Instabilities and Nonequilibrium Structures IV

Transcription

1 Instabilities and Nonequilibrium Structures IV

2 Mathematics and Its Applications Managing Editor: M. HAZEWINKEL Centre for Mathematics and Computer Science, Amsterdam, The Netherlands Volume 267

3 Instabilities and Nonequilibrium Structures IV edited by E. Tirapegui Facultad de Ciencias Fisicas y Matemdticas, Universidad de Chile, Santiago, Chile and W. Zeller Instituto de Flsica, Universidad Catolica de Valparafso, Valparafso, Chile SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.

4 A C.I.P. Catalogue record for this book is available from the Library of Congress. ISBN ISBN (ebook) DOI / Printed on acid-free paper AII Rights Reserved 1993 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 1993 Softcover reprint ofthe hardcover Ist edition 1993 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner.

5 TABLE OF CONTENTS FOREWORD LIST OF SPONSORS OF THE WORKSHOP PREFACE ix x 1 PART I STATISTICAL MECHANICS AND RELATED TOPICS 3 NONEQUILIBRIUM POTENTIALS FOR PERIOD DOUBLING 5 R. Graham and A. Hamm ON SOLITON INSTABILITIES IN DIMENSIONAL 15 INTEGRABLE SYSTEMS F. Lambert, J. Springael and R. Willox A CATASTROPHIC VIEW OF QUASI AND PSEUDOSPIN PHYSICS 27 E.S. Hernandez AN APPROACH TO QUANTUM DISSIPATION 37 G. Crespo, A.M. Kowalski, A. Plastino and A.N. Proto ARNOLD TONGUES IN A PERIODICALLY PERTURBED LOGISTIC 47 OSCILLATOR J. Rossler, E. Lazo and M. Kiwi AXISYMMETRIC COHERENT VORTEX STATES IN AC DRIVEN 53 JOSEPHSON JUNCTIONS ARRAYS D. Domfnguez and J. V. Jose COMMENTS ON THE TOPOLOGICAL ORGANIZATION OF 3D-FLOWS 69 AND 2D-MAPS H.G. Solari, M.A. Natiello, B.G. Mindlin and R. Gilmore PHASE BISTABILITY AND SQUEEZING IN A TWO-PHOTON 77 MICROMASER M. Orszag, L. Roa and R. Ramirez PHASE SPACE FLUCTUATIONS IN NEUTRAL FERMI LIQUIDS 89 B. Benhassine, M. Farine, E.S. Hernandez, D. Idier, B. Remaud and F. Sebille v

6 vi POLAR DECOMPOSITION AND DENSE SIMILARITY TO UNITARY 101 OPERATORS N. Bertoglio, S. Martinez and J. San Martin SITE-EXCHANGE CELLULAR AUTOMATA 109 N. Boccara, and M. Roger STEADY STATE SEGREGATION IN DIFFUSION-LIMITED 119 BIMOLECULAR REACTIONS: EFFECT OF STRONG SPACE DISORDER AND A GALANIN APPROACH H.S. Wio SCHRODINGER'S CAT AND SQUEEZING 133 M. Orszag, R. Ramirez, J.C. Retamal and L. Roa SEQUENTIAL ITERATION FOR EXTREMAL AUTOMATA 141 E. Goles and G. Hernandez A STOCHASTIC APPROACH TOWARDS THE STUDY OF THE 149 ONE-DIMENSIONAL LANDAU GINZGURG DISTRIBUTION C. van den Broeck EFFECTIVE POTENTIAL FOR STOCHASTIC PROCESSES 161 H. Calisto, E. Cerda and E. Tirapegui PART II INSTABILITIES IN NON EQUILIBRIUM SYSTEMS 175 SOME ASYMPTOTIC TIME BEHAVIOR FOR THE REAL GINZBURG 177 LANDAU EQUATION P. Collet ANOMALOUS TRANSPORT IN HETEROGENEOUS MATERIALS 181 E. Guyon, J.P. Bouchaud SUBCRITICAL TRAVELING PULSES AND PATTERN 193 FORMATION IN A FILM DRAGGING EXPERIMENT F. Melo EMPIRICAL DETERMINATION OF THE ONSET OF CONVECTION 199 FOR A HARD DISK SYSTEM D. Risso and P. Cordero 1 D AND 2D NONLINEAR EVOLUTION EQUATIONS FOR 213 BENARD-MARANGONI CONVECTION A.N.Garazo and M.G.Velarde

7 A GENERALIZED SWIFT-HOHENBERG MODEL FOR SEVERAL 225 CONVECTIVE PROBLEMS C. Perez-Garcra, J. Millan-Rodriguez, H. Herrero and M. Bestehorn TWO DIMENSIONAL PATTERNS IN A MODEL FOR THE 235 ELECTRO HYDRODYNAMIC INSTABILITY OF NEMATIC LIQUID CRYSTALS P. de Brouwer and D. Walgraef TURING STRUCTURES IN THE PRESENCE OF GRADIENTS 247 A. De Wit, P. Borckmans and G. Dewel STABILITY LIMITS OF DEFECTS AND SPATIO-TEMPORAL 259 CHAOS IN NONEQUILIBRIUM MEDIA los. Aranson, L. Kramer and A. Weber THE FRAGMENTATION OF A DROP FALLING IN A FLUID: 273 GEOMETRY AND VELOCITY A. Garcimartrn, H.L. Mancini and C. Perez-Garcra THE ROLE OF DISPERSION IN THE GENERALIZED KURAMOTO 281 SIVASHINSKY EQUATION C.M. Alfaro, R.D. Benguria and M.C. Depassier THREE-MODES NONLINEAR STATISTICAL DESCRIPTION FOR A 289 GLOBAL DRIFT WAVE TURBULENCE R. Montagne and A.C. Sicardi Schifino SPREADING OF A DROPLET ON A SOLID SURFACE 297 AND THE HOFFMAN-TANNER LAW V.A. Kuz CORIOLIS FORCE AND CENTRIFUGAL FORCE 301 INDUCED FLOW INSTABILITIES I. Mutabazi and J.E. Wesfreid AMPLITUDE EQUATIONS FOR VISCOELASTIC 317 CONVECTIVE FLUIDS J. Martrnez-Mardones, R. Tiemann, W. Zeller and C. Perez-Garcia INSTABILITIES MEDIATED BY LINE DEFECTS IN THREE 325 DIMENSIONS WITHOUT UNBINDING A.F. Ramrrez, A. Reisenegger and F. Lund GENERATION OF SIDE JETS IN FORCED AXISYMMETRIC JETS 333 M. Abid and M.E. Brachet vii

8 viii PARAMETRIC FORCING OF COUPLED PENDULA F. Belin, P. Coullet, T. Frisch J.C. Robinet TRACER DISPERSION IN THE TAYLOR-COUETTE INSTABILITY WITH AXIAL FLOW M. Piva, A. Calvo, A. Barrantes, S. Gabanelli, M. Rosen, I. Ippolito and J.E. Wesfreid CRITICAL VELOCITIES AND NUCLEATION OF VORTICES IN A MODEL OF SUPERFLOW S. Rica and Y. Pomeau SUBJECT INDEX 365

9 F()REWORD We present here a selection of the lectures given at the Fourth International Workshop on Instabilities and Nonequilibrium Structures in Valparaiso, Chile, in December The Workshop was organized by Facultad de Ciencias Fisicas y Matematicas of Universidad de Chile and by Instituto de Fisica of Universidad Cat6lica de Valparaiso where it took place. This periodic meeting takes place every two years in Chile and aims to contribute to the efforts in Latin America towards the development of scientific research. This development is certainly a necessary condition for progress in our countries and we thank our lectures for their warm collaboration to fulfill this need. We are also very much indebted to the Chilean Academy of Sciences for sponsoring officially this Workshop. We thank CONICYT (Comision Nacional de Investigacion Cientifica y Tecnologica de Chile) and his President Professor E. d'etigny for his valuable help and also Fundacion Andes of Chile. The efforts of M.D. d'ollone, Scientific Advisor at the French Ambassy in Santiago, have been essential for our success and we acknowledge here the generous support of the Scientific Cooperation Program of France for Chile. The organizers are especially grateful to Mr. J.A. Guzman and Mr. B. Philippi, President and Director General of CHILGENER S.A., for their great interest and generous financial support to our Workshop which initiates a new style of collaboration between the chilean private sector and the scientific activity. We also thank Banco de Credito e Inversiones for their support. Ms. AIda Bertoni deserves a special mention for her remarkable work during the realization of the Workshop. We are grateful to Professor Michiel Hazewinkel for including this book in his series and to Dr. David Lamer of Kluwer for his continuous interest and support to this project. E. Tirapegui W. Zeller ix

10 LIST OF SPONSORS OF THE WORKSHOP Academia Chilena de Ciencias Facultad de Ciencias Ffsicas y Matematicas de la U. de Chile Instituto de Ffsica de la Universidad Cat6lica de Valparaiso CONICYT (Chile) Ministere Francais des Affaires Etrangeres International Centre for Theoretical Physics (Trieste) DFG (Germany) FNRS (Belgium) Fundaci6n Andes (Chile) Sociedad Chilena de Ffsica Departamento Tecnico de Investigaci6n y de Relaciones Internacionales de la Universidad de Chile CHILGENER S.A. Banco de Credito e Inversiones x

11 PREFACE We have classified the articles presented here in two Sections according to their general content. In Part I we have included papers which deal with statistical mechanics, mathematical aspects of dynamical systems and sthochastic effects in nonequilibrium systems. Part II is devoted mainly to instabilities and self-organization in extended nonequilibrium systems. The study of partial differential equations by numerical and analytic methods plays a great role here and many works are related to this subject. Most recent developments in this fascinating and rapidly growing area are discussed.