 14 Dear colleagues, the EP2DS-14 conference has been over for quite some time now! The Proceedings were published in Physica E, Volume 12, Issues 1-4, Pages 1-962 (January 2002). The EP2DS-15 conference was hold on July 13-18, 2003 in Nara, Japan. The EP2DS-16 conference will take place in Albuquerque, New Mexico, USA, July 10-15, 2005. Thank you for your interest in these pages. We still have the following links for you: The EP2DS-16 Conference Homepage The EP2DS-15 Conference Homepage The EP2DS-14 Proceedings online. The original EP2DS-14 homepage (not maintained anymore). Some photographs of the Conference. With our best regards, Jan Kucera (on behalf of the organizers) P.S.: You may also wish to visit the Ferromagnetic Semiconductor Spintronics Web Project.
Mindanao Physics Research Group
Temporary official website of Mindanao Physics Research Group, a group of individuals based in Mindanao, Philippines who want to advance physics research and instruction in the Philippines.
Mindanao Physics Research Group Welcome to Group to Advance Physics Research and Education in the Philippines Founded A group of young physicists and educators successfully founded the Physics Research Group with the theme "Advancing Physics Research and Education for National Progress" at Crystal Inn, Tibanga, Iligan City last October 29, 2005. Organized by the Preparatory Committee headed by Mr. Kim Gargar, former Physics Department Chairman of Mindanao Polytechnic State College (MPSC), the Founding Assembly gathered 22 active and new members of the group which is formerly known as Mindanao Physics Research Group. Members came from Iligan, Cagayan De Oro, Davao, Cotabato, and Marawi. Among them were Mr. Hermogenes Gooc, the former Physics Department Chairman of Mindanao State University-Iligan Institute of Technology (MSU-IIT), and Mr. Ruelson Solidum, former Chairman of the then-Department of Natural Sciences in MPSC and a founding member of the original group. Outstanding Young Scientist awardee and Samahang Pisika ng Visayas at Mindanao (SPVM) President Dr. Angelina Bacala graced the event by giving an inspirational message (see related story). Finally, after the ratification of the Constitution and the induction of Executive Committee members, a General Program of Action was discussed. PRG Members vowed to contribute to the advancement of physics research and education in the Philippines and to the progress of the country in any way possible. Einstein's 1905 papers can be downloaded here... PRG in Iligan City! Announcement(Jul1): 7th SPVM National Physics Conference and Workshop Announcement(Mar10): 2005 SPP Physics Congress (First Announcement) This website is listed in Google . geovisit();
Abdus Salam International Centre for Theoretical Physics
Aims to foster the growth of advanced studies and research in developing countries. Includes a database of affiliated scientists, information on activities, and research activities.
the Abdus Salam International Centre for Theoretical Physics Skip navigation . Mission and legacy message from the director ICTP mission governance-tripartite agreement support for the ICTP ICTP prizes and awards history ICTP, Trieste and Italy science, cultural heritage and cooperation statistics on ICTP Organization director's office scientific sections conferences and hosted activities office of external activities (OEA) library scientific publications science dissemination unit (SDU) scientific computing section (SCS) external liaison and information administration ICTP organizational chart Research applied physics condensed matter and statistical physics (CMSP) earth system physics (ESP) high energy, cosmology and astroparticle physics (HECAP) mathematics (Math) ICTP-INFN laboratory (MLab) Training and Education Associate and Federation Schemes Diploma Post Graduate Programmes Visitor's Programme Office of External Activities (OEA) Training and Research in Italian Laboratories (TRIL) Open Access Services Scientific events calendar call for proposals seminars 40th anniversary public lectures ICTP Events portal Collaborations the academy of sciences for the developing world (TWAS) international school of advanced studies (SISSA) dipartimento di fisica, university of Trieste Trieste system Information and Resources ICTP opportunities visiting ICTP virtual tour of the campus general services scientific services press room and logo news search site map contact us ictp net - webmail ICTP Strada Costiera 11 34014 Trieste Italy www.ictp.it OVERVIEW Founded in 1964 by Abdus Salam (Nobel Laureate), the Centre operates under a tripartite agreement among the Italian Government and two United Nations Agencies, UNESCO and IAEA. Its mission is to foster advanced studies and research, especially in developing countries. While the name of the Centre reflects its beginnings, its activities today encompass most areas of physical sciences including applications. ICTP NEWS AND DAILY SCIENCE G-77 and Trieste's scientific institutions posted on November 14, 2005 02:37:58 pm G-77 is exploring avenues of cooperation with ICTP and other Trieste's institutions ... Tosatti Awarded AIP Tate Medal posted on November 09, 2005 02:54:43 pm Former ICTP Acting Director honoured for his efforts to help scientists from developing countries ... Activities 2006 Open Access Physics 2005 ICTP on the web since 1994 disclaimer help
National Society of Black Physicists
NSBP is the largest and most recognizable organization devoted to the African-American physics community.
National Society of Black Physicists - NSBP Einstein on Race and Racism In their upcoming book Fred Jerome and Roger Taylor tell the world about Einstein and his anti-racism activities internationally, nationally and in Princeton's long-established African American community. This unique volume is the first to bring together a wealth of Einstein's writings on the topic of race. Although his activism in this area is less well known than his efforts on behalf of international peace and scientific cooperation, Einstein spoke out vigorously against racism both in the United States and around the world. In addition to the scientist's letters, speeches, and articles with engaging narrative and historical discussions that place his public statements in the context of his life and times, the volume also features a selection of candid interviews with African Americans who as children knew Einstein. Jerome previously authored The Einstein File: J. Edgar Hoover's Secret War Against the World's Most Famous Scientist. More on Einstein and Race NSBP 6704G Lee Highway Arlington VA 22205 Phone: (703) 536-4207 Fax: (703) 536-4203 Privacy Policy
Sigma Pi Sigma: The National Physics Honor Society
Exists to honor outstanding scholarship in physics; to encourage interest in physics among students at all levels; to promote an attitude of service of its members towards their fellow students, colleagues, and the public; and to provide a fellowship of persons who have excelled in physics.
Sigma Pi Sigma - The National Physics Honor Society Hurricane Katrina Assistance -The Katrina Affected Physics and Astronomy (KAPA) bulletin board aids members of the Physics and Astronomy community impacted by Hurricane Katrina. The forum is hosted by the ComPADRE digital library. more details 2004 Congress Reports - Read articles by speakers and attendees from the 2004 Quadrennial Congress of Sigma Pi Sigma. more details Trinity Site Visit - First-hand account of the Trinity Site Visit that preceded the 2004 Congress. more details Inductions - See photos from recent induction ceremonies. more details Society News - SPS Sigma Pi Sigma Council approve statement on teaching science in the classroom. more details Make your Sigma Pi Sigma Experience CountOhio State University's Sigma Pi Sigma Chapter believes that in addition to the honor of induction, members have a responsibility to their community, school, and the scientific community. For the last few years, they have responded strongly to their responsibility by conducting a series of outreach programs. more details Eastern Michigan University Sigma Pi Sigma advisor Diane Jacobs writes "I have attached a very nice photo of our chapter president, Josh Miller, that I thought you might like. He is off to grad school now and SPS truly made a significant difference in his life. Thanks for making great things possible for our students." Marianne Dyson's Home on the Moon wins prestigious science writing award Marianne Dyson's book Home on the Moon has been selected to receive the 2004 American Institute of Physics Science Writing Award in the children's category. Inspired by the Apollo moon landings which she watched as a child, Dyson (UNC-Greensboro, '77) knows firsthand that space motivates kids to achieve. more details James Stith named one of 2004's top Black scientists James H. Stith, a Vice President of the American Institute of Physics, has been named one of the "50 Most Important Blacks in Research Science" for 2004 by the magazines Science Spectrum and US Black Engineer Information Technology, both published by Career Communications Group, Inc. of Baltimore, MD. Dr. Stith (Virginia State University, '64) and the other honorees were featured in the September 2004 issue of the magazine. more details
The International Association of Physics Students (IAPS)
IAPS aims to build a network of contacts between physics students from around the world, to offer them a programme of events and to support them in their academic and professional work.
International Association of Physics Students (IAPS) IAPS International Association of Physics Students Home News Pictures Forum Activities ICPS Organisation Publications Contact information {iaps} Welcome to the website of the International Association of Physics Students We are an association of physics students and student societies from around the globe, working to promote peaceful collaboration among them. Our members are represented by national and local committees, meeting regularly to ensure the relevance of our activities. The results of the past t-shirt competion are now available ! Check out also how to get them from free by participating to flash mobs . Here are some of our members gathered for our Conference in Odense, Denmark 2003. Our next conference will be in Romania in August 2006. Click on ICPS to find out more. The IAPS trip to JET takes places October 20-23. Click here for more info.
Society of Physics Students (SPS) National Website
SPS programs, scholarships, publications, news, career and education resources, science stories of note, physics games, simulations and humor, and physics problems on the web.
Welcome to the SPS National Website
Polish Physical Society
Information on the statutes and members, as well as award winners of the society. Also contains links to other relevant sites.
PTF - Polish Physical Society CURRENTINFORMATION THE SOCIETY PHYSICS, PHYSICISTS, ... Historicalnote Members,MainBoardandCommissions SectionsandBranches Declaration,statute, bank accountandregulations List of ordinary members Honorarymembers Laureates of the PPS prizes Meritorious patrons and patrons of PPS PresidentsofPPS MeetingsofPolishPhysicists Commissions: Rewards and Distinctions ; Didactic Rewards Physics Education in Universities Physics Education in Schools Legislation ; Regulations ; Elections International Cooperation History of Physics; Physical Nomenclature Physics Popularization and Promotion World Year of Physics 2005 Sections: Physics in Economy and Social Sciences Optics SchoolTeachers Young Physicists Branches: Bialystok , Bydgoszcz , Cracow , Czestochowa , Gdansk , Gliwice , Katowice, Kielce , Lublin , Lodz , Opole , Poznan , Rzeszow , Slupsk , Szczecin , Torun , Warsaw , Wroclaw , Zielona Gora Journals: ActaPhysicaPolonicaA ActaPhysicaPolonicaB ReportsonMathematicalPhysics The old and new Concepts of Physics PostepyFizyki (AdvancesinPhysics) Delta ; Foton (Photon) Fizyka i przyroda (Physics and Nature) Moja Fizyka (My Physics) FizykawSzkole (PhysicsEducation) NewJournalofPhysics Other activity: Library of PPS Physnet World Year of Physics 2005 ScienceonStage PhysicsOlympiad YoungPhysicists'Tournament Copernicus-catalogueoftextbooks ZA - www.szukacz.pl Poland PPS
European Committee for Future Accelerators (ECFA)
Works for long-range planning of European high-energy facilities - accelerators, large-scale facilities and equipment - adequate for the conduct of a valid high-energy research programme.
ecfawelcome
American Center for Physics
A brief description of this facility. Includes related links.
American Center for Physics Welcome to the American Center for Physics Directions to the ACP Facility. Announcement ACP Web Mail ACP The American Center for Physics brings together in one building, the American Institute of Physics , The American Physical Society , the American Association of Physics Teachers , and the American Association of Physicists in Medicine . The American Center for Physics is a building providing a permanent home for physics near the Nation's Capital. But it is more than that. The American Center for Physics also is a unifying force for the field of physics and the many programs of physics societies. Purchase of the 24-acre site off Kenilworth Avenue in Prince George's County, Maryland, was completed in the summer of 1992, with the ground breaking taking place July 1992. Staff began working on October 25, 1993. April 24, 1994 marked the official dedication of the American Center for Physics. College Park affords a location close to Washington D.C., and adjacent to the University of Maryland , one of the nation's leading research universities. The wooded site provides a campus-like setting only a short walk from the College Park station of Washington's Metro subway system . In addition to the many societies housed within the facility, American Center for Physics is home to the Niels Bohr Library, which is one of the country's largest collections of material on the history of physics. The library contains some 1,000 transcribed and indexed interviews with physicists such as Niels Bohr, S. Chandrasekar, Richard Feynman, and Robert Oppenheimer while the library's Emilio Segre Visual Archives includes over 20,000 physics related photographs. The American Center for Physics provides a focal point for the physics community, increases the community's interactions with government decision makers, and serves as a resource for scientists, educators, and the public. ACP Societies The American Institute of Physics The American Physical Society The American Association of Physics Teachers The American Association of Physicists in Medicine Questions or comments can be addressed by the webmaster or by sending mail to the webmaster@acp.org.
The Egyptian Society of Solid Science and Applications (ESSA)
Services, news, calendar, links, and details about the Egyptian Journal of Solids, including downloadable versions of archived issues.
The Egyptian Materials Research Society (Eg-MRS) The Egyptian Materials Research Society (Eg-MRS) Egyptian Journal of Solids Free full text electronic edition on our new web site 8 2005 Copyright 2005 The Egyptian Materials Research Society (Eg-MRS) Maher Ahmed
The Egyptian Physicists Association (EPA)
A non-governmental and non-profit association of all those who have interest in physics in Egypt. Membership details and contact information.
EPA The Egyptian Physicists Association (EPA) is a non-governmental and non-porfit association of all those who have interest in Physics in Egypt. The EPA aims to promote the Professional, Academic and Social Communication Between its members and Physics associations, and organizations. And to promote to its members, education, training, career information, Electronic publishing, conferences, workshops, seminars, and meetings. Also aims at representing physics in contacts with authorities dealing with issues concerning education and research, to stimulate the interest for science and to promote the position of the natural sciences in the school system, society, and industry. Founder and chairman Maher Ahmed Send mail to webmaster with questions or comments about this web site. Copyright 2001 Egyptian Physicists Association EPA Maher Ahmed geovisit();
International Liquid Crystal Society
Lists the membership, meetings, news and links to related sites.
International Liquid Crystal Society Home Page International Liquid Crystal Society Directors Membership Bylaws Meetings Liquid Crystals Today Application for 23rd ILCC SocietyNews RelatedLinks Security ILCC 2006 To be held in Keystone, Colorado Awards and Honors 2006 Glenn H. Brown Prize 2006 MultiMedia Prize Nominations for Honored Members Search the ILCS Web Site. Directors Members Meetings Feed Back Post Sites Home Page
Split Physical Society
Official pages of the Physical Society, Split, Croatia.
Index of fdst Index of fdst Name Last modified Size Description Parent Directory 19-Nov-2004 12:15 - astro 18-Feb-2002 23:14 - astroNovo 19-Nov-2001 07:53 - Apache 1.3.33 Server at pubwww.st.carnet.hr Port 80
International Union of Pure and Applied Physics
Sponsors international meetings and fosters the publication of papers.
IUPAP: Home IUPAP News New Study: High Magnetic Fields (pdf) Council and Commissions: Recent Reports Working Group on Women in Physics ICFA International Committee for Future Accelerators New Working Groups International Committee for Ultra-High Intensity Laser - ICUIL Nanoscience Working Group News Archives IUPAP Mission To assist in the worldwide development of physics, to foster international cooperation in physics, and to help in the application of physics toward solving problems of concern to humanity. More about IUPAP . Events and Conferences IUPAP 25th General Assembly October 26-28, 2005 Cape Town, South Africa World Conference on Physics and Sustainable Development October 31-November 2, 2005 Durban, South Africa The World Year of Physics 2005 is a United Nations endorsed, international celebration of physics. International Website | U.S. Website Upcoming Commission Conferences C12.1 International Conference on Particles and Nuclei 2005 October 22-28, 2005, Santa Fe, NM USA C19.1 Scientific Requirements for Extremely Large Telescopes November 14-18, 2005, Cape Town, South Africa All 2005 Conferences Contact IUPAP | Search IUPAP | IUPAP Home
International Research Group on Physics Teaching
Promotes adapting physics teaching to the present knowledge. Fosters friendly contacts between physics teachers and professors above national barriers at all levels of education.
GIREP - Research Group on Physics Teaching International Research Group on Physics Teaching Internationaler Arbeitskreis zur Frderung des Physikunterrichtes This is a GIREP home page that was initialised together with the conference home page New Ways of Teaching Physics. We would like to maintain the permanent GIREP home page with information about GIREP members, the links to their home pages, etc. A word from the President List of members (username and password required) A Brief History of GIREP Statutes of GIREP GIREP newsletters from 1974 (username and password required) GIREP committee Fees Download application form (ZIP compressed) Conferences Conference 1995 - Teaching the science of condensed matter and new materials Conference 1996 - New ways of teaching physics Conference 1998 - Hands-On Experiments in Physics Education Conference 2000 - Physics Teacher Education Beyond 2000 Conference 2002 - Physics in new fields and modern applications, Lund Sweden, August 5 - 9, 2002 Conference 2004 - Teaching and Learning Physics in New Contexts, 19 - 23 July 2004, University of Ostrava, Czech Republic Conference 2006 - Modelling in Physics and Physics Education, 20 - 25 August 2006, AMSTEL institute, Faculty of Science, University of Amsterdam, Netherlands Seminars Seminar 2001 - Developing Formal Thinking in Physics, University of Udine, Italy, 2-6 September 2001 Seminar 2003 - QUALITY DEVELOPMENT IN TEACHER EDUCATION AND TRAINING, 1-6 September 2003 in Udine, Italy. Seminar 2005 - INFORMAL LEARNING AND PUBLIC UNDERSTANDING OF PHYSICS, 5-9 September 2005 in Ljubljana, Slovenia. Events World year of Physics The current home page is maintained by Gorazd Planinsic, University of Ljubljana, Faculty of Mathematics and Physics, Ljubljana, SLOVENIA , e-mail: gorazd.planinsic@fiz.uni-lj.si and Marko Budisa, e-mail: marko.budisa@fiz.uni-lj.si . Information about GIREP was provided by Seta Oblak, Board of Education, Ljubljana, SLOVENIA. E-mail: Seta.Oblak@guest.arnes.si A word from the President Dear GIREP members, As your new President, elected at the 1998 GIREP conference in Duisburg, I would like to address all members and to point out some of the interesting and challenging tasks to be tackled in the future. GIREP has an outstanding tradition in international cooperation in the field of teaching modern physics. It is a great honour and pleasure to work for this highly esteemed community of physics teachers from all over the world, especially now as we make the move into a new millennium. As the past GIREP President Karl Luchner put it, members of GIREP are not only physics teachers. Moreover, they are highly idealistic persons, combining expertise in very different fields. A high degree of competence in the subject area of physics is one important prerequisite, being a great challenge in itself in view of the rapid and still accelerating pace of scientific and technological development. In addition to the progress within physics and to the important developments linking physics with inter- and transdisciplinary areas, we have to keep track of the broader contexts, into which our science is embedded and from which it emerges. In my view, this requires an intelligent balance between tradition and innovation. Physics as a mental challenge is driven by the conviction, that the universe is intelligible by the human mind. The search for unifying principles has been the grand theme, conserved throughout all changes during the development of modern science. As part of our cultural heritage, we have to convey the "big ideas" of our discipline and make them accessible and sensible to our students in a meaningful and authentic way, which meets their expectations and needs. Excellence on the physics side has to be complemented with excellence in terms of pedagogy. Switching the focus from physics to teaching, we have to acknowledge, that during the last decades significant progress has been achieved in research on teaching and learning processes and on using new technologies for teaching and learning. However, a great deal of this valuable knowledge has not been transformed to practical implementations on a broad scale. We still have to try hard to put together threads from different directions, matching the physics oriented view and the learner oriented view on various levels. Science in general and especially physics has been under severe pressure in the last decades, suffering from declining students' interest and enrolments. We are faced with the paradoxical situation of living in a society based on science and technology, the base of which is seemingly thinned out and the gap between the notorious "two cultures" is even increasing. The role of scientific literacy and the public understanding of science have become political issues in view of a globally linked society where knowledge plays an eminent role. As a reaction, different countries have launched programs to promote the quality of science education. Being involved in a national effort to improve the efficiency of mathematics and science education myself, I consider it one of the aims of future GIREP conferences to share our experiences from these different efforts and to make them accessible to the community. At present, an interesting development can be observed on the intern-ational level. Formerly, knowledge used to be transferred from the developed countries to the less developed ones. This situation is about to change: nations, which were newcomers one generation ago, have made a superb progress and have reached a stage, where in turn the developed countries can profit from their approaches and their experience. Let us take this as an indicator for the GIREP philosophy that international cooperation and cross-cultural exchange combined with idealism and enthusiasm will pay in the long run and will help to further the image of physics both as an intellectual endeavour and as one of the central pillars of our modern culture. Manfred Euler Index A Brief History of GIREP In the years 1960-64 OECE (that later became OECD) arranged a series of international meetings to encourage the renewal of Physics teaching. The meetings proved to be a valuable source of inspiration for the participants. However, from 1964 OECD concentrated on other fields and stopped supporting meetings on physics education. - A number of persons who had attended the previuous meetings, led by prof. W. Knecht, Switzerland, believed that the series of international meetings on teaching physics in schools should continue. To this end they formed an international working group: GIREP was founded 15. March 1966 with Prof. Knecht as President. - At the beginning the number of members of GIREP was quite small (a few tens), but it soon grew to over 100 and now, since many years, it is quite stable at about 250. - Very soon GIREP began to organize international meetings, finding sponsorship from Universities, Ministries of Education, UNESCO; ESA and many other national and international organizations. One way the Ministries of Education sponsor the Meetings is paying for the attendance of local school teacher. Here is a list of GIREP meetings from the very beginning: 1. Jan. 1967 (Lausanne, Switzerland): in collaboration with the International Commission of Mathematics Teaching, preliminary informal meeting on the co-ordination of mathematics and physics teaching at the secondary school. 2. 30. Oct.-5.Nov. 1968 (Malvern, UK): Study and discussion of the Nuffield Physics. 3. 30. July-5.Aug. 1969 (Copenhagen, Denmark): Energy in the lower secondary school, Quantum mechanics and Relativity in the higher secondary school. 4. 16.-18. Mar. 1972 (Kiel, Germany): joint GIREP-UNESCO Meeting on the implementation of curricula in science education with sepcial regard to physics teaching. 5. 14.-20. Oct. 1973 (Venezia, Italy): "Electricity, magnetism and mechanics in the secondary school". 6. 6.-10. Sept. 1976 (Montpellier, France): Two main topics: "First steps in teaching physics at the beginning of secondary school", and "Probability and Statistics in physics teaching". 7. 14.-21. July 1978 (Oxford, UK): joint ICPE-GIREP Meeting on "The role of the Laboratory in Physics Teaching". 8. 19.-24. Aug. 1979 (Rehovot, Israel): two topics: "Teaching Waves and Oscillations" and "Current Problems in Physics Teaching". 9. 6.-12. Sept. 1981 (Balatonfred, Hungary): "Nuclear Physics, Nuclear Power". 10. 20.-25. Aug. 1984 (Zeist, Holand): "The many faces of teaching and learning mechanics". 11. 18.-23. Aug. 1986 (Elsinore, Denmark): "COSMOS - an Educational Challenge". 12. 7.-13. Sept. 1989 (Balatonfred, Hungary): "Energy Alternatives - Risk Education". 13. 19.-24. Aug. 1991 (Torun, Poland): "Teaching about Reference Frames - from Copernicus to Einstein". 14. 16.-21. July 1993 (Braga, Portugal): "Light and Information". 15. 24.-30.Aug. 1995 (Udine, Italy): joint ICPE-GIREP Meeting on "Teaching the science of condensed matters and new materials". 16. 21.-27.Aug. 1996 (Ljubljana, Slovenia): joint ICPE-GIREP Meeting on" New Ways of Teaching Physics". 17. 23.-28. Aug. 1998 (Duisburg, Germany): "Hands-On experiments in physics education" 18. 27. Aug - 1. Sept. (Barcelona, Spain): "Physics Teacher Education Beyond 2000" Since 1969 all Meetings published Proceedings, that were distributed to all members. But occasionally Proceedings of other Conferences were also distributed: for example of ICPE Conference on Education for Physics Teaching, Trieste 1980; Microscience Conference on Computers in Science Education, Balaton 1985; ICPE Teaching Modern Physics Conference on Condensed Matter, Munich 1988; and presently RIO FOLLOWUP - International science education conference on environmental issues, Eger 1994. The Presidence of GIREP from foundation 1966 was held by 1966 - 1969 W. Knecht (Switzerland) 1969 - 1972 Soren Sikjaer (Denmark) 1972 - 1979 Poul Thomsen (Royal Danish School of Educational Studies, Copenhagen, Denmark) 1979 - 1984 Arturo Loria (University of Modena, Italy) 1985 - 1991 Paul Black (King's College, London, UK) 1992 - 1995 George Marx (R. Eoetvoes University, Budapest, Hungary) 1995 - 1999 Karl Luchner (University of Munich, Germany) 1999 - 2002 Manfred Euler (Department of Physics Education, IPN (Institute for Science Education), University of Kiel, Germany) Index STATUTES OF GIREP Adopted 1972, revised 1989 and 1995 The Statutes were adopted in Kiel, Germany on March 17, 1972, then revised by the General Assembly on September 12, 1989 in Balatonfred, Hungary (articles 2 and 11) and revised again by the General Assembly on August 29, 1995 in Udine, Italy (article 17). Art .1 The International Research Group on Physics Teaching (GIREP) is an international body of physics professors and teachers who want to cooperate in their work on physics teaching. It enjoys legal status according to the Swiss Common Law. Art. 2 The principal aims and purposes of GIREP are: to use every possible means to promote and encourage every effort made with a view to adapting physics teaching to the present knowledge; to collaborate as closely as possible with any international organisation whose field of activity is connected with that of the Group; to foster friendly contacts between physics teachers and professors above national barriers at all levels of education; to stimulate the exchange of information and team work between its members and to keep them informed of the work of the International Organisations in the field of its activities. Art. 3 The Group is formed of ordinary members, subscribing members and possibly honorary members. Art. 4 The ordinary members are individuals or groups. The individual members are physics teachers or professors. The groups are societies of physics teachers or professors or broadly speaking, national or international scientific bodies interested in the same field of activity as GIREP. The subscribing members are persons, associations, companies or firms who accept to support financially the activities of GIREP but do not participate in its activities. Art.5 It is within the General Assembly(s competence to elect as honorary member of the Group any person whose especially valuable work in favour of physics teaching or GIREP deserves recognition. The honorary members do not pay any membership fee and enjoy the same rights as the ordinary members. Art. 6 Membership is granted to any candidate who applies for it to the Committee and as soon as this application is accepted by the Committee. The members are not personally responsible for the liabilities of GIREP. These liabilities are warranted by the credit of the Group. Art. 7 The different organs of GIREP are: 1) The General Assembly formed of all the active members and the possible honorary members; 2) The National Sections, each of them being formed of the members of the General Assembly living in the same country; 3) The Committee; 4) The Commission of Representatives formed by the Committee and the delegates of the National Sections; 5) The Commission of Auditors. Art. 8 GIREP works mainly through: 1) The working seminar of the Commission of Representatives; 2) The information bulletins draught by the National Sections; 3) The possible international symposiums organised in collaboration with other international institutions. Art. 9 The General Assembly is the highest authority of the Group. It is consulted by letter as often as necessary. The General Assembly delegates its authority to the Commission of Representatives when the latter sits and for the duration of the session. Art. 10 The Commission of Representatives holds an administrative meeting at the same time as the working seminar organised in turn every two years in the various countries represented. It is presided over by the President of the Committee. It takes decisions at the simple majority of the participating members. If necessary the vote of the President will help to sway the decision. The programmes of the working seminars are prepared by the Committee. The Committee convenes the Commission of Representatives. The Chairman of the working seminar is the President of the National Section of the host country. Art. 11 The Committee is the executive organ of the Group. Its members are elected by the General Assembly for four years. They are reelegible. The Committee is formed of the President, two Vice-presidents, the General Secretary and the Treasurer. The President and the Vice-Presidents belong to different countries and, if possible, to two different linguistic regions. The joint signatures of the Treasurer and another member of the Committee involve the financial responsibility of the Group. Art. 12 Each National Section is constituted and is financially run according to its choice. It elects in particular a President, a Secretary and a Treasurer. Several offices may be held by the same person. Once a year - at a seminar or by letter - each National Section will submit to the Committee in the form of an "Information Bulletin" a concise report on the activities carried out in the country in favour of physics teaching. The National Sections represent GIREP before their national authorities and professional associations in their respective countries. A standing invitation is extended to the President of the Committee to participate in the meetings of the National Sections. Art. 13 The Commission of Auditors is formed of two members who are elected in the same way and for the same period as the Committee. Two substitutes are elected for the same period. The Auditors do not reside in the same country as the Treasurer and are not members of the Committee. The same rule applies to the substitutes. Art. 14 GIREP may invite to all or part of the meetings of its various organs any person whose collaboration is thought to be valuable. In particular, representatives of the international organisations are invited to the most important meetings when their field of activity is connected with that of GIREP. Art. 15 When decisions are made by letter, the simple majority of the expressed opinions is required; the documents are kept in the GIREP Records and may be consulted at any time by the members. The decisions made my letter are considered as being made at the headquarters of GIREP. Art. 16 The yearly accounts of GIREP are kept by the Treasurer. The financial year begins on 1st January. Every year the balance sheet and the report of the auditors are sent to the members who may return the sheet within 14 days in case of disapproval. The account books are kept with GIREP(s records. Art. 17 In the October each year, those members who have not paid for the previous two years will be removed from the membership list. Art. 18 The Committee, as well as the General Assembly, may exclude any member of GIREP for serious offence. Art. 19 The present Statutes may be revised by a 2 3 majority of the General Assembly or of the Commission of Representatives entitled to act on the authority of the General Assembly. Art. 20 The dissolution of the association may be decided under the same conditions as the revision of the Statutes. In case of dissolution the credit of GIREP will be given to an international association, whose activities are in favour of physics or scientific teaching. Index GIREP COMMITTEE President: Manfred Euler, Department of Physics Education, IPN (Institute for Science Education), Olshausenstr. 62, 24098 Kiel, Germany (tel 49-431-880-3147, fax 3148, e-mail: euler@ipn.uni-kiel.de ) Vice-presidents: Ton Ellermeijer, e-mail: ellermei@science.uva.nl Michele d'Anna, e-mail: danna@lilo.lic.ti-edu.ch Secretary: Gorazd Planinsic, University of Ljubljana, Faculty of Mathematics and Physics, Jadranska 19, SI-1000 Ljubljana, Slovenia (fax: +386 (1) 2517281, e-mail: gorazd.planinsic@fiz.uni-lj.si ) Treasurer: Rosa Maria Sperandeo-Mineo, Universita` di Palermo Viale delle Scienze (Edificio 18), 90128 PALERMO, Italy (e-mail: sperandeo@difter.unipa.it ) Index FEES The current fee is EURO 20 (+ 1 EURO expenses) for one year. The accounting year runs from January 1 to December 31. Fees paid after September in any year will be credited on the following year, unless the applicant specifies otherwise. The fee can be paid into the following account: Rosa Maria Mineo-Sperandeo MEDIOLANUM BANK-Account N 478971, BIC-code: MEDBITMMXXX IBAN : IT41R0306234210000000478971 For Italian members (national transfer): Rosa Maria Mineo-Sperandeo MEDIOLANUM BANK-Account N 478971 [ ABI: 03062, CAB: 34210]. At the same time, please send a note (by letter, fax or e-mail) to the Treasurer, confirming how much money you sent and when and for what years. The members should pay all bank charges and mailing costs. Please ask your bank for these costs before transferring money! If you prefer to reduce bank or cheque expenses, you may pay several years fees in advance. Please do not send cheques (high expenses!) In cases of real difficulty to arrange payment, please contact the Secretary or the Treasurer who are ready to advise whether special arrangements can be made. The General Assembly of GIREP members in Udine (August 1995) accepted the following supplementary new article for the GIREP statutes: Each year in October, those members who have not paid for the previous two years will be removed from the membership list. Index
Central Michigan University Society of Physics Students
This is the home page of the Central Michigan University chapter of the Society of Physics Students. We are a group of physics students who try to spread the love of physics to everyone.
Central Michigan SPS Society of Physics Students, Central Michigan Chapter We suggest you get a browser that can run frames, because if you're seeing this message, your current browser is outdated and cannot handle frames. Visit Microsoft.com to get the current version of Internet Explorer. Just click on "Downloads" and then find the newest browser available. Sorry, we hope to get a non-frames version of this site up soon!
Landau Institute for Theoretical Physics
Includes details of seminars and conferences, lists of members of research groups, lists of publications.
.. About Us Research Departments Publications Conferences Seminars MIPT chair Inet World OurServices Search LANL APS IOP OJPS EPS ELSEVIER E-LIBRARY PHYSNET PhysTech Library IPP, Moscow. SessionsofITPScientificCouncil, Chernogolovka. 2005, November, 1711.30 2005, November, 1811.30 .. () Dragi Karevski, University Henri Poincare, Nancy, France Scaling and front dynamics in Ising quantum chains MORE LAST SEMINARS MORE LAST SEMINARS QUANTUM FIELD THEORY GROUP SEMINARS (Fridays, 15:00; Chernogolovka) News and events. Last updated:October, 26 2005 , , . : - 9-00 18-00 9-00 15-00 - Posted at:2005-10-26 , 4 2005 . 73- Posted at:2005-08-04 Lars Onsager Prize 2005 . Posted at:2005-06-23 .. Blaise Pascal Medal in Physics and chemistry of European Academy of Sciences. Posted at:2005-05-19 .. http: www4.nationalacademies.org news.nsf isbn 05032005?OpenDocument Posted at:2005-05-03 2005 Wolf Prize Posted at:2005-03-14 , . Posted at:2003-12-15 For Landau ITP staff only. Now it is possible to have your personal internet home page with the hosting on our server. Follow this simple instruction and you will have your personal home page after 10 minutes of work. Posted at:2003-11-04 ! 6 2003 11.30 Posted at:2003-11-03 - local.itp.ac.ru , - . Posted at:2003-05-08 News archive Events archive Forms archive Last Updated: 16 November 2005 12:50:15 For questions or suggestions please send mail to webmaster@itp.ac.ru This site is based on php . Design by Shurik
National Insitute for Theoretical Physics (Australia)
The NITP serves the Australian physics community by acting as an umbrella organisation for Theoretical Physics in Australia.
National Institute for Theoretical Physics National Institute for Theoretical Physics Your browser has requested the non-frames version of this page. It may be found here .
Nordic Institute for Theoretical Physics
Intergovernmental organization, research areas at NORDITA include astrophysics, condensed matter physics and subatomic physics.
NORDITA news institute people research positions meetings today help Nordic Institute for Theoretical Physics funded by Nordisk institut for teoretisk fysik Danmark, Teoreettisen fysiikan pohjoismainen laitos Finland, Norrna stofnunin kennilegri elisfri Island, Nordisk institutt for teoretisk fysikk Norway, and Nordiska institutet fr teoretisk fysik Sweden, through the Nordic Council of Ministers
Croatian Physical Society
The Croatian Physical Society is a public organisation with the purpose of promoting and developing scientific, upbringing, educational and cultural activity in the field of physics and related fields of science
Hrvatsko fizikalno drutvo - O drutvu Hrvatski | English O drutvu Uprava lanstvo Statut Sekcije Izdavatvo Projekti Dokumenti Linkovi Kontakt Pretraga O drutvu Hrvatsko fizikalno drutvo (HFD) osnovano je 19. prosinca 1990. godine, radi promicanja i razvijanja znanstvene, odgojne, obrazovne i kulturne djelatnosti na polju fizike. HFD nastavlja tradiciju okupljanja hrvatskih fiziara, tradiciju koja je zapoela s Matematiko-fizikom sekcijom Hrvatskog prirodoslovnog drutva odnosno Drutvom matematiara i fiziara Hrvatske. Aktivnosti drutva odvijaju se kroz znanstvenu sekciju, nastavnu sekciju, studentsku sekciju, sekciju za popularizaciju i sekciju za industrijsku i primijenjenu fiziku. Drutvo izdaje znanstvene asopise FIZIKA A i FIZIKA B, te (u suradnji s Hrvatskim matematikim drutvom) popularni Matematiko fiziki list za uenike, nastavnike i studente. Ostale aktivnosti HFD-a ukljuuju e-kolu fizike, organizaciju i provedbu Ljetne kole mladih fiziara, te natjecanja iz fizike (opinska, upanijska, dravno te Olimpijada) za osnovne i srednje kole. HFD je lan Europskog fizikalnog drutva (European Physical Society, EPS) i Meunarodne udruge za fundamentalnu i primjenjenu fiziku (International Union of Pure and Applied Physics, IUPAP). Drutvo ima oko 650 lanova, od ega je oko 240 nastavnika fizike te oko 150 studenata fizike. Prof. dr. sc. Amir Hamzi Aktualno Fizika u Hrvatskoj Broja posjeta Posjetitelja: 102634 Design by Vedran erek Dragon Company - Copyright HFD - 2005 Powered by Mambo
Institute of Physics
Devoted to basic research in the fields of physics of atoms, molecules and plasma and solid state physics including surface science. Zagreb, Croatia.
Institute of Physics | about the institute | research | students | seminars | events | library | visit us | links | addressbook | contact 2001. INSTITUTE OF PHYSICS. All rights reserved. Design by Studio8. For comments on these web pages, email wmaster@ifs.hr
International Association of Mathematical Physics
The International Association of Mathematical Physics (IAMP) was founded in 1976 in order to promote research in mathematical physics. The Association invites mathematicians and physicists (including students) interested in this goal to become members.
International Association of Mathematical Physics International Association of Mathematical Physics IAMP information Statement of purpose IAMP News Bulletins Older news bulletins Poincare Prize Membership list (updated Nov. 17, 2005) Associate Members Dues information Joining IAMP IAMP Congress: List of past Congresses Brisbane in 1997 London in 2000 Lisbon in 2003 Rio de Janeiro in 2006 Open Problems in mathematical physics Positions in Mathematical Physics: available, and wanted Conferences: IAMP supported Further listing Links to Interesting New Books and Magazines Executive committee: Current Officers of the Association: President: David Brydges iamp@math.ubc.ca Vice President: Jakob Yngvason yngvason@thor.thp.univie.ac.at Secretary: Ruedi Seiler E-mail: IAMP_secretariat@math.tu-berlin.de Address: FB Mathematik TU Berlin Sekr. MA 7-2 Str. des 17 Juni 136 D-10623 Berlin GERMANY Treasurer: Volker Bach iamp@mathematik.uni-mainz.de Other Executive Committee members: Yosi Avron Percy Deift Jean-Pierre Eckmann Klaus Fredenhagen Giovanni Gallavotti Philippe Martin Vincent Rivasseau Horng-Tzer Yau Other sites of interest (These links are for information purposes only) Mathematical Societies: American Mathematical Society (AMS) AMS Ethics Guidelines European Mathematical Society (EMS) Society for Industrial and Applied Mathematics (SIAM) Other Mathematics References Physical Societies: American Physical Society (APS) European Physical Society Institute of Physics C18 Commission for Mathematical Physics, IUPAP Other Physics References Electronic journals and preprint archives: Advances In Theoretical And Mathematical Physics (ATMP), International Press Los Alamos XXX Physics and Mathematics Archive Front for the mathematics section, including mathematical physics, at the XXX Archive Mathematical Physics Electronic Journal Mathematical Physics Preprint Archive (mp_arc) Institutes and centers The Clay Mathematics Institute (CMI) , Boston Erwin Schrdinger Institute , Vienna MaPhySto , Denmark Max Planck Institute , Leipzig For comments regarding the IAMP web site please contact the webmaster@iamp.org .
European High Pressure Research Group (EHPRG)
Brings together scientists and engineers involved in high pressure research.
The European High Pressure Research Group (EHPRG) Welcome to the homepage of the European High Pressure Research Group (EHPRG)! Back in 1963, a group of scientists and engineers involved in high pressure research decided to meet on an annual basis. The reasonable size of the group, the selection of the topics, the quality of the meetings, the low conference fees and the friendly relationships between the attendants have made the EHPRG meetings attractive. High pressure research is a fast growing discipline, yielding interesting and exciting results in many fields of science, technology and biotechnology. EHPRG contributes to this development by bringing people together. EHPRG is Associated Member of the European Physical Society . Webmaster
American Association of Physicists in Medicine
AAPM homepage with a link to the journal "Medical Physics".
American Association of Physicists in Medicine AAPM Members please login Members only links appear like this. Medical Physicists are... AAPM is... Membership Placement Service Education Meetings Organization Pubs Products Links of Interest Search the Site What's New Pay Your 2006 Dues Online (Individual members, please log in first before clicking on this link. [membership services] NRC Considering Request by Minnesota to be an "Agreement State" [gov't affairs | posted: 11 14 2005 | sunset: 1 14 2006 ] World Congress on Medical Physics and Biomedical Engineering 2006 [meetings | posted: 11 07 2005 | sunset: 1 31 2006 ] Biomedical Imaging Research Opportunities Workshop 4 - Abstract Submission deadline: December 12, 2005 [meetings | posted: 11 07 2005 | sunset: 2 24 2006 ] Educators Resource Guide [education | posted: 11 02 2005 | sunset: 12 31 2005 ] Support for Clinical Residencies in Diagnostic Medical Physics Sponsored by the RSNA Application deadline: February 1, 2006 [announcements | posted: 10 31 2005 | sunset: 2 1 2006 ] Fellowship for Graduate Study in Medical Physics Sponsored by the American Association of Physicists in Medicine Application deadline: April 15, 2006 [announcements | posted: 10 31 2005 | sunset: 4 15 2006 ] AAPM Committee Meetings Scheduled during the 2005 RSNA [meetings | posted: 9 12 2005 | sunset: 12 3 2005] focus on our future ! Contribute to the AAPM Education Research Fund [education | posted: 6 9 2005 | sunset: 12 31 2005] RDCE [education] 8 16 2005 | Radiation Oncology | Real-time 3D surface image guided beam setup in radiotherapy of breast cancer 8 16 2005 | Radiation Oncology | Investigation of secondary neutron dose for 18 MV dynamic MLC IMRT delivery AAPM Fact Sheet | Contact Information | Banner Advertising Information | Site FAQ | Privacy and Security AAPM is the American Association of Physicists in Medicine, One Physics Ellipse, College Park, MD 20740, phone 301-209-3350, fax 301-209-0862. Send general questions to aapm@aapm.org .The AAPM is an educational nonprofit organization devoted to the discipline of physics in medicine. The information provided in this website is offered for the benefit of its members and the general public, however, AAPM does not independently verify or substantiate the information provided on other websites that may be linked to this site.
Institute of Physics (IOP)
Job news, journals, author and referee services, conference diary.
www.iop.org from The Institute of Physics All Journals Online Services Members Books Education Careers Magazines Industry business Physics Policy Branches Groups Constants and Equations Explore the Inside Story of the human body in a new multimedia website News New website explores the Inside Story of the human body Nov16 Skills and cash vital factors for UKs energy future Nov10 Institute of Physics Undergraduate Bursary Scheme Jun16 Awards received by this site | Investor in People award Enhance your browser to view our enhanced content correctly. Cookies Copyright Institute of Physics and IOP Publishing Ltd. 2000 - 2005. The Institute of Physics is a registered charity, No. 293851.
Canadian Association of Physicists
The premier association for physicists living in Canada (or who have any interest in physics)
The Canadian Association of Physicists
American Institute of Physics
This web site allows access to online journals, magazines and has information on other publications. Also has related news and information on its services.
The American Institute of Physics -- Physics Publications and Resources home | contact us | join a society advanced search About AIP Member Societies Organizations Working at AIP Physics Today Events Calendar AIP Store RSS News Feeds current issue Publications AIP Journals | Conference Proceedings | Magazines | Books | Scitation Services Publishing | Careers Jobs | Exhibit Meeting Services Resources Government Relations | Education | History | Statistics | News Media About AIP Member Societies | Awards Prizes | Press Releases | Annual Report MRI Pioneer Wins Industrial Physics Prize The American Institute of Physics has named William Edelstein the winner of its Industrial Applications in Physics Prize "for his pioneering developments leading to commercialization of high-resolution Magnetic Resonance Imaging (MRI) for medical applications." See citation Read press release more stories Magazines Physics Today Physics Today Buyers' Guide The Industrial Physicist Computing in Science Engineering News FYI: Science Policy News Physics News Update Physics News Graphics Inside Science News Service AIP Journals Conference Proceedings Virtual Journals Other Publications Information for: Librarians | Authors | Advertisers Publishing Exhibitions Meetings Careers Government Relations Education History Center Statistical Research News Media Corporate Associates American Institute of Physics | privacy policy | site map
American Physical Society
American Physical Society - for the advancement and diffusion of knowledge of physics Message regarding Hurricane Katrina Congressional Visits for the March meeting Join APS about the society our privacy policy join the APS Our site works best in Netscape 6 Internet Explorer 6 or higher GUI browsers should expand at least this wide for optimal viewing
Encyclopedia.com - Quantum Theory
Includes a basic introduction to what this theory is, and links to relevant journal and magazine articles.
quantum theory on Encyclopedia.com Home | About Us | Contact | Help A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z Home article quantum theory Related: Physics modern physical theory concerned with the emission and absorption of energy by matter and with the motion of material particles; the quantum theory and the theory of relativity together form the theoretical basis of modern physics. Just as the theory of relativity assumes importance in the special situation where very large speeds are involved, so the quantum theory is necessary for the special situation where very small quantities are involved, i.e., on the scale of molecules , atoms , and elementary particles . Aspects of the quantum theory have provoked vigorous philosophical debates concerning, for example, the uncertainty principle and the statistical nature of all the predictions of the theory. Relationship of Energy and Matter Dual Nature of Waves and Particles Evolution of Quantum Theory Bibliography Columbia Encyclopedia, Sixth Edition, Copyright (c) 2005. Related Premium Content from HighBeam Research. Magazines and Newspapers for: quantum theory QUANTUM INFORMATION THEORY: A General Surrenders the Field, But Black Hole Battle Rages On Date: 08 13 2004 Publication: Science; Author: Seife, Charles ; Source: MAGAZINES QUANTUM THEORY CONFERENCE HELD IN MOSCOW. . Date: 12 08 2000 Publication: ITAR-TASS; Author: ; Source: NEWSPAPERS Scientists Eye Quantum Theory, Codes Date: 04 28 2000 Publication: AP Online; Author: JOSEPH B. VERRENGIA, AP Science Writer ; Source: NEWSPAPERS Nobel Prize Winner Dr. Anthony Leggett Merges Quantum Computing Theory and Application in New Book. Date: 01 12 2004 Publication: Business Wire; Author: ; Source: NEWSPAPERS From economics to quantum physics, game theory makes its mark.(The Dallas Morning News) Date: 11 24 2003 Publication: Knight Ridder Tribune News Service; Author: Siegfried, Tom ; Source: NEWSPAPERS From economics to quantum physics, game theory makes its mark. Date: 10 22 2003 Publication: The Dallas Morning News (via Knight-Ridder Tribune News Service); Author: ; Source: NEWSPAPERS Science Technology: A great leap forward; Without quantum theory we wouldn't have computers or nuclear power. And yet no scientist has ever proved it to be true - until now. Marcus Chown reports.(Features) Date: 10 06 2004 Publication: The Independent (London, England); Author: Chown, Marcus ; Source: NEWSPAPERS QUESTIONS ANSWERS Your 'warped' reflection is quantum theory with a twist Date: 02 27 2005 Publication: The Sunday Telegraph; Author: Answer by ROBERT MATTHEWS ; Source: NEWSPAPERS As long as a piece of string: Albert Einstein (left) sought unsuccessfully for a "theory of everything" that would combine quantum mechanics with relativity, and explain both the very tiny (the atom) and the... Date: 07 26 2004 Publication: New Statesman (1996); Author: McKie, Robin ; Source: MAGAZINES Scientists from Lucent Technologies' Bell Labs make microscopic seesaw that moves due to spooky quantum physical force; Experiment supports 50-year-old theory and may lead to practical applications. Date: 02 12 2001 Publication: M2 Presswire; Author: ; Source: NEWSPAPERS Pictures and Maps for: quantum theory Schroeder Attends Unveiling Of Einstein Quotes Date: 02 01 2005 Publication: Getty Images; Author: Carsten Koall ; Source: PICTURES A free trial at HighBeam will give you more info than you can handle. Magazines Newspapers QUANTUM INFORMATION THEORY: A General Surrenders the Field, But Black Hole Battle Rages On QUANTUM THEORY CONFERENCE HELD IN MOSCOW. . Scientists Eye Quantum Theory, Codes Nobel Prize Winner Dr. Anthony Leggett Merges Quantum Computing Theory and Application in New Book. From economics to quantum physics, game theory makes its mark.(The Dallas Morning News) More Magazines Newspapers Pictures Maps Schroeder Attends Unveiling Of Einstein Quotes More Pictures Maps Reference Desk at HighBeam Search for quantum theory in: Dictionaries Thesaurus Almanacs Additional Encyclopedias Home | About Us | Contact | Help Encyclopedia.com is a service of HighBeam Research, Inc . Copyright 2005. All rights reserved. Privacy Policy | Terms Conditions
Mona Lisa - ineffable smile of quantum mechanics
The portrait of Mona Lisa is scrutinized with reference to quantum mechanics
[physics 0302089] Mona Lisa - ineffable smile of quantum mechanics Physics, abstract physics 0302089 From: Slobodan Prvanovic [ view email ] Date: Tue, 25 Feb 2003 11:01:13 GMT (186kb) Mona Lisa - ineffable smile of quantum mechanics Authors: Slobodan Prvanovic Comments: 13 pages, 3 figures Subj-class: Popular Physics; Physics Education; History and Overview The portrait of Mona Lisa is scrutinized with reference to quantum mechanics. The elements of different expressions are firstly recognized on her face. The contradictory details are then classified in two pictures that, undoubtedly representing distinct moods, confirm dichotomous character of the original. Consecutive discussion has lead to conclusion that the mysterious state Mona Lisa is in actually is coherent mixture - superposition, of cheerfulness and sadness. Full-text: PostScript , PDF , or Other formats References and citations for this submission: CiteBase (autonomous citation navigation and analysis) Which authors of this paper are endorsers? Links to: arXiv , physics , find , abs ( - + ), 0302 , ?
How Quantum Entanglement Works
Describes Quantum Entanglement without mathematics, starting from first principles.
Quantum Entanglement Quantum Entanglement Introduction These pages explain quantum entanglement by way of colourful pictures, helpful analogies, and absolutely no math. To understand quantum entanglement, several ideas and words must be explained, especially the idea of a photon. The photon is a key concept in physics, and so critical to entanglement that its behaviours must be fully understood. But before delving into the details of photons, let's take a look at the world of the very tiny, beginning with waves and atoms. Click the arrow to continue. Copyright 2005 by Dave Jarvis. Updated: Tuesday, 25-Oct-2005 04:22:43 PDT Introduction Waves Atoms Photons Entanglement Music Author Questions Applications Addendum End Notes Thanks
Quantum Experiments and the Foundations of Physics
Information about experiments performed in Austria.
QFP - Research Photonic Entanglement Experiments Free-Space Distribution of Entangled Photons Entanglement Purification Long Distance Quantum Communication A PlugPlay System for Quantum Cryptography Experimental Quantum Teleportation-Freely Propagating Teleported Qubits Experimental Two-Photon Three-Dimensional Quantum Entanglement (.pdf) Experimental nonlocality proof of quantum teleportation and entanglement swapping (.pdf) Experimental Demonstration of 4-Photon Entanglement and High-fidelity Teleportation Entanglement of the Orbital Angular Momentum States of Photons A quantum random number generator Entangled State Quantum Cryptography The first experimental demonstration of a three-particle entangled state A Bell-Experiment with independent observers Watch a movie on type-I down-conversion filmed in our lab. (7MB mpeg!)sss Experimental Quantum Teleportation - The Innsbruck Experiment Last updated: 2005-02-15 Layout: Julia Petschinka Code: Rainer Kaltenbaek, Gregor Weihs
Path Integral Methods and Applications
These lectures are intended as an introduction to the technique of path integrals and their applications in physics. The audience is mainly first-year graduate students, and it is assumed that the reader has a good foundation in quantum mechanics.
[quant-ph 0004090] Path Integral Methods and Applications Quantum Physics, abstract quant-ph 0004090 From: Richard MacKenzie [ view email ] Date: Mon, 24 Apr 2000 13:58:03 GMT (56kb) Path Integral Methods and Applications Authors: Richard MacKenzie Comments: 55 pages, 23 figures. Lectures given at Rencontres du Vietnam: VIth Vietnam School of Physics, Vung Tau, Vietnam, 27 December 1999 - 8 January 2000 Report-no: UdeM-GPP-TH-00-71 These lectures are intended as an introduction to the technique of path integrals and their applications in physics. The audience is mainly first-year graduate students, and it is assumed that the reader has a good foundation in quantum mechanics. No prior exposure to path integrals is assumed, however. The path integral is a formulation of quantum mechanics equivalent to the standard formulations, offering a new way of looking at the subject which is, arguably, more intuitive than the usual approaches. Applications of path integrals are as vast as those of quantum mechanics itself, including the quantum mechanics of a single particle, statistical mechanics, condensed matter physics and quantum field theory. After an introduction including a very brief historical overview of the subject, we derive a path integral expression for the propagator in quantum mechanics, including the free particle and harmonic oscillator as examples. We then discuss a variety of applications, including path integrals in multiply-connected spaces, Euclidean path integrals and statistical mechanics, perturbation theory in quantum mechanics and in quantum field theory, and instantons via path integrals. For the most part, the emphasis is on explicit calculations in the familiar setting of quantum mechanics, with some discussion (often brief and schematic) of how these ideas can be applied to more complicated situations such as field theory. Full-text: PostScript , PDF , or Other formats References and citations for this submission: SLAC-SPIRES HEP (refers to , cited by , arXiv reformatted); CiteBase (autonomous citation navigation and analysis) 1 trackback ( What's this? ) (send trackbacks to http: arxiv.org trackback quant-ph 0004090) Which authors of this paper are endorsers? Links to: arXiv , quant-ph , find , abs ( - + ), 0004 , ?
Quantum Cryptography
A recent overview of quantum cryptography.
[quant-ph 0101098] Quantum Cryptography Quantum Physics, abstract quant-ph 0101098 From: Gregoire Ribordy [ view email ] Date ( v1 ): Fri, 19 Jan 2001 16:35:48 GMT (769kb) Date (revised v2): Tue, 18 Sep 2001 19:31:51 GMT (895kb) Quantum Cryptography Authors: Nicolas Gisin , Grgoire Ribordy , Wolfgang Tittel , Hugo Zbinden Comments: 55 pages, 32 figures; to appear in Reviews of Modern Physics Quantum cryptography could well be the first application of quantum mechanics at the individual quanta level. The very fast progress in both theory and experiments over the recent years are reviewed, with emphasis on open questions and technological issues. Full-text: PostScript , PDF , or Other formats References and citations for this submission: SLAC-SPIRES HEP (refers to , cited by , arXiv reformatted); CiteBase (autonomous citation navigation and analysis) 1 trackback ( What's this? ) (send trackbacks to http: arxiv.org trackback quant-ph 0101098) Which authors of this paper are endorsers? Links to: arXiv , quant-ph , find , abs ( - + ), 0101 , ?
Topics in Modern Quantum Optics
This is the written version of lectures presented at the 17th Symposium on Theoretical Physics covering various topics in quantum optics.
[quant-ph 9909086] Topics in Modern Quantum Optics Quantum Physics, abstract quant-ph 9909086 From: Bo-Sture Skagerstam [ view email ] Date ( v1 ): Tue, 28 Sep 1999 17:35:03 GMT (594kb) Date (revised v2): Sat, 6 Nov 1999 15:15:10 GMT (325kb) Topics in Modern Quantum Optics Authors: Bo-Sture Skagerstam Comments: 97 pages, 23 figures, 187 references. Misprints corrected, most figures redrawn and references updated This is the written version of lectures presented at "The 17th Symposium on Theoretical Physics - Applied Field Theory", 29 June - 1 July, 1998, the Sangsan Mathematical Science Building, Seoul National University, Seoul, Korea. Full-text: PostScript , PDF , or Other formats References and citations for this submission: SLAC-SPIRES HEP (refers to , cited by , arXiv reformatted); CiteBase (autonomous citation navigation and analysis) Which authors of this paper are endorsers? Links to: arXiv , quant-ph , find , abs ( - + ), 9909 , ?
An introduction to Quantized Lie Groups and Algebras
We give a selfcontained introduction to the theory of quantum groups according to Drinfeld highlighting the formal aspects as well as the applications to the Yang-Baxter equation and representation theory. Introductions to Hopf algebras, Poisson structures and deformation quantization are also provided.
[hep-th 9111043] An introduction to quantized Lie groups and algebras High Energy Physics - Theory, abstract hep-th 9111043 From: Tjark Tjin [ view email ] Date: Thu, 21 Nov 1991 14:18:58 GMT (29kb) An introduction to quantized Lie groups and algebras Authors: T.Tjin Comments: 38 pages Journal-ref: Int.J.Mod.Phys. A7 (1992) 6175-6213 We give a selfcontained introduction to the theory of quantum groups according to Drinfeld highlighting the formal aspects as well as the applications to the Yang-Baxter equation and representation theory. Introductions to Hopf algebras, Poisson structures and deformation quantization are also provided. After having defined Poisson-Lie groups we study their relation to Lie-bi algebras and the classical Yang-Baxter equation. Then we explain in detail the concept of quantization for them. As an example the quantization of $sl_2$ is explicitly carried out. Next we show how quantum groups are related to the Yang-Baxter equation and how they can be used to solve it. Using the quantum double construction we explicitly construct the universal $R$-matrix for the quantum $sl_2$ algebra. In the last section we deduce all finite dimensional irreducible representations for $q$ a root of unity. We also give their tensor product decomposition (fusion rules) which is relevant to conformal field theory. Full-text: PostScript , PDF , or Other formats References and citations for this submission: SLAC-SPIRES HEP (refers to , cited by , arXiv reformatted); CiteBase (autonomous citation navigation and analysis) 1 trackback ( What's this? ) (send trackbacks to http: arxiv.org trackback hep-th 9111043) Which authors of this paper are endorsers? Links to: arXiv , hep-th , find , abs ( - + ), 9111 , ?
Quantum and Foundational Physics (A. Zeilinger)
The website of the group around Prof. Zeilinger working at the university of Vienna in the field of Quantum Physics.
Quantum Experiments and the Foundations of Physics - Last updated: 2005-06-30 Layout: Julia Petschinka Code: Rainer Kaltenbaek, Gregor Weihs
Path Integral Approach to Quantum Mechanics
An intuitive description of Feynman's version of quantum mechanics written in poetic language.
Chapters II-V of Quantum Mechanics Chapters II-V of Quantum Mechanics of The Bible According to Einstein All rights reserved. No part of this website may be reproduced or transmitted in any form or by any means, electronic or mechanical including photocopying and recording, or by any information storage and retrieval system without written permission from the publisher. Copyright 1999 by Jupiter Scientific Publishing Company To the index of The Bible According to Einstein (Adjust width of browser to the width of the running title (the first line). Much of the formatting of The Bible According to Einstein cannot be implemented in html) To Chapter I To Chapters VI-XIII 212 The Bible According to Einstein Chapter II: Paths Ask among all paths, which is the good way? And walk therein, for ye shall find there peace. Now quantum mechanics has two formulations. And the first is the path integral. Now the position of a moving particle as time evolves shall constitute the particle's trajectory. Thus a trajectory shall be a curve through space and time. And because it is a curve in space and time, it shall also be a path. And a point on the path at a particular time shall be the position of the particle. The New Testament 213 And it is as though thou walkest along a wooded valley trail between two mountains. And thou beginst thy walk at the beginning of the trail. And thirty minutes later, thou hast traversed one mile of track. And one hour later, thou art two miles from the start. And two hours later, thou finishest thy walk. And since thou traverst the trail in a steady manner, anyone knows where thou art at any time. Thy motion is predictable. And thy positions at various times constitute a known trajectory. Thus in this example, the trajectory is the trail itself. Now in classical mechanics, there shall be but one trajectory, or path. And this path shall be computable from Newton's laws. And it shall be called the classical trajectory. And knowledge of this path shall provide knowledge of the position of any object in the future, at the present, or in the past. In classical mechanics, it is as though thou be infinitely lazy. And choosest thou the path of least resistance. And avoidest thou steep mountain slopes, so that thou walkest along the center of the valley. And though thou be tempted to take a short cut, it involves climbing and descending. And thou mightest want to pass along a longer, perhaps-more-scenic route, but lazy as thou art, takest thou the easy path, the lazy path. Only poets choose the path less travelled by. And for thee, the classical trajectory shall be the predictable, well-travelled trail. But in quantum mechanics, thou shalt be free. Thou shalt be allowed to walk along all paths. Quantum mechanics -- it be the democratization of dictatorial classical-mechanics laws. So in a quantum mechanical world, an object shall transverse all paths. But some paths shall be more preferable than others. And the most preferred path of all shall be the classical trajectory. And because all paths are included, it shall be impossible to predict with certainty where an object be at a given moment. Thus uncertainty shall be a property of quantum mechanics. And this effect shall have a name -- the uncertainty principle shall be its name. And suppose thou livest in a quantum world and thou beginst thy walk. Now in this quantum case, thou dost not plan thy walk. And thou art only somewhat lazy. So most of the time, movest thou along the local trail of least resistance. But sometimes, decidest thou to profit from a short cut. And sometimes, thou decidest to ascend a little hill. And sometimes, thou decidest to take a longer route. And these decisions are made randomly but preferably, because preferest thou the easy trails. 213 The Bible According to Einstein And friends who are waiting for thee will be frustrated and annoyed because they do not know where thou be for sure. And although it is most probable that thou art on or near thy favorite well-travelled trail, thou perhaps hast gone astray. And this formulation of quantum mechanics shall be called the path integral because "integral" means "to include all." Chapter III: Quantum Mechanics, Philosophers, Scientists and God And philosophers will debate the meaning and implications of quantum mechanics and be particularly concerned about uncertainty. And many will be frustrated and annoyed. But, as for the uncertainty principle, scientists will understand it. And Nature simply shall obey it. To decide and then revise. To decide and then retreat. Uncertainty will certainly confuse the wise. And theorists using the rules of quantum mechanics will carry out countless computations. And the computations will all agree with countless experiments performed by experimentalists. And scientists will develop a great trust in quantum-mechanical dynamics. And for some scientists, the faith will be as strong as a Christian's faith in God. Now as a consequence of the uncertainty principle, it shall be impossible to know simultaneously and exactly the position and momentum of an object.195 Thus position and momentum in quantum mechanics shall only probabilistically be known. And this shall be completely different from the notion of position and momentum in classical mechanics, where they are known with certainty. Chapter IV: The Planck Constant and Quantum Hills Now quantum mechanical behavior and uncertainty shall be controlled by a fundamental number. And this fundamental parameter shall have a name -- Planck's constant shall be called its name. And theorists will pretend that they can control Planck's constant. And if they play the game of "god" and set the constant to zero, then the classical and quantum worlds will coincide. And making Planck's constant smaller shall be like making the slopes of hills and mountains steeper. And so a somewhat lazy walker will be forced to walk quite near the trail of least resistance. And if the theorists do play "god" and make the constant zero, then they make the slopes of hills and mountains infinitely steep -- with giant hands they fold together mountains. And valleys turn into crevasses. ____________________ 195 This effect becomes particularly important for microscopic objects, such as atoms and electons. The New Testament 215 Walkers become completely trapped. And then even the most energetic motivated hiker is compelled to traverse the crack of least resistance. And since this crack is the classical trajectory, the motion shall be predictable and classical. But in the real world, Planck's constant is 6.6 x 10-34 Joule-seconds. Although miniscule, it is nonetheless not zero. And nobody, neither scientists, nor philosophers, nor holy men, nor theorists can make the constant zero. Such be written in firm stone. But since the constant is so small, classical mechanics shall often be a good approximation. And because the constant is so small, quantum mechanical effects shall only in the microscopic world be manifest at all. Thus atoms, nuclei, nucleons, electrons, quarks and other microscopic bodies shall feel quantum effects, but living bodies, blocks and balls shall not. And even in the microscopic world, the hills and valleys shall be very small. And ants may struggle to pass around a tiny pebble, rock or clump of dirt, but elephants do not. And quantum mechanics shall govern all -- All shall hearken to its song. And quantum mechanics shall dominate the small. Chapter V: Tunnelling And quantum tunnelling and barrier penetration shall be a consequence of the uncertainty of paths. In the quantum world, a marble in a coffee cup, in principle, may suddenly jump out. A path exists which climbs the cup and spout. And from the spout, quickly would the marble fall. But for this path, the probability is very very small. And during the lifetime of the Universe, the marble will not jiggle its way out. But in the subatomic world, a body has a better chance to climb a wall. And sometimes, like an army scout who leaves the troops and climbs a little hill, a particle will jump and manage to get out. How foreign from the world of man be the world of the quantum and the small. And if a microscopic particle should suddenly surmount a wall, one need not shout nor be alarmed -- this is what barrier penetration is about. Now a process, which proceeds along a quantum path through a classically forbidden region, shall by definition be quantum tunnelling or barrier penetration. And the decay of a radioactive nucleus shall take place by means of quantum penetration. Such a nucleus shall be like unto a marble in a cup. Quantum mechanics shall be full of fluctuations for objects of small size. The quantum wings shall flap like unto the wings of butterflies. To Chapter I To Chapters VI-XIII Copyright 1999 by Jupiter Scientific Publishing Company To the index of The Bible According to Einstein
100th Anniversary Of Quantum Theory
A scientific article about a new approach in quantum theory.
To 100 anniversary of quantum theory To 100 anniversary of Quantum Theory Friden Korolkevich The quantum theory is based on constant and quantum But the essence of the constant is not clear. Planck called it the mysterious messenger from the real world[1] and de Broglie called it the mysterious costant[2]. What object of nature does it characterize? It is not clear. It is something like the Cheshire Cats smile in Lewis Carrols tale about Alice: there is a quantity of something, but this something is not yet or already seen. In 1951 Albert Einstein wrote to his friend Michael Besso that a conscious search for half a century had not brought him closer to answering the question: what are quanta of light? And it is still the same[3]. Consequently, the quantum theory is based on two famous but little understood categories, which are accepted without dispute. In 1911 Puancare described the Planck constant as small and unchangeable atoms of energy. Boltsman, Erenfest, Ioffe himself had the same thought. In 1924 Planck proposed we accept that the energy of the single oscillation of the light source be equal to one constant of the value . Consequently, in its most general view and following principles of mechanics, the physical essence of light can be brought down to the notion of radiation energy. From the main formula of quantum theory it follows that light is granular. Experiment proved it. It consists of not only separate quanta, but also of separate intermittent grains of energy of the value. Quantity of these grains depends on frequency of oscillations of the source . This means that every oscillation generates an atom of energy of the value. And the series of these oscillations makes a quantum. The length of the photon is determined by correlation: The number of atoms of energy in the photon is defined by correlation: The distance between atoms in the photon is: where - time of their generation, and - velocity of light. Thus, a photon emitted by the atom of Krypton - 86 at an emitting rate of and time of radiation consists of atoms of energy. The standard meter is 1650763,73 wave length of the orange colour of Krypton-86 contained in the photon with length 299,7924 cm. This leads to the number = 4948864 that is brought to the whole number. The same result is obtained by finding the number with correlation: where is the wavelength of the atom of Krypton-86, equal to 6058 . With this we can suggest that the values of the wave length and the distance between the atoms of energy in photons should be equal: Unbreakable connection of the and values as the consequence of in quantum gives us the reason to suppose that the physical basis of the Planck constant is the atom of the energy radiations and this constant defines the value of the atoms energy. According to Vihman [4] the value corresponds to 4,1355 10 -15 eV and 4,4398 10 -24 a.u.m. Since after leaving the source the photons move in space with the velocity of light and the atoms of energy in them do not have the same value as in the moment of their generation, then it is the value of quantity of movement , i.e. impulse. Thus quantum of light presents by itself the chain of atoms of energy. In almost 3-meter photon of the orange colour, for example, about 5 million atoms of energy move with the distance between each other 6058 And the eternal question What is light? may be answered: Light is the flow of atoms of energy in the photons. As such atoms- impulses of energy make quanta by themselves, then they can be considered as subquanta. This description of the photon and light agrees with the idea of non-sinus waves realized in radiolocation by Chapman in 1976 and developed by Harmuth [5]. If atoms of energy do exist, then they have a measurement. The measurement of the atoms energy solves the problem of infinity in description of microparticles because they are created from the photons and that is why they can be measured. Because of the fact that there are no quarks in the photons neither before photobirth of the particles, nor after their annihilation, we may suggest the qurks presence in subquanta fractions in the adrones. The facts that support this suggestion are the complex structure of particles, the spin and the excitement of rotational type in the nucleus of the atom which probably is also created from the grains of the value. Neither in theory, nor in practice the confluence of the atoms of energy in some sort of formations has not been found, but annihilation of particles and disintegration of nucleus always is accompanied by radiation of the atom energy photons. The metre sizes of the photons cause doubts in rightfulness to include them in the numbers of elementary particles. But corpuscular characteristics of light may be fully explained by the memory of radiation receivers of the subquanta energy effect.It is similar to the period of relaxation in physics of semiconductors. If this memory is defined by correlation: And it is shorter than the period of reception of two consecutive impulses of the photon, then the receiver has time to release from the effect of the first impulse, to forget about it.Corpuscularity of light does not exist. But if the relaxation period of the receiver of electron, atom, or molecule is longer than the interval between the impulses effects, then they supposedly overtake each other and increase the affect of light in proportion to its frequency and memory time of the receiver. While crossing frequency threshold of the photoeffect the effect of the photon becomes similar to the hit of the substantial particle. And that how corpuscularity of light and its dualism have been interpreted. If this memory has not been in existence all the photons will have a hard effect irrespective of their frequency and everything alive will be destroyed. Fortunately the receivers have this memory. It is noticeable that even similar photons have different energy effect on different receivers. Thus copper is fully indifferent to light but it hits out electron from the atom of caesium. The quanta of light with the same frequency are energetic for potassium, sodium and lithium and completely unnoticeable for gold, platinum and tungsten. It means that their memory period is different. Due to this circumstance we may suggest a possibility to create power engineering of cosmic radiations if it becomes possible to increase and control time of relaxation of receiving devices. Practically it is the same to receive either high frequency and intensive rays with ordinary memory or low frequency and dispersed rays with increased memory. The increased memory of the enrgy subquanta can be seen in the organic world. The problem of collection of dispersed photons has been solved long time ago in radioastronomy. It means that radiation energetics is possible. Invariability of the atoms of energy allow us to consider them as primary element of the real world and foundation of the modern atomic science. The decrease of the number of subquanta in the photons and their redness after encounter with different particles along their long way towards us maybe is the reason of red shift of the spectre of galaxies. This corresponds with the known empiric correlation of the red shift: Atoms of energy hit out from the photons together with neutrino probably compose the hidden mass of the Universe. The problem of neutrino mass may be solved by the presence of their energy. The chaotic movement of these atoms and neutrino may determine so called energy of the zero oscillations of the vaccuum. The limitless value of this energy represents a problem in the theory. The benefit of energy atomic understanding of radiations does not end here. It agrees with all optical phenomena and may be combined with electromagnetic theory with correction on mechanical interpretation within the theory of similarity and dynamic analogies. With the subquantum conception transfers in a quantum one and is generalized by it. The notion of the atomic energy of the photons structure opens new opportunities for the development of quantum physics, power engineering and electronics. 15.01.2000. Bibliography 1. M.Planck. Physics,1929,9,193-222. 2. L.de Broglie. Sur les sentiers de la science. A. Michet, Paris,1960 3. Physics Today,v.25,No3,pp.38-47,1972 4. E.Wichman. Quantum Physics. McGrow-Hill,1967 5. H.Harmuth. Sequency Theory. Acad. Press. N.Y.,1977. 135 Hillside Rd., Avoca Beach, NSW 2251 AUSTRALIA Tel: (02) 43 82 18 66 e-mail: rubbo@idl.net.au
QMvideos
Article which teaches the basics of quantum mechanics with help of digital videos showing the time evolution of wave packets in various potentials, with interference, tunneling.
Quantum Mechanics help Preface Quantum mechanics is a mathematical theory that can describe the behavior of objects that are roughly 10,000,000,000 times smaller than a typical human being. Quantum particles move from one point to another as if they are waves. However, at a detector they always appear as discrete lumps of matter. There is no counterpart to this behavior in the world that we perceive with our own senses. One cannot rely on every-day experience to form some kind of "intuition" of how these objects move. The intuition or "understanding" formed by the study of basic elements of quantum mechanics is essential to grasp the behavior of more complicated quantum systems. The approach adopted in all textbooks on quantum mechanics is that the mathematical solution of model problems brings insight in the physics of quantum phenomena. The mathematical prerequisites to work through these model problems are considerable. Moreover, only a few of them can actually be solved analytically. Furthermore, the mathematical structure of the solution is often complicated and presents an additional obstacle for building intuition. This presentation introduces the basic concepts and fundamental phenomena of quantum physics through a combination of computer simulation and animation. The primary tool for presenting the simulation results is computer animation. Watching a quantum system evolve in time is a very effective method to get acquainted with the basic features and peculiarities of quantum mechanics. The images used to produce the computer animated movies shown in this presentation are not created by hand but are obtained by visualization of the simulation data. The process of generating the simulation data for the movies requires the use of computers that are far more powerful than Pentium III based PC 's. Most of the simulations require the use of a supercomputer. Consequently, within this presentation, it is not possible to change the model parameters and repeat a simulation in real time. This presentation is intended for all those who are interested to learn about the fundamentals of quantum mechanics. Some knowledge of mathematics will help but is not required to understand the basics. This presentation is not a substitute for a textbook. The presentation begins by showing the simplest examples, such as the motion of a free particle, a particle in an electric field, etc.. Then, the examples become more sophisticated in the sense that one can no longer rely on one's familiarity with classical physics to describe some of the qualitative features seen in the animations. Classical notions are of no use at all for the last set of examples. However, once all other examples have been "understood", it should be possible to "explain" the behavior of these systems also. Instead of using a comprehensive mathematical apparatus to obtain and analyze solutions of model problems, a computer simulation technique is employed to solve these problems including those that would prove intractable otherwise. Content Introduction Motion in a potential Interference Aharonov-Bohm Stern-Gerlach Tunneling Identical particles The authors FAQs Feedback CD-ROM Copyright
Quantum Physics Primer
Describes some basic concepts of quantum physics.
Quantum Physics Next: Blackbody Radiation Up: Main physics index Previous: Quantum Physics Quantum Physics We have seen in the previous chapter that the properties of refraction, diffraction, and interference all require a wave picture of light. In this chapter we will begin to study other aspects associated with light which cannot be explained with a wave picture, but in fact need a particle picture. The coexistence of phenomena which require both a wave and a particle picture is called a wave-particle duality, and is at the heart of the modern theory of quantum physics. Blackbody Radiation The Photoelectric Effect Compton Scattering Wave-Particle Duality de Broglie Waves The Uncertainty Principle Problems www-admin@theory.uwinnipeg.ca 10 9 1997
Quantum Communication
A short introduction titled "Quantum communication moves into the unknown" by David Deutsch and Artur Ekert.
Quantum Communication - short introduction Quantum communication moves into the unknown By David Deutsch and Artur Ekert Information is physical and any processing of information is always performed by physical means - an innocent-sounding statement, but its consequences are anything but trivial, In the last few years there has been an explosion of theoretical and experimental innovations which, their discoverers claim, are creating a fundamental new discipline: a distinctively quantum theory of information. Quantum physics allows the construction of qualitatively new types of logic gates, absolutely secure cryptosystems (systems that combine communications and cryptography), the cramming of two bits of information into one physical bit and, as has just been proposed, a sort of "teleportation", Here we describe the last two "miracles". Classical information theory agrees with everyday intuition: if you want to send a message using an object which can be put into one of N distinguishable states, the maximum number of different messages that you can send is N. For example, a single photon can have only two distinguishable polarisation states, say "left-handed" and "right-handed". So if you send a message by preparing the polarisation of a single photon and transmitting it, it is obvious that you can send no more than two distinguishable messages, i.e, one bit of information. 0bvious, but false. The state of a classical system can be specified by specifying the states of all its constituent systems. But in quantum theory a combined system can have additional properties, in which case the constituent systems can be said to be "entangled" with one another. Entangled states were first investigated in the famous paper of Einstein, Podolsky and Rosen (EPR). Quantum mechanics is also nonlocal, in that distant and non-interacting systems may be entangled. Last year Charles Bennett of the IBM Thomas J Watson Research Center, Yorktown Heights, New York, and Stephen Wiesner used non-locality to devise a hypothetical quantum communication system in which the receiver reads a two-bit message from two physical bits, but only one of those bits - the transmitted bit - has physically come from the sender of the message (Phys. Rev. Lett. (1992) 69 2881). The other - the reference bit - never leaves the receiver (see (a) in the figure). Strangely, it is the receiver, Bob, who makes the first move. He prepares two photons, or two spin-half particles (which exist in one of two states - spin up or spin down), jointly in an "entangled" state. He stores one particle and sends the other one to the sender, "Alice", who stores it. To ensure that the entanglement is maintained, each particle must be kept isolated from its surroundings. When it is time to send a message, Alice performs one of four special operations on her stored particle before transmitting it back to Bob. For the spin-half particles these four unitary operations, performed by the quantum gate U, are equivalent to: doing nothing (unit operation), or rotating the spin by 180 degrees about the x, y or z axes; for photons these operations correspond to polarisation rotations. The operations have to be unitary to maintain the quantum mechanical coherence of the particle. These operations, although performed only on one particle, affect the joint (entangled) quantum state of the two particles. This cannot be verified by measurements on the two particles separately. But by measuring both of them jointly, using the quantum gate M, Bob can determine which of the four operations Alice performed, and so receive one of the four messages. Thus the technique effectively doubles the peak capacity of an information channel. The other miracle, "quantum teleportation", is also based on quantum nonlocality. In classical physics, the teleportation machines of science fiction present no problem of principle. One simply measures the state of every atom of the object to be teleported, transmits that information, and any number of copies of the object can be reconstructed by any receiver. But quantum physics fundamentally limits the accuracy of any such process because one cannot experimentally determine an unknown state. At most one can distinguish between N mutually orthogonal states, provided one already knows which N states those are. N is determined by the system being used for photons and spinhalf particles, for example, N=2. Cloning (accurately copying) an unknown quantum state would be equivalent to a simultaneous sharp measurement of all observables of the system, including non-commuting ones, which is forbidden by the uncertainty principle. Thus, suppose Alice is given an object in an unknown quantum state . Until recently, it was thought that the only way she could cause Bob to possess an object in that same state, , would be either to send the object itself to Bob, or to transfer its state characteristics to another particle and send that (and irretrievably alter the state of the original object). In either case, the transmission would have to be along a channel that maintains quantum coherence, which requires the complete isolation of the transmitted object. Bennett, Brassard, Crpeau, Jozsa, Peres and Wootters have now shown how an unknown quantum state can be "teleported" from one place to another (Phys. Rev. Lett. (1993) 70 1895). As in the previous example, Alice and Bob are each given one particle of the entangled EPR pair (see (b) in the figure). Then Alice brings together her particle and the particle in an unknown state, and performs jointly on those two particles a special measurement using the quantum gate M. This measurement has four possible outcomes - it is, in fact, the same measurement that is performed at the end of the two-bit communication process. Alice then communicates the result to Bob, by any ordinary channel, such as a telephone or radio transmitter, According to this result, Bob, who has the other member of the EPR pair, performs one of four operations on his particle (the same four operations that were used in the communication scheme) using the quantum gate U. The effect is to leave Bob's particle in exactly the same state that Alice's particle was originally in. So far neither of these miracles is yet practical. Quantum gates such as U can be built, but the operation performed by the gate M, sometimes called a "Bell measurement", is beyond present technology. Harald Weinfirter and Anton Zeilinger from the University of lnnsbruck in Austria have designed optical experiments, using so-called "parametric down-conversion and a simple photodetection scheme, which would allow communication with more than one bit of information per physical bit. They are developing techniques that might allow quantum teleportation too. But the theoretical results, whether they are practicable or not, are already of considerable importance, because they force us to fundamentally revise our concept of information in physics. Figure (a) Two bits for the price of one: starting from the bottom, Bob sends one particle of an entangled (EPR) pair to Alice who performs one of four operations on it with the quantum gate M Alice then returns the particle to Bob who measures the state of the joint (and still entangled) system with the quantum gate M to receive one of four possible messages (two bits of information), although only one particle (which can exist in only one of two states, i.e. carry only one bit of information) has been sent. Ouantum communication channels are represented by thin lines, classical channels by thick lines. (b) Ouantum teleportation: again Bob sends one particle of an entangled state to Alice who measures the joint state of this with the unknown state . She then transmits (classically) this result to Bob. This information can be used to put Bob's remaining particle (the other half of the entangled pair) in the state . Extract from Physics World, June 1993
Fermions and Bosons
A set of notes on fermions and bosons, including a review of angular momentum in quantum mechanics.
Storage Rings and Colliders Next: Proton-Antiproton Collisions Up: Cosmic Rays and Accelerator Previous: Deep Inelastic Scattering of Contents Storage Rings and Colliders Figure 18.7: Schematic model of a particle-antiparticle collider. The particles and antiparticles are injected into the storage rings shown and are made to go in a circle by magnetic fields. The beams cross at two points and apparatus is set up around these points to observe the products of collisions. An alternate way to create interesting collisions is to crash particles and antiparticles of the same energy into each other. This is done via a storage ring, as shown in figure 18.7 . A set of magnets forces particles and antiparticles (which have opposite charges) to move in opposing circles within a high vacuum. The circles are slightly offset so that the beams cross at only two points. Collisions occur at these points and are observed by various types of experimental equipment. An alternate type of collider has two storage rings which intersect at only one point. This type of system can be used to collide particles of the same type together, e. g., protons colliding with protons. Next: Proton-Antiproton Collisions Up: Cosmic Rays and Accelerator Previous: Deep Inelastic Scattering of Contents David Raymond 2004-12-04
Virtual Partical FAQ
This site answers questions about virtual particles.
Part.virtualiFAQ original By Matt McIrvin 1994 Some Frequently Asked Questions About Virtual Particles Contents: What are virtual particles? How can they be responsible for attractive forces? Do they violate energy conservation? Do they go faster than light? Do virtual particles contradict relativity or causality? I hear physicists saying that the "quantum of the gravitational force" is something called a graviton. Doesn't general relativity say that gravity isn't a force at all? What are virtual particles? One of the first steps in the development of quantum mechanics was Max Planck's idea that a harmonic oscillator (classically, anything that wiggles like a mass bobbing on the end of an ideal spring) cannot have just any energy. Its possible energies come in a discrete set of equally spaced levels. An electromagnetic field wiggles in the same way when it possesses waves. Applying quantum mechanics to this oscillator reveals that it must also have discrete, evenly spaced energy levels. These energy levels are what we usually identify as different numbers of photons. The higher the energy level of a vibrational mode, the more photons there are. In this way, an electromagnetic wave acts as if it were made of particles. The electromagnetic field is a quantum field. Electromagnetic fields can do things other than vibration. For instance, the electric field produces an attractive or repulsive force between charged objects, which varies as the inverse square of distance. The force can change the momenta of the objects. Can this be understood in terms of photons as well? It turns out that, in a sense, it can. We can say that the particles exchange "virtual photons" which carry the transferred momentum. Here is a picture (a "Feynman diagram") of the exchange of one virtual photon. \ \ - p ~~~ ^ time ~~~~ | ~~~ | \ --- space \ The lines on the left and right represent two charged particles, and the wavy line (jagged because of the limitations of ASCII) is a virtual photon, which transfers momentum from one to the other. The particle that emits the virtual photon loses momentum p in the recoil, and the other particle gets the momentum. This is a seemingly tidy explanation. Forces don't happen because of any sort of action at a distance, they happen because of virtual particles that spew out of things and hit other things, knocking them around. However, this is misleading. Virtual particles are really not just like classical bullets. How can they be responsible for attractive forces? The most obvious problem with a simple, classical picture of virtual particles is that this sort of behavior can't possibly result in attractive forces. If I throw a ball at you, the recoil pushes me back; when you catch the ball, you are pushed away from me. How can this attract us to each other? The answer lies in Heisenberg's uncertainty principle. Suppose that we are trying to calculate the probability (or, actually, the probability amplitude) that some amount of momentum, p, gets transferred between a couple of particles that are fairly well- localized. The uncertainty principle says that definite momentum is associated with a huge uncertainty in position. A virtual particle with momentum p corresponds to a plane wave filling all of space, with no definite position at all. It doesn't matter which way the momentum points; that just determines how the wavefronts are oriented. Since the wave is everywhere, the photon can be created by one particle and absorbed by the other, no matter where they are. If the momentum transferred by the wave points in the direction from the receiving particle to the emitting one, the effect is that of an attractive force. The moral is that the lines in a Feynman diagram are not to be interpreted literally as the paths of classical particles. Usually, in fact, this interpretation applies to an even lesser extent than in my example, since in most Feynman diagrams the incoming and outgoing particles are not very well localized; they're supposed to be plane waves too. The uncertainty principle opens up the possibility that a virtual photon could impart a momentum that corresponds to an attractive force as well as to a repulsive one. But you may well ask what makes the force repulsive for like charges and attractive for opposite charges! Does the virtual photon know what kind of particle it's going to hit? It's hard even for particle physicists to see this using the Feynman diagram rules of QED, because they're usually formulated in a manner designed to answer a completely different question: that of the probability of particles in plane-wave states scattering off of each other at various angles. Here, though, we want to understand what nudges a couple of particles that are just sitting around some distance apart--to explain the experiment you may have done in high school, in which charged balls of aluminum foil repel each other when hanging from strings. We want to do this using virtual particles. It can be done. In QED, as in quantum mechanics in general, there are wave functions with complex-number values which have to be squared to get probabilities. We want to see that the wave function changes so that the like charges, on average, are repelled from each other, and the unlike charges, on average, are attracted. Suppose, for simplicity, that the charged particles' wave functions are initially Gaussians at rest, that is, normal bell-shaped, real-valued functions, and that they are lined up along the x axis. You can think of the wave functions, schematically, as looking like this: ____ ____ \ \ x -- _ \_ _ \_ 0 _______ \_________________ \__________ where you are supposed to imagine that those ASCII stairs are actually continuous, smooth curves. Imagine, furthermore, that the distance between the two lumps in this diagram is much larger than the width of a lump. If you know some quantum mechanics, you know that in the absence of any forces, the lumps will just spread out symmetrically (well, if the particles are identical we have to worry about other details when they start to overlap substantially, but if the lumps are far apart that won't happen for a while). If there is an overall constant potential energy, that will give the wave functions an additional rotating phase, but we can always ignore that without affecting any physical quantities. Concentrate on one of the particles, say, the one to the left. As well as the ordinary wave functions that are functions of position, I can also define wave functions in "momentum space": there is a probability amplitude for every momentum, which you square to find the probability density. If its wave function in space is Gaussian, then the wave function in "momentum space" is also Gaussian: as a function of the x component of momentum it is also bell-shaped. The narrower the position-space Gaussian is, the wider the momentum-space Gaussian is; that is Heisenberg's uncertainty principle! _____________ __ ^ \__ __ | \__ p -- ____ | \____ 0 ________ zero momentum \____________ In order to make this problem tractable, I should furthermore specify that the momentum-space wave function isn't so wide (in other words, the position-space wave function isn't so narrow) that consequent relativistic effects become large. (For electrons, this doesn't happen until the position wave functions are squeezed into a space much smaller than an atom; and if the particle is more massive you have to squeeze it even more.) Also, I will ignore the particles' magnetic moments, if they have them, because all I care about is the electrostatic force. Now, consider a virtual photon that comes from the particle on the right and is absorbed by the particle on the left. Actually calculating the photon's wave function is a little hairy; I have to consider the possibility that the photon was emitted by the other particle at any prior time. (However, I can save myself a little effort later by automatically including the possibility that the photon actually comes from the particle on the left and is absorbed by the particle on the right, with the recoil nudging the left particle: all I have to do is include situations in which the photon is "emitted on the right" in the future and goes "backward in time," and take its momentum to be minus what it really is! As long as I remember what's really going on, this trick is formally OK and saves a lot of trouble; it was introduced by Richard Feynman.) When I include all of these possibilities, it turns out that I can approximate the photon's momentum-space wave function usably well by the following: the wave function is a function proportional to the electric charge of the emitting particle (in a sense this defines what electric charge is), and it has a few big, narrow spikes in it. One spike is proportional to -i times the charge, and is to the left of the origin; the other spike is minus that and is to the right of the origin. (There is also a third spike at zero momentum that has a real amplitude, but it turns out not to do anything important at the end of the day--it provides a constant potential energy--so I'll ignore it.) The imaginary component of the photon wave function looks like this, if the emitting particle was a negatively charged electron: | +i | zero momentum p -- | | | v 0 ____________|________________________________________ | | | -i | | If the emitting particle was positively charged, this picture is upside down. (A note for experts only: The somewhat QED-savvy may be puzzled by the total nonresemblance of this to any well-known photon propagator. That's because I'm not going into momentum space in every direction, just in the x direction. The more QED-savvy will notice that I am making some pretty monstrous oversimplifications here. Actually they are not so bad; what I'm doing is the equivalent of assuming that the potential can be locally approximated by a sinusoid! If the wave packet is small enough in position space, a Coulomb potential and a sinusoidal one are both effectively a constant-force potential, so I can do this. Neglecting all magnetic effects and taking the nonrelativistic limit, the amplitude for transfer of a given momentum by a single virtual photon -- which is essentially what I am colorfully, and without much prevarication, labeling the "photon's momentum-space wave function"-- has to have an imaginary part odd in p_x because the potential is real, so in any case the qualitative effect will be the same as what I describe below, and for essentially the same reasons. It's just so much easier to convolute spikes. As for the single-particle "wave functions" of the charged particles, I can speak of them with fair correctness because the particles are far apart and slowly moving.) The effect of a virtual photon hit on the charged particle's momentum-space wave function is, then, quite simple. The photon has a certain probability amplitude of knocking the charged particle to the left and a certain amplitude of knocking it to the right. The probability amplitude for each possibility is just proportional to i times the charge of the particle times the photon wave function times the time! (The other constants of proportionality depend on the system of units; we're not being terribly quantitative so don't worry about them.) We multiply the original charged particle's wave function--shifted to the right or left in momentum space, depending on which way it got knocked by the photon--times this amplitude, for each of the two possibilities, and then add the modified wave functions for the two possibilities together. If both particles are negatively charged, or both are positively charged, then we're adding a right-side-up wave function, shifted to the left, to an upside-down wave function shifted to the right. The result is real-valued and looks something like this: _____ + _ \_ zero momentum __ \ | p -- __ \ | 0 ___ \ v \ ________ \ __ \ __ - \_ _ \_____ and it increases in size as time goes on, from zero at the start of the problem. If the particles have opposite charges, then you should flip that picture upside down. The result is proportional to the product of the two charges, because we multiplied in the other particle's charge when finding the photon wave function, and this particle's charge when the interaction happened. Now, by now you might be a little disturbed. We get wave functions by squaring amplitudes. The lump to the right of the origin goes down just as far as the lump to the left goes up. So isn't the probability that the photon knocked the particle's momentum toward the other one just as large as the probability that it knocked it away? No, because there is still some probability amplitude that no photon interaction occurred at all, and since we have no way of unambiguously telling one possibility from the other, we need to add the two wave functions together before squaring them! (There are also amplitudes for larger numbers of interactions, but for short times, we need not worry about those. Also, the "no-hit" wave function is not exactly the unmodified one, because of its own natural time evolution, but for short times all that does to the momentum-space wave function is give it a small imaginary part that we don't care about here.) I said the unmodified wave function was positive, so the post-hit wave function will interfere with it constructively on the left side of the origin, and destructively on the right (or vice versa if the particles have opposite charges). So after a little time has passed, the wave function looks something like this in momentum space: ________ zero momentum _ \___ | \__ v p -- _ \__ _ \______ 0 \________________ Squaring the wave function gives you a probability distribution whose hump is also shifted to the left. The momentum of the particle is skewed leftward--it is being repelled from the other particle! If the charges have the same sign, the interference goes the other way and the particle's momentum is skewed rightward, for a net attraction. The position-space wave function itself will tend to move leftward or rightward as it spreads out, as the case may be. You might wonder: What happens when the time gets late enough that the negative hump in the struck wave function more than cancels the original wave function? Well, at those times, my analysis here is not enough, because there is also a significant amplitude that two photons have hit the particle (and things get gnarlier, because they could have hit it in any order); for still longer times I need to consider three, and so on. The important point is that the photon doesn't "know" that it's going to hit a particle of the same charge as the one that emitted it, or of the opposite charge. The distinction between attraction and repulsion actually arises when the effect of the virtual photon interferes with the unperturbed wave function! In general, the distinction comes from interference between the contributions from odd and even numbers of virtual photons traveling from one particle to the other. Each such photon multiplies a factor of the product of the two charges into its contribution to the wave function; so the odd processes will get a factor of -1 from this product (times other things, of course) if the charges are different and +1 if they are alike, whereas the even processes get a factor of +1 in either case. The interference between "odd" and "even" terms in the wave function yields effects which survive even upon squaring the amplitude to get a probability. In the discussion above, by limiting consideration to short times, I've been able to ignore everything but the no-photon and one-photon processes. This interference, with the amplitude for photon collision increasing smoothly with time, is also part of the reason why you can regard a stately and continuous thing like the evolution of a wave packet as the result of violent particle-collision events. As discordant as these phenomena may seem, they are actually two sides of the same coin. In the classical realm we don't see the spreading of the wave functions, but we do see this gradual net change in momentum, and it is what we call a force. Do they violate energy conservation? We are really using the quantum-mechanical approximation method known as perturbation theory. In perturbation theory, systems can go through intermediate "virtual states" that normally have energies different from that of the initial and final states. This is because of another uncertainty principle, which relates time and energy. In the pictured example, we consider an intermediate state with a virtual photon in it. It isn't classically possible for a charged particle to just emit a photon and remain unchanged (except for recoil) itself. The state with the photon in it has too much energy, assuming conservation of momentum. However, since the intermediate state lasts only a short time, the state's energy becomes uncertain, and it can actually have the same energy as the initial and final states. This allows the system to pass through this state with some probability without violating energy conservation. Some descriptions of this phenomenon instead say that the energy of the system becomes uncertain for a short period of time, that energy is somehow "borrowed" for a brief interval. This is just another way of talking about the same mathematics. However, it obscures the fact that all this talk of virtual states is just an approximation to quantum mechanics, in which energy is conserved at all times. The way I've described it also corresponds to the usual way of talking about Feynman diagrams, in which energy is conserved, but virtual particles can carry amounts of energy not normally allowed by the laws of motion. (General relativity creates a different set of problems for energy conservation; that's described elsewhere in the sci.physics FAQ.) Do they go faster than light? Do virtual particles contradict relativity or causality? In section 2, the virtual photon's plane wave is seemingly created everywhere in space at once, and destroyed all at once. Therefore, the interaction can happen no matter how far the interacting particles are from each other. Quantum field theory is supposed to properly apply special relativity to quantum mechanics. Yet here we have something that, at least at first glance, isn't supposed to be possible in special relativity: the virtual photon can go from one interacting particle to the other faster than light! It turns out, if we sum up all possible momenta, that the amplitude for transmission drops as the virtual particle's final position gets further and further outside the light cone, but that's small consolation. This "superluminal" propagation had better not transmit any information if we are to retain the principle of causality. I'll give a plausibility argument that it doesn't in the context of a thought experiment. Let's try to send information faster than light with a virtual particle. Suppose that you and I make repeated measurements of a quantum field at distant locations. The electromagnetic field is sort of a complicated thing, so I'll use the example of a field with just one component, and call it F. To make things even simpler, we'll assume that there are no "charged" sources of the F field or real F particles initially. This means that our F measurements should fluctuate quantum- mechanically around an average value of zero. You measure F (really, an average value of F over some small region) at one place, and I measure it a little while later at a place far away. We do this over and over, and wait a long time between the repetitions, just to be safe. . . . ------X ------ X------ ^ time ------X me | ------ | you X------ --- space After a large number of repeated field measurements we compare notes. We discover that our results are not independent; the F values are correlated with each other-- even though each individual set of measurements just fluctuates around zero, the fluctuations are not completely independent. This is because of the propagation of virtual quanta of the F field, represented by the diagonal lines. It happens even if the virtual particle has to go faster than light. However, this correlation transmits no information. Neither of us has any control over the results we get, and each set of results looks completely random until we compare notes (this is just like the resolution of the famous EPR "paradox"). You can do things to fields other than measure them. Might you still be able to send a signal? Suppose that you attempt, by some series of actions, to send information to me by means of the virtual particle. If we look at this from the perspective of someone moving to the right at a high enough speed, special relativity says that in that reference frame, the effect is going the other way: . . . X------ ------ ------X you X------ ^ time ------ | ------X me | --- space Now it seems as if I'm affecting what happens to you rather than the other way around. (If the quanta of the F field are not the same as their antiparticles, then the transmission of a virtual F particle from you to me now looks like the transmission of its antiparticle from me to you.) If all this is to fit properly into special relativity, then it shouldn't matter which of these processes "really" happened; the two descriptions should be equally valid. We know that all of this was derived from quantum mechanics, using perturbation theory. In quantum mechanics, the future quantum state of a system can be derived by applying the rules for time evolution to its present quantum state. No measurement I make when I "receive" the particle can tell me whether you've "sent" it or not, because in one frame that hasn't happened yet! Since my present state must be derivable from past events, if I have your message, I must have gotten it by other means. The virtual particle didn't "transmit" any information that I didn't have already; it is useless as a means of faster-than-light communication. The order of events does not vary in different frames if the transmission is at the speed of light or slower. Then, the use of virtual particles as a communication channel is completely consistent with quantum mechanics and relativity. That's fortunate: since all particle interactions occur over a finite time interval, in a sense all particles are virtual to some extent. I hear physicists saying that the "quantum of the gravitational force" is something called a graviton. Doesn't general relativity say that gravity isn't a force at all? You don't have to accept that gravity is a "force" in order to believe that gravitons might exist. According to QM, anything that behaves like a harmonic oscillator has discrete energy levels, as I said in part 1. General relativity allows gravitational waves, ripples in the geometry of spacetime which travel at the speed of light. Under a certain definition of gravitational energy (a tricky subject), the wave can be said to carry energy. If QM is ever successfully applied to GR, it seems sensible to expect that these oscillations will also possess discrete "gravitational energies," corresponding to different numbers of gravitons. Quantum gravity is not yet a complete, established theory, so gravitons are still speculative. It is also unlikely that individual gravitons will be detected any time in the near future. Furthermore, it is not at all clear that it will be useful to think of gravitational "forces," such as the one that sticks you to the earth's surface, as mediated by virtual gravitons. The notion of virtual particles mediating static forces comes from perturbation theory, and if there is one thing we know about quantum gravity, it's that the usual way of doing perturbation theory doesn't work. Quantum field theory is plagued with infinities, which show up in diagrams in which virtual particles go in closed loops. Normally these infinities can be gotten rid of by "renormalization," in which infinite "counterterms" cancel the infinite parts of the diagrams, leaving finite results for experimentally observable quantities. Renormalization works for QED and the other field theories used to describe particle interactions, but it fails when applied to gravity. Graviton loops generate an infinite family of counterterms. The theory ends up with an infinite number of free parameters, and it's no theory at all. Other approaches to quantum gravity are needed, and they might not describe static fields with virtual gravitons. geovisit();
Quantum Mechanics
A survey of quantum mechanics from the Stanford Encyclopedia of Philosophy.
Quantum Mechanics version history HOW TO CITE THIS ENTRY Stanford Encyclopedia of Philosophy A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z This document uses XHTML Unicode to format the display. If you think special symbols are not displaying correctly, see our guide Displaying Special Characters . last substantive content change NOV 29 2000 The Encyclopedia Now Needs Your Support Please Read How You Can Help Keep the Encyclopedia Free Quantum Mechanics Quantum mechanics is, at least at first glance and at least in part, a mathematical machine for predicting the behaviors of microscopic particles or, at least, of the measuring instruments we use to explore those behaviors and in that capacity, it is spectacularly successful: in terms of power and precision, head and shoulders above any theory we have ever had. Mathematically, the theory is well understood; we know what its parts are, how they are put together, and why, in the mechanical sense (i.e., in a sense that can be answered by describing the internal grinding of gear against gear), the whole thing performs the way it does, how the information that gets fed in at one end is converted into what comes out the other. The question of what kind of a world it describes, however, is controversial; there is very little agreement, among physicists and among philosophers, about what the world is like according to quantum mechanics. Minimally interpreted, the theory describes a set of facts about the way the microscopic world impinges on the macroscopic one, how it affects our measuring instruments, described in everyday language or the language of classical mechanics. Disagreement centers on the question of what a microscopic world, which affects our apparatuses in the prescribed manner, is, or even could be, like intrinsically; or how those apparatuses could themselves be built out of microscopic parts of the sort the theory describes.[ 1 ] That is what an interpretation of the theory would provide: a proper account of what the world is like according to quantum mechanics, intrinsically and from the bottom up. The problems with giving an interpretation (not just a comforting, homey sort of interpretation, i.e., not just an interpretation according to which the world isn't too different from the familiar world of common sense, but any interpretation at all) are dealt with in other sections of this encyclopedia. Here, we are concerned only with the mathematical heart of the theory, the theory in its capacity as a mathematical machine, and whatever is true of the rest of it this part of the theory makes exquisitely good sense. 1. Terminology 2. Mathematics 3. Quantum Mechanics 4. Structures on Hilbert Space Bibliography Other Internet Resources Related Entries 1. Terminology Physical systems are divided into types according to their unchanging (or state-independent) properties, and the state of a system at a time consists of a complete specification of those of its properties that change with time (its state-dependent properties). To give a complete description of a system, then, we need to say what type of system it is and what its state is at each moment in its history. A physical quantity is a mutually exclusive and jointly exhaustive family of physical properties (for those who know this way of talking, it is a family of properties with the structure of the cells in a partition). Knowing what kinds of values a quantity takes can tell us a great deal about the relations among the properties of which it is composed. The values of a bivalent quantity, for instance, form a set with two members; the values of a real-valued quantity form a set with the structure of the real numbers. This is a special case of something we will see again and again, viz., that knowing what kind of mathematical objects represent the elements in some set (here, the values of a physical quantity; later, the states that a system can assume, or the quantities pertaining to it) tells us a very great deal (indeed, arguably, all there is to know) about the relations among them. In quantum mechanical contexts, the term observable is used interchangeably with physical quantity, and should be treated as a technical term with the same meaning. It is no accident that the early developers of the theory chose the term, but the choice was made for reasons that are not, nowadays, generally accepted. The state-space of a system is the space formed by the set of its possible states,[ 2 ] i.e., the physically possible ways of combining the values of quantities that characterize it internally. In classical theories, a set of quantities which forms a supervenience basis for the rest is typically designated as basic or fundamental, and, since any mathematically possible way of combining their values is a physical possibility, the state-space can be obtained by simply taking these as coordinates.[ 3 ] So, for instance, the state-space of a classical mechanical system composed of n particles, obtained by specifying the values of 6n real-valued quantities three components of position, and three of momentum for each particle in the system is a 6n-dimensional coordinate space. Each possible state of such a system corresponds to a point in the space, and each point in the space corresponds to a possible state of such a system. The situation is a little different in quantum mechanics, where there are mathematically describable ways of combining the values of the quantities that don't represent physically possible states. As we will see, the state-spaces of quantum mechanics are special kinds of vector spaces, known as Hilbert spaces, and they have more internal structure than their classical counterparts. A structure is a set of elements on which certain operations and relations are defined, a mathematical structure is just a structure in which the elements are mathematical objects (numbers, sets, vectors) and the operations mathematical ones, and a model is a mathematical structure used to represent some physically significant structure in the world. The heart and soul of quantum mechanics is contained in the Hilbert spaces that represent the state-spaces of quantum mechanical systems. The internal relations among states and quantities, and everything this entails about the ways quantum mechanical systems behave, are all woven into the structure of these spaces, embodied in the relations among the mathematical objects which represent them.[ 4 ] This means that understanding what a system is like according to quantum mechanics is inseparable from familiarity with the internal structure of those spaces. Know your way around Hilbert space, and become familiar with the dynamical laws that describe the paths that vectors travel through it, and you know everything there is to know, in the terms provided by the theory, about the systems that it describes. By know your way around Hilbert space, I mean something more than possess a description or a map of it; anybody who has a quantum mechanics textbook on their shelf has that. I mean know your way around it in the way you know your way around the city in which you live. This is a practical kind of knowledge that comes in degrees and it is best acquired by learning to solve problems of the form: How do I get from A to B? Can I get there without passing through C? And what is the shortest route? Graduate students in physics spend long years gaining familiarity with the nooks and crannies of Hilbert space, locating familiar landmarks, treading its beaten paths, learning where secret passages and dead ends lie, and developing a sense of the overall lay of the land. They learn how to navigate Hilbert space in the way a cab driver learns to navigate his city. How much of this kind of knowledge is needed to approach the philosophical problems associated with the theory? In the beginning, not very much: just the most general facts about the geometry of the landscape (which is, in any case, unlike that of most cities, beautifully organized), and the paths that (the vectors representing the states of) systems travel through them. That is what will be introduced here: first a bit of easy math, and then, in a nutshell, the theory. 2. Mathematics Vectors and vector spaces A vector A, written |A , is a mathematical object characterized by a length, |A|, and a direction. A normalized vector is a vector of length 1; i.e., |A| = 1. Vectors can be added together, multiplied by constants (including complex numbers), and multiplied together. Vector addition maps any pair of vectors onto another vector, specifically, the one you get by moving the second vector so that it's tail coincides with the tip of the first, without altering the length or direction of either, and then joining the tail of the first to the tip of the second. This addition rule is known as the parallelogram law. So, for example, adding vectors |A and |B yields vector |C (= |A + |B ) as in Figure 1: Figure 1: Vector Addition Multiplying a vector |A by n, where n is a constant, gives a vector which is the same direction as |A but whose length is n times |A 's length. In a real vector space, the (inner or dot) product of a pair of vectors |A and |B , written A|B is a scalar equal to the product of their lengths (or norms) times the cosine of the angle, , between them: A|B = |A||B|cos Let |A1 and |A2 be vectors of length 1 ("unit vectors") such that A1|A2 = 0. (So the angle between these two unit vectors must be 90 degrees.) Then we can represent an arbitrary vector |B in terms of our unit vectors as follows: |B = b1|A1 + b2|A2 For example, here is a graph which shows how |B can be represented as the sum of the two unit vectors |A1 and |A2 : Figure 2: Representing |B by Vector Addition of Unit Vectors Now the definition of the inner product A|B has to be modified to apply to complex spaces. Let c* be the complex conjugate of c. (When c is a complex number of the form a bi, then the complex conjugate c* of c is defined as follows: [a + bi]* = a bi [a bi]* = a + bi So, for all complex numbers c, [c*]* = c, but c* = c just in case c is real.) Now definition of the inner product of |A and |B for complex spaces can be given in terms of the conjugates of complex coefficients as follows. Where |A1 and |A2 are the unit vectors described earlier, |A = a1|A1 + a2|A2 and |B = b1|A1 + b2|A2 , then A|B = (a1*)(b1) + (a2*)(b2) The most general and abstract notion of an inner product, of which we've now defined two special cases, is as follows. A|B is an inner product on a vector space V just in case (i) A|A = |A|2, and A|A =0 if and only if A=0 (ii) B|A = A|B * (iii) B|A+C = B|A + B|C . It follows from this that (i) the length of |A is the square root of inner product of |A with itself, i.e., |A| = A|A , and (ii) |A and |B are mutually perpendicular, or orthogonal, if, and only if, A|B = 0. A vector space is a set of vectors closed under addition, and multiplication by constants, an inner product space is a vector space on which the operation of vector multiplication has been defined, and the dimension of such a space is the maximum number of nonzero, mutually orthogonal vectors it contains. Any collection of N mutually orthogonal vectors of length 1 in an N-dimensional vector space constitutes an orthonormal basis for that space. Let |A1 , ... , |AN be such a collection of unit vectors. Then every vector in the space can be expressed as a sum of the form: |B = b1|A1 + b2|A2 + ... + bN|AN , where bi = B|Ai . The bi's here are known as B's expansion coefficients in the A-basis.[ 5 ] Notice that: (i) for all vectors A, B, and C in a given space, A|B+C = A|B + A|C (ii) for any vectors M and Q, expressed in terms of the A-basis, |M + |Q = (m1 + q1)|A1 + (m2 + q2)|A2 + ... + (mN + qN)|AN , and M|Q = m1q1 + m2q2 + ... + mnqn There is another way of writing vectors, namely by writing their expansion coefficients (relative to a given basis) in a column, like so: |Q = q1 q2 where qi = Q|Ai and the Ai are the chosen basis vectors. When we are dealing with vector spaces of infinite dimension, since we can't write the whole column of expansion coefficients needed to pick out a vector since it would have to be infinitely long, so instead we write down the function (called the wave function for Q, usually represented (i)) which has those coefficients as values. We write down, that is, the function: (i) = qi = Q|Ai Given any vector in, and any basis for, a vector space, we can obtain the wave-function of the vector in that basis; and given a wave-function for a vector, in a particular basis, we can construct the vector whose wave-function it is. Since it turns out that most of the important operations on vectors correspond to simple algebraic operations on their wave-functions, this is the usual way to represent state-vectors. When a pair of physical systems interact, they form a composite system, and, in quantum mechanics as in classical mechanics, there is a rule for constructing the state-space of a composite system from those of its components, a rule that tells us how to obtain, from the state-spaces, HA and HB for A and B, respectively, the state-space called the tensor product of HA and HB, and written HA HB of the pair. There are two important things about the rule; first, so long as HA and HB are Hilbert spaces, HA HB will be as well, and second, there are some facts about the way HA HB relates to HA and HB, that have surprising consequences for the relations between the complex system and its parts. In particular, it turns out that the state of a composite system is not uniquely defined by those of its components. What this means, or at least what it appears to mean, is that there are, according to quantum mechanics, facts about composite systems (and not just facts about their spatial configuration) that don't supervene on facts about their components; it means that there are facts about systems as wholes that don't supervene on facts about their parts and the way those parts are arranged in space. The significance of this feature of the theory cannot be overplayed; it is, in one way or another, implicated in most of its most difficult problems. In a little more detail: if {viA} is an orthonormal basis for HA and {ujB} is an orthonormal basis for HB, then the set of pairs (viA, ujB) is taken to form an orthonormal basis for the tensor product space HA HB. The notation viA ujB is used for the pair (viA,uj B), and inner product on HA HB is defined as:[ 6 ] viA umB | vjA unB = viA | vjA umB | unB It is a result of this construction that although every vector in HA HB is a linear sum of vectors expressible in the form vA uB, not every vector in the space is itself expressible in that form, and it turns out that (i) any composite state defines uniquely the states of its components. (ii) if the states of A and B are pure (i.e., representable by vectors vA and uB, respectively), then the state of (A+B) is pure and represented by vA uB, and (iii) if the state of (A+B) is pure and expressible in the form vA uB, then the states of A and B are pure, but (iv) if the states of A and B are not pure, i.e., if they are mixed states (these are defined below), they do not uniquely define the state of (A+B); in particular, it may be a pure state not expressible in the form vA uB. Operators An operator O is a mapping of a vector space onto itself; it takes any vector |B in a space onto another vector |B also in the space; O|B = |B . Linear operators are operators that have the following properties: (i) O(|A + |B ) = O|A + O|B , and (ii) O(c|A ) = c(O|A ). Just as any vector in an N-dimensional space can be represented by a column of N numbers, relative to a choice of basis for the space, any linear operator on the space can be represented in a column notation by N2 numbers: O = O11 O21 O12 O22 where Oij = Ai | O|Aj and the |AN are the basis vectors of the space. The effect of the linear operator O on the vector B is, then, given by O|B = = O11 O21 O12 O22 b1 b2 = (O11b1 + O12b2) (O21b1 + O22b2) = (O11b1 + O12b2)|A1 + (O21b1 + O22b2)|A2 = |B Two more definitions before we can say what Hilbert spaces are, and then we can turn to quantum mechanics. |B is an eigenvector of O with eigenvalue a if, and only if, O|B = a|B . Different operators can have different eigenvectors, but the eigenvector operator relation depends only on the operator and vectors in question, and not on the particular basis in which they are expressed; the eigenvector operator relation is, that is to say, invariant under change of basis. Hermitean operators are linear operators, which have only real eigenvalues. A Hilbert space, finally, is a vector space on which an inner product is defined, and which is complete, i.e., which is such that any Cauchy sequence of vectors in the space converges to a vector in the space. All finite-dimensional inner product spaces are complete, and I will restrict myself to these. The infinite case involves some complications that are not fruitfully entered into at this stage. 3. Quantum Mechanics Four basic principles of quantum mechanics are: 3.1 Physical States Every physical system is associated with a Hilbert Space, every unit vector in the space corresponds to a possible pure state of the system, and every possible pure state, to some vector in the space.[ 7 ] In standard texts on quantum mechanics, the vector is represented by a function known as the wave-function, or -function. 3.2 Physical Quantities Hermitian operators in the Hilbert space associated with a system represent physical quantities, and their eigenvalues represent the possible results of measurements of those quantities. 3.3 Composition The Hilbert space associated with a complex system is the tensor product of those associated with the simple systems (in the standard, non-relativistic, theory: the individual particles) of which it is composed. 3.4 Dynamics Contexts of type 1: Given the state of a system at t and the forces and constraints to which it is subject, there is an equation, Schrdinger's equation, that gives the state at any other time U|vt |vt .[ 8 ] The important properties of U for our purposes are that it is deterministic, which is to say that it takes the state of a system at one time into a unique state at any other, and it is linear, which is to say that if it takes a state |A onto the state |A , and it takes the state |B onto the state |B , then it takes any state of the form |A + |B onto the state |A + |B . Contexts of type 2 ("Measurement Contexts"):[ 9 ] Carrying out a "measurement" of an observable B on a system in a state |A has the effect of collapsing the system into a B-eigenstate corresponding to the eigenvalue observed. This is known as the Collapse Postulate. Which particular B-eigenstate it collapses into is a matter of probability, and the probabilities are given by a rule known as Born's Rule: prob(bi) = | A|B=bi |2. There are two important points to note about these two kinds of contexts: The distinction between contexts of type 1 and 2 remains to be made out in quantum mechanical terms; nobody has managed to say in a completely satisfactory way, in the terms provided by the theory, which contexts are measurement contexts, and Even if the distinction is made out, it is an open interpretive question whether there are contexts of type 2; i.e., it is an open interpretive question whether there are any contexts in which systems are governed by a dynamical rule other than Schrdinger's equation. 4. Structures on Hilbert Space I remarked above that in the same way that all the information we have about the relations between locations in a city is embodied in the spatial relations between the points on a map which represent them, all of the information that we have about the internal relations among (and between) states and quantities in quantum mechanics is embodied in the mathematical relations among the vectors and operators which represent them.[ 10 ] From a mathematical point of view, what really distinguishes quantum mechanics from its classical predecessors is that states and quantities have a richer structure; they form families with a more interesting network of relations among their members. All of the physically consequential features of the behaviors of quantum mechanical systems are consequences of mathematical properties of those relations, and the most important of them are easily summarized: (P1) Any way of adding vectors in a Hilbert space or multiplying them by scalars will yield a vector that is also in the space. In the case that the vector is normalized, it will, from (3.1), represent a possible state of the system, and in the event that it is the sum of a pair of eigenvectors of an observable B with distinct eigenvalues, it will not itself be an eigenvector of B, but will be associated, from (3.4b), with a set of probabilities for showing one or another result in B-measurements. (P2) For any Hermitian operator on a Hilbert space, there are others, on the same space, with which it doesn't share a full set of eigenvectors; indeed, it is easy to show that there are other such operators with which it has no eigenvectors in common. If we make a couple of additional interpretive assumptions, we can say more. Assume, for instance, that (4.1) Every Hermitian operator on the Hilbert space associated with a system represents a distinct observable, and (hence) every normalized vector, a distinct state, and (4.2) A system has a value for observable A if, and only if, the vector representing its state is an eigenstate of the A-operator. The value it has, in such a case, is just the eigenvalue associated with that eigenstate.[ 11 ] It follows from (P2), by (3.1), that no quantum mechanical state is an eigenstate of all observables (and indeed that there are observables which have no eigenstates in common), and so, by (3.2), that no quantum mechanical system ever has simultaneous values for all of the quantities pertaining to it (and indeed that there are pairs of quantities to which no state assigns simultaneous values). There are Hermitian operators on the tensor product H1 H2 of a pair of Hilbert spaces H1 and H2 ... In the event that H1 and H2 are the state spaces of systems S1 and S2, H1 H2 is the state-space of the complex system (S1+S2). It follows from this by (4.1) that there are observables pertaining to (S1+S2) whose values are not determined by the values of observables pertaining to the two individually. These are all straightforward consequences of taking vectors and operators in Hilbert space to represent, respectively, states and observables, and applying Born's Rule (and later (4.1) and (4.2)), to give empirical meaning to state assignments. That much is perfectly well understood; the real difficulty in understanding quantum mechanics lies in coming to grips with their implications physical, metaphysical, and epistemological. There is one remaining fact about the mathematical structure of the theory that anyone trying to come to an understanding about what it says about the world has to grapple with. It is not a property of Hilbert spaces, this time, but of the dynamics, the rules that describe the trajectories that systems follow through the space. From a physical point of view, it is far more worrisome than anything that has preceded. For, it does much more than present difficulties to someone trying to provide an interpretation of the theory, it seems to point either to a logical inconsistency in the theory's foundations. Suppose that we have a system S and a device S* which measures an observable A on S with values {a1, a2, a3...}. Then there is some state of S* (the ground state), and some observable B with values {b1, b2, b3...} pertaining to S* (its pointer observable, so called because it is whatever plays the role of the pointer on a dial on the front of a schematic measuring instrument in registering the result of the experiment), which are such that, if S* is started in its ground state and interacts in an appropriate way with S, and if the value of A immediately before the interaction is a1, then B's value immediately thereafter is b1. If, however, A's value immediately before the interaction is a2, then B's value afterwards is b2; if the value of A immediately before the interaction is a3, then B's value immediately after is b3, and so on. That is just what it means to say that S* measures A. So, if we represent the joint, partial state of S and S* (just the part of it which specifies the value of [A on S B on S*], the observable whose values correspond to joint assignments of values to the measured observable on S and the pointer observable on S*) by the vector |A=ai s|B=b i s*, and let "" stand in for the dynamical description of the interaction between the two, to say that S* is a measuring instrument for A is to say that the dynamical laws entail that, |A=a1 s|B=ground state s* |A=a1 s|B=b1 s* |A=a2 s|B=ground state s* |A=a2 s|B=b2 s* |A=a3 s|B=ground state s* |A=a3 s|B=b3 s* and so on.[ 12 ] Intuitively, S* is a measuring instrument for an observable A just in case there is some observable feature of S* (it doesn't matter what, just something whose values can be ascertained by looking at the device), which is correlated with the A-values of systems fed into it in such a way that we can read those values off of S*'s observable state after the interaction. In philosophical parlance, S* is a measuring instrument for A just in case there is some observable feature of S* which tracks or indicates the A-values of systems with which it interacts in an appropriate way. Now, it follows from (3.1), above, that there are states of S (too many to count) which are not eigenstates of A, and if we consider what Schrdinger's equation tells us about the joint evolution of S and S* when S is started out in one of these, we find that the state of the pair after interaction is a superposition of eigenstates of [A on S B on S*]. It doesn't matter what observable on S is being measured, and it doesn't matter what particular superposition S starts out in; when it is fed into a measuring instrument for that observable, if the interaction is correctly described by Schrdinger's equation, it follows just from the linearity of the U in that equation, the operator that effects the transformation from the earlier to the later state of the pair, that the joint state of S and the apparatus after the interaction is a superposition of eigenstates of this observable on the joint system. Suppose, for example, that we start S* in its ground state, and S in the state 1 2|A=a1 s| + 1 2|A=a2 s It is a consequence of the rules for obtaining the state-space of the composite system that the combined state of the pair is 1 2|A=a1 s|B=ground state s* + 1 2|A=a2 s|B=ground state s* and it follows from the fact that S* is a measuring instrument for A, and the linearity of U that their combined state after interaction, is 1 2|A=a1 s|B= b1 s* + 1 2|A=a2 s|B= b2 s* This, however, is inconsistent with the dynamical rule for contexts of type 2, for the dynamical rule for contexts of type 2 (and if there are any such contexts, this is one) entails that the state of the pair after interaction is either |A=a1 s|B=b1 s* or |A=a2 s|B=b2 s* Indeed, it entails that there is a precise probability of 1 2 that it will end up in the former, and a probability of 1 2 that it will end up in the latter. We can try to restore logical consistency by giving up the dynamical rule for contexts of type 2 (or, what amounts to the same thing, by denying that there are any such contexts), but then we have the problem of consistency with experience. For it was no mere blunder that that rule was included in the theory; we know what a system looks like when it is in an eigenstate of a given observable, and we know from looking that the measuring apparatus after measurement is in an eigenstate of the pointer observable. And so we know from the outset that if a theory tells us something else about the post-measurement states of measuring apparatuses, whatever that something else is, it is wrong. That, in a nutshell, is the Measurement Problem in quantum mechanics; any interpretation of the theory, any detailed story about what the world is like according to quantum mechanics, and in particular those bits of the world in which measurements are going on, has to grapple with it. Loose Ends Mixed states are weighted sums of pure states, and they can be used to represent the states of ensembles whose components are in different pure states, or states of individual systems about which we have only partial knowledge. In the first case, the weight attached to a given pure state reflects the size of the component of the ensemble which is in that state (and hence the objective probability that an arbitrary member of the ensemble is); in the second case, they reflect the epistemic probability that the system in question to which the state is assigned is in that state. If we don't want to lose the distinction between pure and mixed states, we need a way of representing the weighted sum of a set of pure states (equivalently, of the probability functions associated with them) that is different from adding the (suitably weighted) vectors that represent them, and that means that we need either an alternative way of representing mixed states, or a uniform way of representing both pure and mixed states that preserves the distinction between them. There is a kind of operator in Hilbert spaces, called a density operator, that serves well in the latter capacity, and it turns out not to be hard to restate everything that has been said about state vectors in terms of density operators. So, even though it is common to speak as though pure states are represented by vectors, the official rule is that states pure and mixed, alike - are represented in quantum mechanics by density operators. Although mixed states can, as I said, be used to represent our ignorance of the states of systems that are actually in one or another pure state, and although this has seemed to many to be an adequate way of interpreting mixtures in classical contexts, there are serious obstacles to applying it generally to quantum mechanical mixtures. These are left for detailed discussion in the other entries on quantum mechanics in the Encyclopedia. Everything that has been said about observables, strictly speaking, applies only to the case in which the values of the observable form a discrete set; the mathematical niceties that are needed to generalize it to the case of continuous observables are complicated, and raise problems of a more technical nature. These, too, are best left for detailed discussion. This should be all the initial preparation one needs to approach the philosophical discussion of quantum mechanics, but it is only a first step. The more one learns about the relationships among and between vectors and operators in Hilbert space, about how the spaces of simple systems relate to those of complex ones, and about the equation which describes how state-vectors move through the space, the better will be one's appreciation of both the nature and the difficulty of the problems associated with the theory. The funny backwards thing about quantum mechanics, the thing that makes it endlessly absorbing to a philosopher, is that the more one learns, the harder the problems get. Bibliography Albert, D., 1992, Quantum Mechanics and Experience, Cambridge, MA: Harvard University Press Halmos, P., 1957, Introduction to Hilbert Space, 2nd edition, Providence: AMS Chelsea Publishing Other Internet Resources Preskill, J., 1998, Quantum Computation (Lecture Notes for Physics 219, California Institute of Technology) Related Entries quantum mechanics: Bohmian mechanics | quantum mechanics: collapse theories | quantum mechanics: Copenhagen interpretation of | quantum mechanics: Everett's relative-state formulation of | quantum mechanics: Kochen-Specker theorem | quantum mechanics: many-worlds interpretation of | quantum mechanics: modal interpretations of | quantum mechanics: relational | quantum mechanics: the role of decoherence in Copyright 2000 Jenann Ismael jtismael@U.Arizona.EDU A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z Stanford Encyclopedia of Philosophy
Quantum Chaos
An essay on the effects Chaos theory would have on traditional quantum mechanics.
Quantum Chaos Genesis of Eden Diversity Encyclopedia Get the Genesis of Eden AV-CD by secure internet order CLICK_HERE Windows Mac Compatible. Includes live video seminars, enchanting renewal songs and a thousand page illustrated codex. Join SAKINA-Weave A transformative network reflowering Earth's living diversity in gender reunion. Return to Genesis of Eden? STATIONARY STATES or wave patterns, associated with the energy levels of a Rydberg atom (a highly excited hydrogen atom) in a strong magnetic field can exhibit chaotic qualities. The states shown in the left two images seem regular, the right two are chaotic. In the third picture the state lies mostly along a periodic orbit; in the fourth, it does not and is difficult to interpret, except for the four mirror symmetries with respect to the vertical horizontal and two diagonal lines. Quantum Chaos Martin Gutzwiller Scientific American Jan 92 In 1917 Albert Einstein wrote a paper that was completely ignored for 40 years. In it he raised a question that physicists have only, recently begun asking themseves: What would classical chaos, which lurks everywhere in our work do to quantum mechanics. the theory describing the atomic and subatomic worlds? The effects of claccical chaos, of course, have long been observed-Kepler knew about the motion of the moon around the earth. and Newton complained bitterly about the phenomenon. At the end of the 19th century the American astronomer William Hill demonstrated that the irregularity is the reswt entirelly of the gravitational pull of the sun. So thereafter, the great French mathematician-astronomer-physicist Henri Poincare surmised that the moon's motion is only mild case of a congenital disease affecting nearlly everything. In the long run Poincare realized, most dynamic systems show no discernible regularity or repetitive pattern. The behavior of even a simple system can depend so sensitively on its initial conditions that the final outcome is uncertain. At about the time of Poincare's seminal work on classical chaos, Max Planck started another revolution, which would lead to the modern theory of quantum mechanics. The simple systems that Newton had studied were investigated again, but this time on the atomic scale. The quantum analogue of the humble pendulum is the laser; the flying cannonballs of the atomic world consist of beams of protons or electrons, and the rotating wheel is the spinning electron (the basis of magnetic tapes). Even the solar system itself is mirrored in each of the atoms found in the periodic table of the elements. Perhaps the single most outstanding feature of the quantum world is its smooth and wavelike nature. This feature leids to the question of how chaos makes itself felt when moving from the classical world to the quantum world. How can the extremelly irregular character of classical chaos be reconciled with the smooth and wavelike nature of phenomena on the atomic scale? Does chaos exist in the quantum world'? Preliminary work seems to show that it does. Chaos is found in the distribution of energy levels of certain atomic systems; it even appears to sneak into the wave patterns associated with those levels. Chaos is also found when electrons scatter from small molecules. I must emphasize, however, that the term 'quantum chaos' serves more to describe a conundrum than to define a well-posed problem. Considering the following interpretation of the bigger picture may be helpful in coming to grips with quantum chaos. All our theoretical discussions of mechanics can be somewhat artificially divided into three compartments [see illustration ] although nature recognizes none of these divisions. Elementary classical mechanics falls in the first compartment. This box contains all the nice, clean systems exhibiting simple and regular behavior, and so I shall call it R, for regular. .Also contained in R is an elaborate mathematical tool called perturbation theory which is used to calculate the effects of small interactions and extraneous disturbances, such as the influence of the sun on the moon's motion around the earth. With the help of perturbation theory, a large part of physics is understood nowadays as making relatively mild modifications of regular systems. Reality though, is much more complicated; chaotic systems lie outside the range of perturbation theory and they constitute the second compartment. Since the first detailed analyses of the systems of the second compartment were done by Poincare, I shall name this box P in his honor. It is stuffed with the chaotic dynamic systems that are the bread and butter of science. Among these systems are all the fundamental problems of mechanics, starting with three, rather than only two bodies interacting with one another, such as the earth, moon and sun, or the three atoms in the water molecule, or the three quarks in the proton. Quantum mechanics, as it has been practiced for about 90 years, belongs in the third compartment, caned Q. After the pioneering work of Planck, Einstein and Niels Bohr. quantum mechanics was given its deftnitive form in four short years, starting in 1924. The seminal work of Louis de Brogbe, Werner Heisenberg, Erwin Schrodinger, Max Born, Wolfgang Pauli and Paul Dirac has stood the test of the laboratory without the slightest lapse. Miraculously. it provides physics with a matheniatical framework that, according to Dirac, has yielded a deep understanding of 'most of phlsics and all of chemistry" Nevertheless, even though most physicists and chemists have learned how to solve special probleins in quantum mechanics, they have yet to come to terms with the incredible subtleties of the field. These subtleties are quite separate from the difficult, conceptual issues having to do with the interpretation of quantum mechanics. The three boxes R (classic, simple sytems), P (classic chaotic systems) and Q (quantum systems) are linked by several connections. The connection between R and Q is known as Bohr's correspondence principle. The correspondence principle claims, quite reasonably, that classical mechanics must be contained in quantum mechanics in the limit where objects become much larger than the size of atoms- The main connection between R and P is the Kolmogorov- Arnold-.Moser (KAM) theorem. The KAM theorem provides a powerful tool for calculating how much of the structure of a regular system survives when a small perturbation is introduced, and the theorem can thus identify perturbations that cause a regular system to undergo chaotic behaviour. Quantum chaos is concerned with establishing the relation between boxes P (chaotic systems and Q (quantum systems). In establishing this relation, it is useful to introduce a concept called phase space. Quite amazingly this concept, which is now so widely exploited by experts in the field of dynamic systems, dates back to Newton. The notion of phase space can be found in Newton's mathematical Principles of Natural Philosophy published in 1687. In the second definition of the first chapter, entitled 'Definitions," Newton states (as translated from the original Latin in 1729): The quantity of motion is the measure of the same, arising from the velocity and quantity of matter conjointly" In modern English this means that for every object there is a quantity. called momentum, which is the product of the mass and velocity of the object. Newton gives his laws of motion in the second chapter, entitled 'Axioms, or Laws of motion.' The second law says that the change of motion is proprotional to the motive force impressed. Newton relates the force to the change of momentum (not to the acceleration as most textbooks do). Momentum is actually one of two quantities that, taken together, yield the complete information about a dynamic system at any instant The other quantity is simply position. which determines the strength and direction of the force. Newton's insight into the dual nature of momentum and position was put on firmer ground some 130 years later by two mathematicians, William Rowan Hamilton and Karl Gustav- Jacob Jacobi. The pairing of momentum and position is no longer viewed in the good old Euclidean space or three dimensions; instead it is viewed in phase space, which has six dimensions, three dimensions for position and three for momentum The introduction of phase space was a powerful step from a mathematical point of view, but it represents a serious setback from the standpoint of human intuition. Who can visualize six dimensions?',' In some cases fortunately phase space can be reduced to three or even better, two dimensions. Such a reduction is possible in examining the behaxior of a hydrogen atom in a strong magnetic field. The hydrogen atom has long been a highily desirable system because of its simplicity. A lone electron moves around a lone proton. And yet the classical motion of the electron becomes chaotic when the magnetic field is turned on. How can we claim to understand physics if we cannot explain this basic problem? POINCARE SECTION OF A HYDROGEN ATOM in a strong magnetic field has regions where the points of the electron's trajectory scatter wildly, indicating chaotic behavior. The section is a slice out of phase space, an abstract six-dimensional space: the usual three for the position of a particle and an additional three for the particle's momentum. Under normal conditions, the electron of a hydrogen atom is tightly bound to the proton. The behavior of the atom is governed by quantum mechanics. The atom is not free to take on any arbitrary energy, it can take on only discrete, or quantized, energies. At low energies, the allowed values are spread relatively far apart. As the eneri,,)- of the atom is increased, the atom grows bigger, because the electron moves farther from the proton, and the allowed energies get closer together. At high enough energies (but not too high. or the atom will be stripped of its electron!), the allowed energies get very close together into what is effectively a continuum, and it now, becomes fair to apply the rules of classical mechanics. Such a highly excited atom is called a Rydberg atom. Rydberg atoms inhabit the middle ground between the quantum and the classical worlds, and they are therefore ideal candidates for exploring Bohr's correspondence principle which connects boxes Q (quantum phenomena) and R (classic phenomenal. If a Rydberg atom could be made to exhibit chaotic behavior in the classical sense, it might provide a clue as to the nature of quantum chaos and thereby shed light on the middle ground between boxes Q and P (chaotic phenomena. A Rdberg atom exhibits chaotic behaviour in a strong magnetic field, but to see this behavior we must reduce the dimension of the phase space. 'The first step is to note that the applied magnetic field defines an axis of symmetry through the atom. The motion of the electron takes place effectively in a two-dimensional plane, and the motion around the axis can be separated out; ornly the distances along the axis and from the axis matter. The symmetty of motion reduces the dimension of the phase space from six to four. Additional help comes from the fact that no outside force does any work on the electron. As a consequence, the total energy does not change with time. By focusing attention on a particular value of the energy, one can take a three-dimensional slice-called an energy shell-out of the four-dimensional phase space. The energy shell allows one to watch the twists and turns of the electron, and one can actually see something resembling a tangled wire sculpture. The resulting picture can be simplffied even further through a simple idea that occurred to Poincare. He suggested taking a fixed two-dimensional plane (called a Poincare section, or a surface of section) through the energy shell and watching the points at which the trajectory intersects the surface. The Poincare section reduces the tangled wire scwpture to a sequence of points in an ordinary plane. A Poincare section for a highly excited hydrogen atom in a strong magnetic field is shown on the opposite page. The regions of the phase space where the points are badly scattered indicate chaotic behavior. Such scattering is a clear symptom of classical chaos, and it aflows one to separate systems into either box P or box R. What does the Rydberg atom reveal about the relation between boxes P and Q? I have mentioned that one of the trademarks of a quantum mechanical system is its quantized energy levels, and in fact the energy levels are the first place to look for quantum chaos. Chaos does not make itself felt at any particular energy level, however; rather its presence is seen in the spectrum, or distribution, of the levels. Perhaps somewhat paradoxically in a nonchaotic quantum system the energy levels are distributed randomly and without correlation, whereas the energy levels of a chaotic quantum system exhibit strong correlations [see illustration] The levels of the regular system are often close to one another, because a regular system is composed of smaller subsystems that are completely decoupled. The energy levels of the chaotic system, however, almost seem to be aware of one another and try to keep a safe distance. A chaotic sytem cannot be decomposed; the motion along one coordinate axis is always coupled to what happens along the other axis. MECHANICS is traditionally (and artificially) divided into the three compartments depicted here, which are linked together by several connections. Quantum chaos is concerned with establishing the relation between boxes P and Q. The spectrum of a chaotic quantum system was first suggested by Eugene P. Wigner, another early master of quantum mechanics. Wigner observed, as had many others, that nuclear physics does not possess the safe underpinnings of atomic and molecular physics: the origin of the nuclear force is still not clearly understood. He therefore asked whether the statistical properties of nuclear spectra could be derived from the assumption that many parameters in the problem have definite, but unknown values. This rather vague starting point allowed him to find the most probable formula for the distribution. Oriol Bohigas and Marie-Joya Giannoni of the Institute of Nuclear Physics in Orsay France, first pointed out that Wigner's distribution happens io be exactly what is found for the spectrum of a chaotic dynamic system. ENERGY SPECTRUM or distribution of energy levels, differs markedly between chaotic and nonchaotic quantum systems. For a nonchaotic system such as a molecular hydrogen ion (H2+), the probability of finding two energy levels close to each other is quite Wgh. In the case of a chaotic system such as a Rydberg atom in a strong magnetic field, the probability is low. The chaotic spectrum closely matches the typical nuclear spectrum derived many years ago by Eugene P. Wigner. Chaos does not seem to limit itself to the distribution of quantum energy levels, however, it even appears to work its way into the wavelike nature of the quantm world. The position of the electron in the hydrogen atom is described by a wave pattern. The electron cannot be pinpointed in space; it is a cloudlike smear hovering near the proton. Associated with each allowed energy level is a stationary state, which is a wave pattern that does not change with time. A stationary state corresponds quite closely to the vibrational pattemrn of a membrane that is stretched over a rigid frame, such as a drum. The stationary states of a chaotic system have surprisingly interesting structure, as demonstrated in the early 1980s by Eric Heller of the University of Washington. He and his students calculated a series of stationary states for a two-dimensional cavity in the shape of a stadium. The corresponding problem in classical mechanics was known to be chaotic, for a typical trajectory quickly covers most of the avai;able ground quite evenly. Such behavior suggests that the stationary states might also look random, as if they had been designed without rhyme or reason. In contrast. Heller discovered that most stationary states are concentrated around narrow channels that form simple shapes inside the stadium, and he called these channels "scars" [see illustration]. Similar structure can also be found in the stationery states of a hydrogen atom in a strong magnetic field [see illustration] The smoothness of the quantum wave forms is preserved from point to point, but when one steps back to view the whole picture, the fingerprint of chaos emerges. It is possible to connect the chaotic signature of the energy spectrum to ordinary classical mechanics. A clue to the prescription is provided in Einstein's 1917 paper, He examined the phase space of a regular system from box R and described it geometrically as filled with surfaces in the shape of a donut; the motion of the system corresponds to the trajectory of a point over the surface of a particular donut. The trajectory winds its way around the surface of the donut in a regular manner, but it does not necessarily close on itself. In Einstein's picture, the application of Bohr's correspondeice principle to find the energy levels of the analogous quantum mechanical system is simple. The only trajectories that can occur in nature are those in which the cross section of the donut encloses an area equal to an integral multiple of Planck's constant, h (2pi times the fundamental quantum of angular momentum having the units of momentum multiplied by length). It tums out that the integral multiple is precisely the number that specifies the corresponding energy level in the quantum system Unfortimately as Einstein clearly saw, his method cannot be applied if the system is chaotic, for the trajectory does not lie on a donut and there is no natural area to enclose an integral multiple of Planck's constant. A new approach must be sought to explain the distribution of quantum mechanical energy levels in terms of the chaotic orbits of classical mechanics. Which features of the trajectory of classical mechanics help us to understand quantum chaos? Hill's discussion of the moon's irregular orbit because of the presence of the sun provides a clue. His work represented the first instance where a particular periodic orbit is found to be at the bottom of a difficult mechanical problem. (A periodic orbit is tike a closed track on which the system is made to run: there are many of them, although they are isolated and unstable.) Inspiration can also be drawn from Poincare, who emphasized the general importance of periodic orbits. In the begining of his three-volume work-, The New Methods of Celestial Mechanics" which appeared in 1892, he expresses the belief that periodic orbits 'offer the only opening through which we might penetrate into the fortress that has the reputation of being impregnable." Phase space for a chaotic system can be organized, at least partially around periodic orbits, even though they are sometimes quite difficult to find. ABSORPTION OF LIGHT by a hydrogen atom in a strong magnetic field appears to vary randomly as a function of energy (top), but when the data are anallzed according to the mathematical procedure called Fourier analysis, a distinct pattern emerges (bottom). Each peak in the bottom panel has associated with it a specific classical periodic orbit. In 1970 I discovered a very general way to extract information about the quantum mechanical spectrum from a complete enumeration of the classical periodic orbits. The mathematics of the approach is too difficult to delve into here, but the main result of the method is a relatively simple expression called a trace formula. The approach has now been used by a number of investigators, including Michael V. Berry of the University of Bristol, who has used the formula to derive the statistical properties of the spectrum. I have applied the trace formula to compute the lowest two dozen energy levels for an electron in a semiconductor lattice, near one of the carefully controlled impurities. (the serriicondoctor, of course, is the basis of the marvellous devices on which modern life depends; because of its impurities, the electrical conductivity of the material is half-way between that of an insulator, such as plastic, and that of a conductor, such as copper.) The trajectory of the electron can be uniquely characterized by a string of symbols, which has a straightforward interpretation. The string is produced by defining an axis through the semiconductor and simply noting when the trajectory crosses the axis. A crossing to the "positive" side of the axis gets the symbol +, and a crossing to the 'negative" side gets the symbol -. A trajectory then looks exactly like the record of a coin toss. Even if the past is known in all detail even if all the crossings have been recorded-the future is still wide open. The sequence of crossings can be chosen arbitrarily. Now, a periodic orbit consists of a binary sequence that repeats itself; the simplest such sequence is (+ -), the next is (+ -), and so on (Two crossings in a row having the same sign indicate that the electron has been trapped temporarily.) All periodic orbits are thereby enumerated, and it is possible to calculate an appropriate spectrum with the help of the trace formula. In other words, the quantum mechanical energy levels are obtained in an approximation that relies on quantities from classical mechanics only. The dassical periodic orbits and the quantum mechanical spectrum are closely bound together through the mathematical process called Fourier analyis. The hidden regularities in one set, and the frequencies with which they show up, are exactly given by the other set. This idea was used by John B. Delos of the College of William and Mary and Dieter Wintgen of the Niax Planck Institute for Nuclear Physics in Heidelberg to interpret the spectrum of the hydrogen atom m a strong magnetic field. Experimental work on such spectra has been done by Karl H. Welge and his colleagues at the University of Bielefeld, who have excited hydrogen atoms nearly to the point of ionization where the electron tears itself free of the proton. The energies at which the atoms absorb radiation appear to be quite random [see illustration], but a Fourier analysis converts the jumble of peaks into a set of well-separated peaks. The important feature here is that each of the well-separated peaks corresponds precisely to one of several standard classical periodic orbits. Poincare's insistence on the iinportance of periodic orbits now takes on a new meaning. Not only does the classical organization of phase space depend critically on the classical periodic orbits, but so too does the understanding of a chaotic quantum spectrum. PARTICLE IN A STADIUM-SHAPED BOX has chaotic stationary states with associated wave patterns that look less random than one might expect. Most of the states are concentrated around narrow channels that form simple shapes, called scars. So far I have talked only about quantum systems in which an S electron is trapped or spatially confined. Chaotic effects are also present in atomic systems where an electron can roam freelly, as it does when it is scattered from the atoms in a molecule. Here energy is no longer quantized, and the electron can take on any value, but the effectiveness of the scattering depends on the energy. Chaos shows up in quantum scattering as variations in the amount of time the electron is temporarily caught inside the molecule during the scattering process. For simplicity the problem can be eexamined in two dimensions. To the electron, a molecule consisting of four atoms looks like a small maze. When the electron approaches one of the atoms, it has two choices: it can turn left or right. Each possible trajectory of the electron through the molecule can be recorded as a series of left and right turns around the atom. until the particle finally emerges. All of the trajectories are unstable: even a minute change in the energy or the initial direction of the approach will cause a large change in the direction in which the electron eventually leaves molecule. The chaos in the scattering process comes from the fact that the number of trajectories increases rapidly with path length. Only an interpretation From the quantum mechanical point of view gives reasonable results; a purely classical calculation yields nonsensical results. In quantum mechanics each classical trajectory is used to deftne a little wavelet that finds its way through the molecule. The quantum mechanical result follows from simply adding up all such wavelets. Recently I have done a calculation of the scattering process for a special case in which the sum of the wavelets is exact An electron of known momentum hits a and emerges with the same momentum The arriarrival time for the electron to reach a fixed monitoring station varies as a function of the momentum and the way in which it varies is so fascinating about this problem. The arrival time fluctuates over small changes in the momentum but over large changes a chotic imprint emerges which never settles down to any simple pattern [see illustration]. TRAJECTORY OIF AN ELECTRON through a molecule during scattering can be recorded as a series of left and right turns ,around the atoms making up the molecule (left). Chaotic variation (right) characterizes the time it takes for a scattered electron of known momentum to reach a fixed monitoring station. Arrival time varies as a function of the electron's momentum. The variation is smooth when changes in the momentum are small but exhibits a complex chaotic pattern when the changes are large. The quantity-shown on the vertical axis the phase shift, is a measure of the time delay. A particularly tantalizing aspect of the chaotic scattering process is that it may connect the mysteries of quantum chaos with the mysteries of number theory. The calculation of the time delay leads straight into what is probably the most enigmatic object in mathematics, Riemann's zeta function. PRIME TIME Fame and fortune await the person who cracks the greatest problem in mathematics. And that could be any day now, says Erica Klarroich Actually it was first emploed by Leonhard Euler in the middle of the 18th century to show the existence of an infinite number of prime numbers (integers that cannot be divided by any smaller integer other than one). About a century later Bernhard Riemann, one of the founders of modem mathematics, employed the function to delve into the distribution of the primes. in his only paper on the subject, he called the function by the Greek letter zeta. The zeta function is a function of two variables, x and y which exist in the complex plane). To understand the distribution of prime numbers, Riemann needed to know when the zeta function has the value of zero. W'ithout giving a valid argument, he stated that it is zero only when x is set equal to 1 2. Vast calculations have shown that he was right without exception for the first billion zeros, but no mathematician has come even close to providing a proof. If Riemann's conjecture is corrcct, all kinds of interesting properties of prime numbers could be proved. The values of y for which the zeta function is zero form a set of numbers that is much like the spectrum of energies of an atom. Just as one can study the distribution of energy levels in the spectrum so can one study the distribution of zeros for the zeta function. Here the prime numbers play the same role as the classical closed orbits of the hydrogen atom in a magnetic field: the primes indicate some of the hidden correlations among the zeros of the zeta function. In the scattering problem the zeros of the zeta function give the values of the momentum where the time delay changes strongly. The chaos of the Riemann zeta function is particularly apparent in a theorem that has only recently been proved: the zeta function fits locally any smooth function. The theorem suggests that the function maydescribe all the chaotic behavior a quantum system can exhibit. If the mathematics of quantum mechanics could be handled more skilfully, many examples of locally smooth, yet globally chaotic, phenomena might be found. Chaotic (magenta) and periodic (cyan) trajectories of an electron through a crystal lattice are contrasted over the wave functions of the lattice (the atoms are the dark ovals). In quantum-confined systems the chaotic trajectories may be eventually quasi-periodic i.e. chaotic orbits may over time become trapped in periodic solutions. Once we release the confinement of the electron, either to a single wave function or to an ordered crystal, as is the case in kinetic interactions in a non-crystalline molecular medium, this quantum break time to periodicity may never become realized explaining the perseverence of chaotic orbits. Where Two Worlds Meet Julian Brown New Scientist 16 May 96 TWICE in 20th-century physics, the notion of unpredictability has shaken scientists' view of the Universe. The first time was the development of quantum mechanics, the theory that describes the behaviour of matter on an atomic scale. The second came with the classical phenomenon of chaos In both areas unpredictable features changed scientists understanding of matter in ways that were totally unforeseen. How ironic then, that these two fields, which have something so fundamental in common, should end up as antagonists when combined. For by rights, chaos should not exist at all in quantum systems- the laws of quantum mechanics actually forbid it. Yet recent experiments seem to show the footprints of quantum chaos in remarkable swirling patterns of atomic disorder. These intriguing patterns could illuminate one of the darkest corners of modern physics: the twilight zone where the quantum and classical worlds meet. The quantum theory is one of the most successful theories in modern science. Developed in the 1920s, it accounts for a vast range of phenomena from the nature of chemical bonds to the behaviour of subatomic particles, making predictions that have been tested to unprecedented levels of accuracy. But at its core there are troublesome features: Prominent among them is Heisenberg's uncertainty principle-if you know the speed of a quantum particle, for instance, you can never know its exact location. The notion that some aspects of nature are simply unknowable has caused sleepless nights for more than a few physicists. Chaos is a younger discipline. Although some of its conceptual elements had already been appreciated by Leibnitz in the 17th century and Poincare in the 19th century, chaos theory did not become fashionable until the 1980s when scientists began to realize that the phenomenon is widespread in the natural world. it arises when a system is unusually sensitive to its initial conditions so that a small perturbation of the system changes its subsequent behaviour in a way that grows exponentially with time. Chaos has been observed in, among other things, pendulums, the growth of populations, planetary dynamics, and weather systems. Probably the most famous example of chaos is the so-called "butterfly effect" in which, in theory, the tiny air disturbance from the flapping of a butterfly's wings can ultimately lead to a dramatic storm. of course, although both these theo.ries place fundamental limits on what we can know about the world, the unpredictabilities in quantum theory and chaos are different in kind. But the particular problem with quantum chaos is that in quantum mechanics small perturbations generally only lead to small perturbations in subsequent states. Without the exponential divergence in evolutionary paths, it is difficult to see how there can be any chaos. This behaviour of quantum systems is often attreibuted to a special property of the quantlani equations: their linearity. Semi-classical description of the stadium illustrates how a wavelet, unlike the classical trajectories begins to display periodic behaviour as a result of the overlapping superposition of wavelets, which unlike classical trajectories cannot densely fillphase space without overlapping. An everyday example of linearity can be seen in a rubber band. When it is stretched a little the extension is proportional to the force. Nonlinearity steps in when you pull too far and the band reaches its limit of elasticity. Stretch even further and it snaps. Because nonlinearity is known to be a crucial ingredient in ch,iotic systems. it is often said that quantum mechanics cannot be chaotic because it is linear. But according to Michael Berry, a leading theorist in the study of quantum chaos at the University of Bristol, this issue of linearity is a red herring. "This is one of the biggest misconceptions in the business he says. Berry's preferred explanation for the difference between what happens in classical and qtiaiitum systenis as they edge towards chaos is that quantum uncertainty iniposes a fundamental limit on the sharpness of the dynamics. The ammount of uncertainty is quantified in Heisenberg's uncertainty principle by a fixed value known as Planck's constantIn classical mechanics, objects can move along infinitely many trajectories," says Berry. This makes it easy to set up complicated dynamics in which an object will never retrace its path-the sort of beliaviour that leads to chaos. But in quantum mechanics, Planck's constant blurs out the fine detail, smoothing away the chaos." This raises some interesting questions. What happens if you scale down a classically chaotic system to atomic size? Do you still get chaos or does quantum regularity suddenly prevail'? Or does someting entirely new happen? And why is it that macroscopic systems can be chaotic, given that ultimately everything is made out of atoms and therefore quantum in nature? These questions have been the subject of intense debate for more than a decade. But now a number of experimental approaches have begun to offer answers. Scrambled spectra One of the earliest clues came from investigations of atomic absorption spectra. If an atom absorbs a photon of light it is possible for one of its electrons to be kicked into a higher energy state. Normally, an atom's energy levels are spaced at mathematically regular intervals, accounted for by aii empirical formula given 19th cent physicist Johannes Rydberg. If an atom absorbs photons with different energies, electrons are kicked into different levels, and the result is a nice tidy absorbtion spectrum whose details are characteristic of the chemical element involved. But when the atom is subjected to a magnetic field the line structure of the spectrum becomes distorted. When the field is sufficiently intense the spectrum becomes so scrambled it looks pretty much random at higher energies. The phenomenon is easier to understand in classical rather than quantum mechanical terms. Viewed classically, atomic electrons movbe in orbits around the nucleus rather like planets round the Sun. A magnetic field, though, introduces an additional force which causes the electrons to swerve from their normal trajectories. It's rather like a stray star encroaching upon the Solar System. If it got sufficiently close the gravitational pull would at some point become comparable to the pull between the Earth and our sun. At this moment the earth would find itself in a tug-of-war between the sun and the interloping star. Such a system would very probably be unstable, with the Earth switching critically between orbits around the sun and the other star. The result would be a chaotic orbit. In the case of excited atoms, for small fields and lower energy states. The electromagnetic swerving is small compared with the electrostatic pull towards the nucleus and the electron continues to follow a stable orbit. But for strong fields and highly excited states where the electron is on average very much further away from the nucleus,the swerving force becomes comparable to the inward pull of the nucleus In this situation, according to vclassical predictions, the motion ought to be chaotic. The effect was first studied back in 1969 by two astronomers Garton and Tonkins of Imperial College, London, who wanted to find out how the spectra of stars would be affected by their powerful magnetic fields. Their experiments on barium atoms produced one of the first surprisesbecause their resulting spectrum still displayed considerable regularity. A grioup at the University of Bielefield in Germany repeated the experiments in the 1980s using higher resolution equipment. Although the randomness was more apparent in their spectra, it was still clear that quantum mechanics was in some strange way superimposing its own order on the chaos. Quantum billiards More recently, signs of quantum suppression of chaos have come from anotheianother experimental approach to quantum chaos: quantum billiards. OOn a conventional billiard table it is quite common for a player to pot a ball by bouncing the cue ball off the cushion first. In the hands of a skilled player, such shots are often quite repeatable. But if you were to try the saine shot on a rounded, stadium-shaped table, the results are far less predictible: the slightest change in starting position alters the ball's trajectory drastically. So what you get if you play stadium billiards is chaos. In 1992 at Boston's Northeastern University, Srinivas Sridhar and colleagues substituted microwaves for billiard balls and a shallow stadium-shaped copper cavity for the table. Sridhar's team then observed how the microwaves settled down inside the cavity. Although their apparatus is not of atomic proportions (a cavity typically measures several millimetres across the experiment exploits the precise similarity between the wave equations of quantum mechanics and the equations of the electromagnetic waves in this two-dimensional situation. If microwaves behaved like billiard balls, you would not expect to see any regular patterns. The experiments, however, reveal structures known its "scars" that suggest the waves concentrate along particular paths. But where do these paths come from? One answer is provided by theoretical work carried out back in the 1970s by Martin Gutzwiller of of the IBM Thomas Watson Center in Yorktown Heights near New York. He produced a key formula that showed how classical chaos might relate to quantum chaos. Basically it indicates that the quantum regularities are related to a very limited range of classical orbits. These orbits are ones that are periodic in the classical system. If, for example, you placed a ball on the stadium table and hit it along exactly the right path, you could get it to retrace its path after only a few bounces off the cushions. however, because the system is chaotic these orbits are unstable. You only need a minuscule error and the ball will move off course within a few bounces. So classically you would not expect to see these orbits stand out. But thanks to the uncertainty in quantum mechanics, which "frizzes" the trajectories of the balls, tiny errors become less significant and the periodic orbits are reinforced in some strange way so that they predominate. Sridhar's millimetre-sized stadium was a good analogy for quantum behaviour, but would the same effects occur in a truly quantum-sized system? This question was answered recently by Laurence Eaves from the University of Nottingham, and his colleagues at Nottingham and at Tokyo University. Eaves conducted his game of quantum billiards inside an elaborate semiconductor "sandwich". He used electrons for balls, and for cushions he used a combination of quantum barriers and magnetic fields. The quantum barriers are formed by the outer layers of the sandwich, which gives the electrons a couple of straight edges to bounce back and forth between, The other edges of the table are created by the restraining effect of the magnetic field, which curves the electron motion in a complicated way. As in Sridhar's stadium cavity, the resulting dynamics ought to be chaotic. Number crunching To do the exeriments, Eaves needed ultra-intense magnetic fields, so he took his device to the High Magnetic Field Laboratory at the University of Tokyo, which is equipped with some of the most powerful sources of pulsed magnetic fields in the world. Meanwhile his colleagues in Noitingham, Paul Wilkinson, Mark Fromhold and Fred Sheard, squared up to a heroic series of calculations, deducing from purely quantum mechanical principles what the results should look like. In a spectacular pape that made the cover of Nature last month, the team produced the first definitive evidence for quantum scarring, and precisely confirmed the quantum mechanical predictions. Sure enough, the current flowing through the device was predominantly carried by electrons moving in certain 'scarred' paths. Quantum regularity was lingering in the chaos rather like the smile of the Cheshire cat in Alice's adventures in wonderland. In case these ideas seem academic it is worth noting that quantum chaos could play an important role in the design of future seniiconductor devices. At the moment, transistor devices on silicon chips are still large enough for the electrons to move through them diffusively like molecules in a gas. But as chip manufacturers squeeze ever more logic gates onto silicon, says Eaves, in the next is years transistors may become so small that electrons will instead flow through them more like quantum billiard balls. "At this point, we may well need the principles of quantum chaos to understand how these devices will work," lie says. But where does that leave the problem of how quantum mechanics turns into the classical world on larger scales? One way of looking at the problem is to investigzite how a quantum chaos system actually evolves with time. Last December, Mark Raizen and his colleagues at. the University of Texas managed to do just that, using an experimental version of a quantum kicked rotor. The idea is to couple two oscillating systems to produce chaos. Imagine pushing a child's swing. If you time your pushes in rhythm with the swing, then it simply rises higher and higher. if you push at a different frequency, the swing will sometimes be given a boost and sometimes slowed down. if this is done too vigorously, the oscillations become chaotic. In Raizen's quantum version, ultra-cold sodium atoms were subjected to a special kind of pulsed laser light. The laser beam was bounced between mirrors to set up a short-lived standing wave-a periodic lattice of light that remains motionless in space rather like the acoustic nodes on a violin string. Depending on their precise location in the standing waves, the sodium atoms are pushed around by the magnetic fields in the lattice. According to classical calculations, the result is that the atoms should be kicked chaotically along an increasingly energetic random walk. Raizen's results confirmed a long- standing prediction of the quantum theoretical descriptions of these systems. The atoms did indeed move in a chaotic way to begin with. But after around 100 microseconds (which corresponds to around 50 kicks) the build-up in energy reached a plateau. Break time In other words. quantum mechanics does suppress the chaos but only after a certain amount of time known as the 'quantum break time'. This turns out to be the crucial feature that distinguishes between quantum and classical predictions of chaotic systems. Before the break time, quantum systems are able to mimic the behaviour of classical systems by looking essentially random. But after the break time, the system simply retraces its path. it is no longer random, but akin to a repeating loop, albeit of considerable complexity. But if this is right, how can classical systems exhibit chaos? Macroscopic objects such as pendulums and planets are, after all, made out of atoms and are therefore, ultimately, quantum systems. it turns out that classical systems are in fact behaving exactly like quantum systems. The only difference is that for classical systems, the quantum break times of macroscopic systems are extraordinarily long-far longer than the age of the Universe. if we could study a classical system for longer than its quantum break time, we would see that the behaviour was not chaotic but quasi-periodic instead. Thus, quantum and classical realities can be reconciled, with the classical world naturally embedded in a larger quantum reality. Or, as physicist Dan Kleppner of ttie Massachusetts Institute of Technology puts it, "Anything classical mechanics can do, quantum mechanics can do better". Since much of the experimental work on quantum chaos has agreed with theoretical predictions, it could be tempting to say "So what?". We already knew that quantum theory was right. Well, research on quantum chaos does hold out the promise of some remarkable discoveries. Berry is excited by what appears to be a deep connection between the problem of finding the energy levels of a quantum system that is classically chaotic and one of the biggest unsolved mysteries in mathematics: the Riemann hypothesis. This concerns the distribution of prime numbers. if you choose a number n and ask how many prime numbers there are less than n it turns out that the answer closely approximates the formula: n log n. The formula is not exact, though: sometimes it is a little high and sometimes it is a little low. Riemann looked at these deviations and saw that they contained periodicities. Berry likens these to musical harmonies: "The question is what are the harmonies in the music of the primes? Amazingly, these harmonies or magic numbers behave exactly like the energy levels in quantum systems that classically would be chaotic." Deep connection This correspondence emerges from statistical correlations between the spacing of the Riemann numbers and the spacing of the energy levels. Berry and his collaborator Jon Keating used them to show how techniques in number theory can be applied to problems in quantum chaos and vice versa. In itself such a connection is very tintisual- Although sonictimes described as the Queen of mathematics, number theory is often thought of as pretty useless, so this deep connection with physics is quite astonishing. Berry is also convinced that there must be a particular chaotic system which when quantised would have energy levels that exactly duplicate the Riemann numbers. 'Finding this system could be the discovery of the century," he says. it would become a model system for describing chaotic systems in the same way that the simple harmonic oscillator is used as a model for all kinds of complicated oscillators. It could play a fundamental role in describing all kinds of chaos. The search for this model system could be the holy grail of chaos. Until we cannot be sure of its properties, but Berry believes the system is likely to be rather simple, and expects it to lead to totally new physics. It is a tantalising thought. out there is a physical structure waiting to be discovered. if we find it, the remarkablee experiments that we have recently witnessed in this discipline would be crowned by an experimental apparatus that could do more than anything to unlock the secrets of quantum chaos. Chaotic Chaos Scientific American Mar 94. Students of chaos have clung to the notion that chaotic systems retain some shreds of order. The shreds manifest themselves in the form of an attractor, a pattern of behavior toward which the system periodically settles. identifying the attractor enables one to predict the final behavior of a chaotic system, at least in a qualitative, statistical sense. That comforting notion has been damaged by Edward Ott of the University of Maryland and John C. Sommerer of Johns Hopkins University and their colleagues. They have shown that for certain systems that have more than one attractor, even qualitative predictions are impossible. "The repeatability of an experiment gets thrown into question," Ott says. The problem is rooted in the way a chaotic system determines which attractor to follow. The initial conditions that control the choice are said to be located in a basin of attraction. Ott and Sommerer have spoiled the party by showing that a basin may be rather leaky: it may have "holes" that make it impossible to predict which attractor the system will follow. Building on earlier mathematical work, the physicists used a computer to conduct numerical experiments in which a particle moving on a frictional surface is occasionally pushed. Consequently, the particle could begin moving either periodically or sporadically. The researchers found that even for this fairly simple system they could not determine which of the two attractors the particle would chase, because one basin is riddled with pieces of the other basin. in fact, every area in one basin, no matter how small, contained pieces of the other basin within it. "Hence, arbitrarily small changes can cause the system to go to a completely different attractor," Ott remarks. The only way to guarantee an outcome is not to have any error or noise whatsoever-a practical impossibility for real systems. And, anyway, what kind of chaos would that be? Ott points out that the results differ from other forms of chaos in which the starting point straddles the boundary between two basins of attraction. In such borderline situations, one might be able to move the starting point away from the boundary so that the attractor can be predicted. The same cannot be done for systems that have riddled basins, because no region is free of holes. "You're always on the borderline," Ott explains. Although riddled basins appear only in situations that have certain spatial symmetries, they are probably not rare. "A lot of physics is based on conservation laws, which are based on symmetries," Sommerer observes. Currently the workers are looking for real physical phenomena that have riddled basins. They suspect that turbulent fluids, chemical mixtures and lasers may be among such systems. Sommerer even speculates that experimentalists have already encountered this kind of chaos. Projects that went awry the second time around could have been a result of the mischievous property of riddled basins. "I have a sneaking suspicion this might be the case for some," he intones. -Philip Yam
The EPR Paradox and Inequality Principle of Bell
A short article from the USENET Physics FAQ.
The EPR Paradox and Bell's Inequality Principle [Physics FAQ] - [Copyright] Updated May 1996 by PEG (thanks to Colin Naturman). Updated August 1993 by SIC. Original by John Blanton. Does Bell's Inequality Principle rule out local theories of quantum mechanics? In 1935 Albert Einstein and two colleagues, Boris Podolsky and Nathan Rosen (EPR) developed a thought experiment to demonstrate what they felt was a lack of completeness in quantum mechanics. This so-called "EPR paradox" has led to much subsequent, and still on-going, research. This article is an introduction to EPR, Bell's inequality, and the real experiments that have attempted to address the interesting issues raised by this discussion. One of the principal features of quantum mechanics is that not all the classical physical observables of a system can be simultaneously known with unlimited precision, even in principle. Instead, there may be several sets of observables which give qualitatively different, but nonetheless complete (maximal possible) descriptions of a quantum mechanical system. These sets are sets of "good quantum numbers," and are also known as "maximal sets of commuting observables." Observables from different sets are "noncommuting observables". A well known example is position and momentum. You can put a subatomic particle into a state of well-defined momentum, but then you cannot know where it is. It's not just a matter of your inability to measure, but rather, an intrinsic property of the particle. Conversely, you can put a particle in a definite position, but then its momentum is completely ill-defined. You can also create states of intermediate knowledge of both observables: if you confine the particle to some arbitrarily large region of space, you can define the momentum more and more precisely. But you can never know both, exactly, at the same time. (Actually, some of the above statements are not quite correct. For one thing, observables that don't commute can still have mutual eigenstates. Such subtleties are very important to those who examine the derivation of Bell's inequality in great detail in order to find hidden assumptions. For the purposes of this short article we'll overlook these finer points.) Position and momentum are continuous observables. But the same situation can arise for discrete observables such as spin. The quantum mechanical spin of a particle along each of the three space axes is a set of mutually noncommuting observables. You can only know the spin along one axis at a time. A proton with spin "up" along the x-axis has undefined spin along the y and z axes. You cannot simultaneously measure the x and y spin projections of a proton. EPR sought to demonstrate that this phenomenon could be exploited to construct an experiment that would demonstrate a paradox which they believed was inherent in the quantum-mechanical description of the world. They imagined two physical systems that are allowed to interact initially so that they will subsequently be defined by a single Schrodinger wave equation. (For simplicity, imagine a simple physical realization of this idea - a neutral pion at rest in your lab, which decays into a pair of back-to-back photons. The pair of photons is described by a single two-particle wave function.) Once separated, the two systems (read: photons) are still described by the same wave equation, and a measurement of one observable of the first system will determine the measurement of the corresponding observable of the second system. (Example: the neutral pion is a scalar particle - it has zero angular momentum. So the two photons must speed off in opposite directions with opposite spin. If photon 1 is found to have spin up along the x-axis, then photon 2 must have spin down along the x-axis, since the total angular momentum of the final-state, two-photon, system must be the same as the angular momentum of the initial state, a single neutral pion. You know the spin of photon 2 even without measuring it.) Likewise, the measurement of another observable of the first system will determine the measurement of the corresponding observable of the second system, even though the systems are no longer physically linked in the traditional sense of local coupling. However, QM prohibits the simultaneous knowledge of more than one mutually noncommuting observable of either system. The paradox of EPR is the following contradiction: for our coupled systems, we can measure observable A of system I (for example, photon 1 has spin up along the x-axis; photon 2 must therefore have x-spin down), and observable B of system II (for example, photon 2 has spin down along the y-axis; therefore the y-spin of photon 1 must be up), thereby revealing both observables for both systems, contrary to QM. QM dictates that this should be impossible, creating the paradoxical implication that measuring one system should "poison" any measurement of the other system, no matter what the distance between them. (In one commonly studied interpretation, the mechanism by which this proceeds is 'instantaneous collapse of the wave function'. But the rules of QM do not require this interpretation, and several other perfectly valid interpretations exist.) The second system would instantaneously be put into a state of well-defined observable A, and, consequently, ill-defined observable B, spoiling the measurement. Yet, one could imagine the two measurements were so far apart in space that special relativity would prohibit any influence of one measurement over the other. For example, after the neutral-pion decay, we can wait until the two photons are a light year apart, and then "simultaneously" measure the x-spin of photon 1 and the y-spin of photon 2. QM suggests that if say the measurement of the photon 1 x-spin happens first, then this measurement must instantaneously force photon 2 into a state of ill-defined y-spin, even though it is light years away from photon 1. How do we reconcile the fact that photon 2 "knows" that the x-spin of photon 1 has been measured, even though they are separated by light years of space and far too little time has passed for information to have travelled to it according to the rules of special relativity? There are basically two choices. You can accept the postulates of QM as a fact of life, in spite of its seemingly uncomfortable coexistence with special relativity, or you can postulate that QM is not complete, that there was more information available for the description of the two-particle system at the time it was created, carried away by both photons, and that you just didn't know it because QM does not properly account for it. So, EPR postulated that the existence of hidden variables, some so-far unknown properties, of the systems should account for the discrepancy. Their claim was that QM theory is incomplete: it does not completely describe the physical reality. System II knows all about System I long before the scientist measures any of the observables, thereby supposedly consigning the other noncommuting observables to obscurity. Furthermore, they claimed that the hidden variables would be local. No instantaneous action-at-a-distance is necessary in this picture, which postulates that each System has more variables than are accounted by QM. Niels Bohr, one of the founders of QM, held the opposite view and defended a strict interpretation, the Copenhagen Interpretation, of QM. In 1964 John Bell proposed a mechanism to test for the existence of these hidden variables, and he developed his inequality principle as the basis for such a test. He showed that if his inequality was ever not satisfied, then it was not possible to have a local theory that accounted for the spin experiment. Using the example of two photons configured in the singlet state, consider this: after separation, each photon will have spin values for each of the three axes of space, and each spin can have one of two values; call them up and down. Call the axes x, y and z and call the spin in the x axis x+ if it is up in that axis, otherwise call it x-. Use similar definitions for the other two axes. Now perform the experiment. Measure the spin in one axis of one particle and the spin in another axis of the other photon. If EPR were correct, each photon will simultaneously have properties for spin in each of axes x, y and z. Next, look at the statistics. Perform the measurements with a number of sets of photons. Use the symbol N(x+, y-) to designate the words "the number of photons with x+ and y-". Similarly for N(x+, y+), N(y-, z+), etc. Also use the designation N(x+, y-, z+) to mean "the number of photons with x+, y- and z+", and so on. It's easy to demonstrate that for a set of photons (1) N(x+, y-) = N(x+, y-, z+) + N(x+, y-, z-) because all of the (x+, y-, z+) and all of the (x+, y-, z-) photons are included in the designation (x+, y-), and nothing else is included in N(x+, y-). You can make this claim if these measurements are connected to some real properties of the photons. Let n[x+, y+] be the designation for "the number of measurements of pairs of photons in which the first photon measured x+, and the second photon measured y+." Use a similar designation for the other possible results. This is necessary because this is all that it is possible to measure. You can't measure both x and y for the same photon. Bell demonstrated that in an actual experiment, if (1) is true (indicating real properties), then the following must be true: (2) n[x+, y+] = n[x+, z+] + n[y-, z-]. Additional inequality relations can be written by just making the appropriate permutations of the letters x, y and z and the two signs. This is Bell's Inequality Principle, and it is proved to be true if there are real (perhaps hidden) variables to account for the measurements. At the time Bell's result first became known, the experimental record was reviewed to see if any known results provided evidence against locality. None did. Thus an effort began to develop tests of Bell's Inequality. A series of experiments was conducted by Aspect ending with one in which polarizer angles were changed while the photons were `in flight'. This was widely regarded at the time as being a reasonably conclusive experiment confirming the predictions of QM. Three years later Franson published a paper showing that the timing constraints in this experiment were not adequate to confirm that locality was violated. Aspect measured the time delays between detections of photon pairs. The critical time delay is that between when a polarizer angle is changed and when this affects the statistics of detecting photon pairs. Aspect estimated this time based on the speed of a photon and the distance between the polarizers and the detectors. Quantum mechanics does not allow making assumptions about where a particle is between detections. We cannot know when a particle traverses a polarizer unless we detect the particle at the polarizer. Experimental tests of Bell's Inequality are ongoing but none has yet fully addressed the issue raised by Franson. In addition there is an issue of detector efficiency. By postulating new laws of physics one can get the expected correlations without any nonlocal effects unless the detectors are close to 90% efficient. The importance of these issues is a matter of judgment. The subject is alive theoretically as well. Eberhard and later Fine uncovered further subtleties in Bell's argument. Some physicists argue that there are assumptions in derivations of Bell's Inequality and that it may be possible to construct a local theory that does not respect those assumptions. The subject is not yet closed, and may yet provide more interesting insights into the subtleties of quantum mechanics. References A. Einstein, B. Podolsky, N. Rosen: "Can quantum-mechanical description of physical reality be considered complete?" Physical Review 41, 777 (15 May 1935). (The original EPR paper) D. Bohm: Quantum Theory, Dover, New York (1957). (Bohm discusses some of his ideas concerning hidden variables.) N. Herbert: Quantum Reality, Doubleday. (A very good popular treatment of EPR and related issues) M. Gardner: Science - Good, Bad and Bogus, Prometheus Books. (Martin Gardner gives a skeptics view of the fringe science associated with EPR.) J. Gribbin: In Search of Schrodinger's Cat, Bantam Books. (A popular treatment of EPR and the paradox of "Schrodinger's cat" that results from the Copenhagen interpretation) N. Bohr: "Can quantum-mechanical description of physical reality be considered complete?" Physical Review 48, 696 (15 Oct 1935). (Niels Bohr's response to EPR) J. Bell: "On the Einstein Podolsky Rosen paradox" Physics 1 3, 195 (1964). J. Bell: "On the problem of hidden variables in quantum mechanics" Reviews of Modern Physics 38 3, 447 (July 1966). D. Bohm, J. Bub: "A proposed solution of the measurement problem in quantum mechanics by a hidden variable theory" Reviews of Modern Physics 38 3, 453 (July 1966). B. DeWitt: "Quantum mechanics and reality" Physics Today p. 30 (Sept 1970). J. Clauser, A. Shimony: "Bell's theorem: experimental tests and implications" Rep. Prog. Phys. 41, 1881 (1978). A. Aspect, Dalibard, Roger: "Experimental test of Bell's inequalities using time- varying analyzers" Physical Review Letters 49 25, 1804 (20 Dec 1982). A. Aspect, P. Grangier, G. Roger: "Experimental realization of Einstein-Podolsky-Rosen-Bohm gedanken experiment; a new violation of Bell's inequalities" Physical Review Letters 49 2, 91 (12 July 1982). A. Robinson: "Loophole closed in quantum mechanics test" Science 219, 40 (7 Jan 1983). B. d'Espagnat: "The quantum theory and reality" Scientific American 241 5 (November 1979). "Bell's theorem and delayed determinism", Franson, Physical Review D, pages 2529-2532, Vol. 31, No. 10, May 1985. "Bell's theorem without hidden variables", P. H. Eberhard, Il Nuovo Cimento, 38 B 1, pages 75-80, (1977). "Bell's theorem and the different concepts of locality", P. H. Eberhard, Il Nuovo Cimento 46 B, pages 392-419, (1978).
Quantum Optics and Foundation of Physics
Pages and Links about Quantum Optics. Created by the group around Anton Zeilinger in Vienna.
Quantum Experiments and the Foundations of Physics - Last updated: 2005-06-30 Layout: Julia Petschinka Code: Rainer Kaltenbaek, Gregor Weihs
Virtual Journal Of Quantum Information
This monthly virtual journal contains articles that have appeared in one of the participating source journals and that fall within a number of contemporary topical areas in quantum information.
Virtual Journal of Quantum Information About this Journal How to Access Articles How to Cite Articles MyArticles Web Links Online Help Feedback Source Journals News 17-Nov-05 Hyper-Entangled Photon Pairs Nobel Focus: Photons at the Forefront 2005 Nobel Prize in Physics Announcements 24-Oct-05 36th Winter Colloquium on the Physics of Quantum Electronics (26 Jan 2006; Snowbird, UT) Int. Conf. on Quantum Computing Many-Body Systems (31 Jan3 Feb 2006; Key West, FL) Quantum Information and Computation IV (1721 Apr 2006; Orlando, FL) Quantum Information Science (712 May 2006; Barga, Italy) Browse Current Issue November 2005 (99 articles) Browse Previous Issue October 2005 (119 articles) Browse All Issues June 2001 - Present E-mail Alerting Service Sign up for FREE contents alerts Other Virtual Journals Applications of Superconductivity Biological Physics Research Nanoscale Science Technology Ultrafast Science Search Quantum Information Recent Review Articles Quantum cloning Electromagnetically induced transparency: Optics in coherent media The density-matrix renormalization group Shor's factoring algorithm and modern cryptography. An illustration of the capabilities inherent in quantum computers Spontaneous and persistent currents in superconductive and mesoscopic structures (Review) Quantum information and relativity theory Solid state quantum computer development in silicon with single ion implantation SPIN Web PROLA Scitation Virtual Journal Service Exit This is one of a series of virtual journals published by the American Institute of Physics and the American Physical Society, in cooperation with other participating publishers. Copyright American Institute of Physics and the American Physical Society
Quantum Physics
A qualitative description of the key aspects, including Heisenburg's Uncertainty Principle, wave-particle duality and related theories.
Quantum physics
Physics Bookshelf - Quantum Mechanics
A collection of articles explaining basic concepts in quantum mechanics.
Physics Virtual Bookshelf: Quantum Mechanics Quantum Mechanics Manhy of the listings are roughly in the order in which these topics might be taught. Topic Description Author Format Wave-Particle Duality A brief summary of wave-particle duality, from a first year physics course that uses minimal mathematics; the entire set of materials from the course is available by clicking here . (14k) Anthony W. Key html Quantum Interference A brief summary of quantum interference and the uncertainty principle, from a first year physics course that uses minimal mathematics; the entire set of materials from the course is available by clicking here . (39k) Anthony W. Key html Double Slit: html pdf A discussion of the "Feynman double slit," which forms the basis of many discussions of Quantum Mechanics. The topic is quite subtle, but the document is equally accessible to students at all levels. (183k 216k) David M. Harrison html and pdf The Bohr Model of the Atom A very brief introduction, originally designed for upper-year liberal arts students. (30k) David M. Harrison html Schrdinger's Cat html pdf A very brief introduction, originally designed for upper-year liberal arts students. (31k 34k) David M. Harrison html and pdf Quantum Mechanics: a Poor Person's Guide An overview of quantum mechanics, from a first year physics course that uses minimal mathematics; the entire set of materials from the course is available by clicking here . (13k) Anthony W. Key html Quantum Mechanics: Interpretation An overview of quantum mechanics, from a first year physics course that uses minimal mathematics; the entire set of materials from the course is available by clicking here . (10k) Anthony W. Key html Black Hole Thermodynamics html pdf Course notes from a one-hour class on black hole thermodynamics for upper-year liberal arts students. (25k 47k) David M. Harrison html and pdf Flash Animations for Physics An index to various Flash animations for physics. (12k). David M. Harrison html Locality and Quantum Mechanics html pdf A brief introduction to the conflict between local cause and effect and Quantum Mechanics. Based on a discussion in an upper year liberal arts course in physics without mathematics. (24k 39k) David M. Harrison html and pdf Complementarity Copenhagen Interpretation html pdf A discussion of Bohr's Principle of Complementarity and its extension to the Copenhagen Interpreation of Quantum Mechnics. Based on a discussion for an upper-year liberal arts course in modern physics without mathematics. (89k 115k) David M. Harrison html and pdf The Development of Quantum Mechanics html pdf A brief survey of the development of Quantum Mechanics in the 1920's by Schrdinger and Heisenberg. Some of the material is non-traditional. Based on a discussion in an upper year liberal arts course in physics without mathematics. (13k 26k) David M. Harrison html and pdf Stern-Gerlach Experiment html pdf This classic experiment introduces the notion of quantum spin; it is a vital introduction to many treatments of the "Einstein-Podolsky-Rosen" paradox and to Bell's theorem. This document is equally accessible to students at all levels. (76k 106k) David M. Harrison html and pdf Bell's Theorem html pdf A derivation of the theorem and a discussion of the consequences. A somewhat subtle topic, but here it is treated in a non-technical fashion. It assumes knowledge of wave-particle duality such as can be found in the Double Slit or the Wave-Particle Duality documents; also assumed is considerable knowledge of the Stern-Gerlach Experiment, for which there is also a document here. (150k 151k) David M. Harrison html and pdf Quantum Teleportation A discussion of Quantum Teleportation, Information, and Cryptography. Based on a presentation to an upper-year course in modern physics without mathematics. (41k) David M. Harrison html This page was last revised (m d y) on 02 18 03 Copyright 2000 David M. Harrison
Quantum Information Dynamics
An overview of work done at Caltech on quantum information dynamics - the study of quantum Information Theory and its application to processes involving the interaction of qubits: the quantum carriers of information
Quantum Information Dynamics Quantum Information Dynamics In quantum information dynamics (1,3,7), we are trying to understand the basic principles of quantum Information Theory and its application to processes involving the interaction of qubits: the quantum carriers of information. In earlier papers, we have shown that quantum conditional entropies are negative for quantum entangled systems (1), which allows for a consistent interpretation of quantum information processes based on Einstein-Podolsky-Rosen (EPR) pairs (5). Furthermore, we showed that the measurement process in quantum mechanics, when analysed within our formalism, is completely natural, unitary, and causal (2). The negativity of quantum entropies can also be related to the violation of Bell inequalities (4). This description can also be used to formulate Kholevo's theorem (on the amount of information that can be obtained from a quantum measurement) simply in terms of arithmetic on Venn diagrams (8) Subsequently, we showed how the quantum mutual entropy (the "mutual entanglement") is at the heart of a natural definition of the von Neumann capacity of noisy quantum channels (6). This capacity is a canonical extension of the classical quantity (defined by C. Shannon) and reverts to it in the classical limit. It was recently discovered by Bennett et al. that the von Neumann capacity is in fact the capacity for classical information transmission when assisted with an unlimited amount of quantum entanglement: the "entanglement-assisted" capacity. A proposal to simulate quantum logic using optical elements opens up the possibility to test simple quantum circuits (such as error-correction circuits) with no more than five to seven qubits using table-top optics (9,12). Mathematical properties of operators introduced in the QIT developed in earlier papers shed light on the separability problem of quantum mechanics. We show (10) that the spectrum of the conditional amplitude operator can reveal inseparability, and leads to the definition of a map (11) which reveals all inseparable systems of dimension 2x2 and 2x3. Quantum information theory is a statistical theory of information, and as such can be useful to examine non-equilibrium processes in quantum statistical mechanics. In (13) we examine QIT from this point of view, and discuss an application to the non-equilibrium thermodynamics of black hole formation and evaporation. A brief review of quantum computation and quantum technology can be found in (14). Quantum information theory can be extended into the relativistic regime. In (15), we discuss the properties of quantum entangled massive fermions under Lorentz transformations. In (16), this formalism is extended to describe beams of entangled photons, such as would be created by the down-conversion process, under relativistic frame changes. Ref. (17) deals with the statistics of perfect and imperfect photon detectors from a Bayesian point of view. In (18), my views on the physics of information are summarized, together with a few surprising new results, among which is the application of information-theoretic tools to the black hole information paradox (19). In (20), we study the adiabatic quantum computation paradigm from the point of view of random matrix theory These are the papers we wrote on this subject: (1) Negative Entropy and Information in Quantum Mechanics (2) Quantum Mechanics of Measurement (3) Quantum Information Theory of Entanglement (4) Entropic Bell inequalities (5) What Information Theory Can Tell Us About Quantum Reality (6) von Neumann Capacity of Noisy Quantum Channels (7) Negative Entropy in Quantum Information Theory (8) Accessible Information in Quantum Measurement (9) Optical Simulation of Quantum Logic (10) Quantum Extension of Conditional Probability (11) Reduction Criterion for Separability (12) Quantum Computation with Linear Optics (13) Prolegomena to a Non-Equilibrum Quantum Statistical Mechanics (14) Quantum Computation--The Ultimate Frontier (15) Quantum Entanglement of Moving Bodies (16) Entangled Light in Moving Frames (17) Towards Photostatistics from Photon-Number Discriminating Detectors (18) The Physics of Information (19) Black Holes Conserve Information in Curved-Space Quantum Field Theory (20) A Random Matrix Model of Adiabatic Quantum Computation
Intro to Quantum Mechanics
This page is intended to give an ordinary person a brief overview of the importance and wonder of quantum mechanics.
Todd's Quantum Intro Intro to Quantum Mechanics This page is intended to give an ordinary person a brief overview of the importance and wonder of quantum mechanics. Unfortunately, most people believe you need the mind of Einstein in order to understand QM so they give up on it entirely. (Interesting side note: Einstein didn't believe QM was a correct theory!) Even some chemists fall into that category-- to represent physical chemistry our departmental T-shirts have a picture of the below atom, which is almost a century out of date. Sigh So please read on, and take a dip in an ocean of information that I find completely invigorating! If the above picture is your idea of an atom, with electrons looping around the nucleus, you are about 70 years out of date. It's time to open your eyes to the modern world of quantum mechanics! The picture below shows some plots of where you would most likely find an electron in a hydrogen atom (the nucleus is at the center of each plot). What is quantum mechanics? Simply put, quantum mechanics is the study of matter and radiation at an atomic level. Why was quantum mechanics developed? In the early 20th century some experiments produced results which could not be explained by classical physics (the science developed by Galileo Galilei, Isaac Newton, etc.). For instance, it was well known that electrons orbited the nucleus of an atom. However, if they did so in a manner which resembled the planets orbiting the sun, classical physics predicted that the electrons would spiral in and crash into the nucleus within a fraction of a second. Obviously that doesn't happen, or life as we know it would not exist. (Chemistry depends upon the interaction of the electrons in atoms, and life depends upon chemistry). That incorrect prediction, along with some other experiments that classical physics could not explain, showed scientists that something new was needed to explain science at the atomic level. If classical physics is wrong, why do we still use it? Classical physics is a flawed theory, but it is only dramatically flawed when dealing with the very small (atomic size, where quantum mechanics is used) or the very fast (near the speed of light, where relativity takes over). For everyday things, which are much larger than atoms and much slower than the speed of light, classical physics does an excellent job. Plus, it is much easier to use than either quantum mechanics or relativity (each of which require an extensive amount of math). What is the importance of quantum mechanics? The following are among the most important things which quantum mechanics can describe while classical physics cannot: Discreteness of energy The wave-particle duality of light and matter Quantum tunneling The Heisenberg uncertainty principle Spin of a particle Discreteness of energy If you look at the spectrum of light emitted by energetic atoms (such as the orange-yellow light from sodium vapor street lights, or the blue-white light from mercury vapor lamps) you will notice that it is composed of individual lines of different colors. These lines represent the discrete energy levels of the electrons in those excited atoms. When an electron in a high energy state jumps down to a lower one, the atom emits a photon of light which corresponds to the exact energy difference of those two levels (conservation of energy). The bigger the energy difference, the more energetic the photon will be, and the closer its color will be to the violet end of the spectrum. If electrons were not restricted to discrete energy levels, the spectrum from an excited atom would be a continuous spread of colors from red to violet with no individual lines. The concept of discrete energy levels can be demonstrated with a 3-way light bulb. A 40 75 115 watt bulb can only shine light at those three wattage's, and when you switch from one setting to the next, the power immediately jumps to the new setting instead of just gradually increasing. It is the fact that electrons can only exist at discrete energy levels which prevents them from spiraling into the nucleus, as classical physics predicts. And it is this quantization of energy, along with some other atomic properties that are quantized, which gives quantum mechanics its name. The wave-particle duality of light and matter In 1690 Christiaan Huygens theorized that light was composed of waves, while in 1704 Isaac Newton explained that light was made of tiny particles. Experiments supported each of their theories. However, neither a completely-particle theory nor a completely-wave theory could explain all of the phenomena associated with light! So scientists began to think of light as both a particle and a wave. In 1923 Louis de Broglie hypothesized that a material particle could also exhibit wavelike properties, and in 1927 it was shown (by Davisson and Germer) that electrons can indeed behave like waves. How can something be both a particle and a wave at the same time? For one thing, it is incorrect to think of light as a stream of particles moving up and down in a wavelike manner. Actually, light and matter exist as particles; what behaves like a wave is the probability of where that particle will be. The reason light sometimes appears to act as a wave is because we are noticing the accumulation of many of the light particles distributed over the probabilities of where each particle could be. For instance, suppose we had a dart-throwing machine that had a 5% chance of hitting the bulls-eye and a 95% chance of hitting the outer ring and no chance of hitting any other place on the dart board. Now, suppose we let the machine throw 100 darts, keeping all of them stuck in the board. We can see each individual dart (so we know they behave like a particle) but we can also see a pattern on the board of a large ring of darts surrounding a small cluster in the middle. This pattern is the accumulation of the individual darts over the probabilities of where each dart could have landed, and represents the 'wavelike' behavior of the darts. Get it? Quantum tunneling This is one of the most interesting phenomena to arise from quantum mechanics; without it computer chips would not exist, and a 'personal' computer would probably take up an entire room. As stated above, a wave determines the probability of where a particle will be. When that probability wave encounters an energy barrier most of the wave will be reflected back, but a small portion of it will 'leak' into the barrier. If the barrier is small enough, the wave that leaked through will continue on the other side of it. Even though the particle doesn't have enough energy to get over the barrier, there is still a small probability that it can 'tunnel' through it! Let's say you are throwing a rubber ball against a wall. You know you don't have enough energy to throw it through the wall, so you always expect it to bounce back. Quantum mechanics, however, says that there is a small probability that the ball could go right through the wall (without damaging the wall) and continue its flight on the other side! With something as large as a rubber ball, though, that probability is so small that you could throw the ball for billions of years and never see it go through the wall. But with something as tiny as an electron, tunneling is an everyday occurrence. On the flip side of tunneling, when a particle encounters a drop in energy there is a small probability that it will be reflected. In other words, if you were rolling a marble off a flat level table, there is a small chance that when the marble reached the edge it would bounce back instead of dropping to the floor! Again, for something as large as a marble you'll probably never see something like that happen, but for photons (the massless particles of light) it is a very real occurrence. The Heisenberg uncertainty principle People are familiar with measuring things in the macroscopic world around them. Someone pulls out a tape measure and determines the length of a table. A state trooper aims his radar gun at a car and knows what direction the car is traveling, as well as how fast. They get the information they want and don't worry whether the measurement itself has changed what they were measuring. After all, what would be the sense in determining that a table is 80 cm long if the very act of measuring it changed its length! At the atomic scale of quantum mechanics, however, measurement becomes a very delicate process. Let's say you want to find out where an electron is and where it is going (that trooper has a feeling that any electron he catches will be going faster than the local speed limit). How would you do it? Get a super high powered magnifier and look for it? The very act of looking depends upon light, which is made of photons, and these photons could have enough momentum that once they hit the electron they would change its course! It's like rolling the cue ball across a billiard table and trying to discover where it is going by bouncing the 8-ball off of it; by making the measurement with the 8-ball you have certainly altered the course of the cue ball. You may have discovered where the cue ball was, but now have no idea of where it is going (because you were measuring with the 8-ball instead of actually looking at the table). Werner Heisenberg was the first to realize that certain pairs of measurements have an intrinsic uncertainty associated with them. For instance, if you have a very good idea of where something is located, then, to a certain degree, you must have a poor idea of how fast it is moving or in what direction. We don't notice this in everyday life because any inherent uncertainty from Heisenberg's principle is well within the acceptable accuracy we desire. For example, you may see a parked car and think you know exactly where it is and exactly how fast it is moving. But would you really know those things exactly? If you were to measure the position of the car to an accuracy of a billionth of a billionth of a centimeter, you would be trying to measure the positions of the individual atoms which make up the car, and those atoms would be jiggling around just because the temperature of the car was above absolute zero! Heisenberg's uncertainty principle completely flies in the face of classical physics. After all, the very foundation of science is the ability to measure things accurately, and now quantum mechanics is saying that it's impossible to get those measurements exact! But the Heisenberg uncertainty principle is a fact of nature, and it would be impossible to build a measuring device which could get around it. Spin of a particle In 1922 Otto Stern and Walther Gerlach performed an experiment whose results could not be explained by classical physics. Their experiment indicated that atomic particles possess an intrinsic angular momentum, or spin, and that this spin is quantized (that is, it can only have certain discrete values). Spin is a completely quantum mechanical property of a particle and cannot be explained in any way by classical physics. It is important to realize that the spin of an atomic particle is not a measure of how it is spinning! In fact, it is impossible to tell whether something as small as an electron is spinning at all! The word 'spin' is just a convenient way of talking about the intrinsic angular momentum of a particle. Magnetic resonance imaging (MRI) uses the fact that under certain conditions the spin of hydrogen nuclei can be 'flipped' from one state to another. By measuring the location of these flips, a picture can be formed of where the hydrogen atoms (mainly as a part of water) are in a body. Since tumors tend to have a different water concentration from the surrounding tissue, they would stand out in such a picture. What is the Schrdinger equation? Every quantum particle is characterized by a wave function. In 1925 Erwin Schrdinger developed the differential equation which describes the evolution of those wave functions. By using Schrdinger's equation scientists can find the wave function which solves a particular problem in quantum mechanics. Unfortunately, it is usually impossible to find an exact solution to the equation, so certain assumptions are used in order to obtain an approximate answer for the particular problem. What is a wave packet? As mentioned earlier, the Schrdinger equation for a particular problem cannot always be solved exactly. However, when there is no force acting upon a particle its potential energy is zero and the Schrdinger equation for the particle can be exactly solved. The solution to this 'free' particle is something known as a wave packet (which initially looks just like a Gaussian bell curve). Wave packets, therefore, can provide a useful way to find approximate solutions to problems which otherwise could not be easily solved. First, a wave packet is assumed to initially describe the particle under study. Then, when the particle encounters a force (so its potential energy is no longer zero), that force modifies the wave packet. The trick, of course, is to find accurate (and quick!) ways to 'propagate' the wave packet so that it still represents the particle at a later point in time. Finding such propagation techniques, and applying them to useful problems, is the topic of my current research. References Claude Cohen-Tannoudji, Bernard Diu, and Franck Lalo, Quantum Mechanics, Volumes 1 and 2, John Wiley Sons, New York (1977). John J. Brehm and William J. Mullin, Introduction to the Structure of Matter: A Course in Modern Physics, John Wiley Sons, New York (1989). Donald A. McQuarrie, Quantum Chemistry, University Science Books, Mill Valley, Calif. (1983). A Few Places That Refer to This Page Links2Go Quantum Physics The American Institute of Physics , as a part of a series about the achievements of Albert Einstein. A Hypernote(7) in an article in Science magazine (vol. 282, 23 Oct 1998, pp. 637-638) about quantum teleportation. Professor David Banach's Philosophy of Science homepage. A science link at Sandhills Community College. Phil Plait's Bad Astronomy pages, dealing with a question about electron probability. Other Links Basic Ideas of Quantum Mechanics. Back to Jnsson group web page. Written by Todd Stedl ( trstedl@u.washington.edu ). Last modified on 25 July 1996. Minor revisions on 25 March 2000. Minor revisions in July 2005.
Quantum Lynx
A collection of quantum mechanic's related sites, with a few metaphysical sites as well.
Quantum Lynx Quantum Lynx Biology | Chemistry | General Science | Math | Physics | Quantum Mechanics | Science Art BIOLOGY Biozone Bio links: Everything from Animal behaviour to Space Biology. CHEMISTRY Periodic Table WebElements Periodic Table (professional edition) See also: WebElements Scholar Edition - for chemistry and other students at universities and schools. Periodic Table: A Visual Interpretation of the Table of Elements The most striking version of the periodic table on the web. "Truly wonderful!" (Bart) Images Murray Robertson 1999. Text The Royal Society of Chemistry 1999. GENERAL SCIENCE Eric Weisstein's World of Science A Wolfram web resource NSDL National Science Digital Library. The Nation's online library of resources for science, technology, engineering, and mathematics education and research. Ology From the American Museum of Natural History. Learn a lot about astronomy, paleontology, and the definitions of other "ologies" on this site by taking journeys through space and the Gobi desert. Print your own dinosaur or space stationery, make a mobile, "excavate" bones, or make cosmic cookies with the instructions found here. Contribute to the planning of the new genetics section by sending topics and questions you want included. Powers of Ten View the Milky Way at 10 million light years from the Earth. Then move through space towards the Earth in successive orders of magnitude until you reach a tall oak tree just outside the buildings of the National High Magnetic Field Laboratory in Tallahassee, Florida. After that, begin to move from the actual size of a leaf into a microscopic world that reveals leaf cell walls, the cell nucleus, chromatin, DNA and finally, into the subatomic universe of electrons and protons. Science and ... Many links. Science and Art, Science and Ethics, Science and Religion, etc. "You can expect many varied and controversial opinions expressed in the pages linked to this page." By Bob Jacobs, Wilton High School, Wilton CT. Science, Mathematics and Beauty Science Learning Network The Science Learning Network (SLN) is an online community of educators, students, schools, science museums and other institutions demonstrating a new model for inquiry science education. Sci-Math World An Interactive Internet Workshop by Robert J. Lackie, Assistant Professor I-Librarian, Rider University. This site contains many resources that today's searchers need, whether they are K-12 or higher education students, educators, or parents. Together, this hands-on class and Web site will provide many of the tools to help locate valuable, reliable science and math information on the ever-changing and rapidly growing World Wide Web. SciSeek A search engine directory of everything scientific, including top rated sites, most popular sites, and most popular searches. Timeline Science One thousand years of scientific thought Windows to the Universe A fun and different Web site about the Earth and Space sciences. MATHEMATICS Binary Numbers www.learnbinary.com. This site is intended to make learning about binary numbers easy by providing a unique interactive experience on the web. EMR Exercises in Math Readiness for University Study. University of Saskatchewan. Fibonacci Numbers and the Golden Section This is the Home page for the Fibonacci numbers, the Golden section and the Golden string. By Dr Ron Knott. Fourth Dimension By Brad Ricca, Case Western Reserve University, Cleveland OH Fourth Dimension: Tetraspace Speculations on the fourth dimension. By Garrett Jones. This page attempts to explain how the world would work if there was a fourth spatial dimension in addition to the three that we already have. You could consider time to be the fourth dimension, but that is not the point of this page. Hyperbolic Tilings By Sascha Rogmann Through Mazes to Mathematics By Anthony Phillips Polyhedra and polytopes The Geometry Junkyard: Polyhedra and polytopes This page includes pointers on geometric properties of polygons, polyhedra, and higher dimensional polytopes (particularly convex polytopes). Other pages of the junkyard collect related information on triangles, tetrahedra, and simplices, cubes and hypercubes, polyhedral models, and symmetry of regular polytopes. Hypercube. Tesseract Hyper-Dimensional Links Unfolding complex polytopes By Joe O'Rourke and Komei Fukuda Zero Zero in Four Dimensions: Cultural, Historical, Mathematical, and Psychological Perspectives PHYSICS Aristotle's Lyceum in Cyberspace By Jeffery Winkler. Pages on Physics, Quantum Physics, Mathematics, etc. Boundaries of Science Yahoo WebRing Cambridge Relativity Public Home Page Cosmology. Black Holes. Cosmic Strings et al. Inflation. Quantum Gravity Fear of Physics Fear not! Physics. Explained. Finally. High Energy Physics By David M. Harrison, Department of Physics, University of Toronto Physics Forums Physics Forums.com: Cosmology. Mathematics. Physics. Science and Religion. String Theory. Theoretical Physics. Homework Help. Physics Encyclopedia. PhysLink Physics Astronomy. "This searchable source for information on physics and astronomy includes material created especially for this site and many links to other online resources. There are sections on reference, ask the experts, software, astronomy, history, new theories, graduate school information, images, YS (young scientists) awards, editorials, and essays. Also included are fun physics; a virtual scientific calculator; a bookstore; links to newsletters, scientific societies, employment resources; and more." ( LII Week ) PSIgate Physical Sciences Information Gateway is an annotated directory of Internet resources for the physical sciences, including chemistry, physics, astronomy, earth sciences, materials, science policy, and science history. Relativity An interactive relativity tutorial in Flash. It's aimed at the layman and its very graphical and fun. By Giles Hogben, Science Spirit Resources. SURE Higher Physics A complete computer based course in physics. It can be used as a resource by high school teachers presenting a class using an interactive white board, or by individual high school students at home. The material covered follows the Scottish Qualifications Authority's Higher Physics subject specification. Interactive simulations allow the user to investigate the phenomena described, and dynamic graphs, interactive equations and questions with fully structured feedback reinforce the learning experience. A free demo can be downloaded . QUANTUM MECHANICS Introductions: Quantumtutorial An interactive quantum tutorial in Flash. It's aimed at the layman and its very graphical and fun. By Giles Hogben, Science Spirit Resources. The Gilestv.com's tutorials. Some Basic Ideas About Quantum Mechanics University of Exeter Visual Quantum Mechanics This project, funded by the National Science Foundation, introduces quantum physics to high school and college students who do not have a background in modern physics or higher level math. Nonlocality This is tutorial No 3 in a series by Giles Hogben. This tutorial also includes a section on EPR. The Gilestv.com's tutorials. ParticleAdventure.org A Tour of the Inner Workings of the Atom and the Tools for Discovery Quantum Theory and Wave Particle Duality By John K. N. Murphy, Kohimarama, Auckland, New Zealand. SCIENCE ART Alchemy Web Site and Virtual Library Art and Mathematics Web Hosted by the New York Journal of Mathematics. Art Science Collaborations, Inc. (ASCI) (Art)n Laboratory Exploratorium Cool sites on art and science The Fractal Microscope Mathematics, Art, and Aesthetics Modularity in Art Slavik Jablan Science and the Arts Tim Love, Cambridge University Science Museum, London Signifying Nothing: The Fourth Dimension in Modernist Art and Literature Brad Ricca, Case Western Reserve University, Cleveland OH. Snelson, Kenneth Teylers Museum, Haarlem YLEM artists using science and technology Quantum Lynx by Bart Rosier. Last updated 7 July 2005. Home . Top . geovisit();
Parity
An overview of Parity in quantum mechanics and of the ways to break quantum mechanical symmetry.
Theory: Parity Parity Many physics processes have a property known as parity invariance. This means that the probability of a particle process occurring is exactly the same as the probability of the same process occurring with the position vectors and directions of travel of all particles reversed. What does it mean to reverse a position vector? Choose any point as your position vector origin and draw a line from the origin to the position of an object. That is the position vector of the object. A parity transformation about that origin would relocate the object at a point found by flipping that position vector so it goes the same distance from the origin but in exactly the opposite direction. It turns up to down, left to right, and front to back! This seems odd because we are used to thinking of up as physically very different from down, but if we reverse everything then the position of the earth changes, too. Consider, for example, a collision of two spheres in space. There would be no way you could tell by looking at a movie whether you were watching an actual collision or a parity reversed simulation of the collision, each would look equally plausible. Parity invariance is true for strong and electromagnetic interactions . This has many consequences for the possible outcomes in decays and scattering events . One of the big surprises of the 1950s was the recognition that parity invariance is not true for weak interactions . Right- and Left-Handed Particles By definition, a right-handed particle is one that rotates in the direction of the fingers while traveling in the direction of the thumb. Similarly, a left-handed particle rotates in the opposite direction. Parity reverses the travel direction without reversing the direction of rotation -- a left-handed particle turns into a right-handed particle. Thus, parity invariance says that left- and right-handed particles must have identical interaction rates. In weak interactions this rule is completely broken -- only left-handed particles (and only right-handed antiparticles ) participate in weak interactions. Biological Parity Breaking It is interesting to note that parity non-invariance is also present in biology. Large spiral molecules can be assigned a handedness from the way they spiral. Left- and right-handed molecules behave very differently in biological function. You may wonder whether this has any connection to the underlying asymmetry of weak interactions or is just the result of random evolutionary selection. Most theories of the origin of life favor the latter interpretation. | Accelerators | Applications | Detectors | Experiments | History | Nobel | SSRL | Theory | | FAQs | Glossary | Guest Book | Photo Tours | Search | Contents | Environment | Paleo | Cosmic Rays | | Home | SLAC | Last update 05 05 03 Owners: mcdunn (design page), quinn (content)
Eurotechnology Japan: Quantum Device Simulations
Visualization and simulation of electron waves propagating through quantum device structures demonstrating solutions to the time-dependent Schroedinger equation
Quantum Device Simulations Visualizing Electron Wave Motion Time-Dependent Schrdinger Equation i-Mode FAQ | HOME | COMPANY | site index | STORE | feedback | Shopping cart | Checkout | Download imode report HOME STORE what we do... - imode, i-mode - camera-phones - L-mode - Internet E-commerce - M A - Negotiation support - Telecom - LSI design outsourcing - Crosscultural - Environmental Techn. - Send us email who we are... - Products Services - Events Publications - Team Management - Corporate Information - Roadmap to our office - Company Profile (pdf) Our R D - Nanotechnology - Device Simulations - Tokyo Univ Lab Record JapanInformation - New opportunities (Stanford Univ. talk) - DoingBusinessInJapan - High-Tech - Blue LEDs Lasers - EuropeJapan - AustriaJapanForum Website index Japanese pages - Blue LEDs Lasers - Crosscultural - AustriaJapanForum - Creative Destruction... Eurotechnology (deutsch) - Produkte Leistungen - JapanInfo (deutsch) Eurotechnology visualizes electron motion in Quantum Devices We simulate quantum devices by solving the time-dependent Schroedinger equation. We apply our software for a variety of problems. Our simulations can be used for simulating electrons in electron microscopes and for simulating electronic devices using quantum effects. Another area is the simulation of electron wave packets prepared by femto-second laser pulses. Femto-second laser technology is a very rapidly growing area, and it is very difficult to imagine how electron wave packets behave on such a short time scale without high quality simulations. Our software can also be used for a range of other simulation technology applications. Slide show In the next few slides we show you an electron wave moving through the potential landscape shown in the image below. (Some of the slides include animated gifs which are approximately 600 kbyte in size. These may take a while to download, but most WWW-browsers should start playing the animations while downloading the remaining frames. The animations will play for ever on most browsers, and the second and further runs will much be quicker than the first. Please respect our copyright on these movies - thank you.) Prize in the Japanese Computer Visualization Contest 1995 This work has been awarded the 2nd Prize in the Japanese Computer Visualization Contest 1995 organized by the Japanese Edition of Scientific American (Nikkei SCIENCE), it has also appeared on the February 1996 page of the Hewlett-Packard Laboratory Calender, and the work has also been presented at a number of scientific conferences and in a number of scientific journals. We have also presented the first simulation of electrons in strong magnetic fields at the 23rd Conference on The Physics of Semiconductors on Berlin (1996). Before you start the slide show.... Below is an image of the potential landscape chosen for this demonstration. There is channel on the left hand side, from which an electron wave packet emerges. The wave packet then propagates through a periodic lattice. This lattice could represent the atoms in a crystal for example. Start Slide Show - Slide No. 1 Click here to go directly to one of the slides: 1 2 3 4 If you have any questions please : email us Welcome to Eurotechnology-Japan in Tokyo! We build the Japan business for European and US corporations. We help Japanese corporations refocus and globalize. Email us or Send Page To a Friend Subscribe to our free newsletter enter your Email address: Copyright (1996-2002), Eurotechnology Japan Corp. All Rights Reserved EUROTECHNOLOGY (R) is a registered trademark or trademark in Japan and other countries. service (at) eurotechnology.com
Student Understanding of Quantum Mechanics
A set of lectures and reports outlining methods of teaching introductory quantum mechanics to a wide range of students.
Student Understanding of Quantum Mechanics University of Maryland Physics Education Research Group Student Understanding of Quantum Mechanics PERG Info | PERG materials | PERG HOMEPAGE | PER on the web | Resources on the web Student Understanding of Quantum Mechanics The University of Maryland Physics Education Research Group is currently involved in two supported projects to study student understanding of quantum mechanics and to build a new course in introductory QM for scientists and engineers. A New Model Course in Quantum Mechanics for Scientists and Engineers E. F. Redish and R. N. Steinberg NSF grant DUE-9652877 Practical Quantum Mechanics (QM):Opening a door for tomorrow's engineers, inventors, and scientists E. F. Redish and R. N. Steinberg Department of Education FIPSE grant 116B70186 Talks Student Misconceptions on Classical Issues at the Boundary of Quantum Mechanics , E. F. Redish (18 April 97 APS AAPT joint meeting ) Student Difficulties with Energy in Quantum Mechanics , E. F. Redish, Lei Bao and Pratibha Jolly ( 8 January 97 AAPT Winter Meeting). Student Difficulties with Quantum Mechanics , Lei Bao, Pratibha Jolly, and Edward F. Redish (8 August 96 AAPT Summer Meeting) QM 708: Seminar in Practical Quantum Physics Schedule for Speakers (Fall 1997) Schedule for Speakers (Spring 1998) Presentations: "Introduction to the Practical Quantum Mechanics Project," E.F. Redish, Practical Quantum Physics Seminar, UMD, September, 1997. "Student Difficulties With Wave Concepts," Michael C. Wittmann, Practical Quantum Physics Seminar, UMD, September, 1997. Maintained by University of Maryland PERG Comments and questions may be directed to E. F. Redish Last modified June 25, 2002
Quantum Physics Online
A series of Java applets illustrating solutions to basic problems in this subject.
Classical Fluid Mechanics Problem Solutions
Solutions to Classical Fluid Flow Momentum Transfer Problems
Fluid Mechanics Momentum Transfer : Problems Problem Solutions in Transport Phenomena BSL K-12 | GMAT | GRE | SAT | USA | Learn Spanish | Quiz | Puzzles | IQ | Downloads | Shopping Cart | Syvum Members | Sign off Search Syvum web site for information or quizzes of your interest. ES.Syvum.com in Spanish BR.Syvum.com in Portuguese Syvum Mobile on your cell phone! Special Features: Christmas Games Christmas Recipes Music Quizzes Foreign Languages - Phrases - Words Hide ALL ADS Online Translation - Dictionary Translation Services One-Click Lookups Language Translation Services $$$ WIN $$$ Syvum Quizenius Trivia Contest! '); ccl9_syvum = 1; } var expDate = new Date(); expDate.setTime(expDate.getTime() + 43200000); document.cookie = "Cl_Syvum_c9="+ ccl9_syvum + "; expires=" + expDate.toGMTString() + "; path= "; if (document.body) { document.cookie = "windoww="+ document.body.offsetWidth + "; path= "; } } -- !-- if (ads == "no") { } else { document.writeln(' IFRAME FRAMEBORDER=0 MARGINWIDTH=0 MARGINHEIGHT=0 SCROLLING=NO WIDTH=468 HEIGHT=60 SRC="http: ad.yieldmanager.com imp?z=4s=74t=3" '); } -- !-- if (document.all) { if (ads == "no") { document.writeln(' span id="syvum_span_link" style="cursor:pointer;" onclick="document.all.syvum_g_link.style.display = \'none\' == document.all.syvum_g_link.style.display ? \'\' : \'none\';document.all.syvum_span_link.style.display = \'none\';" font color=blue face=arial size=-1 b See ads related to this topic '); document.writeln(' '); } } -- google_ad_client = "pub-0582656916058535"; google_ad_width = 728; google_ad_height = 15; google_ad_format = "728x15_0ads_al"; google_ad_channel ="9034378402"; google_color_border = "FFFFFF"; google_color_bg = "FFFFFF"; google_color_link = "0000FF"; google_color_url = "008000"; google_color_text = "000000"; !-- if (document.all) { if (ads == "no") { document.writeln(' '); } } -- Home Engineering Transport Phenomena - Momentum Transfer Fluid Mechanics Problem Solutions in Transport Phenomena : Fluid Mechanics Problems For theory relevant to the fluid mechanics and momentum transfer problems below, please refer to the following books: Bird, R. B., Stewart, W. E., and Lightfoot, E. N., "Transport Phenomena", 2nd edition, John Wiley, New York (2002). Note that BSL is an abbreviation often used for this classic textbook based on the initials of its authors. Geankoplis, C. J., "Transport Processes and Unit Operations", 3rd edition, Prentice-Hall, Englewood Cliffs, New Jersey (1993). The solutions below will also help you solve some of the problems in the books by BSL and Geankoplis. Fluid Mechanics Theory : Differential shell momentum balance in rectangular Cartesian coordinates Fluid Mechanics Theory : Differential shell momentum balance in cylindrical coordinates Fluid Mechanics Problem Solution : Newtonian fluid flow in a plane narrow slit Fluid Mechanics Problem Solution : Newtonian fluid flow in a falling film Fluid Mechanics Problem Solution : Newtonian fluid flow in a circular tube Fluid Mechanics Problem Solution : Newtonian fluid flow in a slightly tapered tube Fluid Mechanics Problem Solution : Newtonian fluid flow in a wire coating die Fluid Mechanics Problem Solution : Tangential annular flow between coaxial rotating cylinders Fluid Mechanics Problem Solution : Free surface shape in tangential annular flow Fluid Mechanics Problem Solution : Parabolic mirror from free surface shape of rotating liquid Fluid Mechanics Problem Solution : Flow between two concentric rotating spheres Fluid Mechanics Problem Solution : Radial fluid flow between two porous concentric spheres Fluid Mechanics Problem Solution : Radial fluid flow between two porous coaxial cylinders Fluid Mechanics Problem Solution : Radial flow of a Newtonian fluid between parallel disks Fluid Mechanics Problem Solution : Newtonian fluid in a parallel - disk viscometer Fluid Mechanics Problem Solution : Power law fluid flow in a plane narrow slit Fluid Mechanics Problem Solution : Power law fluid flow in a falling film Fluid Mechanics Problem Solution : Power law fluid flow in a circular tube Fluid Mechanics Problem Solution : Power law fluid flow in a slightly tapered tube Fluid Mechanics Problem Solution : Power law fluid flow in a wire coating die Fluid Mechanics Problem Solution : Bingham fluid flow in a plane narrow slit Fluid Mechanics Problem Solution : Bingham fluid flow in a circular tube Click here for Problem Solutions in Transport Phenomena : HEAT TRANSFER PROBLEMS Click here for Problem Solutions in Transport Phenomena : MASS TRANSFER PROBLEMS !-- if (document.all) { if (ads == "no") { document.writeln(' p span id="syvum_span_bot" style="cursor:pointer;" onclick="document.all.syvum_g_bot.style.display = \'none\' == document.all.syvum_g_bot.style.display ? \'\' : \'none\';" font color=blue face=arial size=-1 b See ads related to this topic '); document.writeln(' '); } } -- google_ad_client = "pub-0582656916058535"; google_alternate_ad_url = "http: www.syvum.com cgi showad.cgi"; google_ad_width = 336; google_ad_height = 280; google_ad_format = "336x280_as"; google_ad_type = "text"; google_ad_channel ="9034378402"; google_color_border = "FFFFFF"; google_color_bg = "FFFFFF"; google_color_link = "0000FF"; google_color_url = "008000"; google_color_text = "000000"; !-- if (document.all) { if (ads == "no") { document.writeln(' '); } } -- !-- if (ads == "no") { } else { document.writeln(' IFRAME FRAMEBORDER=0 MARGINWIDTH=0 MARGINHEIGHT=0 SCROLLING=NO WIDTH=300 HEIGHT=250 SRC="http: ad.yieldmanager.com imp?z=2s=74t=3" '); } -- Syvum in other languages: Spanish Espaol , Portuguese Portugus document.write(' table width="100%" bgcolor='+syvum_bs_a[2]+' cellspacing=0 border=0 style="font: normal 10pt arial;" '); Contact Info 1999-2005, Syvum Technologies Inc. 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Irrotational Plane Flows of an Inviscid Fluid
Lecture for those who need a refresher course on hydrodynamics fundamentals.
IRROTATIONAL PLANE FLOWS OF AN INVISCID FLUID Choose your language ... ... and good navigation. John S. Denker has been so kind to host a mirror of these webpages for US readers. The official site is www.diam.unige.it and I will try to keep the mirror updated without abusing of John's patience. Please don't bother him with questions related to these pages but contact me instead. During the lecture you will encounter some Java Applets. They have been developed using the Java Developer Kit (JDK), version 1.1. If they do not work on your browser, please let me know. Be patient ... animations take some time to travel. If you are not patient at all, you can download a .tar.gz or a .zip archive of the whole tree. Here you can find a gallery of some nice photos and images people sent me. I would like to extend this section, so please email me any image you feel is pertinent to this project. Be sure to include a few lines of description of what can be seen in the image. ACKNOWLEDGEMENTS This webpages would never have seen the light without the help from the following persons I would like to thank: Marco Colombini ... well, after all I think I can put myself on top of the thanks list ... this work has been done in my spare time :-( Marco Galiani who has been, as always, willing to help solving all (well, almost all) the technical problems. Tilman Buntz , who is a maths and physics student at the University of Munchen and is writing a thesis which shall become a guided tour on the principles of flight for the Deutsches Museum of Munchen for students. Tilman will use some material from these webpages for his thesis and proposed himself for arranging the german version of this lecture ... so choosing to receive all the honours and the blames about it. Rita Wodzinski , who teaches physics at the University of Munchen and is the supervisor of Tilman. Her curiosity on the problem ``longer path = higher velocity'' stimulated an interesting discussion. The sections devoted to the streaklines pattern are the ultimate result of this discussion and I hope they will help to clarify this common misconception. John S. Denker , who wrote some very enojable pages on the principles of aerodynamics. John has been very helpful in the building of the code needed for the streakline animations. A particular thank for his willingness and for his suggestions. Jay M. Khodadadi , who teaches Fluid Mechanics at Auburn University and, with the help of Mr. Nitesh Nimkar, did a very good job in checking the english version of the site. His work went well beyond a mere spell check so that I really would like to thank him for his willingness. After all he was the only one of many volunteers who actually completed the job. Anyway, I take this chance to thank also all the people who spent some time on this tedious work. The students of the course of Fluid Mechanics for Chemical Engineers, who were the actual reason I started this project. In the last few years I have mercilessly forced them to carefully study these pages, asking them to correct, at least, the typos in the italian version. No hope. (Well, well, actually they found two in the english version ... hope is the last to die). A note to the german version, written by Tilman (I don't understand a word in german, but I've seen my name in it so ...) Vorwort zur deutschen bersetzung: Hiermit danke ich nochmal ganz herzlich Marco Colombini fr die grozgige Bereitstellung seiner Seiten und Rita Wodzinski, die viel Zeit fr die berarbeitung der bersetzung geopfert hat. This project has been developed on HP-Ux and Linux systems making use of the following software: Gsharp from AVS Java from SUN Latex2html from Nikos Drakos ImageMagick from John Cristy
Flow optimization
The site demonstrates a method of flow visualisation by using an optically active liquid. The advantages of the method and some example applications are described.
flow optimization - Strmungsoptimierung und Projektmanagement im Ingenieurbro Dr. Jan Forkert Berlin Flow optimization in components and machinery of flow technology Ingenieurbro Dr. Jan Forkert Allee der Kosmonauten 28 D-12681 Berlin Germany Phone: +49(0)30 548 00 450 Fax: +49(0)30 548 01 706 eMail: info@flow-optimization.com English Deutsch Strmungsoptimierung in Komponenten und Maschinen der Strmungstechnik Achtung: Diese web-site ist nur zur Information. Rechtliche und andere Ansprche knnen hieraus nicht abgeleitet werden. Letzte nderung am 16.10.2004. Attention: This web-site is only for information. Juridical and other pretensions can not be related. Last modification: 16.10.2004
Fluid Mechanics
Site contains a collection of tutorials, javascript calculators, and links of interest to those doing teaching and research in fluid mechanics, wave propagation, applied physics, and mechanical and aerospace engineering.
Main Fluid Mechanics Site: Introduction Fluid Mechanics My Homepage My Gallery Navier-Stokes.Net Cambridge University Press Contact Index Home About This Site Our Sponsor What's New? Tutorials Introduction Aurora Bernoulli Eqn Lubrication Raindrops Sound Barrier Water Waves Calculators Introduction Engr Fluid Mech Waves Phys. Properties Links My Homepage My Gallery Navier-Stokes.Net WELCOME Fluid mechanics is one of the oldest and richest branches of mechanics and applied physics. Fluid mechanics has been studied (formally or informally) since the beginning of recorded history. We are literally immersed in fluids, our bodies are primarily water, and we simply cannot live without air and water. Not only are fluids and their complex physics of general interest, but it is widely recognized that fluid mechanics is an essential part of the comprehensive design and manufacture of nearly all modern machinery, structures, and devices. And, yes, even the design of your computer requires some form of cooling and the manufacture of its chips requires a proper understanding of fluid flow. Over the years, I've tried to pass on what is currently understood about fluid flows (and even a little bit of my fascination with them) in the classroom and my websites. The idea of the present site is to act as an umbrella for most of my fluids-related online material. Links to this material are found in the navigation column at the left. You will find that the material here will be representative of fluid mechanics itself in that it ranges from the moderately mathematical (in the Navier-Stokes.Net site) to purely visual physical (in the Gallery of Fluid Mechanics ). In between these extremes are the Tutorials which are just short (and not-so-short) discussions of fluids-related topics. These Tutorials were originally intended to demonstrate how a knowledge of fluid mechanics can be applied to day-to-day phenomena. The math tends to be minimized and in many cases limited to order of magnitude analysis so that at least some of the material in each tutorial ought to be accessible to those without a background in engineering. Hopefully, everyone can take something useful away from these notes. The Javascript Calculators are another major section of the site. Here I've provided some online calculators which can be of use to a wide variety of visitors. The advantage of these calculators is that they require no detailed knowledge of the physics or mathematics of fluids in order to generate useful numbers. This site will continue to be updated so check back often to see what's new. I'm also happy to receive suggestions or reports of problems with the site. Copyright 1998-2004 M.S.Cramer, All Rights Reserved | My Homepage | Navier-Stokes.Net | Gallery of Fluid Mechanics | | Cambridge University Press | Contact Me |
History of Fluid Mechanics, Mathematics, and Science
Links to historical information for mathematics, science and fluid mechanics.
Links to History of Mathematics and Science Sites Fluid Mechanics My Homepage My Gallery Navier-Stokes.Net Cambridge University Press Contact Index Home About This Site Our Sponsor What's New? Professional Info Short Vita Research Teaching On-Site Material My Link Pages JS Boutique Tutorials Related Sites My Gallery Fluidmech.Net Navier-Stokes.Net Click on the above animation to learn a bit more about a few of the best mathematicians and fluid mechanists of history. HISTORY OF SCIENCE SITES These are the history of science, technology, aviation, and mathematics sites which I've collected. I'm always looking for more of these. Drop me a line if I've missed a good one. General History of Math and Science Pages: Mathematicians of the 17th and 18th Centuries. These are the guys and gals who invented 20th century engineering. Here's another page on both Galileo and Einstein from UVa. This is a History of Mathematics site . The Museum of the History of Science at Oxford has a nice on-line exhibit page . Eric's Treasure Trove of Scientific Biographies . This used to be a UVa site, but has since moved to the Wolfram (Mathematica) site. A short list of contributors to science and technology . The level may also be geared to the more general reader. This site appears to be a reasonable list of biographies of Women Mathematicians . History of Fluid Mechanics, Aviation, Etc: A fairly extensive site dedicated to the History of Flight can be found at the highlighted link. Click on the essays icon in the right column (next to the Wright Brother's airplane) to see much of the historical content. Articles describing the physics of flight can be found at the Theories of Flight (Aerodynamics) link. Here is a synopsis entitled Highlights in the History of Hydraulics by Hunter Rouse. The page also includes a nice reference list. Speaking of hydraulics, here is a site with biographical information on Henry Darcy , a major contributor to the theory of pipe flow and porous media. Here is a list of links to information about Ludwig Prandtl compiled by Niall McMahon at the Dublin City University . A short bio of Daniel Bernoulli can be found by clicking at the highlighted text. Here's a list of the Pioneers of Heat Transfer along with short bios for each scientist. These include Prandtl, Fourier, and Reynolds. Beware: this is a Journal of Heat Transfer site. These seem to vanish every few years as the editor changes. This is another historical article on the first supersonic flight . Nasa maintains this History of Aviation site. It also has a small Aircraft Gallery and a Principles of Flight page. History of Electromagnetics This is a Gallery of Contributors to E M ----- Students should note the overlap with the Fluid Mechanics Applied Math Heat Transfer Halls of Fame. Here's a list of links to scientists with an emphasis on electricity and magnetism. Happy surfing, MSC Copyright 1998-2004 M.S.Cramer, All Rights Reserved | My Homepage | My Gallery | Navier-Stokes.Net | | Cambridge University Press | Contact Me |
Navier Stokes Equations
A brief summary of the Navier-Stokes equations governing fluid dynamics and fluid mechanics.
Navier-Stokes Equations: Introduction Foundations of Fluid Mechanics My Homepage Gallery of Fluid Mechanics Cambridge University Press Contact Index Introduction Web Stuff Our Sponsor What's New? Navier-Stokes Eqns Overview Notation Definition Continuum Hypoth. Balance Laws Cauchy's Hypoth. Local Bal. Laws Constitutive Assumpt. Constitutive Relations Field Equations Physical BC Shock Jump Cond. Summary Misc. Topics Constant Properties Inviscid Flows Incompressible Flows Conservative Forms Bernoulli Equations Vorticity Special Fluid Models Potential Flows Introduction Restrictions Aerodynamics Water Waves Acoustics Math Identities Vector Calculus Stokes' Theorem Gauss' Theorem Transport Theorems Great Books Introduction Continuum Mech. General Fluid Mech. Aero Hydrodyn. Viscous Flow Compressible Flow Miscellaneous Navier-Stokes Equations Introduction The Navier-Stokes equations are the foundation of fluid mechanics and, strangely enough, are rarely recorded in their entirety. The motivation for developing this site was to help plug this gap and to also provide an easily accessible, i.e., web-based, source which lists the full set of equations normally associated with fluid mechanics. Please note that you won't find any detailed derivations or proofs here, although the presentation style is intended to provide enough development to give the reader a feel for the overall structure of the theory. I hope that the efficiency of the presentation will enable my visitors to identify the key results more easily. There are many excellent texts which can be used to fill in the details of the derivation. Many of these texts are listed in the Great Books section. You should also be warned that you won't be seeing any animations or cute graphics here. Again, this is in the spirit of the no-nonsense, plain-jane approach of the site. If you are interested in seeing great images and movies of fluids in motion, have a look at my Gallery of Fluid Mechanics . I think that the most likely audience for these notes are mathematicians, physicists, computational fluid dynamicists, graduate students, and working engineers who need a quick, complete, and correct statement of the Navier-Stokes equations without all the development, derviation, and motivation that is (appropriately, I hasten to add) included in fluid mechanics texts and courses. This material is certainly not for the typical undergraduate who is just starting their first plumbing (engineering fluid mechanics) or aerodynamics course. However, there are no proofs and the mathematical notation will be familiar to most undergraduates who have had junior level courses on fluids (or aerodynamics) and vector calculus. Perhaps there are a few bright and ambitious undergraduates out there who will find my scribblings interesting. If there are any questions, suggestions, or corrections on the material please drop me a note at any of the Contact links. The site is constantly being fine-tuned and I'm always eager to improve it. Copyright 2002-2004 M.S.Cramer, All Rights Reserved | My Homepage | Gallery of Fluid Mechanics | Cambridge University Press | | Contact Me | Remarks
Funneller - Single Vortex Technology
Introduction to a propulsion technique that utilizes a rotating cone.
Funneller Single Vortex Technology www.funneller.com - official Funneller website concerning Single Vortex Viscostic Vector Management and patent info. Funneller Single Vortex Technology Enter site - German English Russian Funneller History and Technical Links 17 April 2002 Funneller Principle Discovered 23 Nov 2004 Preparing 1st Cavitation Tunnel Test 23 July 2002 Single-Funneller VMU 12 Apr 2005 First Official Cavitation Tunnel Test .. 14 Sept 2003 Viscostic Pump 1 May 2005 Finding the Traction Quotient .......... 27 Dec 2003 Duel-Funneller VMU 8 May 2005 Measuring VMU Impedance VSD . Official Funneller Website. Stand: 11. May 2005. The Funneller patent application is registered at The International Bureau of WIPO PCT 1B03 01727. All Rights Reserved.
Fluid dynamics course material
139 pages script at undergraduate level on the fundamental aspects of non-relativistic fluid dynamics in pdf format.
MAS209 course material MAS209 Fluid Dynamics Course Material September-December 2002 From here you can take copies of the key objectives, lecture notes and the coursework problems for the course MAS209: Fluid Dynamics. Key objectives Key objectives Lecture notes MAS209: Fluid Dynamics (139 pages, *.pdf) Chapter 1: Describing fluids and fluid flows (26 pages, *.pdf) Chapter 2: Mathematical techniques (16 pages, *.pdf) Chapter 3: Introduction to fluid flows (20 pages, *.pdf) Chapter 4: Analysis and classification of fluid motion (10 pages, *.pdf) Chapter 5: Irrotational flows of incompressible fluids (18 pages, *.pdf) Chapter 6: Fluid equations of motion (20 pages, *.pdf) Chapter 7: Incompressible viscous flows (12 pages, *.pdf) Chapter 8: Waves in fluids (17 pages, *.pdf) Coursework 2002 Exercise sheet 1 -- Due: Fri, 11-10-2002, 10:00h. Exercise sheet 2 -- Due: Fri, 18-10-2002, 10:00h. Exercise sheet 3 -- Due: Fri, 25-10-2002, 10:00h. Exercise sheet 4 -- Due: Fri, 01-11-2002, 10:00h. Exercise sheet 5 -- Due: Fri, 08-11-2002, 10:00h. Exercise sheet 6 -- Due: Fri, 15-11-2002, 10:00h. Exercise sheet 7 -- Due: Fri, 22-11-2002, 10:00h. Exercise sheet 8 -- Due: Fri, 29-11-2002, 10:00h. Exercise sheet 9 -- Due: Fri, 06-12-2002, 10:00h. Exercise sheet 10 -- Due: Fri, 13-12-2002, 10:00h. Coursework 2001 Exercise sheet 1 Exercise sheet 2 Exercise sheet 3 Exercise sheet 4 Exercise sheet 5 Exercise sheet 6 Exercise sheet 7 Exercise sheet 8 Exercise sheet 9 Henk van Elst (H.van.Elst%%qmul.ac.uk -- replace "%%" by "@") May 24, 2004
Engineers Edge - fluid flow, hydraulic and pneumatic
Fluids section of engineering directory. Provides definitions and practical applications.
Table of Contents Fluids Flow Hydraulic and Pneumatic - Engineers Edge Fluid Flow Hydraulic and Pneumatic Table of Contents PipeFlow.co.uk - Flow Pressure Drop Calculations Software Pressure Check FlowCalc Check NPSH Fluid Database Included Free TRIAL DOWNLOAD Use Code EE2005 For 10% Discount Product and Services Directory CONTINUITY EQUATION Properties of Fluids Buoyancy Compressibility Relationship Between Depth and Pressure Pascals Law Control Volume Volumetric Flow Rate Mass Flow Rate Conservation of Mass Steady-State Flow Continuity Equation LAMINAR AND TURBULENT FLOW Flow Regimes Laminar Flow Turbulent Flow Flow Velocity Profiles Average (Bulk) Velocity Viscosity Ideal Fluid Reynolds Number BERNOULLIS EQUATION General Energy Equation Simplified Bernoulli Equation Head Energy Conversions in Fluid Systems Restrictions on the Simplified Bernoulli Equation Extended Bernoulli Application of Bernoullis Equation to a Venturi HEAD LOSS Head Loss Friction Factor Darcys Equation Minor Losses Equivalent Piping Length NATURAL CIRCULATION Forced and Natural Circulation Thermal Driving Head Conditions Required for Natural Circulation Example of Natural Circulation Cooling Flow Rate and Temperature Difference TWO-PHASE FLUID FLOW Two-Phase Fluid Flow Flow Instability Pipe Whip Water Hammer Pressure spike Steam Hammer Operational Considerations Practical Application CENTRIFUGAL PUMPS Energy Conversion in a Centrifugal Pump Operating Characteristics of a Centrifugal Pump Cavitation Net Positive Suction Head Pump Laws System Characteristic Curve System Operating Point System Use of Multiple Centrifugal Pumps Centrifugal Pumps in Parallel Centrifugal Pumps in Series Engineering Design Data Engineering Forum Products and Services Engineers Store Engineering Career Engineering News Engineering Calculators Asme Y14.5M-1994 Geometric Dimensioning and Tolerancing GDT Training Free Magazine Subscriptions: Pump World Water and Waste International Pipeline and Gas Technology Copyright 2000 - 2005, by Engineers Edge, All rights reserved Disclaimer
Bernoulli's Principle Animation
Interactive animation shows how pressure and velocity in a fluid behave according to Bernoulli's Principle.
Bernoulli's Principle Animation Animated Demonstration of Bernoulli's Principle M. Mitchell Bernoulli's Principle states that as the speed of a moving fluid increases, the pressure within the fluid decreases. Introduction The Bernoulli's Principle animation on this page explores the behavior of an ideal fluid passing through a pipe. You can interact with the animation, and immediately see the effects on the fluid velocity and pressure. The animation is accompanied by two discussions - an introductory discussion without any math, and a more advanced discussion involving algebra and calculus. The fluid can be either a liquid or a gas. For Bernoulli's Principle to apply, the fluid is assumed to have these qualities: fluid flows smoothly fluid flows without any swirls (which are called "eddies") fluid flows everywhere through the pipe (which means there is no "flow separation") fluid has the same density everywhere (it is "incompressible" like water) As a fluid passes through a pipe that narrows or widens, the velocity and pressure of the fluid vary. As the pipe narrows, the fluid flows more quickly. Surprisingly, Bernoulli's Principle tells us that as the fluid flows more quickly through the narrow sections, the pressure actually decreases rather than increases! Demonstration A cutout view of a rectangular pipe is shown below, with fluid flowing through it from left to right. This pipe demonstrates the physics of fluid flow and Bernoulli's Principle. In this pipe, you can change the shape of the pipe by clicking and dragging the yellow handles ( ). Underneath, the cross-sectional area, pressure, flow rate and velocity curves are graphed so you can see how they are affected by the pipe shape. In the fluid, there are flow markers that show how the fluid travels through the pipe. Each flow marker may be thought of as a small ball having the same density as the surrounding fluid, and traveling along with that fluid. Java must be enabled to use the Bernoulli's Principle Demonstration Suggested Shapes Shape Title Comments Narrow pipe widens As cross-sectional area increases, velocity drops and pressure slightly increases Rocket nozzle Exhaust is shot at high speed out of narrow opening Drifting Rafters drift in lazy current between rapids Discussions Two discussions are available: An introductory discussion without any math A more advanced discussion involving algebra and calculus The meaning of the flow separation flag ( ) is explained in the more advanced discussion. Simply put, this flag is telling you when the demonstration should be modeling flow separation, so the displayed pressure and velocity values are not quite right because the demonstration ignores flow separation effects. Since flow separation is an advanced topic, beginners should just ignore it. Links There are other useful resources for Bernoulli's Principle and the Bernoulli Equation: Calculations, curving baseballs, and airfoils Advanced Bernoulli Equation This demonstration of Bernoulli's Principle has to be seen to be believed! While blowing through the narrow part, remove your finger that is holding the ball inside the inverted funnel. The ball will hover in the funnel until your breath runs out. Ball in funnel demonstration When describing why curve balls curve, Bernoulli's Principle is sometimes invoked. However, the Magnus Effect (which is not discussed here) is more appropriate for explaining curve balls, as explained at: Simple explanation of curve balls Advanced explanation of curve balls When describing how airplane wings work, many textbooks claim that the air traveling above the wing must travel faster over the wing so it can "catch up" with the air that went under the wing, so there is less air pressure above according to Bernoulli's Principle. This "catch up" explanation of airplane lift is seriously flawed. For clear and thorough explanations of airplane wings, start with the following links: Airfoils and Airflow How do airplane wings really work? Why does an airplane wing produce lift?
Incompressible Navier-Stokes equations reduce to Bernoulli's Law
Integrates the vector Navier-Stokes equation to obtain a vector form of Bernoulli's law. Provides interpretation and a mathematical basis for doing calculations.
Incompressible Navier-Stokes equations reduce to Bernoulli's Law Incompressible Navier-Stokes equations reduce to Bernoulli's Law Clyde M. Davenport cmdaven@usit.net 2003 Introduction Complementary Equation Quaternion Form Hypercomplex Integration Interpretation of Result Numerical Calculations Conclusions Introduction The incompressible Navier-Stokes vector-form equation is a nonlinear partial differential equation of second order (in dimensionless variables), as follows: where is a vector representing the velocity of an infinitesimal element of mass at a point in 3-D space, p is the scalar pressure at the same point, is the mass density at the point and is assumed constant throughout the medium, is the viscosity of the medium, and g is a constant vector acceleration due to some constant external force on the infinitesimal element, usually taken to be gravity. In other words, the N-S vector equation represents a force-mass-energy-momentum balance about an infinitesimal mass element of the field. The N-S equation addresses the motion of a single, tiny particle of the fluid field, not the overall motion of the fluid. However, it can be used to calculate the flow of incompressible gases and fluids past objects of arbitrary shape, as we shall explain. It is used in fluid dynamics teaching and in engineering as a standard model for turbulence, boundary layer behavior, shock wave formation, and mass transport. Among other things, it is used to calculate the pattern of air flow past airplane wings [The last time that you flew in an airplane, did you realize that your life depended upon this equation holding true?]. It has been studied and applied for many decades. Many different closed-form, series approximation, and numerical solutions are known for particular sets of boundary and initial conditions. Top Our objective, here, is to show that, under laminar flow conditions, the above equation reduces to a simple Bernoulli's Law in 4-D vector form: where V is the analytic 4-D velocity, P is the 4-D analytic vector pressure field (we shall explain), g is a constant acceleration which we shall allow to be imposed in an arbitrary direction, and Z is a vector representing arbitrary displacement in 4-D space, as we shall explain. We shall show how to recover the traditional scalar Bernoulli's Law, as a special case, from this expression. Top We shall supply the necessary mathematics for interpreting this expression and using it in applications. The informed reader will realize that, if we can do this, then a quantum leap in efficiency and reduction in cost of an enormous array of engineering calculations, from weather patterns to hydraulics to the flight of airplanes, can be made. We all remember Bernoulli's Law from our introductory physics courses. It was most often illustrated by flow through a constriction in a pipe, as in a Pitot airspeed gage. More significantly, it was also explained as the basis for lift by an airplane wing. The air travels a greater distance over the bulged upper surface than over the relatively flat underside, hence must flow faster over the top. By Bernoulli's Law, this creates a net drop in pressure, hence lift, on the top of the wing. Only much later, when we got to much more advanced courses, did we learn that there is also a complicated set of partial differential equations, called the Navier-Stokes equations, that can be used to calculate the flow of air and the pressure pattern around an airplane wing, consequently the lift. Until now, apparently no has ever said, "Wait a minute - what is the connection between these two formulas?" We intend to elucidate the connection, right here. Top We shall show, below, that any system of PDEs written in the form of a vector equation, using vector algebra and operators, is only an incomplete statement of some corresponding quaternion expression. The approach that we shall take toward integrating the N-S equation is start with the N-S vector equation, find terms that complete it to its corresponding quaternion expression, and then solve the latter by use of commutative hypercomplex analysis. The Hypercomplex Math page explains the mathematical system. It obeys the same axioms, algebraic rules, function theory, and scheme of analysis as the classical complex variables, while treating a 4-D variable. It is based upon a particular commutative group ring with an expanded definition of "the zero element." No snake oil is necessary, nor is any applied. In order to illuminate the argument, we first need to examine a particular, odd feature of vector mathematics that was put there by Heaviside and Gibbs at the outset. We begin with a short review of the development of multidimensional algebras and vector analysis, concentrating on those aspects that will be relevant to our argument, here. We urge the reader to follow along, because we shall construct an interpretation and point of view that is not generally seen in the literature. The interested reader may refer to the Hypercomplex Math page for supporting references for the following discussion. Top In the 1830s, Sir William Rowan Hamilton set out to create the first multidimensional algebra and associated analysis (beyond complex variables). He wanted to apply it to 3-D problems in optics and mechanics, in much the same way that we use vector analysis, today. As a guide, he had only a few rudimentary concepts from the algebra of complex variables. There was no matrix analysis, group theory, or ring theory at that time. Hamilton initially desired to create an algebra involving multiplication and division over a variable of the form Z = ix + jy + kz, where i,j,k are unit basis vectors and x,y,z are real coordinates. By trial and error, he was unable to do so, because, as we know today, no division algebra exists for three-dimensional numbers. He found that he could create a division algebra over 4-D elements of the form Z = + ix + jy + kz, which we now know as the quaternion algebra, the only division algebra of order four. He called the scalar part, and ix + jy + kz the vector part, and neither he nor his immediate successors quite knew what to make of the scalar part. Although Hamilton knew that the basis elements for his new algebra were 1,i,j,k, he could not bring himself to associate the 1 element with the "scalar part" and view the result as a 4-D vector. Apparently, the one thing upon which they were in unanimous agreement was that could not be a "fourth dimension," neither time nor anything else. They began to treat and think of these components as fundamentally different kinds of things, when in actuality all four coefficients (coordinates) are treated qualitatively the same by the algebra. Top This is an important insight for our present objectives. Apparently, neither Hamilton nor any of his nineteenth-century successors could quite get their minds around the concept of a four-dimensional space. What would be the "direction" of the supposed "fourth dimension?" How could it possibly be orthogonal to the other three? Because of this bafflement, scientists and engineers of the time steadfastly refused to use quaternion mathematics in their calculations. In the mid-1850s, James Maxwell published four major papers that developed the first formulation of electromagnetic theory, using the clumsy component-by-component calculations of the time. In 1873, he published a treatise on electromagnetic theory that included his earlier papers and in which he reformulated all of the fundamental equations in terms of the algebra and notation of quaternions and keeping Hamilton's view that the vector and scalar parts were somehow fundamentally different in nature. This formulation was absolutely rejected out of hand by the scientific community. Instead, they struggled along with a crude, component-by-component means of calculation. In the period 1873-1893, there was an acrimonious, running argument in the scientific literature as to whether quaternion mathematics had a proper place anywhere in science! Top There it lay until 1893, when J. W. Gibbs in America and O. W. Heaviside in Britain began to develop and apply what we now know as vector analysis. They based it upon the quaternion algebra, but knew that they could never mention that fact, lest it be rejected instantly. Their notation is basically a modification shorthand version of the full quaternion notation. Apparently, their thought processes ran something like the following: "Look, we believe that the scalar and vector parts are mathematically fundamentally-different things. The scalar part is 1-D and the vector part is 3-D, so let's just use those two things separately and independently as the basic elements, if you will, and drop all mention of anything that is 4-D. The 4-D objectionists will be left with nothing to argue about." All calculations would appear as separate manipulations in terms of the scalar or vector parts of a quaternion, as if they were independent, and they would never be identified as components of a quaternion. This gave it the desired 3-D look. Heaviside reformulated Maxwell's electromagnetic theory in these terms, and was aided by the circumstance that the dot and cross products involving the del operator with various field variables could be identified with fundamental, physically-measurable electromagnetic field parameters. The subterfuge worked. Scientists and engineers accepted it, and the rest is history. Top However, and this is why we have struggled through this tedious chain of events, when Gibbs and Heaviside dropped the full quaternion product in favor of manipulations with the scalar and vector parts, separately, they had to make an ad hoc change to the algebra that is inconsistent with quaternion mathematics. They wanted to assure that no product of two 3-D vectors would ever have a scalar part (i.e., a dreaded "fourth dimension.") They found that they could achieve this end by arbitrarily setting ii=jj=kk=0 in the cross product of two 3-D vector components of a quaternion, but ii=jj=kk=-1 in the dot product of the same! Then, they were free to treat the scalar and vector parts of a quaternion product as independent entities. Their introduction of the nonstandard notation ii = jj = kk = 0 does not change the fact that they were working with a quaternion algebra. This is the "odd feature" that we alluded to, earlier. However, when they arbitrarily set certain terms of a product to zero, something was lost. The full quaternion product of two 3-D vectors is a b = - a183b b + b a 215 b b , hence if we go off and do calculations using only the cross product operation, then every time that we do a product, we lose the scalar part (here, denoted as the usual dot product). That is why the Heaviside-Maxwell's equations require the addition of a i continuity condition i (additional, seemingly-unrelated equation, not generated by the original derivation) to make them consistent. That the resulting system of mathematics worked in practical terms is abundantly testified to by our space-age, technological society, fully undergirded by vector calculations, but is there more insight to be gained? img src="spacer.gif" width="20" height="5" a href="top" Top a p p align="justify" Indeed, we can see from the above that any typical vector algebra expression, equation, etc., such as the vector N-S equation, must represent only i part i of a true quaternion expression (i.e., without dot or cross products). There must exist a complementary expression that, when combined with added to the original will result in a valid quaternion expression. Moreover, the resulting quaternion expression will nearly always allow some consolidation among its components, making it easier to solve. That is the notion that we are pursuing, here. [Aside: It is the author's opinion that if Hamilton, Gibbs, Heaviside, and their nineteenth-century compatriots had not been so abstractly-challenged, there would be no "vector analysis" today, but only quaternion analysis.] a href="top" Top a p p align="justify" There is another observation that we need to make, before proceeding. Both the full quaternion and the commutative hypercomplex algebras can be based upon an element of the form b Z b = b 1 b i ct i + b i b i x i + b j b i y i + b k b i z i , where b 1,i,j,k b are unit direction vectors (or algebraic basis elements) and i ct,x,y,z i are real. [Of course, the b 1,i,j,k b elements obey different rules in the two different systems.] The element i c i is the speed of transmission of disturbances in a quiescent N-S medium. Moreover, the notation for all of the elementary operations of the associated analyses are the same in both systems, and they have the same abstract meaning. Some examples are the 4-D product, the 3-D del operator, and the scalar Laplacian operator. Consequently, if we have an elementary quaternion equation or expression, not containing dot or cross product forms, then we can accept it as a valid commutative hypercomplex expression and proceed from there to solve it. img src="spacer.gif" width="20" height="5" a href="top" Top a p a name="comple" a p font size="5" color="teal" Complementary Equation font p p align="justify" We shall now construct the complementary equation for the vector Navier-Stokes equation. We shall take each term in the N-S equation in turn and construct a complementary expression that completes a valid quaternion expression (i.e., having no dot or cross product terms). Note that, because of what we pointed out above, all terms of the N-S equation are 3-D or less. That is no problem, because the application of an operator is handled exactly like multiplication, and quaternion multiplication is still valid even if one or more components of either or both multiplicands are zero or absent altogether. img src="spacer.gif" width="20" height="5" a href="top" Top a p p align="justify" The first term in the N-S equation is a partial derivative, img src="vt.gif" align="top" alt="v sub t" , where img src="v.gif" align="top" alt="velocity v" is the 3-D velocity. We first note that, in quaternion notation, p p align="center" img src="pvt.gif" align="middle" alt="k v_ct" p p align="justify" The parenthetical quantity is a part of a 4-D gradient operation, p p align="center" img src="quadv.gif" align="middle" alt="quad v" p p align="justify" Consequently, the complementary part for the img src="vt.gif" align="absbottom" alt="v sub t" term is img src="cdelv.gif" align="bottom" alt="c del v" , where the latter is a quaternion operation. Note that, although the quad operator is 4-D and img src="v.gif" align="top" alt="velocity v" is 3-D, the operation is performed like a quaternion multiplication, hence is valid. img src="spacer.gif" width="15" height="5" a href="top" Top a p p align="justify" The second term of the N-S vector equation is img src="vdotdelv.gif" align="absbottom" alt="v dot del v" . The obvious complementary part is img src="vcrsdelv.gif" align="absbottom" alt="- v cross del v" , the sum of the two parts then yielding img src="vdelv.gif" align="absbottom" alt="- v del v" , a quaternion expression. p p align="justify" Recall that quaternion multiplication is noncommutative, and note that we are maintaining the proper left-right orientation of all operators and variables, hence we are maintaining quaternion algebraic rules. The quaternion algebra is also associative and distributive. img src="spacer.gif" width="20" height="5" a href="top" Top a p p align="justify" The third term of the N-S vector equation is img src="delp.gif" align="absmiddle" alt="del p" . This brings up a different kind of problem because, looking ahead, we are going to integrate once and obtain i p i as a free-standing entity, without further specification of its functional form. However, we must remember that the original Bernoulli's Law was developed to show the co-dependent relationship between speed and pressure in a flowing medium. If the pressure was specified at a given point, then the corresponding speed could be calculated from Bernoulli's Law; conversely, if the speed at a given point was specified, then the pressure could be calculated. The formula was expressed in all-real terms. Here, we will have a i vector velocity i img src="v.gif" align="absmiddle" alt="v symbol" , rather than scalar speed, consequently i p i will have to have a vector form in order to have the proper co-dependence with velocity. img src="spacer.gif" width="20" height="5" a href="top" Top a p p align="justify" We could just i assume i that a real, analytic function i p(x,y,z,ct) i can be analytically continued into 4-D hypercomplex form, and work with the vector Bernoulli's Law and numerical values without ever having to know its precise analytical form. However, we can actually show that this is a good assumption, in concrete terms. Suppose that we are given a scalar (real) analytic function i p(x,y,z,ct) i , even allowing some of the independent variables to be missing. If we make the substitutions img src="spacer.gif" width="20" height="5" a href="top" Top a p p align="center" img src="4dargs.gif" alt="1-D to 4-D args" p p align="justify" for whatever independent variables i x,y,z,ct i that are present, then we have a hypercomplex-valued, analytic function i p i ( b Z b ) that subsumes the original scalar function. This works even if we start with a function of only one independent variable, say i p(x) i . Moreover, we have preserved the form of the function, and the commutative hypercomplex mathematics always tell us how to interpret and manipulate the extended form. img src="spacer.gif" width="20" height="5" a href="top" Top a p p align="justify" All that being said, we can assume that i p i can always be represented in an analytic, 4-D vector form. If the vector field img src="v.gif" align="absmiddle" alt="v symbol" is given, then the corresponding vector i p i field can be calculated from the Bernoulli's Law formula. Conversely, if a 4-D scalar i p(x,y,z,ct) i field is given, then we know how to construct its 4-D vector extension. Having that, we can calculate the vector field img src="v.gif" align="absmiddle" alt="v symbol" from the Bernoulli's Law. In conclusion, the img src="delp.gif" align="absmiddle" alt="del p" term can be assumed to be a quaternion expression as is. No complementary term is needed. img src="spacer.gif" width="20" height="5" a href="top" Top a p p align="justify" The fourth term of the N-S vector equation is img src="delsqv.gif" align="absmiddle" alt="del-square v" . The del-squared operator is a scalar operator. We note that p p align="center" img src="quadsqv.gif" align="absmiddle" alt="quad-square v" p p align="justify" Therefore, the necessary complementary term is: p p align="center" img src="pvpctsq.gif" align="absmiddle" alt="d2 v dct2" p p align="justify" The fifth and last term of the N-S vector equation is img src="rhog.gif" align="absmiddle" alt="rho g" . Both elements are constant, rho being a scalar and i b g b i being a 3-D acceleration which we intend to allow being imposed in any direction, and as such their product is a valid quaternion expression. No complementary term is needed. This concludes our derivation of the complementary terms. img src="spacer.gif" width="20" height="5" a href="top" Top a p a name="fullhy" a p font size="5" color="teal" Quaternion Form font p p align="justify" Now we can summarize our findings and show the N-S equation, the complementary vector equation, and their sum, which is the associated quaternion equation, as follows: p p align="center" img src="quatsum.gif" align="absmiddle" alt="2 vect eqns" p p align="justify" Remember that, in the quaternion equation, we are assuming that i b p b i will be treated as a 4-D analytic (vector) function, rather than a scalar function, and that we showed earlier how to construct it, if given a scalar function as part of the initial conditions. img src="spacer.gif" width="20" height="5" a href="top" Top a p p align="justify" The reader might notice that some of the elements of the quaternion equation are not 4-D, for example the del operator and i b g b i . That is no problem, because the application of an operator is handled exactly like multiplication, and quaternion multiplication is still valid even if one or more components of either or both multiplicands are zero or absent. It is a valid quaternion expression because we eliminated the dot and cross products. img src="spacer.gif" width="20" height="5" a href="top" Top a p a name="integ" a p font size="5" color="teal" Hypercomplex Integration font p p align="justify" The quaternion-form N-S equation, p p align="center" img src="quateqn.gif" align="absmiddle" alt="quaternion eqn" p p align="justify" is also a valid commutative hypercomplex equation, because every element and operation has an equivalent interpretation in the latter system. From this point forward, we shall treat it as such, and solve it by means of commutative hypercomplex functional analysis techniques. Are we entitled to do this? Yes, as long as we are consistent throughout, because we can verify the result by substitution into the original N-S equation. We do not use quaternion functional analysis because a classical function theory for a quaternion variable does not exist, as a consequence of the noncommutativity of quaternion multiplication. img src="spacer.gif" width="20" height="5" a href="top" Top a p p align="justify" The commutative hypercomplex mathematics is a system that obeys the axioms of the classical complex variables, including the function theory, and behaves in all ways like the classical complex analysis, while treating a 4-D independent variable. The algebra has much of the notation and appearance of quaternions, the main difference being that quaternion multiplication is noncommutative. Refer to the a href="http: home.usit.net ~cmdaven nhyprcpx.htm" Hypercomplex Math a page for details. In this system of mathematics, the vector Bernoulli's Law as given earlier has a rational and consistent interpretation in the same way as would a classically-complex expression, as we shall show. img src="spacer.gif" width="20" height="5" a href="top" Top a p p align="justify" We shall now convert the Navier-Stokes PDE to an ODE by use of the 4-D Cauchy-Riemann conditions. In doing so, we shall analytically continue the dependent variables img src="v.gif" align="absmiddle" alt="v symbol" and i p i into 4-D. At the end, we shall extract the lower-dimensional solution. Recall that, to this point, img src="v.gif" align="absmiddle" alt="v symbol" and i p i are 3-D and 1-D scalar, respectively. We showed how to analytically extend a scalar function i p(x,y,z,ct) i to a 4-D vector function. Here, we are going to be integrating in terms of a 4-D variable b Z b = b 1 b i ct i + b i b i x i + b j b i y i + b k b i z i , which analytically continues the results into 4-D. Therefore, to emphasize the enlarged problem, we write the broadened variables with capital letters: img src="spacer.gif" width="20" height="5" a href="top" Top a p p align="center" img src="hypxeqn.gif" align="absmiddle" alt="hypercomplex eqn" p p align="justify" Also, recalling the definition of the quad operator, we expand the second and third terms as follows: p p align="center" img src="vdelvexp.gif" align="absbottom" alt="- v del v expanded" p p align="justify" The " b 1 b " element is just that - the unity element. Here, it can be explicitly displayed or not, as desired. Now, as consequences of the 4-D Cauchy-Riemann conditions, for b V,P b , or i any other i analytic function, img src="spacer.gif" width="20" height="5" a href="top" Top a p p align="center" img src="boxvp.gif" align="absbottom" alt="box v,p =0" p p align="justify" Folding all of this back into the broadened N-S equation, we arrive at a dramatically simplified ODE expression: p p align="center" img src="finleqn.gif" align="absmiddle" alt="ODE eqn" p p align="justify" In the process of making this conversion, we have introduced the Cauchy-Riemann conditions, so that when we integrate, our results will automatically be analytically continued into 4-D. We are operating under axioms and functional behavior exactly like that for real or classically-complex variables, so without further ado, we integrate by inspection to get: img src="spacer.gif" width="20" height="5" a href="top" Top a p p align="center" img src="finlbern.gif" alt="4-D Bernoulli's Law" p p align="justify" This is our result in 4-D terms, from which we shall extract special cases for the traditional scalar Bernoulli's Law and a 3-D vector form. All of this leadup may have seemed obscure, and the reader might have difficulty in believing the result, but a closer reading of the a href="http: home.usit.net ~cmdaven nhyprcpx.htm" Hypercomplex Math a page can verify that everything that we have done is valid. If it were not, then it would be quite a coincidence that after letting logic take us where it will, we arrived at a conclusion that, upon reflection, makes great intuitive sense, because both Bernoulli's Law and the incompressible Navier-Stokes equations deal with laminar flows of incompressible liquids or gasses. p p align="justify" The result of integrating the vector N-S equation has produced an atypical characteristic function. There is not a single function of the 4-D coordinates, i f i ( b Z b ), but i two i : b V b ( b Z b ) and b P b ( b Z b ). The characteristic function reveals the exact relationship between b V b and b P b , and how they must interact and play off of each other in a dynamic situation. For example, if we are given the velocity field in the form of an analytic function b V b ( b Z b ) (or enough information to construct it by use of the 4-D Cauchy-Riemann conditions), then the pressure field b P b ( b Z b ) is: img src="spacer.gif" width="20" height="5" a href="top" Top a p p align="center" img src="pfz.gif" alt="P(Z) function" p p align="justify" Note that all elements are manipulated by use of the same axioms and functional rules as for the real or complex variables. Conversely, if we are given a 4-D pressure field b P(Z) b (or enough information to construct it by use of the 4-D Cauchy-Riemann conditions), then the velocity field b V b ( b Z b ) is: img src="spacer.gif" width="20" height="5" a href="top" Top a p p align="center" img src="vfz.gif" alt="V(Z) function" p p align="justify" The commutative hypercomplex mathematics tell us how to interpret these expressions. We can even break them down into 4-D vector functions of the form b 1 b i u(x,y,z,ct) i + b i b i q(x,y,z,ct) i + b j b i w(x,y,z,ct) i + b k b i s(x,y,z,ct) i . Although every element in these expressions can be written in 4-D vector form, i we do not use classical vector algebra when manipulating them i . Instead, we use the rules and function theory of the commutative hypercomplex mathematics, which are the same as for the classical complex variables, with a few, minor notational differences. img src="spacer.gif" width="2" height="5" a href="top" Top a p p align="justify" The reader might notice that the viscosity factor, img src="mu.gif" align="top" alt="mu" , does not appear in the 4-D Bernoulli's Law. There is a reason. i The commutative hypercomplex, analytic treatment makes it unnecessary. i Go back and review where in the solution process that img src="mu.gif" align="top" alt="mu" was eliminated: In the middle of the "Hypercomplex Solution" section, we asserted that we were going to use analytic function theory to solve the quaternion form of the N-S equation (which is also a valid commutative hypercomplex expression). We want the flow field b V(Z) b to be continuous and single-valued (analytic). Consequently, as for any analytic function, the 4-D scalar Laplacian of b V b is zero, causing img src="mu.gif" align="top" alt="mu" to drop out. We rationalize this as follows. img src="spacer.gif" width="20" height="5" a href="top" Top a p p align="justify" In the original, vector-form Navier-Stokes equation, it is the img src="delsqv.gif" align="absmiddle" alt="mu del sq v" term that causes a differential flow between different streamlines. It is the term that produces conformal flow lines. When we go to a 4-D, commutative hypercomplex, analytic treatment, i it is the mathematical system, itself, that produces the conformal flow lines, i making img src="mu.gif" align="top" alt="mu" superfluous. It so happens that laminar flow is i analytic i in the complex variable sense. Indeed, classical complex function theory has been used since the 1930s to calculate conformal flow over an airfoil shape. See [ a name="kober" a a href="nrefrncs.htmkober" Kober, 1957 a ] for examples and a long list of references. We should not be surprised at all by our result, here. We do, however, need to check beforehand that our fluid parameters are such that laminar flow is possible. This is indicated by a Reynolds number, which is proportional to (fluid velocity viscosity), less than about 2,000 (even less near sharp edges). If this is exceeded, then turbulent flow ensues. img src="spacer.gif" width="10" height="5" a href="top" Top a p a name="interp" a p font size="5" color="teal" Interpretation of Result font p p align="justify" We have a 4-D expression that looks like a Bernoulli's Law, but the original Bernoulli's Law was all-scalar, and the vector form that we wanted to obtain as our objective in this paper is 3-D. Therefore, some interpretation is required. Let us first address Bernoulli's original, all-scalar form and see if we can recover it from the 4-D form. Consider the following special case: Let i x,y,z i be the usual three-space coordinates, with b k b i z i in the vertical direction. Let the scalar speed img src="v.gif" align="top" alt="vel v" be in the + i x i direction. Let i b g b i be the acceleration due to gravity (in a vertical direction), and let the displacement b Z b = b k b i h i be in a true vertical direction. We shall also have to convert the scalar i v i back from a dimensionless form. In these terms, img src="spacer.gif" width="20" height="5" a href="top" Top a p p align="center" img src="origlaw.gif" alt="Scalar Bernoulli's Law" p p align="justify" Up to now, we are still allowing b P b to be 4-D. But here, all other terms of the equation are scalar, meaning that the equation holds true only with the first (scalar) component of b P b , b 1 b i p i , which, if one recalls, is the same i p i as in the original Navier-Stokes equation. Therefore, in all-scalar terms, img src="spacer.gif" width="20" height="5" a href="top" Top a p p align="center" img src="origlw1.gif" alt="Original Bernoulli's Law" border="1" p p align="justify" This is the original Bernoulli's Law, as given in most any college introductory physics textbook. This result is significant, but it would be even more useful if we could express it in three dimensions. Indeed, we can do so. In this example, we shall use the dimensionless variable i v i from the initial N-S equation as given in the Introduction. Consider the special case (stated in commutative hypercomplex mathematics): img src="spacer.gif" width="20" height="5" a href="top" Top a p p align="center" img src="origlw2.gif" alt="3-D Bernoulli's Law" p p align="center" img src="origlw3.gif" alt="3-D Bernoulli's Law" border="1" p p align="justify" Here, img src="v.gif" align="top" alt="vel v" , i b g b i , and b X b are 3-D, each with b i,j,k b components, but their indicated products will be 4-D, with b 1,i,j,k b components. Therefore, b P b must be manipulated as a 4-D entity. We must go "outside the 3-D box" in order to do calculations. If we are given a scalar i p(x,y,z,ct) i pressure field in the form of an analytic function, then we must construct its 4-D extension as indicated earlier. If the velocity field is given in the form of an analytic function, and the external force and displacement are given, then we merely calculate b P b from the above equation, then select its b 1 b -component as the scalar i p(x,y,z,ct) i pressure field. img src="spacer.gif" width="20" height="5" a href="top" Top a p a name="numer" a p font size="5" color="teal" Numerical Calculations font p p align="justify" All of the above is well and good, but when solving engineering problems, the problem statement usually does not give any part of the field configuration in the form of an analytic function. Typically, we receive only the boundary and initial conditions in the form of numerical data. We must compute the rest. img src="spacer.gif" width="20" height="5" a href="top" Top a p p align="justify" One might recall that partial differential equations, especially those used to model the behavior of some material substance, typically describe the behavior of some variable, parameter, or physical effect i about a point i . They are typically derived from a force-energy-momentum-mass balance on an infinitesimal element at a point. If we achieve an integration of the Navier-Stokes equation by whatever means, then the integrated form (characteristic function) will embody the same description of physical effects as the PDE and must be viewed and applied in the same way; i.e., as describing the variation of effects about a point, and not necessarily the macro behavior over all space. That is to say, the behavior of the integrated function about its origin of coordinates describes the qualitative variation of physical effects about i any i point in the region of validity of the PDE. The region of acceptable approximation of the real, physical effects about a given point might be small, so we might have to do a numerical solution, this time using the characteristic function instead of the PDE. We could use the 4-D constant of integration and the playoff between img src="v.gif" align="top" alt="vel v" and i b p b i in the Bernoulli formula to fit together a mosaic of small-area solutions on a grid, quite analogous to what is done in a numerical, finite-element solution of the PDE. img src="spacer.gif" width="5" height="5" a href="top" Top a p p align="justify" Another way to view the Navier-Stokes equation is that it was developed to describe the immediate, localized reaction of a tiny, incremental element of mass in the fluid field to given external forces and momentum and energy inputs. In physics terms, the integrated result is expressed in i body-centered coordinates i whose origin moves with the subject particle of mass and whose axes slide parallel to themselves. At any given instant of time and for given local conditions, the integrated result indicates how the particle of mass will move next within the body-centered frame. We continue to emphasize: The integrated result describes an immediate, localized reaction, and says nothing about the long-term motion of a given particle of mass. For that reason, we must do a finite-element-like numerical calculation in order to coordinate the motions and interactions of all the particles, thereby obtaining a view of the overall motion of the fluid. This view explains why there is not any analytic-function solution of the N-S equation that models turbulent behavior in the large. Any "solution" is point-localized. img src="spacer.gif" width="20" height="5" a href="top" Top a p p align="justify" However, the Bernoulli's Law formula might not be the best choice for use in a numerical solution. Instead, consider the ODE that we integrated to obtain the Bernoulli formula. From it, we can write: p p align="center" img src="odedif.gif" alt="ODE differentials" p p align="justify" We would use this expression in a finite-difference scheme. Here, d b Z b can be viewed as an incremental movement on the problem grid as our numerical solution proceeds, and not just a displacement against the constant force associated with b g b . As we have seen, even when we are working with 3-D quantities, the commutative hypercomplex algebra returns a 4-D result from a product operation, so it is necessary that we carry all results in 4-D terms. In this approach, we would generate at least two four-component numbers b V sub small i i i small sub img src="spacer.gif" width="1" height="5" , P sub small i i i small sub b for each 3-D grid point. Starting from a boundary, we could "walk" a solution throughout the problem volume by advancing an increment d b Z b to a new mesh point, then using the formula to calculate the new pressure b P sub small i i i small sub b and velocity b V sub small i i i small sub b img src="spacer.gif" width="1" height="5" . At the end, on a point-by-point basis, we would extract the 3-D velocity as the b i,j,k b components of b V sub small i i i small sub b img src="spacer.gif" width="1" height="5" , and the scalar pressure as the b 1 b -component of b P sub small i i i small sub b img src="spacer.gif" width="1" height="5" . The unused 4-D components can be viewed as only intermediate data storage registers. Not being a practicing numerical analyst, I leave the details of the scheme to more-experienced specialists. img src="spacer.gif" width="20" height="5" a href="top" Top a p p align="justify" Yet another way to view the characteristic function solution of the Navier-Stokes equation is as follows. Consider an infinite, uniform, incompressible fluid medium. Let an infinite-magnitude, point impulse be introduced at some arbitrary point in the fluid. The disturbance will assume the functional form of the characteristic function and will move away from the originating point at the characteristic speed for disturbances in the medium. The outwardly-moving disturbance will be radially symmetrical because, as we have shown, the solution is rotationally invariant, given the proper frame of reference. img src="spacer.gif" width="20" height="5" a href="top" Top a p a name="conclus" a p font size="5" color="teal" Conclusions font p p align="justify" For more than sixty years, we have had ample illustration that Bernoulli's Law addresses the same laminar flow phenomena as does the Navier-Stokes equation, and that classical analytic function theory can be used to calculate 2-D laminar flow around an airfoil. Here, we have used 4-D analytic function theory to show that under an assumption of laminar flow, the N-S equation integrates directly to a 4-D form of Bernoulli's Law. From this, we can recover Bernoulli's original, all-scalar formula as a special case. Even better, we have a general formula that accommodates 3-D vector values for flow velocity, and the commutative hypercomplex math provides a comprehensive basis for doing calculations. We can use the 4-D Bernoulli's Law in place of the Navier-Stokes equation when doing laminar flow calculations, with potentially great savings in computational expense. p p align="justify" All that aside, possibly the greatest gain is the expanded theoretical insight that we now have about laminar flow in three dimensions. img src="spacer.gif" width="20" height="5" a href="top" Top a p hr p align="center" !-- Gostats.com web hit code. Please do not change this-- script type="text javascript" var go_mem="navier"; script script type="text javascript" src="http: c2.gostats.com go.js" script noscript a href="http: c2.gostats.com gogi viewstats.pl?mn=navier" target="_top" img src="http: c2.gostats.com gogi count.pl?mn=navier" border=0 alt="Free Hit Counter" a noscript br a href="http: gostats.com" free hit counter a !-- End of Gostats.com web hit code -- p p align="center" a href="top" Top a | a href="http: home.usit.net ~cmdaven cmdaven1.htm" target="_top" Home a br copy 2003 br font size="small" Clyde M. Davenport br cmdaven@usit.net br First edition, 12 2 03 font p p td tr table !-- Close formatting table that was opened at top -- body html
eMicroNano
A free one-stop information resource for bio-, micro-, and nano-fluidic systems.
emicron: A Free One-stop Resource For bio, micro, and nano fluids and systems Home Site Map Search New User Contact Us Gallery Event Calendar Education Publications Buyers Guide Jobs Who's Who Companies Vendors Research Professional Societies Consultants Other Links * Please send news items to contact@emicronano.com * Support this website by buying items from Amazon through eMicroNano Welcome to eMicroNano A Free One-Stop Resource For Bio, Micro, and Nano Fluids and Systems Useful tools for students and professionals: * Compressible Flow Calculator * Molecular Dynamics Simulation Codes * Boltzmann Equation Solvers * Direct Simulation Monte Carlo codes * Potential Flow Machine * Vortex Panel Method * Unit Conversion Calculator by LMNO Engineering New Users: List Yourself for free in our Directory . Other Related Websites: Gallery of eMicroNano Images: Send new contributions to contact@emicronano.com About eMicroNano Editors Discussion Forum Sponsorship Gallery of eMicroNano Images Editorial Advisory Board List of Contributors Education Focus Forgot your password?
Convection in a box.
Experiments with smoke inside a plexiglass box challenge convectional wisdom. Smoke can unexpectedly act heavier than air and then spontaneously reverse.
airbox experiments Convection in a box e-mail...id@synapse9.com (delete spaces drop me a line) These are convection experiments with smoke that can be performed using a Plexiglas box and a burning stick of incense. I used solvent glue to make 6"x6" boxes of varying depth, using 1 8" plexiglas on the faces and 1 16" plexiglas on the edges, making gaps in the edge pieces for openings as needed. Several observed behaviors pose challenging questions. Click on the pictures for image popups. Have fun. A single 2D vortex ring - displaying apparent contradictions Detailed diagrams of vortex flow - the winding wrapping of layers Smoke pool - with branching columns of clear air Very strange indeed - a clear confusion between up and down One thing these experiments demonstrate is Organized Molecular Motion , fluid states that store and release energy. This is clearly evident from experiment 4, and then can help explain experiments 1, 2 3. There is a simpler way to perform experiment 4 that usually works. On a table in a quiet place stand a burning cigarette on its end and patiently watch. After a while smoke will be seen pouring down the outside to form a pool of smoke around the base. Wisps will then sometimes be seen spontaneously rising from the smoke pool, storage and release , QED. Perhaps several repetitions will be needed for you to believe what you see. With an opening in the bottom of a ~1 4" deep box, a burning incense stick is inserted and the rising smoke generates a convection loop. At first the flow may look like a large circle, two 'D' shaped spirals back to back, nearly filling the chamber (left). Curiously the none of the smoke rises to spread out at the top. After a few seconds, with a continuing introduction of heat and smoke, the double spiral curiously becomes smaller and denser (center). Both of these behaviors seem wrong when you think about them. First, the smoke should rise and spread out at the top, like in open air, but it doesn't. Second the vortex should get larger the more heat and smoke are added, not smaller. After removing the incense stick and covering the hole in the bottom of the box the 2D vortex ring continues, firmly sitting on the bottom of the box (right). When you try it with a 1 2" deep box the self-confined cell does not develop. Smoke goes to the top and spreads out (in a 6"x6" box at least) just like you'd expect it to. The image at the left shows a recent test of both 1 2" and 1 4" depth containers, and using color changing heat sensitive film on the back surface, to help show where the heat goes. In the 1 4" box, the heat introduced almost seems to disappear. Of course it does not, but there is an increase in density in the confined smoke cell and no indication of a corresponding heat loss. There are surely other things to be resolved too, but I think this is unambiguous evidence of fluid-partical gels. That could explain why something hot acts heavy, a problem observed in all these studies. The key observation is that the smoke comes to circulate entirely within itself. The rising plume flows down from above and is then drawn in at the bottom and up at the center. It's possible to interpret this as smoke being pulled downward on the outside by the central current. A possibly important observation is that in an 1 8" deep box the smoke cell that forms is about the size of a quarter, very small, and the circulation is so confined that the incense stick is snuffed out almost immediately. In the 1 4" deep box the ember can go out for lack of oxygen as well, though not for some time. What's wrong with the idea suggested by some, that the walls drain enough heat from the smoke to make it heavier than air, is that : 1) the effect increases over time, rather than slowing as the walls get hotter, and 2) the smoke would spread out over time, not compress, seeking the cooler portions of the surface 3) Plexiglas has a very low specific heat and the smoke is not in circulating contact with it. Others have suggested that it's just the proximity of vertical surfaces. If the same smoke source is held close to a similar surface in quiet open air, smoke is seen easily drifting upward even within the near ('sticky' ~1 32") boundary layer where all flow is laminar. The proximity of the surface alone is not what makes the smoke turn and go down, but proximity must have something to do with it, since proximity is a controlling variable. After removing the incense stick and covering the hole at the bottom the 2D vortex ring settles into the shape at the right, similar to an apple upside down. This continues without outwardly changing shape or size for a very long time. It seems to just spiral slower and slower until the smoke particles settle to the bottom of the chamber. top The details of the spiral path of circulation can be seen after generating a double spiral, removing the smoke source, and covering the bottom hole. Briefly removing the cover on the bottom hole introduces a pulse of clear air to be drawn up into the convection vortex and trace the circulation shape.. The actual movement of the layers is quite simple, after moving up the center and splitting at the top the new material begins an infinite regression of stretching and wrapping around itself while also migrating outward toward the outer surface. Material from the outer surface may then be drawn back in the bottom to start the process over. At first it looks like circular motion, but it is composed entirely of winding. top Some interesting shapes result from blowing smoke into the box. Do it gently so as not to mix it by forced turbulence. Then momentarily open a hole in the bottom to let in cool room air. Oddly, the smoke sits on the bottom and the 'cool' air rises through it, displaying a number of fascinating circulation patterns. Introducing an incense stick near the edge of the 1 4" deep box stimulates a single 'D' shaped loop, with the same characteristics as the more normal double 'D' shaped shrinking convection cell. After removing the incense stick and watching it sit there spinning by itself, crammed into the corner instead of spreading out either along the top or bottom, seems very strange! top One of the strangest things found were these two examples of 'heavy smoke' spontaneously becoming buoyant. In both cases warm smoke was blown into the boxes gently so as not to turbulently mix, and was found to first settle in a pool on the bottom. In the first example the box was then sealed and left alone. In the second, openings were made at the top and bottom, in completely still surroundings, and the smoke was allowed to gently drain out the bottom with room air entering at the top. The circulation shown in the first example developed after a few minutes. Instead of remaining motionless the smoke pool took on the shape shown, oddly sloped, necking upward on one side and flowing toward the top of the box in a loose, lopsided, double spiral. There are quite a long list of things wrong with this one! What explains both this and the following example seems impossible, energy storage and release in a fluid in some form other than heat. In the second example the smoke pool in the box flows gently out over the table surface. It forms a thick spreading film as if a puddle of syrup. On occasion (~1 10 or so), and clearly only when the room air is quite still, little vigorous rising currents develop. They're not normal convection cells, but twisting slivers of smoke. Warm smoke should not have settled in a pool in the first place, and especially not spontaneously rise again from it. Back to top , Other Airwork Phil Henshaw
ePower Propulsion and Combustion
A one-stop resource for professionals working in propulsion, power, and combustion fields.
ePower-Propulsion: A Free One-stop Internet Resource For Propulsion and Power Engineering Community Home Site Map Search New User Contact Us Event Calendar Education Publications Buyers Guide Jobs Who's Who Companies Vendors Research Professional Societies Consultants Other Links HEADLINES* Re-Living the Wright Way (A website developed by NASA) Current Funding News News Archive * Please send news items to Contact Us Welcome to ePower-Propulsion A Free One-Stop Resource For Power and Propulsion Engineering Editors Useful tools for students and professionals: * Engine Simulation Software by NASA * Compressible Flow Calculator Research Funding: See the database of Current Funding News Education: See Education Focus for further details. New Users: You can list yourself in the Directory of our Professionals for free. Interesting Images: The Gallery is continually being updated. Please send new contributions to Contact Us . About ePower-Propulsion Gallery of Images Editorial Advisory Board List of Contributors Create a link to this site Sponsorship Discussion Forum iCentral: an ePower Gold Sponsor
PivNet 2
An introduction to the European Collaboration on Particle Image Velocimetry. Links to participating partners, information about courses, conferences and literature.
PivNet 2 - A European collaboration on Particle Image Velocimetry
The Effects of Water Hammer And Pulsations
Explanation of water hammer and pulsation inclusive the formula used to calculate the pressure increase.
"Water Hammer Pulsation" Tech Brief: The Effects of Water Hammer And Pulsations Quick closing valves, positive displacement pumps, and vertical pipe runs can create damaging pressure spikes, leading to blown diaphragms, seals and gaskets also destroyed meters and gauges. Liquid for all practical purposes is not compressible, any energy that is applied to it is instantly transmitted. This energy becomes dynamic in nature when a force such as quick closing valve or a pump applies velocity to the fluid. Surge (Water Hammer) Surge or water hammer, as it is commonly known is the result of a sudden change in liquid velocity. Water hammer usually occurs when a transfer system is quickly started, stopped or is forced to make a rapid change in direction. Any of these events can lead to catastrophic system component failure. Without question, the primary cause of water hammer in process applications is the quick closing valve, whether manual or automatic. A valve closing in 1.5 sec. or less depending upon valve size and system conditions, causes an abrupt stoppage of flow. The pressure spike(acoustic wave)created at rapid valve closure can be high as five(5) times the system working pressure. Unrestricted, this pressure spike or wave will rapidly accelerate to the speed of sound in liquid, which can exceed 4000 ft sec. It is possible to estimate the pressure increase by the following formula. Importance of Using this Formula While there are many online water hammer calculators, we have found wide variety in the results. We therefore recommend using old fashioned pencil and paper and this formula: Water Hammer Formula: P = (0.070) (V) (L) t + P1 Where P = Increase in pressure P1 = Inlet Pressure V = Flow velocity in ft sec t = Time in sec.(Valve closing time) L = Upstream Pipe Length in feet Here's an example of pressure hammer when closing an EASMT solenoid valve, with a 50 ft long upstream pipe connection: L = 50 ft V = 5.0 ft sec( recommended velocity for PVC piping design) t = 40 ms(solenoid valve closing time is approx. 40-50 ms) P1 = 50 psi inlet pressure therefore, P = 0.07 x 5 x 50 0.040 + P1 or P = 437.5 psi + P1 Total Pressure = 437.5 + 50 = 487.5 psi Pulsation Pulsation generally occurs when a liquids motive force is generated by reciprocating or peristaltic positive displacement pumps. It is most commonly caused by the acceleration and deceleration of the pumped fluid. This uncontrolled energy appears as pressure spikes. Vibration is the visible example of pulsation and is the culprit that usually leads the way to component failure. Unlike centrifugal pumps(which produce normally non-damaging high-frequency but low-amplitude pulses), the amplitude is the problem because its the pressure spike. The peak, instantaneous pressure required to accelerate the liquid in the pipe line can be greater than ten (10) times the steady state flow pressure produced by a centrifugal pump. Damage to seals gauges, diaphragms , valves and joints in piping result from the pressure spikes created by the pulsating flow. Remedy Suggest that you install a pulsation dampener. Dampeners provide the most cost efficient and effective choice to prevent the damaging effects of pulsation. A surge suppressor is in design essentially the same as pulsation dampener. The difference primarily lies in sizing and pressurizing. The most current pulsation dampener design is the hydro-pneumatic dampener, consisting of a pressure vessel containing a compressed gas, generally air or Nitrogen separated from the process liquid by a bladder or diaphragm. The dampener is installed as close as possible to the pump or quick closing valve and is charged to 85% of the liquid line pressure. Proper sizing of the pulsation or surge suppressor requires several calculations. A close contact with the suppressors manufacturer will ensure the correct sizing for a particular application. Conclusion By knowing how to avoid situations that will create water hammer or pulsations during the specification process, or while trouble shooting, you can eliminate a lot of problems, failed valves and equipment, and costly downtime. Plast-O-Matic Valves, Inc. 1384 Pompton Avenue Cedar Grove, NJ 07009-1095 USA Voice: (973) 256-3000 Fax: (973) 256-4745 Top of Page Copyright 1997-2002 Plast-O-Matic Valves, Inc.
Transforming Ellipsodial Into Translatory Motion
A report in pdf format describes how ellipsoidal water wave motion can be transformed into translatory motion to exchange polluted water in an almost closed sea bay.
:: MARMARIS PROJECT Transforming ellipsoidal motion into translatory motion Adem Kader - Cagatay Bircan - Ersen Bilgin - Zafer Faydali home | introduction | experiments | numerical modeling | animations | conclusion | acknowledgements | references | appendix Marmaris Bay is one of the important touristic places in Turkey. Since it has only one connection with the open seas it is said to be a closed bay. Pollution is a major problem in this kind of bays; therefore we tried to make a mechanism that would, by using wave energy, clean the bay. We could also use the same mechanism to generate electricity. According to our results, the application of such a mechanism can flush most of the bay clean approximately every thirty days. We worked on this project while we were students at Inanc Lisesi . All of the experiments were conducted at Istanbul Technical University with the guidance of Prof. Ali Riza Gunbak and Dr. Simon Butterworth and the numerical modeling was done at Arti Proje. This project won the Jury Special Award in the MEF 11th Annual National Research Project Contest in Istanbul and was presented at the International Conference for Physics Students 2002 and at the 12th European Physical Society Conference in Budapest as well as at STFA Holding Co (leading construction company in Turkey). Cagatay Bircan was selected the "Best Lecturer" at the International Conference for Physics Students. Adem Kader is now a student at Swarthmore College and is majoring in Engineering and minoring in Math and Computer Sciences. Cagatay Bircan and Ersen Bilgin are both at Williams College . Ersen is double majoring in Physics and Computer Sciences while Cagatay is pursuing a degree in Economics and Math. Zafer Faydali is at Istanbul Technical University ( ITU ) studying Electrical Engineering. home | introduction | experiments | numerical modeling | animations | conclusion | acknowledgements | references | appendix Sign Guestbook - View Guestbook geovisit();
University of Colorado Flow Visualization Course
A course in the physics and art of fluid flow for engineering and fine arts photography students at the University of Colorado, Boulder. The student gallery has a wide assortment of images ranging from soap films to clouds.
Flow Visualization Course : Physics and Art of Fluid Flow Sanjeev Sharma Graduate Student Mechanical Engineering Flow Visualization Flow visualization is the process of making the physics of fluid flows (gases, liquids) visible. In this course, we explore a range of techniques for creating images of fluid flows. Our work is motivated not just by the utility and importance of fluid flows, but also by their inherent beauty. The Flow Visualization course is designed for mixed teams of engineering and fine arts photography students at the University of Colorado, but anybody who has paid attention to the patterns while stirring milk into coffee or stared at the curl of a rising tendril of smoke has participated in flow visualization, and will understand the purpose of this course. Please explore this site; there are resources for teachers and students of all levels, as well as amazing images that anyone can enjoy Explore the class galleries A paper on the course that was presented at the American Society for Engineering Education 2004 Annual Conference won the "Best Paper" PIC III award at the conference. PDF (345 K) Next course offering: Spring 2006! MCEN 4228 5228 001, and crosslisted in ARTS. Lecture: MW 2:00 - 2:50 in ECCR 151 Lab: F 2:00 - 4:50 in ITLL 2B50 Recent publication: "Images of Fluid Flow: Art and Physics by Students," by Hertzberg, J. and Sweetman, A. Journal of Visualization, Vol. 8, No. 2 (2005)145-152. 2005 Jean Hertzberg. All rights reserved.-Web Site: Corey Simpson
Turbulent Scalar Transport
Heat and mass transfer studies using direct numerical simulations of turbulent channel, Couette, and shear flows as well as experiments with tube banks.
Turbulent Scalar Transport in Reacting and Non-Reacting Flows.
Cinema Particle Image Velocimetry Investigation of Turbulence and Combustion
High-speed "movies" of time-evolving velocity fields in turbulent and combusting gas flows are obtained using a newly developed kilohertz frame-rate cinema Particle Image Velocimetry system.
Cinema Particle Image Velocimetry Investigation of Turbulence and Combustion The information on this page is displayed in frames. If this page is not displayed properly, your browser may not capable of displaying frames or the frame viewing feature may be turned off. Check your browser settings, or get a browser that can display frames.
Fluid Power Net International (FPN)
Provides information and links to fluid power (hydraulics pneumatics).
Fluid Power Net - International Fluid Power Research Network FPN International (Fluid Power Net) is an International Fluid Power Research Network of National FPN sites which provide information about, and links to world-wide research and industrial activities in the field of fluid power. The FPN website provides overview of fluid power research, development and education activities carried out at the Universities and RD Centres and contains on-line directories of leading fluid powr engineers involved in academic, research, consulting and industrial areas; research and development (RD) projects in the field of fluid power; conferences, workshops, seminars and professional courses on fluid power. It also contains on-line bibliography of books, conference and journal papers and report on fluid power as well as links to bibliographies dealing with associated fields (simulation, modelling, mechatronics). (Keywords: fluid power net, fluid power research, fluid power systems, research fluid power, fluid power automation, fluid power control, hydraulics research, hydraulic control, pneumatic, rd center, rd centre, fluid power education, valves, pumps, cylinders, filters, accumulators, proportional valves, servovalves).
Investigation into Aerodynamic Flutter Test Systems
An investigation into aerodynamic vibration excitation systems for in-flight flutter testing of general aviation aircraft. Richard R. Western, Melbourne, 1999.
Undergraduate thesis - Richard Western Search: Lycos Angelfire G'Night G'Luck Share This Page Report Abuse Edit your Site Browse Sites Previous | Top 100 | Next The development of in-flight vibration excitation systems for flutter certification of GA aircraft Richard R. Western 1999 Department of Aerospace Engineering Royal Melbourne Institute of Technology Mail me!
Fluid Dynamics of Bioreactors
This site summarizes the research currently conducted at the Georgia Institute of Technology on the fluidic characterization of bioreactors.
SKY@Tech - Philippe Sucosky's website TYPE="application x-shockwave-flash" PLUGINSPAGE="http: www.macromedia.com go getflashplayer" Skip Intro Copyright 2004 - Philippe Sucosky OneStat
Fluid Salients in Air, Water, and Solids
Site discusses fluid salients as a cause for ocean wave formation, cloud formation and geologic structure formation. Several small physical models of salients are also discussed.
The Structuring of Moving Fluids Fluid Salients and The Structuring of Moving Fluids Michael A. Gorycki, Ph.D., January, 2002 CONTENTS ABSTRACT INTRODUCTION THE MECHANISM OF ALIGNED PLANAR SALIENT FORMATION A Physical Model RELATED PHENOMENA Beach Cusps Longitudinal Sand Dunes Gravity Currents Langmuir Circulation Cells Thunderstorm Squall Lines Tornado Swarms Windshear TAYLOR-COUETTE FLOW Taylor Vortices Spherical Flow RADIAL PLANAR SALIENTS Centrifugal Radial Salients Centripetal Radial Salients CUMULOUS SALIENTS Globoidal Cumulous Structures Planar Cumulous Structures and Bnard Convection Cells Linear Cumulous Structures TECTONIC ARC SERIES CONCLUSIONS REFERENCES FOOTNOTES and WEBSITES EXPLANATION OF FIGURES ABSTRACT The development of aligned, evenly-spaced lobate salients, separated by zones of retarded flow, can be observed at the leading edge of a fluid traversing a planar surface in many natural environments and during certain man-made events. Physical models presented here reveal the mechanism of salient formation and associated processes. Salients can be recognized in diverse phenomena including hairpin vortices (which are transitional between laminar flow and turbulence), beach cusp series, most types of sand dunes, gravity currents, and turbidites. It is suggested here that fluid salients appear to be responsible for Langmuir circulation. They also may be recognized in thunderstorm squall lines, tornado swarms, wind shear, and haboobs. Taylor vortices and the large-scale structure of Jupiters atmosphere may result from salient formation acting against cylindrical or spherical surfaces. All cumulous and related structures, including hurricanes, cloud rows, and Bnard cells appear to derive from fluid salients, as do falling drop patterns. It is also argued here that primary and secondary tectonic arc series may owe their general structure to fluid salients modifying lithospheric plates. Salients, therefore, range in size from a few mm to thousands of km, and can take from a few milliseconds to millions of years to form. INTRODUCTION The recognition and study of the structuring of moving fluids derive from an early observation of the leading edge of a small amount of water moving across the bottom of a small, flat-bottomed tray. If the energy of the system is sufficent, the fluid is frictionally impeded, its edge overrolls, thins, and, everywhere restrained from extending axially by adjacent parcels, is thrown into a series of evenly-spaced salients. The extension generated by overolling material effects an axial compression relieved by the formation of salients and retarded zones. Either term; extension or compression, will be used in this paper depending on the context of the various discussions of salient formation. Adjacent salients mutually interfere, producing rearward-pointing zones of retarded flow between each salient (Gorycki, 1973a). If flow continues, weaker salients can become cannibalized and become absorbed as they are overwhelmed by the overrolling sides of adjacent salients which then become larger and less numerous. Continued discernment of fluid salient structuring in a variety of natural environments reveals that it is ubiquitous, legion, and likely responsible for a variety of geologic, marine, atmospheric, and even extraterrestrial phenomena. Additionally, fluid salients may be discerned in some laboratory and even kitchen phenomena. Depending on the environment of formation, aligned, evenly-spaced salients and zones of retarded flow exhibit diverse morphologies. In addition, second-, third-, and even higher-order (smaller) salients can develop on primary salients. Fluid salients and zones of retarded flow can: 1) occur aligned at the leading edge of a fluid overriding a planar surface, 2) be generated against a cylindrical or spherical surface, 3) form radially, either centrifugally or centripetally, against a planar surface, 4) develop globoidally as cumulous structures diverging radially from a central point, 5) be uniformly distributed on a two-dimensional plane which is perpendicular to salient motion, and 6) form linear structures. Following are a variety of phenomena in which fluid salients may be recognized. The Mechanism of Salient Formation A Physical Model A simple physical model to demonstrate aligned, evenly-spaced salients involves placing a straight 5 cm length of 0.4 mm diameter cylindrical rubber monofilament (taken from a new elastic cloth waistband) between two pieces of plate glass. The apposed glass surfaces are first coated with a thin film of light mineral oil. This reduces friction between the glass and the monofilament, and allows strains in the rubber to be relieved in an unhindered manner. Pressing down on the upper glass, the monofilament is flattened to about half its diameter. At this point, a spherical tri-axial ellipsoid in the monofilament becomes oblate. As the upper plate is translated in a direction perpendicular to the monofilaments axis, one would expect the cylinder to overroll and remain straight. Instead, it extends axially (as the oblate spheroid becomes prolate in that direction) and simultaneously forms a series (with overolling) of nearly identical waves (salients) with amplitude parallel to the motion of the upper plate (Fig. 1), but with virtually no change in the straight-line distance between its ends. Obviously, the monofilament greatly increases its length at the expense of a reduction in cross-sectional area. More familiarly, rolling dough by hand across a flat surface thins the worked material and causes it to lengthen, but, lacking axial constraint, without the production of salients. The anterior salients of the rubber cylinder closely resemble a uniform series of hairpin vortices, detected in the laminar flow of fluids. All overrolling in the monofilament is in the same direction. In a discussion of the generation of turbulence in fluids, Tesar (1997) [1] (Click here to view this reference online) (see his figures I-26 and I-27), describes a hairpin vortex as forming from a roller vortex, becoming elevated, thinning, and forming a number of thinner secondary salients (his instabilities), which degenerate into turbulent spots. He describes a cascade as the energy in turbulence being continuously transferred from large vortices to smaller ones. In the context of the present paper, I would describe cascading as second- and higher-order salients forming on primary salients as is commonly seen in the swash zone of beaches (Fig. 2). Second- and higher-order salients also suggest chaos theory fractals [2] (Click here to view this reference online) . Importantly, the development of salients requires energy in a system sufficent for their formation, just as does turbulence beyond the condition of laminar flow. RELATED PHENOMENA Beach Cusps The most obvious illustration in nature of the action of aligned, evenly-spaced salients would be in the formation of beach cusps (Gorycki, 1973a). Beach cusps have been found to vary in size from a few cm up to 360 m apart and are separated by bays which oppose submerged seaward deltas. Over the years, various authors have presented disparate, conflicting observations and theories concerning the process of beach cusp formation. They involve such parameters as cusp shape, size and spacing, sediment particle size, erosion versus deposition, wave refraction, swash directions, effects of long-shore currents, beach face irregularities, angle of wave fronts, and two-wave cycles. Russell McIntires (1965) early study is detailed, but still leads them to conclude that they have not been able to explain the reasons for cusp spacing. Later research by Inman and Guza (1982), based on a standing wave model, is in conflict with the more recent self-organization computer simulation model of Werner and Fink (1993). However, both teams also admit that their studies have not provided a solution to the cause of beach cusp series [3]. Werner feels that an understanding as to how local interactions between fluid and sediment leads to globally uniform patterns is lacking in the standing wave model, but also admits that more detailed observations of morphology and swash flow during cusp formation are needed for the self-organized theory. In still later work on cusps, Masselink (1998) concludes that the cause of beach cusp formation requires "...further numerical and experimental investigations...". Finally, Coco, OHare and Huntley (1999), assert that, "...it is not possible to produce conclusive support for one theory above the other...". My experimentation with a large (75 cm wide and 245 cm long), flat-bottomed rocking trough, containing a small amount of water, routinely produces numerous evenly-spaced aligned water salients (Fig. 3), which, with distance, become fewer and larger through cannibalization (through absorption and or upward displacement), and are separated by invaginating zones of retarded flow. In the monofilament model the lower plate represents the shallowing sea floor close to the beach face, the monofilament is the forward-rolling water of a wave, and the upper plate represents the force of gravity combined with the forward kinetic energy of the wave. Examination of air photos of well-formed beach cusp series strongly suggests that plunging waves, which directly bottom and impinge on the submerged portion of a relatively steeply-dipping beach face close to the water's edge, apparently contain energy sufficent for the initiation, formation, and maintenance of cusp series [4] (Click here to view an image online) and are reminiscent of the simple action seen in the rocking trough (Gorycki, 1973a). If a thin layer of sand and silt is strewn on the trough bottom, it quickly forms rearward-projecting deposits (Fig. 4) as a line of salients flows over the sediment. The sand is frondescently swept both forward and bilaterally to the sides of each salient, depositing in the inter-salient zones of retarded flow. In nature, the evenly-spaced rearward projections of sand develop into the submarine deltas with overdeepening of the beach face just seaward of each cusp. Midway between salients, well-developed deltas and associated seaward-rushing water can be seen to impede their portion of the incoming wave (Fig. 5). The water, flowing from the cusps into the intercusp areas and back to the sea, further erodes the beach face to deepen the bays and add sediment down-slope to the submarine deltas. Once partially developed, the inter-cusp deltas (and associated return flow of water) and the fore-cusp overdeepening would continue to control the location of retarded zones and salients, respectively, as they develop from successive waves of similar strength and adequate wavelength (Fig. 6). As a consequence, evenly-spaced cusps, bays, and deltas would continue to develop and be maintained (Fig. 7). If a larger set of waves reaches the beach face, established cusps and deltas would be replaced by a larger set. If wave action becomes random, established cusps might initially control the swash, causing larger waves to passively rush up the beach face in the intercusp bays and refract toward the beach cusps (Gorycki, 1973a). Weaker waves would have little effect. In time, however, established cusps and deltas would be destroyed. Werner and Fink (1993) find that cusps are rare on most beaches, but tend to form when normally incident, nonbreaking waves surge against high beach slopes in regions where the range between high and low tide is small. Rudowski (1964) notes that beach cusps form readily in the relatively restricted Baltic Sea, where the tidal range is very small. After exhaustive field observations, he concludes that beach cusps usually form as the result of erosive activity, when the force of the surf is not too strong, and when waves approach parallel to the beach. He finds that cusps can form if the wave front is not parallel to the shore, but that the angle to the shoreline must be less than 40 degrees and the resulting cusps would be asymmetrical. By observing aligned, evenly-spaced salients operating on the beach face and considering the rubber monofilament model and the rocking trough salients with their ability to organize sand on the trough bottom into spaced "deltas", we have a simple and obvious mechanism for beach cusp formation. As a consequence, the diverse, often contradictory field observations of many workers can be readily accommodated (Gorycki, 1973a). It appears then, that an initializing incoming wave can become intrinsically structured, inaugurating the formation and location of a series of cusps and deltas. These incipient cusps and deltas then control the location of later salients and retarded zones, resulting in the further development of the cusp series. Cusp spacing would be determined by a combination of such parameters as water density, beach face slope, wave size, etc., but the role played by sediment during cusp and delta initiation, erosion, transportation, and deposition, would seem to be essentially collateral. Longitudinal Sand Dunes Folk (1971) describes great chains of incredibly parallel dunes which dominate the vast inland deserts of the world and extend over areas of as much as 100,000 sq mi. They follow the orientation of the great geostrophic trade wind systems, are widely spaced if large, are narrow compared to the interdune space, have tuning fork junctures invariably in an upwind direction, and, "...like stripes in a convict suit...", exhibit uniform lateral spacing in any one area. These dunes and a variety of other, more or less parallel, evenly-spaced structures such as cirrus cloud mares' tails, sand strips, parabolic, and possibly barchan sand dunes, as well as a variety of elongate subaqueous structures (Folk, 1971), could be attributed to salients initially developing in the wind or water along a straight front just as sand is moved into streaks on the rocking trough (Fig. 4). Once established, the dunes would determine the location of developing retarded zones, with salients forming in the interdune areas (Fig. 8). The spacing of dunes, whether they are the result of erosion or deposition, would be a function of an optimal, consistent wind velocity and persistent direction. Folks observation (1971) that the processes which formed and maintain the Simpson Desert dunes are fixed because the dunes have cores of old alluvial sediment and, "...thus have not shifted laterally in position since dune formation began...", supports the control which established structures may have on the positioning of fluid salients. The stability of oghurd dunes will also be discussed later. Folk (1971), however, referencing Bagnold (1953), ascribes the uniform spacing of dunes to paired horizontal roller vortices in the wind and attributes it to Langmuir circulation operating in the atmosphere, but admits there is no satisfactory explanation for the uniform spacing or the, "... vitally important junctures." Also, in a personal (Internet) communication Husar [5] (Click here to view this reference online) agrees with Tsoar that helicoidal flow is not a proven explanation for long km-spaced dunes, and Tsoar, in that communication, maintains that no one has ever observed or measured helicoidal flow in connection with the formation of dunes in deserts. He offers his own smoke candle experiments as proof. Sparrow and Husars figure 1 (1969) showing black dye moving up the upper surface of a submerged, heated, inclined plate mimics my observations in the rocking trough experiments (Gorycki, 1973a). The dye appears to be gently swept by salients into evenly-spaced, thin, dark streaks which then become more widely spaced and fewer in number in a process similar to the cannibalization (absorbtion and or upward displacement) of water salients in the rocking trough and the lateral movement of sediment into zones of retarded flow (Gorycki, 1973a). As a consequence, up-current tuning fork junctions are also present in the dye streaks of Sparrow and Husars (1969) figure 1. Slightly editing Husar's [5] sketch on his figure 2 of dye motion would have each light-colored thermal (here, salient) displacing dye to the streak (here, retarded zone) on either side. Hanna (1969) discusses counter-rotating horizontal helical vortices observed in the trajectories of simultaneously released neutral density balloons moving downwind, but these might be explained by a detail of salient formation described in the following section. Gravity Currents Aligned, evenly-spaced salients may be observed in a slow-moving gravity current formed by pouring 10 ml of a saturated sodium chloride solution, colored with ink, down an 8 by 40 cm trough (Gorycki, 1973a). The trough has walls 3 cm high, is filled with standing fresh water, and is tilted 3 degrees. As it travels downslope (Fig. 9), the leading edge of the current is modified by the retarding effect of the overlying water into a head, neck, and body region (Komar, 1972). Elevation of the head region, caused by interaction with the invaded fluid, is similar to that seen in hairpin vortices [1]. The current also forms long salients separated by retarded zones (Komar, 1972), and the leading portion of the flow can be seen to lighten in color by incorporation of the fresh water through which it flows. Allen (1971) describes the well-known admixing of the ambient medium at the upper surface of gravity currents, but he pointedly describes additional inmixing, with a spatial periodicity, of ambient medium into what he calls clefts and tunnels (here, retarded zones) between fingers or lobes (here, salients) at the head of a gravity current, which also serves to increase the total volume of the current. This sub-current addition finds its way, "...into the body of the flow...close to the lower boundary...", where it, "...can be transported upward through the effects of shearing and buoyancy much more readily than fluid mixed at the upper surface can be transported downward.", (Allen, 1971). Note also that Simpson (1969) describes similar structuring of density currents in air (and water) into the clefts and tunnels of which ambient air (and water) may enter. His figures 4 (Simpson, 1969), and 7 and 11 (Simpson, 1972), showing cleft development and decrease in numbers of lobes with distance traveled, mimic my rocking trough observations with water alone, and he relates the lobes to bulges observed at the edge of powder snow avalanches. Idso (1974) lists a number of phenomena, which exhibit salient-like structures, including nues ardentes. I would also include the commonly lobate, dust-laden haboobs seen in drier climates (Simpson, 1969) [6] (Click here to view an image online) . Hannas (1969) comments on balloon trajectories might be explained by the paired, oppositely rotating structuring within a single cleft as presented by Simpson (1969, 1972). Allens (1971) depiction (his figure 3) of a hypothetical gravity current is typical of salient formation discussed in this section, but he deduces an implied spatially periodic variation of the bed shear stresses across the region of the head resulting in, "...very probably a system of oppositely rotating (horizontal) longitudinal vortices...", again, like Folk (1971), suggestive of Langmuir circulation acting within a moving fluid. Allen maintains that these vortices must operate in the head of turbidity currents in order to explain the criss-crossing of tool marks commonly observed in turbidites (Allen, 1971). However, the intrinsic structure of fluid salients as described in the present paper (Fig. 4) would explain the morphology of gravity currents and also the uniform spacing of flute marks and the criss-cross of tool marks seen in some turbidites [7] (Click here to view an image online) . The plumose flow of sand in each salient would also explain development of frondescent sole markings seen in other turbidites [8] (Click here to view an image online) . It should be noted, too, that mud and lava flows can exhibit evenly-spaced salients. Langmuir Circulation Cells The lack of support in the literature for oppositely rotating (horizontal) longitudinal vortices motivates the following discussion. Here, evidence is presented for fluid salients as being the operative mechanism for those phenomenon usually attributed to Langmuir circulation. Langmuir (1938) describes relatively narrow (2 to 6 m wide) streaks of seaweed on the surface of the ocean having spacings of approximately 100 to 200 m (not unlike Folk's (1971) description of longitudinal dunes), and smaller-scale (1-10 m) alignments of floating debris (streaks) on Lake George. He ascribes the streaks to multiple, paired, horizontal, cylindrical, roller-vortices developing within the water caused by (ostensibly structureless) wind blowing across the water parallel to the streaks. Paired vortices would roll the surface water toward the streaks, thus sweeping floating debris together. Interestingly, a number of later workers describe mixing of upper surface lake or sea water with deeper water as being very important to the distribution of heat, oxygen, plankton, organic matter and nutrients, and also to oil spill dispersion, organization of bubble clouds, etc. The mixing is usually ascribed to Langmuirs roller vortices operating in the water. Similarly, evenly-spaced, streaks of trade wind cumulus clouds over the ocean are common and have been attributed to Avsec (1939) rolls by Malkus (1963) who presents schematic maps of evenly-spaced cloud rows which are considered to require strong vertical wind shear as in plane Couette flow (Brown, 1991). She also suggests that the cloud rows are the result of vertical displacement of warm moist air (to colder regions) between apposed, elongate, helical, Avsec rolls or Ekman helical vortices generated in the plane Couette flow of the planetary boundary layer (Brown, 1991). Hanna (1969) similarily describes longitudinal vortices in the atmosphere and couples longitudinal dune formation and cloud row formation to the same mechanism operating where the sides of vortices are thought to converge toward each other near the ground and diverge at altitude. These cloud rows are more simply interpreted in the present paper as due, rather, to vertical displacement of air in zones of retarded flow between fluid salients (Fig. 10) operating in a moving layer of the atmosphere either on or above the earth's surface, rather than Langmuir-like helical roller vortices. These observations, and recalling Folks (1971) and Bagnolds (1953) suggestion that some sort of structuring must be present in the wind blowing over land, leads to the conclusion that Langmuir circulation in sensu stricto, that is, only within the water, is not necessarily responsible for the development of streaks on the surfaces of bodies of water. Also, importantly, no evidence as to why evenly-spaced, paired horizontal roller vertices should develop, in any medium, to produce the various structures is presented by Folk (1971), later workers (Allen, 1971), [5] or even by Langmuir (1938) himself. I have noted fog blown from a quiet pool surface and snow crystals blown across a frozen lake surface becoming organized into elongate streaks, parallel to wind direction (McLeish, 1968). Any aerial, sub-aerial, or sub-aqueous aligned structures may be more simply ascribed to the essentially two-dimensional, lateral component of motion of structured air in the evenly-spaced fluid salients operating above an interface in the atmosphere; on the surface of water or land; or within the moving water acting on subaqueous surfaces, as experimentally shown here. The lateral component of flow of a supposed pair of roller vortices, with bases rotating away from each other, would comprise a single fluid salient. Adjacent, converging bases, would comprise a retarded zone for the location of a streak, dune, or cloud row. Consequently, the upper half of the more elaborate, presumed system of paired horizontal roller vortices could thus be eliminated (Fig. 10), resulting in the simpler mechanism experimentally described here with the rubber monofilament, the rocking trough, or the gravity current. As a consequence, any evidential structuring of the near-surface water ascribed to Langmuir circulation would therefore be passive and shallow. It should be noted here that Langmuir himself provides strong evidence for fluid salients and against his horizontal roller vortices. Using his "velocity indicator", he observed that shallow water at depths of less than 5 m drifted under a streak, whereas water at 10 m, "...had no tendency to do so." That is, only surface water is involved. He only assumes that, "...perhaps at a greater depth the indicator would move into a position midway between streaks since there must be horizontal currents which converge under the rising currents between the streaks." He, "...never observed in Lake George any reverse flow in the lower part of the epilimnon...", except a (usually windless) nocturnal flattening (leveling) of the epilimnon along the lakes axis, which is also parallel to the usual, daily wind direction (Langmuir, 1938). Also, if steaks and adjacent interstreak surface waters are generated by a series of paired, subaqueous horizontal roller vortices, it would seem streaks and interstreak areas should both be conveyed in a downwind direction at the same speed (see Hannas (1969) figure 4a which diagrammatically shows longitudinal vortices acting in the wind to produce evenly-spaced longitudinal dunes). To maintain their structure, these simplistic vortices must retain the same velocity throughout. In this respect, Langmuir, again, provides evidence against his horizontal roller vortices acting in the water. Employing a string with floats stretched across streaks, he describes water motion in the streaks to be faster downwind than in the broader areas between (Langmuir, 1938). Langmuir also notes that the longitudinal and transverse velocities of the water have their maximum values at the surface and gradually decrease to zero as his vortices become, "...increasingly diffuse at greater depths." If, instead, we assume that it is aligned wind salients centered on the broad inter-streak areas, they would push surface water and debris bilaterally and downwind toward the streaks and expose relatively still subsurface water underneath the salients. Since the debris would present a frictional drag on the wind, the wind would also preferentially move the streak areas more quickly downwind compared to the upwelling water in intervening areas, which would initially have comparatively little of a down-wind component to its motion. Since established seaweed streaks would determine the location of a series of retarded zones, wind salients would develop in the zones between streaks, characterized by debris-free water and a spreading of the water surface with concomitant upwelling of slightly deeper water. However, if surface debris is not present, then no determining factor for the location of retarded zones and associated salients should be present. This would account for the less than remarkable wind slick patterns observed by McLeish (1968) (employing thin floating layers of sulfur dust), which often seem to intersect and are irregular in width and direction. The lack of evidence for: 1) deeper return water flow, 2) the variation in velocity of surface water and 3) the diminution of assumed horizontal roller vortex structure (and water motion) at depth, all strongly suggest that, as stated previously, paired horizontal roller vortices in nature (and Langmuir circulation cells within the water) apparently do not exist. It would seem that the accumulation, spacing, and motion of seaweed streaks are, therefore, dependent on evenly-spaced fluid salients and retarded zones developing in the wind just above the waters surface. Langmuir additionally mentions that the surfaces of larger vortices contain smaller and shallower vortices. These are reminiscent of second- and higher-order salients as previously described here. Thunderstorm Squall Lines Powerful cold fronts are known to generate rather evenly-spaced thunderstorms (Fig. 11) along squall lines located just forward of the fronts (Strahler, 1969). This spacing strongly suggests the development of aligned planar salients providing clefts or tunnels (Allen, 1971; Simpson, 1969 and 1972) (zones of retarded flow) which can engulf warmer, moist air which then rises as thunderheads, at spaced intervals, through the colder air. Tornado Swarms Accumulating data concerned with the structure of tornadoes and their development in the Midwest and Southeast strongly suggests that it is a complicated process which is based on the production of planar salients. In a typical scenario, tornadoes commonly develop at the leading edge of a massive, southeasterly or easterly-moving cold front as it invades a region overlain by warm, moist air which is itself usually moving in an east or northerly direction from the Gulf of Mexico. This normally results in a front moving to the east-northeast. Some of the warm air near the ground will be trapped within overriding and overrolling cooler air and will, in conjunction with opposition from the invaded warm air mass, as in the head region of turbidity currents (Komar, 1972), form a series of elevating hairpin vortices. Idso (1974) observed, on two occasions, an elevated hairpin vortex, which visibly formed at the fronts of dust-laden wind. He maintains, however, that the overrolling vortices require a topographic disturbance, such as a mountain, to uplift and form the twin, oppositely-rotating funnels. No such topography would be necessary in the production of a fluid salient series as described in the present paper. Also, the counterclockwise rotation of the southern limb of each vortex would tend to be enhanced by the northward flowing warmer air at the eastern edge of the front and it is this direction of rotation which is most commonly observed in tornadoes, whereas, conversely, the clockwise rotating northern limb of each vortex would tend to be inhibited (Fig. 12) [9]. This limb is also, "...generally in the storms precipitation downdraft.", (Snow, 1984). As the southern limb of a hairpin vortex assumes a vertical axis (Snow, 1984), it would entrain rising warmer air engulfed by the tunnel or cleft structure from which it emanates, and this would increase its vorticity and generate a tornado. It is also the weight of the overlying colder air pressing down which facilitates upward motion of the warmer air near the ground. It is this combination of events, as suggested here, which may explain the parallel, and often uniformly-spaced, paths of destruction generated by swarms of counter-clockwise-rotating tornadoes so often seen as a single cold front traverses the Midwest or Southeast. Four evenly-spaced tracks produced by seven tornadoes in east-central Florida on Feb. 22-23, 1998; four tracks produced by 15 tornadoes on March 1, 1997 in central Arkansas; and a similar swarm on May 3, 1999 in Oklahoma City, are good examples of spaced swarms. An explanation for, and even the recognition of, the even-spacing in thunderstorm squall lines and tornado swarms is generally lacking in the literature. Wind Shear Examining information and data related to aircraft disasters attributed to near-ground-level clear air wind shear suggests that aligned planar salients could also be responsible for this phenomenon. Wind shear can be defined as any fast and dramatic variation in wind speed, or horizontal or vertical wind direction, such that the velocity of air moving over a planes wings is swiftly changed. Disasters are commonly the consequence of three sequential factors: 1) increased lift caused by a sudden headwind for which the pilot compensates by a decrease in power, 2) a sudden downward flow of air, and 3) a sudden tail wind. As a result, the plane will drastically lose altitude and may also catastrophically stall. Wind shear can occur at or near the ground, and often involves a plane attempting either to take off or land into the wind on fixed runways and at near-stall velocity. It is suggested here that under conditions during which aligned fluid salients can develop, the plane will likely traverse a salient at an angle to the salients axis. This encounter will initially result in an increase on the air-speed indicator as the plane approaches the rising head region of a salient for which the pilot compensates with a decrease in power and elevation to reduce the effects of the increased lift. Continuing on a straight flight path, however, the plane would enter the portion of the salient where overrolling, or downward motion of the air might cause the plane to again loose altitude. (This downward motion is often attributed to a localized, single, inopportune, "microburst" of downward-moving air.) Continued traverse of the salient will cause the plane to cross the opposite edge of the salient where it encounters a tail wind as it enters the region of retarded flow between two salients where slow-moving turbulent air would be encountered. This last factor will further reduce the planes altitude and velocity. A schematic diagram (Fig. 13) shows a plane experiencing the sequence of events normally attributed to wind shear as it traverses one of a series of fluid salients. It is suggested here that at least some wind shear occurrences may be attributed to "clear air" fluid salients, similar in size and structure to dust-laden haboobs (which also usually exhibit salients), but which are invisible to both pilot and radar. The action of an inopportune microburst is also not required. Possibly, as the angle between the line of flight and the general wind direction increases, the more likely a plane will traverse salients and encounter a greater risk of windshear. Frondescent air motion within a salient may also cause crabbing motion (horizontal rotation) of aircraft. TAYLOR-COUETTE FLOW Taylor Vortices Fluid salient formation may also be invoked to explain the development of Taylor vortices formed in the annulus fluid between two vertical, concentric cylinders [10] (Click here to view this reference online) . In the situation where the outer cylinder is stationary and the inner cylinder is rotating, there is a diminution in the rotational velocity (circular Couette flow) as the outer wall is approached, and the subsequent development of vortices if a given rotational rate (Reynolds number) is attained. To understand this process in light of fluid salient formation, it helps to consider a quickly-stirred cup of coffee. The spoon acts as the inner cylinder. The stirring generates a coffee "annulus" having an angular velocity which, through wall shear, diminishes as the wall of the cup is approached (Taylor-Goertler instability). That is, the fluid moving over the cup wall is frictionally slowed. There is also an elevation (axial extension) of the coffee at the wall of the cup produced by the outward radial (centrifugal) motion of the fluid. In the closed Taylor-Couette apparatus, this extension would be inhibited, generating compressional axial stresses. Since there is no leading edge, these stresses would be relieved by fluid structuring on the concave surface of the outer cylinder resulting in quickly-formed, evenly-spaced, annular rings (Taylor vortices) if the energy of the system is sufficient. Since plane Couette flow is defined as flow in a fluid between two plates on which a force is applied to move one plate, this definition is identical to the mechanism in my rubber monofilament model which generates aligned salients in the rubber monofilament sheared between two glass plates, one of which moves in a direction perpendicular to the long axis of the monofilament (and parallel to the axes of the salients). Paired rings (or ring portions) which rotate toward each other (close to the outer glass wall) would represent a salient; and each pair rotating away from each other, a zone of retarded flow. Also, a comparison of Taylor vortex formation with the rubber monofilament model would have adjacent arms of an elongated salient close together and rotating away from each other. Conversely, adjacent arms of a zone of retarded flow would rotate toward each other. The requisite features, therefore, of salient formation as seen on the beach face (overrolling of a frictionally impeded liquid moving over a surface, and inhibited lateral extension) are present in the Taylor-Couette apparatus. Once established by the leading edge of fluid salient formation subsequent (Taylor) vortices, acting against a planar surface, could be responsible for the maintenance of the various longitudinal forms such as sand dunes, subaqueous structures and gravity currents previously described, as the fluid continues to flow. To support the argument for fluid salients it has already been experimentally shown, using a porous inner cylinder (Lueptow and Min, 1994a), that fluid pumped axially inhibits the development of vortices (salients), at a given Taylor number. Pumping and fluid transfer into the inner cylinder would diminish the prerequisite inhibited axial extension in the fluid so necessary to salient formation. Alternatively, employing two porous cylinders where any radially inward flow or strong radially outward flow of annular fluid occurs also inhibits vortex formation (Lueptow and Min, 1994b) apparently by destroying the incipient structuring necessary for inhibited axial extension and fluid salient formation. The same is true if the speed of the inner, rotating cylinder is modulated, or if the cylinder is moved up and down in a sinusoidal fashion, or, again, if fluid is pumped in an axial direction. In most experiments, Taylor vortices are initiated near the ends of the cylinders where the additional drag at the ends of the annulus may induce incipient salient formation. However, in one experiment, the early development of Taylor vortices occurs at the base of the annulus (Weisberg, Kevrekidis, and Smits, 1997). These early vortices may be explained by the hydrostatic head inducing slightly greater axial pressure, friction, and salient formation in that region [11] (Click here to view this reference online) . Taylor vortices become wavy if the Reynolds number is increased. Sinuosity has been displayed in a physical model for the mechanism of stream meandering (Gorycki, 1973b) where a straight rubber monofilament, flattened between two lightly-oiled glass plates, becomes simultaneously structured because of axial compression from slightly to strongly sinuous if the upper glass plate is translated in a direction parallel to the monofilaments axis (Fig. 14). The sinuosity in the monofilament results from a waveform, probably initially developing in a vertical plane but, being inhibited by the overlying glass surface, becoming confined to a horizontal plane. Continued flattening and overolling of the cylinder causes it to further extend axially, thereby increasing the sinuosity with each bend moving progressively away from the axis of the initially straight cylinder. Overolling of both limbs of a bend is in the same "downslope" direction with twisting at the bend. The increase in sinuosity increases the length of the monofiliment, but with virtually no increase in the straight line distance between the ends of the essentially unmoving cylinder. The sinuosity is aided both by the cylindrical shape of the monofilament and the strains relieved in an otherwise unhindered manner by the presence of the lubricating oil. The energy for this model is supplied by the "downslope" motion of the upper plate pressing against the monofilament. Sinuous flow in an initially straight, 4 mm wide, sediment-free stream of water flowing down an inclined, smooth, planar, hydrophobic surface (stream plate) can be demonstrated by injecting multiple ink filaments, simultaneously produced from a single micropipette orifice, into the stream of water. Sinuosity is shown to be due to the presence of increasingly frictionally slowed and sinuously distorted water filaments progressively deeper in the stream (hydraulic drag)(Gorycki, 1973b). By increasing the flow of water, the maximum sinuosity of the stream (stream distance ) in one experiment reached at least 1.79, indicating it is possible to demonstrate true meandering under laboratory conditions. It should be mentioned that the only overolling on the stream plate (or in natural streams) is at each bend, with practically straight line motion of water filaments between bends. The energy for the development of sinuosity in these streams is, of course, gravity. Sediment added to the stream also deposits point bars and reveals a meandering thalweg where these are normally observed in the field. These laboratory streams bear the closest of relationships to sinuous and meandering streams, of any size, in nature (Gorycki, 1973b) and presents a simple, easily studied and understood explanation for meandering. The point of this discussion is that once Taylor vortices (salients) become established in the Taylor-Couette apparatus and the rotation is increased, they can become elongated and, therefore, sinuously distorted in a fashion similar to that of the rubber monofilament, by differential motion (hydraulic drag = Couette flow) on the vortices held between the surfaces of the cylinders. In the situation where Taylor vortices become merely tilted with respect to the axis of rotation, the circular vortices deform to ellipses by simple elongation prior to becoming sinuous. A futher increase in rotation can lead to smaller (higher-order) Taylor vortices (salients) and, eventually, turbulence. Spherical Flow In spherical flow, Taylor-like vortices (Fechtmann, Wulf, Egbers, and Rath, 1997) [12] (Click here to view this reference online) may be seen in the belts and zones of Jupiter and are considered in the present paper to also be the result of fluid salient formation in that planets atmosphere for the same reasons. The planet is a large oblate spheroid (PD ED = 0.93) due to its rapid rate of rotation. Equatorial winds of its 1000 km thick, helium-hydrogen, gaseous atmosphere reach 600 km h and shift eastward 11 degrees in 24 hours relative to the planets supercritical fluid interior. As a consequence, there is a compression of the atmosphere (due to gravity), a circumferential restriction (from pole to pole), and a relative eastward motion of the atmosphere over the planets mid-latitude and equatorial "surface". As discussed here, with regard to Taylor vortices, these, again, are the requisites for salient formation. A similar vortical wind motion also exists in the region close to the earths equator. RADIAL PLANAR SALIENTS Centrifugal Radial Salients Centrifugal, radial salients develop due to extension along a circular periphery when a frictionally impeded fluid spreads across a flat surface from a central point. They can be observed as the scalloped exhaust cloud of a rocket radially dilates against the earths surface (Fig. 15) and also in some nuclear explosions as the rising cloud, at a great height, flattens and spreads radially as its specific gravity matches that of the adjacent ambient atmosphere, or if the cloud dilates at the earths surface [13] (Click here to view these images online) (see 1945, Fatman; 1953, Annie; 1955, Apple II; 1957, Smoky). Parenthetically, ink splotches depicted here (Fig. 16) seem to be good examples of similar, radial fluid salient formation. They are produced by drops of India ink falling onto heavy paper. The further the drop falls, the smaller and more numerous the salients, and the larger the splotch. Surface tension certainly may be invoked as a cause for the patterns, and many published images captured by high-speed stroboscopic photography suggest this. Recent workers in the field describe them as fingering patterns based on an "impact Reynolds number", which is a function of surface tension, inertia and viscosity (Marmanis and Thoroddsen, 1966). However, the nature of the substrate is also important. In one set of "drop spreading" Internet photos, drops impact smooth or rough wax or glass surfaces [14] (Click here to view these images online) (see roughness, perturbations). For the smooth wax or glass, the expanding, toroidal lamellae are featureless, but for the rough wax or glass, evenly-spaced "perturbations" (salients) are obvious in the lamellae. The rough surface apparently inhibits (frictionally impedes) the advance of the overrolling edge and thus induces peripheral extension and salient formation. If we assume these salients are the result of surface tension only, then the perturbations should also be induced on the smooth surfaces. Lim's website describing the collision of vortex rings also supports radial planar salient formation [15] (Click here to view this reference online) . The planar circular membrane produced by the collision of two vortices generates a number of evenly-spaced small rings, or vortices (here salients) similar to the ink splotch pattern (Fig. 16) but without any influence from surface tension. Note also that the membrane becomes crenulated by what is again suggested here to be a peripheral extension of the dilating membrane caused by resistance as it expands through the stationary supporting fluid in the water tunnel. Drops of molten solder which flatten and crystallize against a horizontal surface also exhibit radial planar salient formation. Elongate salients are separated by thickened, raised zones of retarded flow at the drop's edge. This suggests that the retardation at the spreading drop's edge, induced by overolling and crystallization, is breached by evenly-spaced salients, and that the formation of retarded zones and salients is, therefore, integral to falling drop patterns. In the kitchen, a much larger (20 cm diameter) version of Figure 16 can form on the bottom of a hydrophobic plastic sink if the faucet is very quickly turned on and off. Centrifugal salients may also be produced by quickly pouring a thin stream of milk, from a height of 10 cm, into a 1 cm deep layer of the "heavy" syrup from canned fruit. The point to be made, in this instance, is that (as in Fig. 15, [13] and [15]), the centripetal, radial milk salients also obviously form without the influence of surface tension. Incidentally, centrifugal salients can also form at the edges of omelets and thin-batter pancakes if fried in a well-oiled skillet. Centripetal Radial Salients Folk (1971) maintains that star-shaped oghurd (star) sand dunes apparently form by radially inblowing wind converging as vertical drafts. This is consistent with radial centripetal salient formation, casued by peripheral compression with apparent concomitant salient cannibalization and or their vertical expulsion (Gorycki, 1973a). Some of these dunes are stationary for periods of time long enough for them to have long-lived geographic names given them indicating that, once formed (like longitudinal dunes), they are capable of maintaining their structure and location. Folk, however, maintains that the dunes are created by rising air setting up roller vortices having vertical axes, another version of Langmuir paired circulation cells considered, in the present paper, as not being a viable mechanism. Additionally, the gross, counter-clock-wise structure of cyclonic air masses and hurricanes, common to the Caribbean, develop when surface air tangentially approaches a central area of low-pressure, increases its angular velocity, and accordionizes due to mutual peripheral compression. This causes spaced upwellings (vertical expulsion) of warm air into colder regions of the atmosphere where moisture then condenses and forms the familiar spiral clouds or rain feeder bands [16] (Click here to view this image online) (see previous page, spiral bands). A solid model of the radial centripetal salients of a hurricane can be generated using a pencil and an inflated balloon. The tip of the eraser (first made sticky with rubber cement) is pressed into the side of an inflated balloon, and the pencil is then twisted. CUMULOUS SALIENTS Globoidal Cumulous Structures Observations of the cauliflower-like structure of rapidly expanding cumulus clouds, as well as some man-made (including nuclear) explosions, violently-burning fire and or smoke clouds, and pyroclastic flows, are all similar in appearance [13] (Click here to view some images online) . (See 1956, Mosaic; 1957, Smoky). Cumuli exhibit second-, third- and higher order salients which, in each category, tend to be uniform in size and spacing. This structuring suggests an equant, three-dimensional version of salient formation generated radially from one or more points operating without interaction against a planar substrate. Cumuli occur when a rapidly expanding gas forms globoidal first-order salients, which displace and distort the interfacing atmosphere and are comprised of second-order and smaller salients. Adding milk to a cup of tea produces the same structuring. To quote Benoit Mandlebrot, regarding fractal geometry, "...clouds are not spheres...". Planar Cumulous Structures and Bnard Convection Cells Cumulostratus and mammatus clouds commonly exhibit evenly-spaced two-dimensional arrays of salients associated with the essentially planar atmospheric interface at which condensation occurs. Cumulostratus clouds are similar to experimentally produced Bnard (1901) convection cells which are evenly-spaced, vertically-moving, fluid salients exhibiting a horizontal, two-dimensional, mutual interference due to a plumose, radial extension from each of their centers. Concurrent downward motion occurs at the edge of each cell where mutual interference results in a zone of retarded flow. It is suggested here that Bnard cells are globoidal cumuli (salients) confined to a planar distribution [17] (Click here to view this reference online) (see 3 second video). The plane along which Bnard cells form and are viewed is perpendicular to their direction of motion as opposed to most fluid structures which develop in a plane parallel to their direction of motion. A similar Bnard convective pattern of warm patches of ocean surface water surrounded by cold has been shown using infrared imagery (Stewart, 1969). Also, elongate, wind-generated, warm and cold streaks may be the result of stretching of the Bnard pattern, or due to fluid salient formation at the ocean surface. In addition, Husar [5] (Click here to view this reference online) (see his figure 4), describes the periodic rising of groups of thermals in a liquid above a heated, horizontal hot surface. This, again, suggest a Bnard convective pattern. If the hot surface is tilted, these cells could give rise to longitudinal thermals, as described by Sparrow and Husar (1969) just as Bnard convection cells, if sheared, can give rise to elongate cloud rows (Malkus, 1963). Planar salient formation may also be responsible for the relatively uniform, random outcrop pattern exhibited by non-tectonic salt dome swarms seen in various regions. Large regions of uniformly spaced oghurd (star) dunes such as at the eastern edge of Grand Erg Oriental, Algeria-Tunisia-Libya [18] (Click here to view this image online) (see Plate E-6), also suggest a Bnard convection cell forming above each dune because it becomes hotter than the surrounding denuded desert floor [5]. Radially inblowing winds shape the dune and support the cell above. Bnard convection has also been considered to be the mechanism for convection within the earths mantle, which is responsible for plate tectonics. Another version of this instability is also considered possibly responsible for the "Pillars of Creation" seen in the Eagle Nebula [19]. These Pillars are considered by some workers to be generated as a molecular cloud is heated by ultra-violet light from nearby stars and, being less dense, penetrates the cooler portion of the cloud which mutually responds by producing salients. It should also be noted that snow avalanches may exhibit a planar cumulous structure in the central mass of the flow as air becomes increasingly incorporated into the snow. Linear Cumulous Structures Energetic volcanic plumes usually develop a uniform series of expanding 1st order cumuli spaced along an axis and they also exhibit higher order (smaller) salients [20] (Click here to view this image online) . More energetic eruptions can produce projectiles which take initially linear, vertical trajectories. The eruption of Mount St. Helens on May 18, 1980, again, affords a good example. Less energetic eruptions may exhibit a periodicity of evenly-spaced first-order globoidal salients with the loss of second- and higher order (smaller) salients with distance (and energy dissipation) from the vent [21]. Burning fuels from ruptured pipes also produce similar plume structures. All of these first-order linear cumuli are similar to bubbles escaping from the end of submerged tubing where parameters such as the difference in specific gravity, bubble size, orifice size, velocity, pressure, viscosity, ambient currents etc., all control bubble size, path and spacing. A simple experiment reveals a surprising aspect of this kind of linear flow which bears on 1st order cumuli. If the end of a 1 cm diameter length of tubing is positioned at the bottom of a 2 liter graduated cylinder and the flow of nitrogen (or, likely, any other) gas is increased to generate an ascending stream of approximately 1 cm diameter bubbles spaced at about 10 cm intervals, each bubble rises to the surface in a linear stream. A further increase in gas flow tends to disturb the water column. As a consequence of the induced turbulence, each bubble takes a separate, erratic path to the surface as it expands slightly due to decreased water pressure. Interestingly, if the gas flow is slightly further increased, every third or fourth bubble can be seen to accelerate, follow, overtake, and merge with the one just above it. This is apparently due to an otherwise invisible vortex ring-like channel of upward-moving water created by the captured bubble, which entrains the pursuing bubble. The coalesced (enlarged and flat) bubble usually then immediately breaks into several smaller bubbles, possibly as the result of Bnard convection. The bubble cannibalization process described here apparently is similar to Lim's (1997) leapfrogging vortex rings [15]. It is suggested in the present paper that the implied channeling structure in the water should be considered the cause of the linear cohesiveness of the volcanic plume cumuli or the smoke from a chimney or fire. Apparently, it is this type of channel which second-place race car drivers and ice skaters utilize as they more easily follow leading competitors. This is often called drafting, considered to result simply from a low pressure zone created behind the lead driver or skater. In the case of volcanic plumes, a first-order cumulus forms, rises quickly after reaching an optimum size, and both displaces the overlying atmosphere and entrains the air beneath to form a constriction which gives the cloud its spheroidal shape. As it expands and cools, produces higher-order salients, and loses some buoyancy, it slows and is impinged upon by the following first order cumulus. The entire plume of clumuli thereby expands due to axial compression aided by subsequent first-order cumuli. Rocket exhaust also can exhibit a linear stream of first order cumuli (see Fig. 15) as can the contrails of jet planes [22] (Click here to see an image online) (see last image). A similar pattern, produced by fine sediment, is all too often seen in television commercials for fast-moving cars racing across playa lakebeds in the American Southwest, but all these linear structures appear to be examples of Von Karman vortex streaks. Of greater importance, however, are the linear patterns, which develop in cloud rows, as previously described. Significantly, each cloud row is itself commonly comprised of evenly-spaced first-order cumulus clouds [23] (Click here to view this image online) . Distortion imposed by Couette flow on cloud rows may be similar to that generated within the rubber monofilament model as described here for stream meandering, except the sinuosity generated by axial compression is in the vertical plane (into colder regions) because of the lack of any strong physical constraint (the glass plate surfaces (or gravity for the stream)). To demonstrate this concept, another physical model comprised of a 50 by 3 by 0.5 mm thick strip of fugative hot melt adhesive flattened between clean plate glass surfaces can be distorted by axial compression, due to spaced overrolling, into vertically thickened and thinned portions as the upper glass plate is moved parallel to the long dimension of the strip (Fig. 17). This model mimics ascending evenly-spaced cumulus clouds in cloud rows. It is important to note that the thickened, clearer portions of the adhesive strip also elongate horizontally (due to overrolling), perpendicular to the motion of the upper plate or strip length, and represent troughs deepening and elongating in a direction perpendicular to the direction of the current. The thinner regions represent crests. The model therefore also represents wind or water current structure during the development of ripple marks in sand, rippled altocumulus clouds (mackerel sky), or drag folds in rock strata. As with my beach cusp and stream meander observations and the ripple model mentioned here (Fig. 17), it appears that the incoming wave, the flowing stream, or the surface wind can become intrinsically structured, and the role played by sediment in all three environments during erosion, transportation, and deposition is, again, essentially collateral. TECTONIC ARC SERIES Another familiar phenomenon that could be ascribed to aligned salient formation is the development of island arcs and associated structures. If we consider that a series of arcs is the result of extensive tectonic plates overriding a portion of the crust, and that salients of a similar magnitude all point toward the overridden surface and are separated by angular, rearward-pointing zones of retarded motion, we then have the definition of fluid salient formation operating on a grand scale over millions of years. Arcuate tectonic structure series of similar size have long been recognized but no satisfactory explanations were provided prior to the general acceptance of plate-tectonics (Jacobs, Russell, and Wilson, 1974). The familiar suggestion that an arc is structurally similar to a portion of the circular indented surface of a ping pong ball (Frank, 1963) may account for the general shape and cross-sectional structure of an arc in light of plate tectonics, but it does not explain the development of a connected series of segments of circles (arcs) of similar size and orientation. Scholz and Page (1970) suggest that the surface area of the lithosphere must be reduced either by thickening of the downthrust plate or conserved by lateral buckling. They prefer buckling, similar to that seen at the edge of an old-fashioned bottle cap, as the cause of the development of island arc series in the North Pacific. Utilizing earthquake foci to contour the tops and bottoms of descending lithospheric plates, Stoiber and Carr (1971) indicate that the resulting downplunging folds in the plates represent a (lateral) shortening of the plates. Both papers, therefore, are not in conflict with the concept of lateral compression being involved in the development of salient-like arcs in the overriding plates. Scholz and Page (1970) also argue that if one end (edge) of the downgoing slab is free, the result would be a straight hinge line as in the case of the Tonga-Kermadec "arc". In a similar fashion, the unusually straight coast of Chile, with its lack of a southern off-shore trench or deep focus earthquakes to the east, the presence of islands in the sinking portion of the coast in the south, and the southern tapering of the continent could all be attributed to a lack of lateral (northward) compression of the southern end of the Chilean "arc". This is expressed by the separation of southern Chile from Antarctica as evidenced by the eastward thrust of the intervening Scotia plate. This plate abuts the southern free edge (Scholtz and Page, 1970) of the Chilean slab resulting in the straight hinge ("arc") and coastline of Chile, and may represent the return flow of Pacific mantle material into the expanding Atlantic Ocean basin. The motion of the Scotia plate only modestly affects the shapes of both Cape Horn and the Antarctic Peninsula. The arcuate shape of the west coast of South America from Peru northward would result from the lateral compression of the northern