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Ehrenfest
Ehrenfest is a surname. Notable people with the surname include: *Paul Ehrenfest (1880-1933), Austrian physicist and mathematician **Ehrenfest equations **Ehrenfest model **Ehrenfest paradox **Ehrenfest theorem The Ehrenfest theorem, named after Paul Ehrenfest, an Austrian theoretical physicist at Leiden University, relates the time derivative of the expectation values of the position and momentum operators ''x'' and ''p'' to the expectation value of th ... ** 32796 Ehrenfest * Tatjana Ehrenfest-Afanassjewa (1876-1964), Ukrainian-Russian mathematician, wife of Paul * Tanja van Aardenne-Ehrenfest (1905–1984), Austrian Dutch mathematician, daughter of Paul See also * Ehrenfeld (other) * Ehrenfels (other) * Ehrenbaum * Ehrenberg (other) * Ehrenburg (other) * Ehrenhaft * Ehrenpreis * Ehrenstein * Ehrenthal {{surname, Ehrenfest German-language surnames ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paul Ehrenfest
Paul Ehrenfest (18 January 1880 – 25 September 1933) was an Austrian theoretical physicist, who made major contributions to the field of statistical mechanics and its relations with quantum mechanics, including the theory of phase transition and the Ehrenfest theorem. He bonded with Albert Einstein on a visit to Prague in 1912 and became a professor in Leiden, where he frequently hosted Einstein. Biography Paul Ehrenfest was born and grew up in Vienna to Jewish parents from Loštice in Moravia (now part of the Czech Republic). His parents, Sigmund Ehrenfest and Johanna Jellinek, ran a grocery store. Although the family was not overly religious, Paul studied Hebrew and the history of the Jewish people. Later, he always emphasized his Jewish roots. Ehrenfest excelled in grade school but did not do well at the Akademisches Gymnasium, his best subject being mathematics. After transferring to the Franz Josef Gymnasium, his marks improved. In 1899, he passed the final exams. He m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tatyana Afanasyeva
Tatyana Alexeyevna Afanasyeva (russian: link=no, Татья́на Алексе́евна Афана́сьева) (Kiev, 19 November 1876 – Leiden, 14 April 1964) (also known as Tatiana Ehrenfest-Afanaseva or spelled Afanassjewa) was a Russian/Dutch mathematician and physicist who made contributions to the fields of statistical mechanics and statistical thermodynamics. On 21 December 1904, she married Austrian physicist Paul Ehrenfest (1880–1933). They had two daughters and two sons; one daughter, Tatyana Pavlovna Ehrenfest, also became a mathematician. Early life Afanasyeva was born in Kiev, Ukraine, then part of the Russian Empire. Her father was Alexander Afanassjev, a chief engineer on the Imperial Railways, who would bring Tatyana on his travels around the Russian Empire. Her father died while she was still young, so she moved to St Petersburg in Russia to live with her aunt Sonya, and uncle Peter Afanassjev, a professor at the Peter the Great St. Petersburg Polytech ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ehrenfest Theorem
The Ehrenfest theorem, named after Paul Ehrenfest, an Austrian theoretical physicist at Leiden University, relates the time derivative of the expectation values of the position and momentum operators ''x'' and ''p'' to the expectation value of the force F=-V'(x) on a massive particle moving in a scalar potential V(x), The Ehrenfest theorem is a special case of a more general relation between the expectation of any quantum mechanical operator and the expectation of the commutator of that operator with the Hamiltonian of the system where is some quantum mechanical operator and is its expectation value. It is most apparent in the Heisenberg picture of quantum mechanics, where it amounts to just the expectation value of the Heisenberg equation of motion. It provides mathematical support to the correspondence principle. The reason is that Ehrenfest's theorem is closely related to Liouville's theorem of Hamiltonian mechanics, which involves the Poisson bracket instead of a com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ehrenfest Paradox
The Ehrenfest paradox concerns the rotation of a "rigid" disc in the theory of relativity. In its original 1909 formulation as presented by Paul Ehrenfest in relation to the concept of Born rigidity within special relativity, it discusses an ideally rigid cylinder that is made to rotate about its axis of symmetry. The radius ''R'' as seen in the laboratory frame is always perpendicular to its motion and should therefore be equal to its value R0 when stationary. However, the circumference (2''R'') should appear Lorentz-contracted to a smaller value than at rest, by the usual factor γ. This leads to the contradiction that ''R'' = ''R''0 ''and'' ''R'' < ''R''0. The has been deepened further by , ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tatyana Pavlovna Ehrenfest
Tatyana Pavlovna Ehrenfest, later van Aardenne-Ehrenfest, (Vienna, October 28, 1905 – Dordrecht, November 29, 1984) was a Dutch mathematician. She was the daughter of Paul Ehrenfest (1880–1933) and Tatyana Alexeyevna Afanasyeva (1876–1964). Under her married name, Tanja van Aardenne-Ehrenfest, she is known for her contributions to De Bruijn sequences, low-discrepancy sequences, and the BEST theorem. Education Tatyana Ehrenfest was born in Vienna and spent her childhood in St Petersburg. In 1912 the Ehrenfests moved to Leiden where her father succeeded H.A. Lorentz as professor at the University of Leiden. Until 1917 she was home schooled; after that, she attended the Gymnasium in Leiden and passed the final exams in 1922. She studied mathematics and physics at the University of Leiden. In 1928 she went to Göttingen where she took courses from Harald Bohr and Max Born. On December 8, 1931, she obtained her Ph.D. in Leiden. After that, she was never employed and, in part ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ehrenfest Model
The Ehrenfest model (or dog–flea model) of diffusion was proposed by Tatiana and Paul Ehrenfest to explain the second law of thermodynamics. The model considers ''N'' particles in two containers. Particles independently change container at a rate ''λ''. If ''X''(''t'') = ''i'' is defined to be the number of particles in one container at time ''t'', then it is a birth–death process with transition rates * q_ = i\, \lambda for ''i'' = 1, 2, ..., ''N'' * q_ = (N-i\,) \lambda for ''i'' = 0, 1, ..., ''N'' – 1 and equilibrium distribution \pi_i = 2^ \tbinom Ni. Mark Kac proved in 1947 that if the initial system state is not equilibrium, then the entropy, given by :H(t) = -\sum_ P(X(t)=i) \log \left( \frac\right), is monotonically increasing (H-theorem). This is a consequence of the convergence to the equilibrium distribution. Interpretation of results Consider that at the beginning all the particles are in one of the containers. It is expected that over time the num ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ehrenfest Equations
Ehrenfest equations (named after Paul Ehrenfest) are equations which describe changes in specific heat capacity and derivatives of specific volume in second-order phase transitions. The Clausius–Clapeyron relation does not make sense for second-order phase transitions,Sivuhin D.V. General physics course. V.2. ''Thermodynamics and molecular physics''. 2005 as both specific entropy and specific volume do not change in second-order phase transitions. Quantitative consideration Ehrenfest equations are the consequence of continuity of specific entropy s and specific volume v, which are first derivatives of specific Gibbs free energy – in second-order phase transitions. If one considers specific entropy s as a function of temperature and pressure, then its differential is: ds = \left( \right)_P dT + \left( \right)_T dP. As \left( \right)_P = , \left( \right)_T = - \left( \right)_P , then the differential of specific entropy also is: d = dT - \left( \right)_P dP, where i= ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ehrenburg (other)
Ehrenburg may refer to: Castles and palaces * Ehrenburg Palace, Bavaria, Germany * Ehrenburg (Brodenbach), Rhineland-Palatinate, Germany * Ehrenburg (Plaue), Thuringia, Germany Places * Ehrenburg, Arizona * Ehrenburg, Lower Saxony, a municipality in the district of Diepholz, Lower Saxony, Germany People * Ilya Ehrenburg (1891–1967), Soviet poet, translator, and writer Other uses * Ehrenbürg The Ehrenbürg is a double-peaked butte on the edge of the Franconian Jura in Bavaria, Germany. It is in the district of Forchheim in Upper Franconia, in the municipalities of Kirchehrenbach, Leutenbach and Wiesenthau. The north peak is the ..., a hill in Bavaria, Germany See also * Ehrenberg (other) {{Disambig, geo, surname ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ehrenstein
Ehrenstein is a German surname. Notable people with the surname include: *Albert Ehrenstein (1886-1950), Hungarian-Austrian writer * David Ehrenstein (born 1947), American critic Ehrenstein may also refer to: *Schloß Ehrenstein (Ehrenstein Castle), a castle in Ohrdruf, Thuringia, Germany. See also *Ehrenstein illusion The Ehrenstein illusion is an optical illusion studied by the German psychologist (1899 – 1961) in which the sides of a square placed inside a pattern of concentric circles take an apparent curved shape. File:Ehrenstein.svg, Original Ehren ... {{surname, Ehrenstein German toponymic surnames German-language surnames Jewish surnames ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ehrenpreis
Ehrenpreis is a surname. Notable people with the surname include: *Leon Ehrenpreis (1930–2010), American mathematician ** Ehrenpreis conjecture **Malgrange–Ehrenpreis theorem *Mordecai Ehrenpreis Mordecai Ehrenpreis (25 June 1869 – 26 February 1951) was a Hebrew author, publisher and Zionist activist. From 1914 until his death he served as chief rabbi of Stockholm. Biography Mordechai (Marcus) Ehrenpreis was born in Lviv. As a young man ..., (1869–1951), Polish-Swedish rabbi See also * Veronica (plant), German name: Ehrenpreis {{surname, Ehrenpreis German-language surnames ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ehrenhaft
Felix Ehrenhaft (24 April 1879 – 4 March 1952) was an Austrian physicist who contributed to atomic physics, to the measurement of electrical charges and to the optical properties of metal colloids. He was known for his maverick and controversial style. His fearless iconoclasm was greatly admired by philosopher Paul Feyerabend. He won the Haitinger Prize of the Austrian Academy of Sciences in 1917. Biography Early years Ehrenhaft was born in Vienna to physician Leopold Ehrenhaft and Louise Eggar, the daughter of a Hungarian industrialist. Ehrenhaft earned his doctorate from the University of Vienna in 1903, working on the optical properties of metallic colloids. He subsequently became assistant to Franz S. Exner. Middle years In 1907, the reality of atoms was still disputed but Albert Einstein and Marian Smoluchowski had both recently given accounts of Brownian motion in liquids, strongly supporting the atomic theory. Though Theodor Svedberg had made important demonstrati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ehrenfeld (other)
Ehrenfeld is "field of honor" in German. Ehrenfeld may refer to: * Ehrenfeld, Pennsylvania * Ehrenfeld, Cologne, borough of the city of Cologne, Germany * Ehrenfeld Group The Ehrenfeld Group (german: Ehrenfelder Gruppe, ; sometimes called the Steinbrück Group, german: Steinbrück-Gruppe, ) was an anti-Nazi resistance group, active in the summer and autumn of 1944. The group, which consisted of over one hundred pe ..., an anti-Nazi resistance group centered in Cologne * Ehrenfeld (surname) {{disambig, geo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
