DOCSLIB.ORG

Introduction to Soliton Theory: Applications to Mechanics Fundamental Theories of Physics

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Introduction to Soliton Theory: Applications to Mechanics Fundamental Theories of Physics Introduction to Soliton Theory: Applications to Mechanics Fundamental Theories of Physics An International Book Series on The Fundamental Theories of Physics: Their Clarification, Development and Application Editor: ALWYN VAN DER MERWE, University of Denver, U.S.A. Editorial Advisory Board: GIANCARLO GHIRARDI, University of Trieste, Italy LAWRENCE P. HORWITZ, Tel-Aviv University, Israel BRIAN D. JOSEPHSON, University of Cambridge, U.K. CLIVE KILMISTER, University of London, U.K. PEKKA J. LAHTI, University of Turku, Finland ASHER PERES, Israel Institute of Technology, Israel EDUARD PRUGOVECKI, University of Toronto, Canada FRANCO SELLERI, Università di Bara, Italy TONY SUDBURY, University of York, U.K. HANS-JÜRGEN TREDER, Zentralinstitut für Astrophysik der Akademie der Wissenschaften, Germany Volume 143 Introduction to Soliton Theory: Applications to Mechanics by Ligia Munteanu Institute of Solid Mechanics, Romanian Academy, Bucharest, Romania and Stefania Donescu Technical University of Civil Engineering, Department of Mathematics, Bucharest, Romania KLUWER ACADEMIC PUBLISHERS NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW eBook ISBN: 1-4020-2577-7 Print ISBN: 1-4020-2576-9 ©2005 Springer Science + Business Media, Inc. Print ©2004 Kluwer Academic Publishers Dordrecht All rights reserved No part of this eBook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Springer's eBookstore at: http://ebooks.kluweronline.com and the Springer Global Website Online at: http://www.springeronline.com Contents Preface ix Part 1. INTRODUCTION TO SOLITON THEORY 1. MATHEMATICAL METHODS 1 1.1 Scope of the chapter 1 1.2 Scattering theory 1 1.3 Inverse scattering theory 12 1.4 Cnoidal method 17 1.5 Hirota method 25 1.6 Linear equivalence method (LEM) 31 1.7 Bäcklund transformation 39 1.8 Painlevé analysis 46 2. SOME PROPERTIES OF NONLINEAR EQUATIONS 53 2.1 Scope of the chapter 53 2.2 General properties of the linear waves 53 2.3 Some properties of nonlinear equations 59 2.4 Symmetry groups of nonlinear equations 62 2.5 Noether theorem 66 2.6 Inverse Lagrange problem 69 2.7 Recursion operators 73 3. SOLITONS AND NONLINEAR EQUATIONS 78 3.1 Scope of the chapter 78 3.2 Korteweg and de Vries equation (KdV) 78 3.3 Derivation of the KdV equation 86 vi INTRODUCTION TO SOLITON THEORY: APPLICATIONS TO MECHANICS 3.4 Scattering problem for the KdV equation 90 3.5 Inverse scattering problem for the KdV equation 95 3.6 Multi-soliton solutions of the KdV equation 101 3.7 Boussinesq, modified KdV and Burgers equations 107 3.8 The sine-Gordon and Schrödinger equations 112 3.9 Tricomi system and the simple pendulum 115 121 Part 2. APPLICATIONS TO MECHANICS 4. STATICS AND DYNAMICS OF THE THIN ELASTIC ROD 121 4.1 Scope of the chapter 121 4.2 Fundamental equations 122 4.3 The equivalence theorem 132 4.4 Exact solutions of the equilibrium equations 134 4.5 Exact solutions of the motion equations 146 5. VIBRATIONS OF THIN ELASTIC RODS 149 5.1 Scope of the chapter 149 5.2 Linear and nonlinear vibrations 149 5.3 Transverse vibrations of the helical rod 155 5.4 A special class of DRIP media 159 5.5 Interaction of waves 163 5.6 Vibrations of a heterogeneous string 166 6. THE COUPLED PENDULUM 173 6.1 Scope of the chapter 173 6.2 Motion equations. Problem E1 173 6.3 Problem E2 177 6.4 LEM solutions of the system E2 180 6.5 Cnoidal solutions 185 6.6 Modal interaction in periodic structures 191 7. DYNAMICS OF THE LEFT VENTRICLE 197 7.1 Scope of the chapter 197 7.2 The mathematical model 198 7.3 Cnoidal solutions 206 7.4 Numerical results 209 7.5 A nonlinear system with essential energy influx 213 CONTENTS vii 8. THE FLOW OF BLOOD IN ARTERIES 220 8.1 Scope of the chapter 220 8.2 A nonlinear model of blood flow in arteries 221 8.3 Two-soliton solutions 228 8.4 A micropolar model of blood flow in arteries 235 9. INTERMODAL INTERACTION OF WAVES 242 9.1 Scope of the chapter 242 9.2 A plate with Cantor-like structure 243 9.3 The eigenvalue problem 248 9.4 Subharmonic waves generation 249 9.5 Internal solitary waves in a stratified fluid 255 9.6 The motion of a micropolar fluid in inclined open channels 259 9.7 Cnoidal solutions 265 9.8 The effect of surface tension on the solitary waves 269 10. ON THE TZITZEICA SURFACES AND SOME RELATED 273 PROBLEMS 10.1 Scope of the chapter 273 10.2 Tzitzeica surfaces 273 10.3 Symmetry group theory applied to Tzitzeica equations 276 10.4 The relation between the forced oscillator and a Tzitzeica 283 curve 10.5 Sound propagation in a nonlinear medium 285 10.6 The pseudospherical reduction of a nonlinear problem 291 References 298 Index 305 Preface This monograph is planned to provide the application of the soliton theory to solve certain practical problems selected from the fields of solid mechanics, fluid mechanics and biomechanics. The work is based mainly on the authors’ research carried out at their home institutes, and on some specified, significant results existing in the published literature. The methodology to study a given evolution equation is to seek the waves of permanent form, to test whether it possesses any symmetry properties, and whether it is stable and solitonic in nature. Students of physics, applied mathematics, and engineering are usually exposed to various branches of nonlinear mechanics, especially to the soliton theory. The soliton is regarded as an entity, a quasi-particle, which conserves its character and interacts with the surroundings and other solitons as a particle. It is related to a strange phenomenon, which consists in the propagation of certain waves without attenuation in dissipative media. This phenomenon has been known for about 200 years (it was described, for example, by the Joule Verne's novel Les histoires de Jean Marie Cabidoulin, Éd. Hetzel), but its detailed quantitative description became possible only in the last 30 years due to the exceptional development of computers. The discovery of the physical soliton is attributed to John Scott Russell. In 1834, Russell was observing a boat being drawn along a narrow channel by a pair of horses. He followed it on horseback and observed an amazing phenomenon: when the boat suddenly stopped, a bow wave detached from the boat and rolled forward with great velocity, having the shape of a large solitary elevation, with a rounded well-defined heap of water. The solitary wave continued its motion along the channel without change of form or velocity. The scientist followed it on horseback as it propagated at about eight or nine miles an hour, but after one or two miles he lost it. Russell was convinced that he had observed an important phenomenon, and he built an experimental tank in his garden to continue the studies of what he named the wave of translation. The wave of translation was regarded as a curiosity until the 1960s, when scientists began to use computers to study nonlinear wave propagation. The discovery of mathematical solutions started with the analysis of nonlinear partial differential equations, such as the work of Boussinesq and Rayleigh, independently, in the 1870s. Boussinesq and Rayleigh explained theoretically the Russell observation and later reproduction in a laboratory experiment. Korteweg and de Vries derived in 1895 the equation for water waves in shallow channels, and confirmed the existence of solitons. x INTRODUCTION TO SOLITON THEORY : APPLICATIONS TO MECHANICS An explosion of works occurred when it was discovered that many phenomena in physics, electronics, mechanics and biology might be described by using the theory of solitons. Nonlinear mechanics is often faced with the unexpected appearance of chaos or order. Within this framework the soliton plays the role of order. The discovery of orderly stable pulses as an effect of nonlinearity is surprising. The results obtained in the linear theory of waves, by ignoring the nonlinear parts, are most frequently too far from reality to be useful. The linearisation misses an important phenomenon, solitons, which are waves, which maintain their identity indefinitely just when we most expect that dispersion effects will lead to their disappearance. The soliton as the solution of the completely integrable partial differential equations are stable in collision process even if interaction between the solitons takes place in a nonlinear way. The unexpected results obtained in 1955 by Fermi, Pasta and Ulam in the study of a nonlinear anharmonic oscillator, generate much of the work on solitons. Their attempt to demonstrate that the nonlinear interactions between the normal modes of vibrations lead to the energy of the system being evenly distributed throughout all the modes, as a result of the equipartition of energy, failed. The energy does not spread throughout all the modes but recollect after a time in the initial mode where it was when the experiment was started. In 1965, Zabusky and Kruskal approached the Fermi, Pasta and Ulam problem from the continuum point of view. They rederived the Korteweg and de Vries equation and found its stable wave solutions by numerical computation. They showed that these solutions preserve their shape and velocities after two of them collide, interact and then spread apart again. They named such waves solitons. Gardner, Green, Kruskal and Miura introduced in 1974 the Inverse Scattering Transform to integrate nonlinear evolution equations. The conserved features of solitons become intimately related to the notion of symmetry and to the construction of pseudospherical surfaces. The Gauss–Weingarten system for the pseudospherical surfaces yields sine-Gordon equation, providing a bridge to soliton theory.
Load more

Recommended publications
  • Finslerian Geometries Fundamental Theories of Physics
    Finslerian Geometries Fundamental Theories of Physics An International Book Series on The Fundamental Theories of Physics: Their Clarification, Development and Application Editor: ALWYN VAN DER MERWE, University of Denver, U.S.A. Editorial Advisory Board: LAWRENCE P. HORWITZ, Tel-Aviv University, Israel BRIAN D. JOSEPHSON, University of Cambridge, u.K. CLIVE KILMISTER, University of London, U.K. PEKKA J. LAHTI, University of Turku, Finland GUNTER LUDWIG, Philipps-Universitiit, Marburg, Germany NATHAN ROSEN, Israel Institute of Technology, Israel ASHER PERES, Israel Institute of Technology, Israel EDUARD PRUGOVECKI, University of Toronto, Canada MENDEL SACHS, State University of New York at Buffalo, U.S.A. ABDUS SALAM, International Centre for Theoretical Physics, Trieste, Italy HANS-JURGEN TREDER, Zentralinstitut fur Astrophysik der Akademie der Wissenschaften, Germany Volume 109 Finslerian Geometries A Meeting of Minds edited by P.L. Antonell i DeJXlrlmem of Mathematical Sciences, University ofAlberta, EdmonlOn. Alberta, Canada SPRINGER-SCIENCE+BUSINESS MEDIA, B.V. A C .I.P. Catalogue record for this book is available from the Library of Congress. ISBN 978-94-010-5838-4 ISBN 978-94-011-4235-9 (eBook) DOI 10.1007/978-94-011-4235-9 Printed an arid1ree paper AH Rights Reserved © 2000 Springer Science+Business Media Dordrecht Originally published by K!uwer Academic Publishers in 2000 Soticovcr repri Il! of the hardcover l s( cd ition in 20()(} No part of the material protected by this copyright natice may be reproduced Of utilized in any farm Of by any means, electronic or mechanical, induding pholocopying, recording or by any informat ion slorage and relrieval system, withoUI wrinen permissian from the copyright owner.
    [Show full text]
  • Can Croatia Join Europe As Competitive Knowledge-Based Society by 2010?
    Editorial Can Croatia Join Europe as Competitive Knowledge-based Society by 2010? Mladen Petrovečki1, Vladimir Paar2, Dragan Primorac1 1Ministry of Science, The 21st century has brought important changes in the paradigms of eco- Education and Sports of the nomic development, one of them being a shift toward recognizing knowl- Republic of Croatia, Zagreb, Croatia edge and information as the most important factors of today. The European 2Croatian Academy of Union (EU) has been working hard to become the most competitive knowl- Sciences and Arts, edge-based society in the world, and Croatia, an EU candidate country, has Zagreb, Croatia been faced with a similar task. To establish itself as one of the best knowl- edge-based country in the Eastern European region over the next four years, Croatia realized it has to create an education and science system correspon- dent with European standards and sensitive to labor market needs. For that purpose, the Croatian Ministry of Science, Education, and Sports (MSES) has created and started implementing a complex strategy, consisting of the following key components: the reform of education system in accordance with the Bologna Declaration; stimulation of scientific production by sup- porting national and international research projects; reversing the “brain drain” into “brain gain” and strengthening the links between science and technology; and informatization of the whole education and science sys- tem. In this comprehensive report, we describe the implementation of these > Correspondence to: measures, whose coordination with the EU goals presents a challenge, as well as an opportunity for Croatia to become a knowledge-based society Mladen Petrovečki Assistant Minister for Science by 2010.
    [Show full text]
  • Introduction to Soliton Theory: Applications to Mechanics Fundamental Theories of Physics
    Introduction to Soliton Theory: Applications to Mechanics Fundamental Theories of Physics An International Book Series on The Fundamental Theories of Physics: Their Clarification, Development and Application Editor: ALWYN VAN DER MERWE, University of Denver, U.S.A. Editorial Advisory Board: GIANCARLO GHIRARDI, University of Trieste, Italy LAWRENCE P. HORWITZ, Tel-Aviv University, Israel BRIAN D. JOSEPHSON, University of Cambridge, U.K. CLIVE KILMISTER, University of London, U.K. PEKKA J. LAHTI, University of Turku, Finland ASHER PERES, Israel Institute of Technology, Israel EDUARD PRUGOVECKI, University of Toronto, Canada FRANCO SELLERI, Università di Bara, Italy TONY SUDBURY, University of York, U.K. HANS-JÜRGEN TREDER, Zentralinstitut für Astrophysik der Akademie der Wissenschaften, Germany Volume 143 Introduction to Soliton Theory: Applications to Mechanics by Ligia Munteanu Institute of Solid Mechanics, Romanian Academy, Bucharest, Romania and Stefania Donescu Technical University of Civil Engineering, Department of Mathematics, Bucharest, Romania KLUWER ACADEMIC PUBLISHERS NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW eBook ISBN: 1-4020-2577-7 Print ISBN: 1-4020-2576-9 ©2005 Springer Science + Business Media, Inc. Print ©2004 Kluwer Academic Publishers Dordrecht All rights reserved No part of this eBook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Springer's eBookstore at: http://ebooks.kluweronline.com and the Springer Global Website Online at: http://www.springeronline.com Contents Preface ix Part 1. INTRODUCTION TO SOLITON THEORY 1. MATHEMATICAL METHODS 1 1.1 Scope of the chapter 1 1.2 Scattering theory 1 1.3 Inverse scattering theory 12 1.4 Cnoidal method 17 1.5 Hirota method 25 1.6 Linear equivalence method (LEM) 31 1.7 Bäcklund transformation 39 1.8 Painlevé analysis 46 2.
    [Show full text]
  • Relativity in Rotating Frames Fundamental Theories of Physics
    Relativity in Rotating Frames Fundamental Theories of Physics An International Book Series on The Fundamental Theories of Physics: Their Clarification, Development and Application Editor: ALWYN VAN DER MERWE, University of Denver, U.S.A. Editorial Advisory Board: JAMES T. CUSHING, University of Notre Dame, U.S.A. GIANCARLO GHIRARDI, University of Trieste, Italy LAWRENCE P. HORWITZ, Tel-Aviv University, Israel BRIAN D. JOSEPHSON, University of Cambridge, U.K. CLIVE KILMISTER, University of London, U.K. PEKKA J. LAHTI, University of Turku, Finland ASHER PERES, Israel Institute of Technology, Israel EDUARD PRUGOVECKI, University of Toronto, Canada TONY SUDBURY, University of York, U.K. HANS-JÜRGEN TREDER, Zentralinstitut für Astrophysik der Akademie der Wissenschaften, Germany Volume 135 Relativity in Rotating Frames Relativistic Physics in Rotating Reference Frames Edited by Guido Rizzi Politecnico di Torino and Istituto Nazionale di Fisica Nucleare, Torino, Italy and Matteo Luca Ruggiero Politecnico di Torino and Istituto Nazionale di Fisica Nucleare, Torino, Italy SPRINGER-SCIENCE+BUSINESS MEDIA, B.V. A C.I.P. Catalogue record for this book is available from the Library of Congress. ISBN 978-90-481-6514-8 ISBN 978-94-017-0528-8 (eBook) DOI 10.1007/978-94-017-0528-8 Printed on acid-free paper All Rights Reserved © 2004 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 2004 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work.
    [Show full text]
  • Notices of the American Mathematical Society
    OF THE AMERICAN MATHEMATICAL SOCIETY Edited by Everett Pitcher and Gordon L. Walker CONTENTS MEETINGS Calendar of Meetings ................ 578 Program for the june Meeting in Corvallis, Oregon 579 Abstracts for the Meeting: Pages 611-617 PRELIMINARY ANNOUNCEMENTS OF MEETINGS 583 NEWS ITEMS AND ANNOUNCEMENTS . 582, 589 MATHEMATICAL OFFPRINT SERVICE 590 LETTERS TO THE EDITOR . 592 SPECIAL MEETINGS INFORMATION CENTER 595 MEMORANDA TO MEMBERS . 600 Policy on Recruitment PERSONAL ITEMS 601 NEW AMS PUBLICATIONS .. 605 ABSTRACTS OF CONTRIBUTED PAPERS 608 ERRATA TO ABSTRACTS ........• 617 ABSTRACTS PRESENTED TO THE SOCIETY 618 INDEX TO ADVERTISERS. 687 RESERVATION FORM •.. 688 MEETINGS Calendar of Meetings NOTE: This Calendar lists all of the meetings which have been approved by the Council up to the date at which this issue of the cJ{oticti) was sent to press. The summer and annual meetings are joint meetings of the Mathematical Association of America and the American Mathematical Society. The meeting dates which fall rather far in the future are subject to change. This is particularly true of the meetings to which no numbers have yet been assigned. Meet· Deadline ing Date Place for No. Abstracts• 687 August 30-September 3, 1171 University Park, Pennsylvania July 7, I 'n I (76th Summer Meeting) 688 October 30, 1971 Cambridge, Massachusetts Sept. 9, 1971 689 November 19-20, I971 Auburn, Alabama Oct. 4, 1971 690 November 27, 1971 Milwaukee, Wisconsin Oct. 4, 1971 691 January 17-21, 1972 Las Vegas, Nevada Nov. 4, 1971 (78th Annual Meeting) March 29-April 1, 1972 St. Louis, Missouri August 28-September 1, 1972 Hanover, New Hampshire (77th Summer Meeting) January 25-29, 1973 Dallas, Texas (79:h Annual Meeting) August 20-24, 1973 Missoula, Montana (78th Summer Meeting) January 13-19, 1974 San Francisco, California (80th Annual Meeting) January 23-27, 1975 Washington, D.C.
    [Show full text]
  • Relativistic Elementary Particles 47 1
    Kinematical Theory of Spinning Particles Fundamental Theories of Physics An International Book Series on The Fundamental Theories of Physics: Their Clarification, Development and Application Editor: ALWYN VAN DER MERWE, University of Denver, U.S.A. Editorial Advisory Board: JAMES T. CUSHING, University of Notre Dame, U.S.A. GIANCARLO GHIRARDI, University of Trieste, Italy LAWRENCE P. HORWITZ, Tel-Aviv University, Israel BRIAN D. JOSEPHSON, University of Cambridge, U.K. CLIVE KILMISTER, University of London, U.K. PEKKA J. LAHTI, University of Turku, Finland ASHER PERES, Israel Institute of Technology, Israel EDUARD PRUGOVECKI, University of Toronto, Canada TONY SUDBURY, University of York, U.K. HANS-JÜRGEN TREDER, Zentralinstitut für Astrophysik der Akademie der Wissenschaften, Germany Volume 116 Kinematical Theory of Spinning Particles Classical and Quantum Mechanical Formalism of Elementary Particles by Martin Rivas The University of the Basque Country, Bilbao, Spain KLUWER ACADEMIC PUBLISHERS NEW YORK,BOSTON, DORDRECHT,LONDON, MOSCOW eBook ISBN 0-306-47133-7 Print ISBN 0-792-36824-X ©2002 Kluwer Academic Publishers New York, Boston, Dordrecht, London, Moscow All rights reserved No part of this eBook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Kluwer Online at: http://www.kluweronline.com and Kluwer's eBookstore at: http://www.ebooks.kluweronline.com To Merche This page intentionally left blank. Contents List of Figures xi Acknowledgment xvii Introduction xix 1. GENERAL FORMALISM 1 1. Introduction 1 1 . 1 Kinematics and dynamics 3 2 . Variational versus Newtonian formalism 4 3.
    [Show full text]
  • Assistantships and Fellowships in the Mathematical Sciences in 1982-1983 Supplementary List
    il16 and 17)-Page 257 ta~Aellnformation- Page 27 5 ematical Society < 2. c 3 II> J~ cz 3 i"... w Calendar of AMS Meetings THIS CALENDAR lists all meetings which have been approved by the Council prior to the date this issue of the Notices was sent to press. The summer and annual meetings are joint meetings of the Mathematical Association of America and the Ameri· can Mathematical Society. The meeting dates which fall rather far in the future are subject to change; this is particularly true of meetings to which no numbers have yet been assigned. Programs of the meetings will appear in the issues indicated below. First and second announcements of the meetings will have appeared in earlier issues. ABSTRACTS OF PAPERS presented at a meeting of the Society are published in the journal Abstracts of papers presented to the American Mathematical Society in the issue corresponding to that of the Notices which contains the program of the meet­ ing. Abstracts should be submitted on special forms which are available in many departments of mathematics and from the office of the Society in Providence. Abstracts of papers to be presented at the meeting must be received at the headquarters of the Society in Providence, Rhode Island, on or before the deadline given below for the meeting. Note that the deadline for ab· stracts submitted for consideration for presentation at special sessions is usually three weeks earlier than that specified below. For additional information consult the meeting announcement and the list of organizers of special sessions.
    [Show full text]
  • A Selected Bibliography of Publications By, and About, Paul Adrien Maurice Dirac
    A Selected Bibliography of Publications by, and about, Paul Adrien Maurice Dirac Nelson H. F. Beebe University of Utah Department of Mathematics, 110 LCB 155 S 1400 E RM 233 Salt Lake City, UT 84112-0090 USA Tel: +1 801 581 5254 FAX: +1 801 581 4148 E-mail: [email protected], [email protected], [email protected] (Internet) WWW URL: http://www.math.utah.edu/~beebe/ 08 June 2021 Version 1.195 Title word cross-reference (1 + 1) [Das93]. (2 + 1) [JM99]. −1=2 [CT67a]. −1=2; 1=2; 3=2; 5=2 [Mac98]. − 1 1 2 ; 2 [CT67b]. 1 [CG07]. 1 + 1 [Fei02]. 1=2 [CT67a, FA01, Ogu96, dB51, dB52a]. 2:7◦ [Noe73]. $250.00 [War96]. $26.00 [Ryc17]. $29.95 [RS10, Dys10]. 3 [RRS06]. 3 + 1 [Nak00]. 3 + 2 [Dir63b]. 3=2 [CT67a]. $44.50 [Dre90]. $49.50 [Sch85]. $7.50 [Suc67]. 6 [DN96]. α [BM98, LT04]. α, β; γ; δ [Som36]. c [IC04, MBS02, Mag15]. D [DSP03]. δ ˇ 2 3 [DES89, IP56, IP57, Lut07, Sch72]. e [IC04, MBS02]. e [CP68]. [GGS04]. 2 + [CT67b]. G [AWW 81, Dir75f, Dir78b, Dir80g, Dir82f]. GF [FA10]. m+2 s 3 Gr2(C ) [Mil98].RH (R ) [EV97].h ¯ [IC04]. mp=me [BBSF10, FK07]. F ∞ p −η p(η)=1=Γ(p +1) 0 [ =(1 + e )]d [GFG01]. SU (2) [yRSBSV99]. H2 [SBK+08]. N [Ata89, KY01, MHN98, MB90, Mor85, Won90]. ∇2n=n [MHN98]. ∇n=n [MHN98]. π [JT10]. q [CPV10, JT10]. R [Szm98, Szm99]. Rn [Bet83]. rt [BBR85]. s>1 [EV97]. SL(2; C) [Hos82, Hos83]. SO(4) [LH86].
    [Show full text]
  • July 2012 Contents
    International Association of Mathematical Physics News Bulletin July 2012 Contents International Association of Mathematical Physics News Bulletin, July 2012 Contents Mathematical Physics at Princeton in the 1970s 3 Celebration of Elliott Lieb’s 80th birthday in Berlin 9 On ground-state phases of quantum spin systems 12 News from the IAMP Executive Committee 18 Bulletin editor Valentin A. Zagrebnov Editorial board Evans Harrell, Masao Hirokawa, David Krejˇciˇr´ık, Jan Philip Solovej Contacts http://www.iamp.org and e-mail: [email protected] Cover photo: Princeton University. Holder Hall, Court and Tower. The views expressed in this IAMP News Bulletin are those of the authors and do not necessarily represent those of the IAMP Executive Committee, Editor or Editorial board. Any complete or partial publication or reproduction made without the consent of the author or of his successors in title or assigns shall be unlawful. All reproduction rights are henceforth reserved, and mention of the IAMP News Bulletin is obligatory in the reference. (Art.L.122-4 of the Code of Intellectual Property). ISSN 2304-7348 News Bulletin (International Association of Mathematical Physics) 2 IAMP News Bulletin, July 2012 Mathematical Physics at Princeton in the 1970s Mathematical Physics at Princeton in the 1970s by Barry Simon (Pasadena, USA) Barry Simon got his PhD. in Physics under Arthur Wightman in 1970, was on the Princeton Faculty for 12 years and, since 1981, has been at Caltech where he is currently IBM Professor of Mathematics and Theoretical Physics and Executive Officer (aka Chair) of Mathematics. He is the author of 384 research articles and 16 scientific monographs including the Reed-Simon series.
    [Show full text]
  • April 2013 2) Treasurer Report
    International Association of Mathematical Physics ΜUΦ Invitation Dear IAMP Members, according to Part I of the By-Laws we announce a meeting of the IAMP General Assembly. It will convene on Monday August 3 in the Meridian Hall of the Clarion NewsCongress Hotel in Prague opening Bulletin at 8pm. The agenda: 1) President report April 2013 2) Treasurer report 3) The ICMP 2012 a) Presentation of the bids b) Discussion and informal vote 4) General discussion It is important for our Association that you attend and take active part in the meeting. We are looking forward to seeing you there. With best wishes, Pavel Exner, President Jan Philip Solovej, Secretary Contents International Association of Mathematical Physics News Bulletin, April 2013 Contents Nine Lessons of my Teacher, Arthur Strong Wightman3 Quantum ergodicity and beyond. With a gallery of pictures. 10 Algebraic tools for evolutionary biology 29 Obituary: G´erardGustav Emch 44 News from the IAMP Executive Committee 46 Bulletin Editor Editorial Board Valentin A. Zagrebnov Rafael Benguria, Evans Harrell, Masao Hirokawa, Manfred Salmhofer, Robert Sims Contacts. http://www.iamp.org and e-mail: [email protected] Cover picture: Circle billiards; see the article of Anantharaman and B¨acker in this issue The views expressed in this IAMP News Bulletin are those of the authors and do not necessarily represent those of the IAMP Executive Committee, Editor or Editorial Board. Any complete or partial performance or reproduction made without the consent of the author or of his successors in title or assigns shall be unlawful. All reproduction rights are henceforth reserved, and mention of the IAMP News Bulletin is obligatory in the reference.
    [Show full text]
  • January 2013 2) Treasurer Report
    International Association of Mathematical Physics ΜUΦ Invitation Dear IAMP Members, according to Part I of the By-Laws we announce a meeting of the IAMP General Assembly. It will convene on Monday August 3 in the Meridian Hall of the Clarion NewsCongress Hotel in Prague opening Bulletin at 8pm. The agenda: 1) President reportJanuary 2013 2) Treasurer report 3) The ICMP 2012 a) Presentation of the bids b) Discussion and informal vote 4) General discussion It is important for our Association that you attend and take active part in the meeting. We are looking forward to seeing you there. With best wishes, Pavel Exner, President Jan Philip Solovej, Secretary Happy New Year 2013 Contents International Association of Mathematical Physics News Bulletin, January 2013 Contents About the Code of Practice of the European Mathematical Society3 The Kardar-Parisi-Zhang Equation and Universality Class6 Some Simple Questions From Nonequilibrium Physics 17 The Myth of Academic Excellence and Scientific Curiosity 26 Obituary: Nicolae Angelescu 32 Obituary: Arthur S. Wightman 34 News from the IAMP Executive Committee 37 Bulletin Editor Editorial Board Valentin A. Zagrebnov Rafael Benguria, Evans Harrell, Masao Hirokawa, Manfred Salmhofer, Robert Sims Contacts. http://www.iamp.org and e-mail: [email protected] Cover photo: Heidelberg: view of the castle and the old bridge. The views expressed in this IAMP News Bulletin are those of the authors and do not necessarily represent those of the IAMP Executive Committee, Editor or Editorial Board. Any complete or partial performance or reproduction made without the consent of the author or of his successors in title or assigns shall be unlawful.
    [Show full text]
  • Can Croatia Join Europe As Competitive Knowledge-Based Society by 2010?
    Editorial Can Croatia Join Europe as Competitive Knowledge-based Society by 2010? Mladen Petrovečki1, Vladimir Paar2, Dragan Primorac1 1Ministry of Science, The 21st century has brought important changes in the paradigms of eco- Education and Sports of the nomic development, one of them being a shift toward recognizing knowl- Republic of Croatia, Zagreb, Croatia edge and information as the most important factors of today. The European 2Croatian Academy of Union (EU) has been working hard to become the most competitive knowl- Sciences and Arts, edge-based society in the world, and Croatia, an EU candidate country, has Zagreb, Croatia been faced with a similar task. To establish itself as one of the best knowl- edge-based country in the Eastern European region over the next four years, Croatia realized it has to create an education and science system correspon- dent with European standards and sensitive to labor market needs. For that purpose, the Croatian Ministry of Science, Education, and Sports (MSES) has created and started implementing a complex strategy, consisting of the following key components: the reform of education system in accordance with the Bologna Declaration; stimulation of scientific production by sup- porting national and international research projects; reversing the “brain drain” into “brain gain” and strengthening the links between science and technology; and informatization of the whole education and science sys- tem. In this comprehensive report, we describe the implementation of these > Correspondence to: measures, whose coordination with the EU goals presents a challenge, as well as an opportunity for Croatia to become a knowledge-based society Mladen Petrovečki Assistant Minister for Science by 2010.
    [Show full text]