James Clerk Maxwell - Poems
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James Clerk Maxwell
James Clerk Maxwell JAMES CLERK MAXWELL Perspectives on his Life and Work Edited by raymond flood mark mccartney and andrew whitaker 3 3 Great Clarendon Street, Oxford, OX2 6DP, United Kingdom Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries c Oxford University Press 2014 The moral rights of the authors have been asserted First Edition published in 2014 Impression: 1 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by licence or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this work in any other form and you must impose this same condition on any acquirer Published in the United States of America by Oxford University Press 198 Madison Avenue, New York, NY 10016, United States of America British Library Cataloguing in Publication Data Data available Library of Congress Control Number: 2013942195 ISBN 978–0–19–966437–5 Printed and bound by CPI Group (UK) Ltd, Croydon, CR0 4YY Links to third party websites are provided by Oxford in good faith and for information only. -
Acta Technica Jaurinensis
Acta Technica Jaurinensis Győr, Transactions on Engineering Vol. 3, No. 1 Acta Technica Jaurinensis Vol. 3. No. 1. 2010 The Historical Development of Thermodynamics D. Bozsaky “Széchenyi István” University Department of Architecture and Building Construction, H-9026 Győr, Egyetem tér 1. Phone: +36(96)-503-454, fax: +36(96)-613-595 e-mail: [email protected] Abstract: Thermodynamics as a wide branch of physics had a long historical development from the ancient times to the 20th century. The invention of the thermometer was the first important step that made possible to formulate the first precise speculations on heat. There were no exact theories about the nature of heat for a long time and even the majority of the scientific world in the 18th and the early 19th century viewed heat as a substance and the representatives of the Kinetic Theory were rejected and stayed in the background. The Caloric Theory successfully explained plenty of natural phenomena like gas laws and heat transfer and it was impossible to refute it until the 1850s when the Principle of Conservation of Energy was introduced (Mayer, Joule, Helmholtz). The Second Law of Thermodynamics was discovered soon after that explanation of the tendency of thermodynamic processes and the heat loss of useful heat. The Kinetic Theory of Gases motivated the scientists to introduce the concept of entropy that was a basis to formulate the laws of thermodynamics in a perfect mathematical form and founded a new branch of physics called statistical thermodynamics. The Third Law of Thermodynamics was discovered in the beginning of the 20th century after introducing the concept of thermodynamic potentials and the absolute temperature scale. -
Kinetyczno-Molekularnego Modelu Budowy Materii
Roskal Z. E.: Prekursorzy kinetycznej teorii gazów. Zenon E. Roskal Prekursorzy kinetycznej teorii gazów Twórcy kinetycznej teorii gazów są dobrze znani zarówno fizykom jak i filozo- fom przyrody1, ale wiedza na temat prekursorów tej teorii jest na ogół mniej dostępna i równie słabo rozpowszechniona. Według opinii S. Brusha2 kinetyczno-molekularny model budowy materii, a ściślej kinetyczną teorię gazów3, w istotny sposób inicjuje4 dopiero publikacja niemieckiego przyrodnika A. K. Kröniga z 1856. W tym roku mija zatem dokładnie 150 lat od tego wydarzenia5. Praca Kröniga nie pozostała niezauważona w XIX wieku. Powoływał się na nią – obok prac Joule’a i Clausiusa – J. C. Maxwell6. Twórcy kinetyczno-molekularnego mo- 1 W pierwszej kolejności zaliczamy w poczet twórców tej teorii R. Clausiusa (1822-1888) J. C. Maxwella (1831-1879), L. Boltzmanna (1844-1906) i J. W. Gibbsa (1839-1903). Popularne i skrótowe przedstawienie historii kinetycznej teorii gazów można znaleźć m.in. w E. Mendoza, A Sketch for a History of the Kinetic Theory of gases, ,,Physics Today’’ 14 nr 3 (1961): 36-39. 2 Por. S. G. Brush, The development of the kinetic theory of gases: III. Clausius, ,,Annals of Science’’, 14 (1958): 185-196. Na opinię tę powołuje się m.in. E. Daub, Waterston, Rankine, and Clausius on the Kinetic Theory of Gases, ,,Isis’’ 61 nr 1 (1970): 105, ale mylnie podaje, imię niemieckiego fizyka pisząc o Adolfie Krönigu. Tamże, s. 105. 3 W pierwotnym sformułowaniu tej teorii podanym przez J. C. Maxwella była ona nazywana dynamiczna teorią gazów. Taką nazwę zawierał np. tytuł wykładu Maxwella (Illustrations of the Dynamical Theory of Gases) przedstawionego w Aberdeen w 1859 r. -
TERMODYNAMIK En Kort Historik Christoffer Norberg
ISRN LUTMDN/TMHP-08/3032-SE ISSN 0282-1990 Institutionen f¨or Energivetenskaper TERMODYNAMIK en kort historik Christoffer Norberg Joules skovelanordning fr˚an 1845/7 f¨or att best¨amma den mekaniska v¨armeekvivalenten. Phil. Trans. Roy. Soc. 140 (1850). januari 2008 F¨orord Denna skrift g¨or inga anspr˚ak p˚aatt vara komplett eller utt¨ommande. D¨aremot har jag i m¨ojligaste m˚an f¨ors¨okt vara korrekt n¨ar det g¨aller ˚artal, biografiska data och prioritet av originalarbeten. F¨or en mer utt¨ommande beskrivning (fram till 1800-talets slut) re- kommenderas From Watt to Clausius av Donald Cardwell ([5]). Kommentarer och f¨orslag till korrigeringar emottages tacksamt. Portr¨att ¨ar huvudsakligen h¨amtade fr˚an Internet samt [2, 6, 25, 28, 20, 27], biografiska data v¨asentligen ur [1, 28, 7, 12, 21, 26, 30] och originalreferenser mestadels ur bibliotekss¨okningar, tillg¨angliga tidskrifter inom LU-n¨atet samt [23, 30]. 8 januari 20081 Christoffer Norberg Tel. 046-2228606 Christoff[email protected] Levnads˚ar f¨or 35 pionj¨arer inom termodynamikens historiska utveckling. Tjocka linjer motsvarar ˚aldern 20–65 ˚ar. “But although, as a matter of history, statistical mechanics owes its origin to investigations in thermodynamics, it seems eminently worthy of an independent development, both on account of the elegance and simplicity of its principles, and because it yields new results and places old truths in a new light in departments quite outside of thermodynamics.” Willard Gibbs 1Sedan tryckningen fr˚an januari 2008 har det gjorts ett par uppdateringar av biografiska data, liksom sm¨arre justeringar och till¨agg i texten samt i den bibliografiska delen; 15 december 2013. -
John James Waterston a Pioneer of the Kinetic Theory of Gases Jaime Wisniak*
PARA QUITARLE EL POLVO La química en la historia, para la enseñanza. John James Waterston A pioneer of the kinetic theory of gases Jaime Wisniak* Resumen mostly in straight lines, except when deflected with John James Waterston (1811-1883) puede ser consid- occasional collisions with the walls of the containing erado el último de los pioneros de la teoría cinética. vessel and with each other. The colliding particles El mejoró en forma notable la teoría desarrollada por are supposed to act upon each other only within very Herapath y demostró que la velocidad cuadrática small distances and for very short times before and media de las moléculas de un gas, puro o mezclado, after collision, their motion being free in the intervals está conectada directamente con su temperatura ab- between such distances and times (free path). The soluta. Fue el primero en publicar el teorema de duration of free paths are assumed to be indefinitely equipartición de la energía y demostró cómo su large as compared to the durations of the encounters teoría podía ser utilizada para calcular la velocidad and of the mutual actions. The motion as a whole is del sonido así como el diámetro de una molécula. conserved by reason of the absolute elasticity of the Lamentablemente su publicación fundamental su- moving particles, while the directions of the move- frió el mismo destino que la de Herapath: su rechazo ments of the individual particles are persistently por la Sociedad Real y, por tanto, desconocida por changed by their mutual collisions. Molecules of el mundo científico. Afortunadamente, Lord different gases differ in mass, but all molecules of the Rayleigh la encontró y publicó años después de la same gas have the same mass. -
Efficient Sampling of SAT and SMT Solutions for Testing
Efficient Sampling of SAT and SMT Solutions for Testing and Verification by Rafael Tupynamb´aDutra A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Computer Science in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Koushik Sen, Chair Adjunct Assistant Professor Jonathan Bachrach Professor Sanjit Seshia Professor Theodore Slaman Fall 2019 Efficient Sampling of SAT and SMT Solutions for Testing and Verification This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License by Rafael Tupynamb´aDutra 2019 To view a copy of this license, visit https://creativecommons.org/licenses/by-sa/4.0/ 1 Abstract Efficient Sampling of SAT and SMT Solutions for Testing and Verification by Rafael Tupynamb´aDutra Doctor of Philosophy in Computer Science University of California, Berkeley Professor Koushik Sen, Chair The problem of generating a large number of diverse solutions to a logical constraint has important applications in testing, verification, and synthesis for both software and hardware. The solutions generated could be used as inputs that exercise some target functionality in a program or as random stimuli to a hardware module. This sampling of solutions can be combined with techniques such as fuzz testing, symbolic execution, and constrained-random verification to uncover bugs and vulnerabilities in real programs and hardware designs. Stim- ulus generation, in particular, is an essential part of hardware verification, being at the core of widely applied constrained-random verification techniques. For all these applications, the generation of multiple solutions instead of a single solution can lead to better coverage and higher probability of finding bugs. -
Nascimentos Da Fısica
56 Revista Brasileira de Ensino de F´ısica, vol. 20, no. 1, marc¸o, 1998 Nascimentos da F´ısica Jose´ Maria Filardo Bassalo Departamento de F´ısica da UFPA, 66075-900 - Belem,´ Para´ e-mail:[email protected] home-page: http://amazon.com.br/bassalo Trabalho recebido em 6 de junho de 1996 Com este trabalho, iniciamos uma nova saga. Desta vez, a exemplo do escritor uruguaio Eduardo Hughes Galeano (1940- ) em sua fantastica´ trilogia Memoria´ do Fogo (Nascimentos, 1986; As Caras e as Mascaras´ , 1985; OSeculo´ do Vento, 1988 - Editora Nova Fronteira), apresentaremos em forma de verbetes, e na ordem cronologica´ (seguindo a divisao˜ classica´ das idades historicas),´ os principais fatos (nascimentos) referentes aos conceitos f´ısicos, os quais serao˜ apresentados por temas separados. Para isso, basicamente, usaremos os dados que coletamos nos quatro tomos de nossas Cronicasˆ da F´ısica (EUFPA: 1987, 1990, 1992, 1994) e nas referenciasˆ a´ı indicadas. With this work, we begin a new saga. This time, as the Uruguayan writer Eduardo Hughes Galeano (1940- ) made in his fantastic trilogy Memoria´ do Fogo (Nascimentos, 1986; As Caras e as Mascaras´ , 1985; OSeculo´ do Vento, 1988 - Editora Nova Fronteira), we present in entries, and in chronological order (following the classical division of historical ages), the main events (births) concerned to the physical concepts, which will be presented in separated subjects. For that, basically, we use the data that we gather in our four books Cronicasˆ da F´ısica (EUFPA: 1987, 1990, 1992, 1994) and in the references therein. Idade Moderna: Calor Dalton demonstrou que se um gas´ e´ composto de uma mistura de gases, entao˜ a pressao˜ total e´ a soma das pressoes˜ Primeira Metade do Seculo´ 19 (1801-1850) parciais dos gases componentes. -
Principle of Equipartition of Energy -Dr S P Singh (Dept of Chemistry, a N College, Patna)
Principle of Equipartition of Energy -Dr S P Singh (Dept of Chemistry, A N College, Patna) Historical Background 1843: The equipartition of kinetic energy was proposed by John James Waterston. 1845: more correctly proposed by John James Waterston. 1859: James Clerk Maxwell argued that the kinetic heat energy of a gas is equally divided between linear and rotational energy. ∑ Experimental observations of the specific heat capacities of gases also raised concerns about the validity of the equipartition theorem. ∑ Several explanations of equipartition's failure to account for molar heat capacities were proposed. 1876: Ludwig Boltzmann expanded this principle by showing that the average energy was divided equally among all the independent components of motion in a system. ∑ Boltzmann applied the equipartition theorem to provide a theoretical explanation of the Dulong-Petit Law for the specific heat capacities of solids. 1900: Lord Rayleigh instead put forward a more radical view that the equipartition theorem and the experimental assumption of thermal equilibrium were both correct; to reconcile them, he noted the need for a new principle that would provide an "escape from the destructive simplicity" of the equipartition theorem. 1906: Albert Einstein provided that escape, by showing that these anomalies in the specific heat were due to quantum effects, specifically the quantization of energy in the elastic modes of the solid. 1910: W H Nernst’s measurements of specific heats at low temperatures supported Einstein's theory, and led to the widespread acceptance of quantum theory among physicists. Under the head we deal with the contributions of translational and vibrational motions to the energy and heat capacity of a molecule. -
1 the Course Is Taught on the Basis of Lecture Notes Which Can Be
1 I. SYLLABUS The course is taught on the basis of lecture notes which can be obtained from my web site ( http://www.niu.edu/ veenendaal/563.htm ). These notes contain the following topics: ∼ I. LITERATURE II. INTRODUCTION A. History up to Newton B. Daniel Bernoulli and the foundations of statistical mechanics C. History from Newton to Carnot D. Thermodynamics E. Atomism III. SYSTEMS OF NONINTERACTING ARTICLES OR SPINS A. Two-level spin system B. History of statistical mechanics: Clausius and Maxwell C. Thermal equilibrium and entropy D. History of statistical mechanics: Boltzmann E. Boltzmann factor G. Free energy H. Ideal gas I. Pressure J. The ideal gas law K. Gibbs' paradox L. History of statistical mechanics: Gibbs M. Link to classical partition function IV. Quantum mechanics A. Planck's quantum hypothesis B. Many-particle wavefunctions C. The chemical potential D. Quantum distribution functions V. Systems of interacting particles or spins A. Van der Waals gas B. Critical points C. The Ising model: mean field D. Relations between liquid-gases transition and magnetism E. Ising model: exact solution in one Dimension VI. Applications A. Superfluidity in Helium II 2 A. Literature Thermodynamics R. J. Baxter, Exactly Solved Models in Statistical Mechanics (Academic Press, London, 1982). A. H. Carter, Classical and Statistical Thermodynamics (Prentice Hall, Upper Saddle River, NJ, 2001). R. L. Pathria, Statistical Mechanics (Butterworth-Heinemann, Oxford, 1972). F. Reif, Statistical and Thermal Physics (McGraw-Hill, Boston, 1965). C. Kittel and H. Kroemer, Thermal Physics (W. H. Freeman and Company, New York, 1980) H. E. Stanley, Introduction to Phase Transitions and Critical Phenomena (Oxford University Press, Oxford, 1971). -
Ludwig Boltzmann, Transport Equation and the Second
Ludwig Boltzmann, Transport Equation and the Second law K. P. N. Murthy ∗ Theoretical Studies Section, Materials Science Division, Indira Gandhi Centre for Atomic Research, Kalpakkam 603 102, Tamilnadu, INDIA Abstract Ludwig Boltzmann had a hunch that irreversibility exhibited by a macroscopic system arises from the reversible dynamics of its microscopic constituents. He derived a nonlinear integro-differential equation - now called the Boltzmann equation - for the phase space density of the molecules of a dilute fluid. He showed that the Second law of thermodynamics emerges from Newton’s equations of motion. However Boltzmann realized that stosszahlansatz, em- ployed in the derivation, smuggles in an element of stochasticity into the transport equation. He then proposed a fully stochastic description of entropy which laid the foundation for statis- tical mechanics. Recent developments, embodied in different fluctuation theorems, have shown that Boltzmann’s hunch was, in essence, correct. Based on the invited talk given at the arXiv:cond-mat/0601566v3 [cond-mat.stat-mech] 6 Apr 2006 Sixteenth National Symposium on Radiation Physics, Meenakshi College for Women, Chennai, January 18-20, 2006. See A. K. Jena, R. Mathiyarasu and V. Gopalakrishnan (Eds.), Proc. Sixteenth National Symp. Rad. Phys., Indian Society for Radiation Physics (2006)p1. ∗[email protected] Everything existing in the Universe is the fruit of chance and necessity Diogenes Laertius IX 1 Prologue OLTZMANN transport equation has played an important role in basic and applied sciences. BIt is a nonlinear integro-differential equation for the phase space density of the molecules of a dilute gas. It remains today, an important theoretical technique for investigating non-equilibrium systems. -
CSE370: Introduction to Digital Design
Announcements • Reading assignments CSE 311 Foundations of – 7th Edition, Section 9.1 and pp. 594-601 – 6th Edition, Section 8.1 and pp. 541-548 Computing I – 5th Edition, Section 7.1 and pp. 493-500 Lecture 19 • Upcoming topics – Relations Relations – Finite State Machines Autumn 2011 Autumn 2011 CSE 311 1 Autumn 2011 CSE 311 2 Definition of Relations Relation Examples Let A and B be sets, R1 = {(a, 1), (a, 2), (b, 1), (b, 3), (c, 3)} A binary relation from A to B is a subset of A B R2 = {(x, y) | x ≡ y (mod 5) } Let A be a set, A binary relation on A is a subset of A A R3 = {(c1, c2) | c1 is a prerequisite of c2 } R4 = {(s, c) | student s had taken course c } Autumn 2011 CSE 311 4 Properties of Relations Combining Relations Let R be a relation on A Let R be a relation from A to B R is reflexive iff (a,a) R for every a A Let S be a relation from B to C The composite of R and S, S R is the relation R is symmetric iff (a,b) R implies (b, a) R from A to C defined S R = {(a, c) | b such that (a,b) R and (b,c) S} R is antisymmetric iff (a,b) R and a b implies (b,a) / R R is transitive iff (a,b) R and (b, c) R implies (a, c) R Examples Examples (a,b) Parent: b is a parent of a Using the relations: Parent, Child, Brother, (a,b) Sister: b is a sister of a Sister, Sibling, Father, Mother express What is Parent Sister? Uncle: b is an uncle of a What is Sister Parent? Cousin: b is a cousin of a S R = {(a, c) | b such that (a,b) R and (b,c) S} Powers of a Relation How is Anderson related to Bernoulli? R2 = R R = {(a, c) | b such -
Mathematicians Timeline
Rikitar¯oFujisawa Otto Hesse Kunihiko Kodaira Friedrich Shottky Viktor Bunyakovsky Pavel Aleksandrov Hermann Schwarz Mikhail Ostrogradsky Alexey Krylov Heinrich Martin Weber Nikolai Lobachevsky David Hilbert Paul Bachmann Felix Klein Rudolf Lipschitz Gottlob Frege G Perelman Elwin Bruno Christoffel Max Noether Sergei Novikov Heinrich Eduard Heine Paul Bernays Richard Dedekind Yuri Manin Carl Borchardt Ivan Lappo-Danilevskii Georg F B Riemann Emmy Noether Vladimir Arnold Sergey Bernstein Gotthold Eisenstein Edmund Landau Issai Schur Leoplod Kronecker Paul Halmos Hermann Minkowski Hermann von Helmholtz Paul Erd}os Rikitar¯oFujisawa Otto Hesse Kunihiko Kodaira Vladimir Steklov Karl Weierstrass Kurt G¨odel Friedrich Shottky Viktor Bunyakovsky Pavel Aleksandrov Andrei Markov Ernst Eduard Kummer Alexander Grothendieck Hermann Schwarz Mikhail Ostrogradsky Alexey Krylov Sofia Kovalevskya Andrey Kolmogorov Moritz Stern Friedrich Hirzebruch Heinrich Martin Weber Nikolai Lobachevsky David Hilbert Georg Cantor Carl Goldschmidt Ferdinand von Lindemann Paul Bachmann Felix Klein Pafnuti Chebyshev Oscar Zariski Carl Gustav Jacobi F Georg Frobenius Peter Lax Rudolf Lipschitz Gottlob Frege G Perelman Solomon Lefschetz Julius Pl¨ucker Hermann Weyl Elwin Bruno Christoffel Max Noether Sergei Novikov Karl von Staudt Eugene Wigner Martin Ohm Emil Artin Heinrich Eduard Heine Paul Bernays Richard Dedekind Yuri Manin 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000 Carl Borchardt Ivan Lappo-Danilevskii Georg F B Riemann Emmy Noether Vladimir Arnold August Ferdinand