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Scientific Phenomena Named After People

Scientific phenomena named after people

This is a list of scientific phenomena named after people (eponymous phenomena). For other lists of eponyms, see eponym.

The list

A to J


- Abney effectW. Abney
- Abrikosov latticeAlexei Abrikosov
- Aharonov-Bohm effectYakir Aharonov and David Bohm
- Allais effectMaurice Allais
- Allee effectW. C. Allee
- Auger electronPierre Victor Auger
- Balmer lineJohann Jakob Balmer
- Barnett effectS. J. Barnett
- Barkhausen effectHeinrich Barkhausen
- Baskerville effect – the fictional Charles Baskerville of the novel The Hound of the Baskervilles
- Benioff zone (also called Wadati-Benioff zone) – Hugo Benioff and Kiyoo Wadati
- Bernoulli's principleDaniel Bernoulli
- Betz limitAlbert Betz
- Biefeld-Brown effectPaul Alfred Biefeld and Thomas Townsend Brown
- Bloch waveFelix Bloch
- Bohr modelNeils Bohr
- Bose-Einstein condensate, Bose-Einstein statisticsSatyendra Nath Bose and Albert Einstein
- Boson, Satyendra Nath Bose
- Brackett linesFrederick Sumner Brackett
- Bragg diffractionWilliam Lawrence Bragg
- Bragg angle, Bragg planeWilliam Henry Bragg and his son William Lawrence Bragg
- Brewster's angleDavid Brewster
- Brillouin zoneLeon Brillouin
- Brownian motionRobert Brown
- Calvin cycle, or Calvin-Benson cycleMelvin Calvin and Andy Benson
- Carnot cycleNicolas Leonard Sadi Carnot
- Casimir effectHendrik Casimir
- Chandrasekhar limitSubrahmanyan Chandrasekhar
- Cherenkov radiationPavel Alekseyevich Cherenkov
- Christofilos effectNicholas Christofilos
- Coanda effectHenri Coanda
- Compton effect, Compton scatteringArthur Compton
- Cooper pairLeon Cooper
- Coriolis effectGaspard-Gustave Coriolis
- Curie pointPierre Curie
- De Broglie wavelengthLouis de Broglie
- Doppler effect, Doppler profileChristian Doppler
- Eagle effectHarry Eagle
- Early effectJames Early
- Edison effectThomas Edison
- Einstein-de Haas effectAlbert Einstein and Wander Johannes de Haas
- Eddington limitArthur Eddington
- Evershed effectJohn Evershed
- Faraday effectMichael Faraday
- Fermat's principle, – Pierre de Fermat
- Fermi energy, Fermi paradox, Fermi surface, FermionEnrico Fermi
- Fermi-Dirac statisticsEnrico Fermi and Paul Dirac
- Fraunhofer lines, Fraunhofer diffractionJoseph von Fraunhofer
- Fresnel zoneAugustin Fresnel
- Frey effectAllan H. Frey
- Froude numberWilliam Froude
- Fujiwhara effectSakuhei Fujiwhara
- Gibbs phenomenonJosiah Willard Gibbs
- Grashof numberFranz Grashof
- Hall effectEdwin Hall
- Hayflick limitLeonard Hayflick
- Heisenberg uncertainty principleWerner Heisenberg
- Hertz effectHeinrich Hertz
- Heusler alloyFritz Heusler
- Higgs Field, Higgs bosonPeter Higgs
- Hubble constant, Hubble expansionEdwin Hubble
- Huygens' principleChristiaan Huygens
- Jahn-Teller effect – ? Jahn and Edward Teller
- Josephson effect, Josephson junctionBrian David Josephson
- Joule-Thomson effectJames Prescott Joule and William Thomson

K to P


- Kapitsa-Dirac effectPyotr Leonidovich Kapitsa and Paul Dirac
- Kennelly-Heaviside layerArthur Edwin Kennelly and Oliver Heaviside
- Keeling CurveCharles David Keeling
- Kerr effectJohn Kerr (physicist)
- Kirkendall effectErnest Kirkendall
- Kohn-Sham equationsWalter Kohn and Lu Jeu Sham
- Kohn effectWalter Kohn
- Krebs cycleHans Adolf Krebs
- Kuiper BeltGerard Kuiper
- Lagrangian mechanics, Lagrange pointsJoseph Louis Lagrange
- Landau damping, Landau poleLev Davidovich Landau
- Lennard-Jones potentialJohn Lennard-Jones
- Lense-Thirring effectJosef Lense and Hans Thirring
- Little-Parks effectW. A. Little and R. D. Parks
- London forceFritz London
- Lorentz forceHendrik Lorentz
- Loschmidt's paradoxJohann Loschmidt
- Love wavesAugustus Love
- Marangoni effectCarlo Marangoni
- Magnus effectHeinrich Gustav Magnus
- Maxwell-Boltzmann distributionJames Clark Maxwell and Ludwig Boltzmann
- McGurk effectHarry McGurk
- Meissner effect (or Meissner-Ochsenfeld effect) – Walter Meissner (and Robert Ochsenfeld)
- Metonic cycle4th Century BC astronomer Meton
- Mikheyev-Smirnov-Wolfenstein effect
- Misznay-Schardin effect – ? Miznay and Hubert Schardin
- Mohorovičić discontinuity (Moho) – Andrija Mohorovičić
- Morse potentialPhilip M. Morse
- Mossbauer effectRudolf Mössbauer
- Mpemba effectErasto B. Mpemba
- Munroe effectCharles E. Munroe
- Newton's rings, Newtonian mechanicsIsaac Newton
- Oort cloud (or Öpik-Oort Cloud) – Jan Oort (Ernst Julius Öpik)
- Pauli exclusion principleWolfgang Pauli
- Peltier effectJean Charles Athanase Peltier
- Petkau effectAbram Petkau
- Pearson-Anson effectS O Pearson and H St G Anson
- Planck mass, Planck lengthMax Planck
- Pockels effectFriedrich Carl Alwin Pockels
- Poynting vectorJohn Henry Poynting
- Poynting-Robertson effectJohn Henry Poynting and Howard Percy Robertson
- Pulfrich effectCarl Pulfrich

R to Z


- Raman scatteringChandrasekhara Venkata Raman
- Rayleigh scattering, Rayleigh fading, Rayleigh wavesLord Rayleigh
- Richardson numberLewis Fry Richardson
- Roche limitEdouard Rouche
- Runge's phenomenonCarle David Tolmé Runge
- Sagnac effectGeorges Sagnac
- St. Elmo's fireSaint Elmo
- Schwarzschild metric, Schwarzschild radiusKarl Schwarzschild
- Schottky effectWalter H. Schottky
- Seebeck effectThomas Johann Seebeck
- Shapiro effectIrwin Shapiro
- Stark effect, Stark ladderJohannes Stark
- Stroop effectJohn Ridley Stroop
- Sunyaev-Zel'dovich effectRashid Sunyaev and Yakov Zel'dovich
- Tesla effectNikola Tesla
- Thomas precessionLlewellyn Thomas
- Thomas-Fermi modelEnrico Fermi and Llewellyn Thomas
- Van Allen radiation beltJames Van Allen
- Van der Waals forceJohannes Diderik van der Waals
- Venturi effectGiovanni Battista Venturi
- Von Restorff effectHedwig von Restorff
- Wadati-Benioff zone (or just Benioff zone) – Kiyoo Wadati and Hugo Benioff
- Wannier orbitalGregory Wannier
- Wannier-Stark ladder (sometimes just Stark ladder) – Gregory Wannier and Johannes Stark
- Wigner energy, Wigner effectEugene Wigner
- Wigner-Seitz cellEugene Wigner and Frederick Seitz
- Wilson CycleJohn Tuzo Wilson
- Yarkovsky effectIvan Osipovich Yarkovsky
- Zeeman effectPieter Zeeman

See also


- Eponyms
- List of scientists
- List of science topics Category:Eponyms

Phenomena

phenomenon.

Abney effect

The Abney Effect is one of many documented phenomena related to color perception. Specifically the Abney effect relates to the apparent shift in hue that a light source takes when white light is added. That is, a blue light would seem to become more red when white light is added.

Other color illuminance changes


- Stevens Effect
- Hunt Effect
- Bezold-Brücke Effect

References


-
- Category:Color

Alexei Abrikosov

Alexei Alexeevich Abrikosov (Алексей Алексеевич Абрикосов) (born June 25 1928, in Moscow, Russian SFSR, USSR.) is a Soviet/Russian theoretical physicist whose main contributions are in the field of condensed matter physics. He graduated from the Moscow State University in 1948. In 1948-1965 he worked in the Institute for Physical Problems of the USSR Academy of Sciences, where he received his Ph.D. (in 1951) for the theory of thermal diffusion in plasmas and then the next degree, Doctor of Physical and Mathematical Sciences (in 1955) for a thesis on quantum electrodynamics at high energies. After that, in 1965-1988 he worked in the Landau Institute for Theoretical Physics (USSR Academy of Sciences). Professor of the Moscow State University since 1965.Academician of the USSR Academy of Sciences in 1987-1991, since 1991 he is academician of Russian Academy of Sciences. In 1952 Abrikosov discovered the way in which magnetic flux can penetrate a superconductor. The phenomenon is known as type-II superconductivity, and the accompanying arrangement of magnetic flux lines is called the Abrikosov vortex lattice. Since 1991 he works in the Materials Science Division at Argonne National Laboratory in Illinois, USA on contract basis. He is a citizen of both Russia and the United States.

Awards

Alexei Abrikosov was awarded Lenin Prize (in 1966), USSR State Prize (in 1982), Fritz London Memorial Prize (in 1972). He was the co-recipient of the 2003 Nobel Prize in Physics, with Vitaly Ginzburg and Anthony James Leggett.

External links


- [http://www.msd.anl.gov/groups/cmt/people/abrikosov.html A Short Biography], on the website of the Material Science Division of Argonne National Laboratory
- [http://phys.unn.ru/Gazeta/03/ An article about 2003 Nobel Prize in Physics (in Russian)], includes a short biography of Alexei Abrikosov
- [http://abrikosov.sytes.net/ Alexei A. Abrikosov], Autobiography in English Abrikosov, Alexei Abrikosov, Alexei Abrikosov, Alexei Abrikosov, Alexei Category:Superconductivity Abrikosov, Alexei Abrikosov, Alexei ja:アレクセイ・アブリコソフ

David Bohm

David Joseph Bohm (December 20, 1917 Wilkes-Barre, PAOctober 27, 1992 London, UK) was an American quantum physicist who made significant contributions in the fields of theoretical physics, philosophy and neuropsychology, and to scientists working on the Manhattan Project.

Biography

Youth and college

Born at Wilkes-Barre, Pennsylvania, Bohm attended Pennsylvania State College, graduating in 1939, and then heading west to work with theoretical physicist Robert Oppenheimer, first at the California Institute of Technology for a year, and then at the University of California, Berkeley. Along with a few of Oppenheimer's other graduate students (Giovanni Rossi Lomanitz, Joseph Weinberg, and Max Friedman, all of whom lived in the same neighborhood), Bohm became increasingly involved not only with physics, but with radical politics. Like many young idealists in the late 1930s (including Oppenheimer himself), Bohm gravitated to alternative models of society and became active in organizations like the Young Communist League, the Campus Committee to Fight Conscription, and the Committee for Peace Mobilization (all of which the FBI under J. Edgar Hoover would brand as Communist fronts).

Work and doctorate

Manhattan Project Contributions

During World War II, the Manhattan Project mobilized much of Berkeley's physics research in the effort to produce the first atomic bomb. Though Oppenheimer had asked Bohm to work with him at the Los Alamos, the top-secret laboratory established in 1942 to design the bomb, the head of the Manhattan Project, General Leslie Groves, would not approve Bohm's security clearance, after tip-offs about his politics (Bohm's friend, Joseph Weinberg, had also come under suspicion for espionage). Bohm remained in Berkeley, teaching physics, before completing his Ph.D. in 1943, under an unusually ironic circumstance. According to Peat(see reference below, p.64), "the scattering calculations (of collisions of protons and deuterons) that he had completed proved useful to the Manhattan Project and were immediately classified. Without security clearance, Bohm was denied access to his own work; not only would he be barred from defending his thesis, he was not even allowed to write his own thesis in the first place!" To satisfy the university, Oppenheimer certified that Bohm had successfully completed the research. He would later, however, work on the theoretical calculations for the Calutrons at the Y-12 facility in Oak Ridge, used to electromagnetically enrich uranium for use in the bomb dropped on Hiroshima in 1945.

Victim of McCarthyism

After the war, Bohm became an assistant professor at Princeton University, where he worked closely with Albert Einstein. In May, 1949, at the beginning of the McCarthyism hysteria period, the House Un-American Activities Committee called upon Bohm to testify before it— because of his previous ties to suspected Communists. Bohm, however, pleaded the Fifth amendment right to decline to testify, and refused to give evidence against his colleagues. In 1950, Bohm was charged for refusing to answer questions before the Committee and arrested. He was acquitted in May, 1951, but Princeton had already suspended him. After the acquittal, Bohm's colleagues sought to have his position at Princeton re-instated, and Einstein reportedly wanted Bohm to serve as his assistant; the university, however, did not renew the contract. Bohm then left for Brazil to take up a Chair in Physics at the University of São Paulo.

Quantum theory and Bohm-diffusion

During this early period, Bohm made a number of significant contributions to physics, particularly in the area of quantum mechanics and relativity theory. While still a post-graduate at Berkeley, he discovered the electron phenomenon now known as Bohm-diffusion. His first book, Quantum Theory published in 1951, was well-received by Einstein, among others. However, Bohm became dissatisfied with the orthodox approach to quantum theory, which he had written about in that book, and began to develop his own approach (Bohm interpretation)— a non-local hidden variable deterministic theory whose predictions agree perfectly with the nondeterministic quantum theory. His work and the EPR argument became the major factor motivating John Bell's inequality, whose consequences are still being investigated.

The Aharonov-Bohm effect

In 1955, Bohm moved to Israel, where he spent two years at the Technion at Haifa. Here he met his wife Saral, who became an important figure in the development of his ideas. In 1957, Bohm moved to the UK as a research fellow at the University of Bristol. In 1959, with his student Yakir Aharonov, he discovered the Aharonov-Bohm effect, showing how an electro-magnetic field could affect a region of space in which the field had been shielded, although its vector potential did exist there. This showed for the first time that the vector potential, hitherto a mathematical convenience, could have real physical (quantum) effects. In 1961, Bohm was made Professor of Theoretical Physics at Birkbeck College London, where his [http://www.aim25.ac.uk/cgi-bin/search2?coll_id=3070&inst_id=33 collected papers] are kept.

Bridging science, philosophy, and cognition

Bohm's scientific and philosophical views were inseparable. In 1959, his wife Sarel had found a book by the Indian philosopher J. Krishnamurti in a library and recommended it to him. He was impressed by the way his own ideas on quantum mechanics meshed with the philosophical ideas of Krishnamurti. Bohm's approach to philosophy and physics receive expression in his 1980 book Wholeness and the Implicate Order, and in the book Science, Order and Creativity.

The holonomic model of the brain

Bohm also made significant theoretical contributions to neuropsychology and the development of the holonomic model [http://www.acsa2000.net/bcngroup/jponkp/#chap4] of the functioning of the brain. In collaboration with Stanford neuroscientist Karl Pribram, Bohm helped establish the foundation for Pribram's theory that the brain operates in a manner similar to a hologram, in accordance with quantum mathematical principles and the characteristics of wave patterns. These wave forms may compose hologram-like organizations, Bohm suggested, basing this concept on his application of Fourier analysis, a form of calculus that transforms complex patterns into component sine waves. The holonomic brain model developed by Pribram and Bohm posits a lens defined world view— much like the textured prismatic effect of sunlight refracted by the churning mists of a rainbow— a view which is quite different from the more conventional "objective" approach. Pribram believes that if psychology is to understand the conditions that produce the world of appearances, it must look to the thinking of physicists like Bohm.

Thought As a System (TAS)

Bohm showed a deep concern for humankind and life in general, and was alarmed by what he considered an increasing imbalance of not only Man and nature, but among peoples, as well as people, themselves. Bohm: "So one begins to wonder what is going to happen to the human race. Technology keeps on advancing with greater and greater power, either for good or for destruction." And he goes on to ask: "What is the source of all this trouble? I'm saying that the source is basically in thought. Many people would think that such a statement is crazy, because thought is the one thing we have with which to solve our problems. That's part of our tradition. Yet it looks as if the thing we use to solve our problems with is the source of our problems. It's like going to the doctor and having him make you ill. In fact, in 20% of medical cases we do apparently have that going on. But in the case of thought, its far over 20%." In Bohm's view: "the general tacit assumption in thought is that it's just telling you the way things are and that its not doing anything - that 'you' are inside there, deciding what to do with the info. But you don't decide what to do with the info. Thought runs you. Thought, however, gives false info that you are running it, that you are the one who controls thought. Whereas actually thought is the one which controls each one of us." "Thought is creating divisions out of itself and then saying that they are there naturally. This is another major feature of thought: Thought doesn't know it is doing something and then it struggles against it is doing. It doesn't want to know that it is doing it. And thought struggles against the results, trying to avoid those unpleasant results while keeping on with that way of thinking. That is what I call 'sustained incoherence.'" Bohm proposes thus in his book "Thought as a System" (TAS) a pervasive, systematic nature of thought:
What I mean by 'thought' is the whole thing - thought, 'felt', the body, the whole society sharing thoughts - it's all one process. It is essential for me not to break that up, because it's all one process; somebody else's thought becomes my thought, and vice versa. Therefore it would be wrong and misleading to break it up into my thought, your thought, my feelings, these feelings, those feelings. I would say that thought makes what is often called in modern language a SYSTEM. A system means a set of connected things or parts. But the way people commonly use the word nowadays it means something all of whose parts are mutually interdependent - not only for their mutual action, but for their meaning and for their existence. A corporation is organized as a system - it has this department, that department, that department... they don't have any meaning separately; they only can function together. And also the body is a system. Society is a system in some sense. And so on.
Similarly, thought is a system. That system not only includes thought and feelings, but it includes the state of the body; it includes the whole of society - as thought is passing back and forth between people in a process by which thought evolved from ancient times. Thought has been constantly evolving and we can't say when that system began. But with the growth of civilization it has developed a great deal. It was probably very simple thought before civilization, and now it has become very complex and ramified and has much more incoherence than before.
Now, I say that this system has a fault in it - a 'systematic fault'. It is not a fault here, there or here, but it is a fault that is all throughout the system. Can you picture that? It is everywhere and nowhere. You may say "I see a problem here, so I will bring my thoughts to bear on this problem". But 'my' thought is part of the system. It has the same fault as the fault I'm trying to look at, or a similar fault.
Thought is constantly creating problems that way and then trying to solve them. But as it tries to solve them it makes it worse because it doesn’t notice that it's creating them, and the more it thinks, the more problems it creates.

Bohm Dialogue

In his later years, he developed the technique that has become known as "Bohm Dialogue", in which equal status and "free space" form the most important prerequisites of discourse. He suggested that if carried out on a sufficiently wide scale, such dialogues could help overcome fragmentation in society.

Later years

Bohm continued his work in quantum physics past his retirement in 1987. His final work, the posthumously published The Undivided Universe: An ontological interpretation of quantum theory (1993), was the fruit of a decades-long collaboration with his colleague Basil Hiley. At the same time, he continued his conversations with Jiddu Krishnamurti, resulting in a series of publications; he also spoke to audiences across Europe and North America on the importance of dialogue as a form of sociotherapy, a concept he borrowed from London psychiatrist Patrick de Mare. He was elected Fellow of the Royal Society in 1990. David Bohm died of a heart attack in London on October 27, 1992.

Publications


- 1951 Quantum Theory, New York: Dover, ISBN 0-486-65969-0 (1989 reprint).
- 1957 Causality and Chance in Modern Physics, Philadelphia: U of Pa Press, ISBN 0-8122-1002-6 (1980 reprint)
- 1965 The Special Theory of Relativity, New York: W.A. Benjamin.
- 1980 Wholeness and the Implicate Order London: Routledge, ISBN 0-710-00971-2.
- 1985 Unfolding Meaning: a weekend of dialogue with David Bohm (Donald Factor, editor), Gloucestershire: Foundation House, ISBN 0-948-32500-3.
- 1985 The Ending of Time, with Jiddu Krishnamurti, San Francisco, CA: Harper, ISBN: 0-060-64796-5.
- 1987 Science, Order and Creativity, with F. David Peat. London: Routledge. 2nd ed. 2000. ISBN 0-415-17182-2.
- 1992 Thought as a System (transcript of seminar held in Ojai, California, from November 30 to December 2, 1990), London: Routledge. ISBN 0-415-11980-4.
- 1993 The Undivided Universe: An ontological interpretation of quantum theory, with B.J. Hiley, London: Routledge, ISBN 0-415-12185-X (final work)
- 1996 On Dialogue. Ed. Lee Nichol. London: Routledge, ISBN 0-415-14911-8
- 1999 Limits of Thought: Discussions, with Jiddu Krishnamurti, London: Routledge, ISBN 0-415-19398-2.
- 1999 Bohm-Biederman Correspondence: Creativity and Science, with Charles Biederman. Ed. P. Pylkkänen. ISBN: 0-415-16225-4.
- 2002 The Essential David Bohm. Ed. Lee Nichol. London: Routledge, ISBN: 0-415-26174-0.

See also


- Aharonov-Bohm effect
- Bohm diffusion of a plasma in a magnetic field
- Bohm interpretation
- Correspondence principle
- EPR paradox
- Holomovement
- Implicate and Explicate Order
- John Stewart Bell
- Karl Pribram
- McCarthyism
- The Bohm sheath criterion, which states that a plasma must flow with at least the speed of sound toward a solid surface

References


- "Bohm's Alternative to Quantum Mechanics", David Z. Albert, Scientific American (May, 1994)
- Brotherhood of the Bomb: The Tangled Lives and Loyalties of Robert Oppenheimer, Ernest Lawrence, and Edward Teller, Herken, Gregg, New York: Henry Holt (2002) ISBN 080506589X (information on Bohm's work at Berkeley and his dealings with HUAC)
- Infinite Potential: the Life and Times of David Bohm, F. David Peat, Reading, MA: Addison Wesley (1997), ISBN 0201406357 [http://www.fdavidpeat.com/ DavidPeat.com]
- Quantum Implications: Essays in Honour of David Bohm, (B.J. Hiley, F. David Peat, editors), London: Routledge (1987), ISBN 0415069602

External links


- More about David Bohm's ideas on Dialogue at a German [http://www.muc.de/~heuvel/dialogue/ site] maintained to carry on his concepts of Dialogue.
- [http://www.david-bohm.net English site] for David Bohm's ideas about Dialogue.
- [http://www.david-bohm.org/mailman/listinfo/bohm_dialogue Moderated Dialogue Group] Participate in an international English-speaking Bohm Dialogue group, by list server email.
- [http://thinkg.net/TT TT The Table] David Bohm dialogue online.
- [http://www.thinkg.net/david_bohm/ the David_Bohm_Hub] A site that compiles parts of David Bohm's life and work in form of texts, audio, video, and pictures.
- [http://thinkg.net/david_bohm/martin_gardner_on_david_bohm_and_krishnamurti.html David Bohm and Krishnamurti] Skeptical Inquirer, July, 2000, by Martin Gardner.
- [http://arxiv.org/abs/physics/?0508184 Science and exile]: David Bohm, the hot times of the Cold War, and his struggle for a new interpretation of quantum mechanics. Bohm, David Bohm, David Bohm, David Bohm, David Bohm, David

Maurice Allais

Maurice Allais (born May 31, 1911) was the 1988 winner of The Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel for his pioneering contributions to the theory of markets and efficient utilization of resources. He was born in Paris, France. Allais made contribution to economics and was an accomplished physicist. As a scientist, he made two controversial contributions to the scientific community: # The Allais effect first reported in 1954 was the result of anomalous readings of a paraconical pendulum during two separate eclipse events. Initially this was thought to be a gravitational shielding effect inconsistent with general relativity but other conventional interpretations take precedence in mainstream physics. # More recently Dr. Allais performed a statistical analysis of the thousands of interferometer measurements of Dayton Miller and found a corresponding periodicity with the sidereal day, the equinoxes and other celestial events thus invalidating the Robert S. Shankland rufutation of Miller's work. This [http://www.anti-relativity.com/allaisarticle21stcentury.htm analysis], if confirmed, either casts doubt on the second postulate of Special Relativity or opens possibilities for expansion of the theory.

Notable quotes


- "In essence, the present creation of money, out of nothing by the banking system, is similar - I do not hesitate to say it in order to make people clearly realize what is at stake here - to the creation of money by counterfeiters, so rightly condemned by law."

External links


- "[http://www.nobel.se/economics/laureates/1988/allais-autobio.html Maurice Allais -Autobiography]" Nobel Prize, nobel.se.
- "[http://allais.maurice.free.fr/ Maurice Allais]" - Internet Site (French)
- [http://kilop.atspace.com/allais-cv.html pioneering contributions to the theory of markets and efficient utilization of resources.]
- [http://www.geocities.com/econ_555jim/allais-autobio.html Maurice Allais – Autobiography] Allais, Maurice Allais, Maurice Allais,Maurice Allais, Maurice Allais, Maurice Allais, Maurice

W. C. Allee

Warder Clyde Allee (June 5, 1885 - March 18, 1955) was an American zoologist and ecologist who taught animal ecology at the University of Chicago. He is best known for his research on animal behavior, protocooperation, and for identifying the Allee effect. Allee was born in Bloomingdale, Indiana and died in Gainesville, Florida. The Animal Behavior Society offers the W.C. Allee Award in a juried competition held at their annual meeting.

See also


- Population density

Bibliography


- Alee, W. C. (1931). Animal Aggregations. A study in General Sociology. University of Chicago Press, Chicago. ISBN 0404145019
- Allee, W. C. (1949). [http://chla.library.cornell.edu/cgi/t/text/text-idx?c=chla;idno=3110087 Principles of Animal Ecology]. W.B. Saunders Co., Philadelphia. ISBN 0721611206

External links


- [http://maps.uchicago.edu/northwest/allee.html WC Allee Laboratory of Animal Behavior] Biopsychological Research Building at the University of Chicago Allee, W. C. Allee, W. C. Allee, W. C. Allee, W. C. Allee, W. C.

Auger electron

Auger emission (pronounced Oh-zhay) is a phenomenon in physics in which the emission of an electron from an atom causes the emission of a second electron. This second ejected electron is called an Auger electron. The name Auger electron comes from one of its discoverer, Pierre Victor Auger, see below. The name does not come from the device by the same name, the auger. When an electron is removed from a core level of an atom, leaving a vacancy, an electron from a higher energy level may fall into the vacancy, resulting in a release of energy. Although sometimes this energy is released in the form of an emitted photon, the energy can also be tranfered to another electron, which is then ejected from the atom. Upon ejection the kinetic energy of the Auger electron corresponds to the difference between the energy of the initial electronic transition and the ionization energy for the shell from which the Auger electron was ejected. These energy levels depend on the type of atom and the chemical environment in which the atom was located. Auger electron spectroscopy stimulates the emission of Auger electrons by bombarding a sample with either X-rays or energetic electrons and measures the intensity of Auger electrons as a function of the Auger electron energy. The resulting spectra can be used to determine the identity of the emitting atoms and some information about their environment.

History

The Auger emission process was discovered in the 1920s by Lise Meitner, an Austrian physicist. Subsequently Pierre Victor Auger, a French Physicist, also discovered the process. Auger reported the discovery in the journal Radium in 1925 and it was Auger that had the process named after him. A similar Auger effect occurs in semiconductors. An electron and electron hole can recombine giving up their energy to an electron in the conduction band, increasing its energy. The reverse effect is known as impact ionization. Category:Atomic physics Category:Foundational quantum physics

Balmer line

In physics, the Balmer series is the series of transitions and resulting emission lines of the hydrogen atom. The Balmer series are characterized by the Balmer formula, discovered by Johann Balmer in 1885. While the emission lines had been seen long before, previous attempts to characterize the spectrum mathematically had failed. The Balmer series is characterized by the electron transitioning from n ≥ 3 to n = 2, where n refers to the radial quantum number or principal quantum number of the electron. The transitions are named sequentially by Greek letter: n = 3 to n = 2 is called H-α, 4 to 2 is H-β, 5 to 2 is H-γ, etc. As the spectral lines associated with this series are located in the visible part of the electromagnetic spectrum, these lines are historically referred to as H-alpha, etc., rather than Balmer-alpha, etc.

Balmer's formula

:\frac = R_H\left(\frac - \frac\right), n=3,4,5,... where λ is the wavelength of the emitted light and RH is the Rydberg constant for hydrogen. The Rydberg constant for an infinitely heavy nucleus is 10,973,735.3 m−1.

Role in Astronomy

In astronomy, lines of the Balmer series appear in a great variety of objects, as hydrogen is the most common chemical element in the universe. Balmer lines can appear in absorption or emission. In stars they appear in absorption, and they are "strongest" when radiating from a star with a temperature of 10,000K. In nebulae such as H II regions, planetary nebulae, and AGNs they appear in emission.

See also


- Bohr model
- Hydrogen spectral series
- H-alpha
- Rydberg formula Category:Emission spectroscopy ja:バルマー系列

Johann Jakob Balmer

Johann Jakob Balmer (May 1 1825March 12 1898) was a Swiss mathematician and an honorary physicist. He was born in Lausen, Switzerland, the son of a Chief Justice also named Johann Jakob Balmer. His mother was Elizabeth Rolle Balmer, and he was the oldest son. During his schooling he excelled in mathematics, and so decided to focus on that field when he attended university. He studied at the University of Karlsruhe and the University of Berlin, then completed his Ph.D. from the University of Basel in 1849 with a dissertation on the cycloid. Johann then spent his entire life in Basel, where he taught at a school for girls. He also lectured at the University of Basel. In 1868 he married Christine Pauline Rinck at the age of 43. The couple had a total of six children. Despite being a mathematician, he is not remembered for any work in that field; rather, his major contribution (made at the age of sixty, in 1885) was an empirical formula for the spectral lines of the hydrogen atom. Balmer's formula computed the wavelength as follows: :\lambda\ = \frac for n = 2, h = 3.6546 10-7 m, and m = 3, 4, 5, 6, and so forth. Balmer then used this formula to predict the wavelength for m = 7, and a colleague at the university was able to confirm a match to a high degree of accuracy. A full explanation of why the formula worked, however, had to wait until the presentation of the Bohr model of the atom by Niels Bohr in 1913. Johann Balmer died in Basel.

Honors


- Balmer lines and Balmer series are named after him.
- Balmer crater on the Moon is named after him.

External links


- [http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Balmer.html Biography] Balmer, Johann Balmer, Johann Balmer, Johann Balmer, Johann Balmer, Johann Balmer, Johann

Heinrich Barkhausen

Barkhausen is also a locality in Detmold, see Detmold-Barkhausen Heinrich Georg Barkhausen (December 2,1881 - February 20, 1956), born at Bremen was a German physicist. Born into a patrician family in Bremen, he showed interest in natural sciences from an early age. He studied at the universities of Munich and Berlin before obtaining a doctorate at the University of Göttingen in 1907. He became Professor for Electrical Engineering at the Technische Hochschule Dresden in 1911 at the age of 29, thus obtaining the world's first chair in this discipline. He discovered in 1919 an effect named after him, the Barkhausen effect, which suggested that ferromagnetic materials contain regions of like-oriented atoms. Induced changes in the magnetic orientation of these domains affect the whole domain and not individual atoms. With suitable equipment, these changes of orientation (jumps) can be heard. Another contribution of his, the Barkhausen Criterion states that an oscillator will oscillate when the total phase shift from input to output back to input is 360 degrees and the system gain is at least 1. [http://web.mit.edu/klund/www/weblatex/node4.html]

Publications

Four volume teaching text: "Lehrbuch der Elektronenröhren, Elektronenröhren und ihre technischen Anwendungen."

External links


- "[http://www.geocities.com/neveyaakov/electro_science/barkhausen.html Heinrich Georg Barkhausen ]" Barkhausen, Heinrich Barkhausen, Heinrich Barkhausen, Heinrich

Baskerville effect

The Baskerville effect, or the Hound of the Baskervilles effect is a statistical observation that mortality through heart attacks is increased by psychological stress. It is named after the fictional Charles Baskerville from the Sherlock Holmes novel The Hound of the Baskervilles who died as a result of the stress of encountering the fierce dog after which the story is named. It was discovered by David Phillips and his colleagues at the University of California, San Diego, who found that daily number of deaths of the 200,000 Chinese and Japanese Americans who died from heart attacks between 1973 and 1988 was 7 percent higher on the fourth of the month compared to the average for the other days in that week. Four (四, formal writing: 肆, pinyin si4) is considered an unlucky number in Chinese and Japanese (as well as Korean) cultures because it sounds like "death" (死 pinyin si3). Some Chinese and Japanese hotels and hospitals do not use it as a room number[http://www.japan-guide.com/e/e2209.html]. His hypothesis was that the peak was caused by stress induced by the superstition surrounding this number. Previous research had also shown a complementary effect, mortality falling before auspicious occasions and rising again afterwards.

References


- [http://www.newscientist.com/article.ns?id=dn1724 New Scientist magazine, 2001]
- [http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=61045 British Medical Journal - The Hound of the Baskervilles effect: natural experiment on the influence of psychological stress on timing of death] Category:Cardiology

Benioff zone

A Benioff zone (also Benioff-Wadati zone or Wadati-Benioff zone) is a deep active seismic area in a subduction zone. Differential motion along the zone produces deep seated earthquakes. They develop beneath volcanic island arcs and continental margins above active subduction zones. The deep earthquakes along the zone allow seismologists to map the three dimensional surface of a subducting slab of oceanic crust and mantle. The term was named for the two seismologists, Hugo Benioff of the California Institute of Technology, and Kiyoo Wadati of the Central Meteorological Observatory of Japan who independently discovered the zones.

External link


- [http://earthquake.usgs.gov/image_glossary/benioff.html USGS]

See also


- Subduction Category:Seismology Category:Plate tectonics

Daniel Bernoulli

Daniel Bernoulli (Groningen, February 9, 1700Basel, March 17, 1782) was a Dutch-born mathematician who spent much of his life in Basel, Switzerland. He worked with Leonhard Euler on the equations bearing their names. Bernoulli's principle is of critical use in aerodynamics. It is applicable to steady, inviscid, incompressible flow, along a streamline. Born as the son of Johann Bernoulli,nephew of Jakob Bernoulli, younger brother of Nicolaus Bernoulli II, Daniel Bernoulli was by far the ablest of the younger Bernoullis. He is said to have had a bad relationship with his father. Upon both of them entering and trying for first place in a scientific contest at the University of Paris, Johann, unable to bear the "shame" of being compared to his offspring, banned Daniel from his house. Johann Bernoulli also tried to steal Daniel's book Hydrodynamica and rename it Hydraulica. Despite Daniel's attempts at reconciliation, his father carried the grudge until his death. When Daniel was five, his younger brother Johann Bernoulli II was born. He was a contemporary and intimate friend of Euler. He went to St. Petersburg in 1724 as professor of mathematics, but did not like it there, and a temporary illness in 1733 gave him an excuse for leaving. He returned to the University of Basel, where he successively held the chairs of medicine, metaphysics and natural philosophy until his death. His earliest mathematical work was the Exercitationes (Mathematical Exercises), published in 1724, which contains a solution of the differential equation proposed by Jacopo Riccati (the Riccati equation). Two years later he pointed out for the first time the frequent desirability of resolving a compound motion into motions of translation and motions of rotation. His chief work is his Hydrodynamique (Hydrodynamica), published in 1738; it resembles Lagrange's Méchanique Analytique in being arranged so that all the results are consequences of a single principle, namely, in this case, the conservation of energy. This was followed by a memoir on the theory of the tides, to which, conjointly with the memoirs by Euler and Colin Maclaurin, a prize was awarded by the French Academy: these three memoirs contain all that was done on this subject between the publication of Isaac Newton's Principia and the investigations of Laplace. Bernoulli also wrote a large number of papers on various mechanical questions, especially on problems connected with vibrating strings, and the solutions given by Brook Taylor and by d'Alembert. He is the earliest writer who attempted to formulate a kinetic theory of gases, and he applied the idea to explain the law associated with the names of Robert Boyle and Edme Mariotte. Daniel Bernoulli also was the author in 1738 of the "Exposition of a New Theory on the Measurement of Risk", (Econometrica vol 22 (1954), pp23-36; Stanford Encyclopaedia of Philosophy) which St. Petersburg paradox was the base of the economic theory of risk aversion, risk premium and utility.

See also


- Bernoulli's equation
- Euler-Bernoulli beam equation

External links


-
- Mathematik.ch Biography: http://www.mathematik.ch/mathematiker/daniel_bernoulli.php Original entry based on the public domain Rouse History of Mathematics Bernoulli, Daniel Bernoulli, Daniel Bernoulli, Daniel Bernoulli, Daniel Bernoulli, Daniel ko:다니엘 베르누이 ja:ダニエル・ベルヌーイ

Paul Alfred Biefeld

Dr. Paul Alfred Biefeld (? - 1940) was a Swiss scientist, who emigrated to the United States of America. He was an astronomer and physicist. At points in his career, he taught at Denison University in Granville, Ohio and the California Institute of Technology. He is best known for research into the Biefeld-Brown effect with Thomas Townsend Brown. Biefeld, Paul Alfred Biefeld, Paul Alfred Biefeld, Paul Alfred

Bloch wave

A Bloch wave or Bloch state is the wavefunction of a particle (usually, an electron) placed in a periodic potential. It consists of the product of a plane wave and a periodic function (Bloch envelope) unk(r) which has the same periodicity as the potential: :\psi_(\mathbf)=e^u_(\mathbf). The result that the eigenfunctions can be written in this form for a periodic system is called Bloch's theorem. The plane wave wavevector (or Bloch wavevector) k (multiplied by Planck's constant, this is the particle's crystal momentum) is unique only up to a reciprocal lattice vector, so one only needs to consider the wavevectors inside the first Brillouin zone. For a given wavevector and potential, there are a number of solutions, indexed by n, to Schrodinger's equation for a Bloch electron. These solutions, called bands, are separated in energy by a finite spacing at each k; if there is a separation that extends over all wavevectors, it is called a (complete) band gap. The band structure is the collection of energy eigenstates within the first Brillouin zone. All the properties of electrons in a periodic potential can be calculated from this band structure and the associated wavefunctions, at least within the independent electron approximation. More generally, a Bloch-wave description applies to any wave-like phenomenon in a periodic medium. For example, a periodic dielectric in electromagnetism leads to photonic crystals, and a periodic acoustic medium leads to phononic crystals. A corollary of this result is that the Bloch wavevector k is a conserved quantity in a crystalline system (modulo addition of reciprocal lattice vectors), and hence the group velocity of the wave is conserved. This means that electron can propagate without scattering through a crystalline material, almost like free particles, and that electrical resistance in a crystalline conductor only results from things like imperfections that break the periodicity. It can be shown that the eigenfunctions of a particle in a periodic potential can always be chosen this form by proving that translation operators (by lattice vectors) commute with the Hamiltonian. More generally, the consequences of symmetry on the eigenfunctions are described by representation theory. The concept of the Bloch state was developed by Felix Bloch in 1928, to describe the conduction of electrons in crystalline solids. The same underlying mathematics, however, was also discovered independently several times: by George William Hill (1877), Gaston Floquet (1883), and Alexander Lyapunov (1892). As a result, a variety of nomenclatures are common: applied to ordinary differential equations, it is called Floquet theory (or occasionally the Lyapunov-Floquet theorem), and the one-dimensional periodic wave equation is sometimes called Hill's equation.

References


- Charles Kittel, Introduction to Solid State Physics (Wiley: New York, 1996).
- Neil W. Ashcroft and N. David Mermin, Solid State Physics (Harcourt: Orlando, 1976).
- Felix Bloch, "Über die quantenmechanik der electronen in kristallgittern," Z. Physik 52, 555-600 (1928).
- George William Hill, "On the part of the motion of the lunar perigee which is a function of the mean motions of the sun and moon," Acta. Math. 8, 1-36 (1886). (This work was initially published and distributed privately in 1877.)
- Gaston Floquet, "Sur les équations différentielles linéaires à coefficients périodiques," Ann. École Norm. Sup. 12, 47-88 (1883).
- Alexander Mihailovich Lyapunov, The General Problem of the Stability of Motion (London: Taylor and Francis, 1992). Translated by A. T. Fuller from Edouard Davaux's French translation (1907) of the original Russian dissertation (1892). Category:Condensed matter physics



Bose-Einstein condensate

A Bose-Einstein condensate is a phase of matter formed by bosons cooled to temperatures very near to absolute zero. The first such condensate was produced by Eric Cornell and Carl Wieman in 1995 at the University of Colorado at Boulder, using a gas of rubidium atoms cooled to 170 nanokelvins (nK). Under such conditions, a large fraction of the atoms collapse into the lowest quantum state. quantum state

Theory

The collapse of the atoms into a single quantum state is known as Bose condensation or Bose-Einstein condensation. This phenomenon was predicted in the 1920s by Satyendra Nath Bose and Albert Einstein, based on Bose's work on the statistical mechanics of photons, which was then formalized and generalized by Einstein. The result of the efforts of Bose and Einstein is the concept of a Bose gas, governed by the Bose-Einstein statistics, which describes the statistical distribution of certain types of identical particles now known as bosons. Bosonic particles, which include the photon as well as atoms such as helium-4, are allowed to share quantum states with each other. Einstein speculated that cooling bosonic atoms to a very low temperature would cause them to fall (or "condense") into the lowest accessible quantum state, resulting in a new form of matter. The critical temperature (in a uniform three-dimensional gas consisting of particles with no apparent internal degrees of freedom, and with no or uniform external potential) at which this happens can be derived to be: :T_c=\left(\frac\right)^\frac where:

Discovery

In 1938, Pyotr Kapitsa, John Allen and Don Misener discovered that helium-4 became a new kind of fluid, now known as a superfluid, at temperatures below 2.17 kelvins (K) (lambda point). Superfluid helium has many unusual properties, including zero viscosity (the ability to flow without dissipating energy) and the existence of quantized vortices. It was quickly realized that the superfluidity was due to Bose-Einstein condensation of the helium-4 atoms, which are bosons. In fact, many of the properties of superfluid helium also appear in the gaseous Bose-Einstein condensates created by Cornell, Wieman and Ketterle (see below). However, superfluid helium-4 is not commonly referred to as a "Bose-Einstein condensate" because it is a liquid rather than a gas, which means that the interactions between the atoms are relatively strong. The original Bose-Einstein has to be heavily modified in order to describe it. The first "true" Bose-Einstein condensate was created by Cornell, Wieman, and co-workers at JILA on June 5, 1995. They did this by cooling a dilute vapor consisting of approximately 2000 rubidium-87 atoms to 170 nK using a combination of laser cooling (a technique that won its inventors Steven Chu, Claude Cohen-Tannoudji, and William D. Phillips the 1997 Nobel Prize in Physics) and magnetic evaporative cooling. About four months later, an independent effort led by Wolfgang Ketterle at MIT created a condensate made of sodium-23. Ketterle's condensate had about a hundred times more atoms, allowing him to obtain several important results such as the observation of quantum mechanical interference between two different condensates. Cornell, Wieman and Ketterle won the 2001 Nobel Prize for their achievement. The initial results by the JILA and MIT groups have led to an explosion of experimental activity. For instance, the first molecular Bose-Einstein condensates were created in November 2003 by teams surrounding Rudolf Grimm at the University of Innsbruck, Deborah S. Jin at the University of Colorado at Boulder and Wolfgang Ketterle at MIT. Jin also went on to create the first fermionic condensate. Bose-Einstein condensates are extremely fragile, compared to other states of matter more commonly encountered. The slightest interaction with the outside world can be enough to warm them past the condensation threshold, causing them to break back down into individual atoms again; it is likely to be some time before any practical applications are developed for them.

Slowing light

Despite our inability to fully understand these new states of matter, several interesting properties have already been observed in experiments. Bose-Einstein condensates can be made to have an extremely high gradient in optical density. Normally, condensates do not have a particularly special refractive index, due to having an atomic density far less than normal solid materials. However, additional pump lasers can be used at frequencies designed to alter the state of atoms in the Bose-Einstein condensate, increasing drastically the index for a beam of a precise target frequency recorded at a probe point. This results in an extremely low measured speed of light within the condensate; some have slowed beams of light down to mere meters per second, speeds which can be exceeded by a human on a bicycle. This apparent speed of light is slower than c, since although it travels at the speed of light between the atoms, it is absorbed by the atoms for a long time before being re-emitted, so giving at outward appearance of travelling slowly. Rotating Bose-Einstein condensates could be used as a model black hole, allowing light to enter but not to escape. Condensates could also be used to "freeze" pulses of light, to be released again when the condensate breaks down. This is done by shutting off the pumping lasers with pulses still in transit and allowing the photons to be absorbed. Reapplying the pump lasers can then release the pulses of light, and due to the coherence of the Bose-Einstein condensate, there may be very little degradation. Research in this field is still young and ongoing.

See also


- Bose gas
- Electromagnetically induced transparency
- Fermionic condensate
- Gas in a box
- Gravastar
- Slow glass
- Superfluid
- Supersolid
- Super-heavy atom
- Tonks-Girardeau gas

External links


- [http://nobelprize.org/physics/laureates/2001/index.html Nobel Prize in Physics 2001] - for the achievement of Bose-Einstein condensation in dilute gases of alkali atoms, and for early fundamental studies of the properties of the condensates
- [http://jilawww.colorado.edu/bec/ Bose-Einstein Condensates at JILA]
- [http://www.physics.uq.edu.au/atomoptics/ Atom Optics at UQ]
- [http://www.europhysicsnews.com/full/26/article1/article1.html Europhysics News Report on Slowed Light]
- [http://www.lorentz.leidenuniv.nl/history/Einstein_archive/ Einstein's manuscript on the Bose-Einstein condensate discovered at Leiden University]
- [http://arxiv.org/abs/cond-mat/0310067 Bose-Einstein Condensation of Helium and Hydrogen inside Bundles of Carbon Nanotubes]

References


- S. N. Bose, Z. Phys. 26, 178 (1924)
- A. Einstein, Sitz. Ber. Preuss. Akad. Wiss. (Berlin) 22, 261 (1924)
- L.D. Landau, J. Phys. USSR 5, 71 (1941)
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- C. J. Pethick and H. Smith, "Bose-Einstein Condensation in Dilute Gases", Cambridge University Press, Cambridge, 2004. Category:Albert Einstein Category:Quantum mechanics Category:Condensed matter physics ja:ボース=アインシュタイン凝縮

Bose-Einstein statistics

:For other topics related to Einstein see Einstein (disambiguation). In statistical mechanics, Bose-Einstein statistics determines the statistical distribution of identical indistinguishable bosons over the energy states in thermal equilibrium. Bose-Einstein (or B-E) statistics are closely related to Maxwell-Boltzmann statistics (M-B) and Fermi-Dirac statistics (F-D). While F-D statistics holds for fermions, M-B statistics holds for classical particles, i.e. identical but distinguishable particles, and represents the classical or high-temperature limit of both F-D and B-E statistics. (M-B, B-E, and F-D statistics are all derived from the Boltzmann factor probability weight applied to the problem of classical particles and discrete energy quanta with boson/fermion behavior, respectively.) Bosons, unlike fermions, are not subject to the Pauli exclusion principle: an unlimited number of particles may occupy the same state at the same time. This explains why, at low temperatures, bosons can behave very differently than fermions; all the particles will tend to congregate together at the same lowest-energy state, forming what is known as a Bose-Einstein condensate. B-E statistics was introduced for photons in 1920 by Bose and generalized to atoms by Einstein in 1924. Einstein's original sketches were recovered in August 2005 in the Academical Library of Leiden, the Netherlands, where they were found by a student (Rowdy Boeyink). The expected number of particles in an energy state i  for B-E statistics is: : n_i = \frac where: :ni  is the number of particles in state i :gi  is the degeneracy of state i : εi  is the energy of the i-th state :μ is the chemical potential :k is Boltzmann's constant :T is absolute temperature :exp is the exponential function This reduces to M-B statistics for energies ( εi-μ ) >> kT.

Derivation of the Bose-Einstein distribution

Suppose we have a number of energy levels, labelled by index i, each level having energy εi  and containing a total of ni  particles. Suppose each level contains gi  distinct sublevels, all of which have the same energy, and which are distinguishable. For example, two particles may have different momenta, in which case they are distinguishable from each other, yet they can still have the same energy. The value of gi  associated with level i is called the "degeneracy" of that energy level. Any number of bosons can occupy the same sublevel. Let w(n,g) be the number of ways of distributing n particles among the g sublevels of an energy level. There is only one way of distributing n particles with one sublevel, therefore w(n,1) = 1. Its easy to see that there are n + 1 ways of distributing n particles in two sublevels which we will write as: : w(n,2)=\frac. With a little thought it can be seen that the number of ways of distributing n particles in three sublevels is w(n,3) = w(n,2) + w(n−1,2) + ... + w(0,2) so that : w(n,3)=\sum_^n w(n-k,2) = \sum_^n\frac=\frac where we have used the following theorem involving binomial coefficients: : \sum_^n\frac=\frac. Continuing this process, we can see that w(n,g) is just a binomial coefficient : w(n,g)=\frac. The number of ways that a set of occupation numbers ni  can be realized is the product of the ways that each individual energy level can be populated: : W = \prod_i w(n_i,g_i) = \prod_i \frac \approx\prod_i \frac where the approximation assumes that g_i>>1. Following the same procedure used in deriving the Maxwell-Boltzmann statistics, we wish to find the set of ni  for which W is maximised, subject to the constraint that there be a fixed number of particles, and a fixed energy. The maxima of W and \ln(W) occur at the value of N_i and, since it is easier to accomplish mathematically, we will maximise the latter function instead. We constrain our solution using Lagrange multipliers forming the function: : f(n_i)=\ln(W)+\alpha(N-\sum n_i)+\beta(E-\sum n_i \epsilon_i) Using the g_i>>1 approximation and using Stirling's approximation for the factorials \left(\ln(x!)\approx x\ln(x)-x\right) and taking the derivative with respect to ni, and setting the result to zero and solving for ni yields the Fermi-Dirac population numbers: : n_i = \frac It can be shown thermodynamically that β = 1/kT where k  is Boltzmann's constant and T is the temperature, and that α = -μ/kT where μ is the chemical potential, so that finally: : n_i = \frac Note that the above formula is sometimes written: : n_i = \frac where z=exp(\mu/kT) is the absolute activity.

See also


- Maxwell Boltzmann statistics (derivation)
- Fermi-Dirac statistics
- Parastatistics
- Planck's law of black body radiation Category:Statistical mechanics Category:Quantum mechanics Category:Quantum field theory Category:Probability distributions Category:Albert Einstein

Eastman Kodak

Eastman Kodak - to jeden z największych koncernów na świecie zajmujących się produkcją szeroko rozumianego sprzętu fotograficznego i filmowego. Posiada on status międzynarodowej spółki akcyjnej. Firmą, od której pierwotnie wywodzi się obecny Eastman Kodak, jest Eastman Dry Plate Company, która została założona przez wynalazcę Georga Eastmana i inwestora Henry Stronga, w 1881 r. Centrala firmy znajduje się w Rochester, w stanie New York, w USA. Słowo Kodak zostało wprowadzone do nazwy firmy ze względu na popularność pierwszego aparatu małoobrazkowego współpracującego z filmami w rolkach, który był sprzedawany przez Eastman Dry Plate Company pod nazwą Kodak. Popularność tego aparatu była tak wielka, że firma była bardziej kojarzona ze słowem Kodak, niż z nazwiskiem Eastmana. Słowo to miało w zamyśle kojarzyć się z dźwiękiem wydawanym przez aparat w trakcie wykonywania zdjęcia i wg relacji Eastmana zostało wymyślone przez jego kilkuletnią córkę. Firma wprowadziła na rynek wiele podstawowych obecnie technologii fotograficznych takich jak film fotograficzny w rolkach 35 mm oraz pierwszy aparat fotograficzny dla amatorów. Aktualnie firma jest wciąż największym producentem sprzętu fotograficznego na świecie, zarówno dla profesjonalistów jak i amatorów. Oprócz stworzenia standardu fotografii małoobrazkowej firma była też pionierem w fotografii kolorowej, wprowadzając jako pierwsza standard automatycznego wywoływania filmów znany jako proces C-41, który obecnie stosują praktycznie wszyscy wytwórcy kolorowych filmów małoobrazkowych na świecie. Równolegle z firmą Polaroid rozwijała ona technologię fotografii błyskawicznej, jednak po przegraniu sprawy patentowej przeciw Polaroidowi 19 stycznia 1986 wycofała się całkowicie z tego segmentu rynku. W latach 90. XX wieku firma forsowała nową technologię fotografii tradycyjnej o nazwie Advanced Photo System, mającą zastąpić aparaty małoobrazkowe. Technologia ta umożliwia radykalne zmniejszenie rozmiarów aparatów, stosowanie filmów umożliwiających zapisanie do 135 zdjęć na jednej rolce i automatyczne ich katalogowanie. Firma jest też silnie zaangażowana w rynek fotografii cyfrowej, którego opanowanie jest obecnie głównym celem strategicznym koncernu. 13 stycznia 2004 koncern ogłosił zaprzestanie produkcji aparatów małoobrazkowych w USA i Europie Zachodniej i zarzucenie całkowicie rozwijania technologii Advanced Photo System, która nie cieszy się specjalnym zainteresowaniem klientów. Produkcja i rozwój technologii tradycyjnych filmów fotograficznych będzie jednak kontynuowana.

Zobacz też


- przegląd zagadnień z zakresu fotografii
- Canon
- Nikon Kategoria:Fotografia kategoria:Firmy ja:コダック

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