Instabilities and Nonequilibrium Structures VI

Transcription

1 Instabilities and Nonequilibrium Structures VI

2 Nonlinear Phenomena and Complex Systems VOLUMES The Centre for Nonlinear Physics and Complex Systems (CFNL), Santiago, Chile, and Kluwer Academic Publishers have established this series devoted to nonlinear phenomena and complex systems, which is one of the most fascinating fields of science today, to publish books that cover the essential concepts in this area, as well as the latest developments. As the number of scientists involved in the subject increases continually, so does the number of new questions and results. Nonlinear effects are essential to understand the behaviour of nature, and the methods and ideas introduced to treat them are increasingly used in new applications to a variety of problems ranging from physics to human sciences. Most of the books in this series will be about physical and mathematical aspects of nonlinear science, since these fields report the greatest activity. Series Editors Enrique Tirapegui (Centre for Nonlinear Physics and Complex Systems, Santiago, Chile) Servet Martinez (Centre for Nonlinear Physics and Complex Systems, Santiago, Chile) Advisory Editorial Board Marc Etienne Brachet (Ecole Normale Superieure, Paris, France) Pierre Collet (Ecole Poly technique, Paris, France) Pierre Coullet (Institut Nonlineaire de Nice, France) Gregoire Nicolis (Universite Libre de Bruxelles, Belgium) Yves Pomeau (Ecole Normale Superieure, Paris, France) Daniel Walgraef (Universite Libre de Bruxelles, Belgium) The titles published in this series are listed at the end of this volume.

3 Instabilities and N onequilibrium Structures VI Edited by Enrique Tirapegui Facultad de Ciencias Ffsicas y Matemdticas, Universidad de Chile, Santiago, Chile Javier Martfnez Instituto de Ffsica, Universidad Catolica de Valparafso, Valparafso, Chile and Rolando Tiemann Facultad de Ciencias, Universidad de Playa Ancha, Valparaiso, 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 DOI / ISBN (ebook) Printed on acid-free paper AlI Rights Reserved 2000 Springer Science+Business Media Dordrecht Origina11y published by Kluwer Academic Publishers in 2000 Softcover reprint ofthe hardcover lst edition 2000 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.... Biographical Sketch of Professor Walter Zeller. Acknowledgements Vll ix xi Preface.... Part I. Review Lectures A primer in classical turbulence theory M. E. Brachet Stochastic effects in physical systems M. San Miguel and R. Toral Part II. Pattern Selection, Defects and Granular Matter Spatio-temporal intermittency in the spatial unfolding of Andronov's Bifurcations M. Argentina and P. Coullet Thermodynamics and dynamics of supersolids Y. Pomeau Large Amplitude Patterns in Bistable Reaction-Diffusion Systems S. Metens, P. Borckmans and G. Dewel Benard Cell: A Centennial Puzzle C. Perez-Garcia and B. Echebarria A parametric oscillator in a highly viscous fluid E. Cerda Spiral waves and target waves in single cells A. Babloyantz and N. Ellis Pattern Selection and Stability in Polymeric Fluid Convection J. Martinez-Mardones, R. Tiemann, D. Walgraef and W. Zeller Wavelength Selection of Spiral Waves in Liquid Crystals E. Hamm, S. Rica and A. Vierheilig

6 VI Surface Waves Scattering by a Vertical Vortex: A progress report F. Vivanco, L. Caballero and F. Melo Spreading of molecularly thin wetting films on solid interfaces S. F. Burlatsky, A. M. Cazabat, M. Moreau, G. Oshanin and S. Villette Developable Cones and Crumpled Paper: An experimental point of view S. Chai:eb and F Melo Quantum Topological Defects and the Schwinger mechanism C. Elphick Imperfect Coagulation reaction A + A --+ A : An analitical approach M. Hoyuelos Mixing and Segregation in Granular Matter E. Guyon and D. Bideau Pressure and Surface Dilation measurements in vibrated granular layers N. Mujica, E. Tirapegui and F. Melo Part III. Stochastic Behavior and Statistical Mechanics Quantum Coherence and Decoherence by Spontaneous Emission in a Quantum Optical Realization of a Driven Pendulum R. Graham Covariant Non-Linear Non-Equilibrium Thermodynamics and the Ergodic Theory of Stochastic and Quantum Flows D. Rapaport Stochastic Inflation: A Semiclassical Approach M. Bellini, H. Casini, R. Montemayor and P. Sistema Upper Bounds for Correlation Functions: Bose Systems M. Corgini and D. P. Sankovich Multifractal Behavior of a Fibonacci Crystal built over p coupled chains E. Lazo Stationary probability for systems presenting weak noise transitions O. Descalzi, J. Lauzeral and E. Tirapegui. 393 Subject Index

7 FOREWORD This sixth Volume of the International Workshop on Instabilities and Nonequilibrium Structures is dedicated to the memory of my friend Walter Zeller, Professor of the Universidad C'at6lica df' Valparaiso and Vice-Director of the Workshop. Walter Zeller was much more than an organizer of this meeting: his enthusiasm, dedication and critical views were many times the essential ingredients to continue with a task which in occasions faced difficulties and incomprehensiolls. It is in great part due to him that the workshop has adquired to-day tradition. maturity and international recognition. This Volume should have been coedited by Walter and it is with df'ep emotion that I learned that his disciples Javier Martinez and Rolando Tiemann wanted as a last hommage to their Professor and friend to coedit tfus book. No me seria posible terminal' estas lineas sin pensar en la senora Adriana Gamonal de Zelln. quf' ella encuentre en este libro la admiraci6n y reconocimiento hacia su marido de quipilf's [l\prall sus discipulos, colegas y amigos. Enrique Tirapcglli vii

8 Walter Zeller

9 BIOGRAPHICAL SKETCH Walter Zeller was Born on June, 13, 1943, in Antofagasta, in the north of Chile. Later on. his family moves to La Union, in the south of the country, where he is sent to Colegio Alelmin to do his elementary education. He continues his studies in the Colegio Aleman of Valparaiso and obtains his secondary Education Diploma in In 1961 he starts his universitary studies in the Pedagogical Institute of the Universidad de Chile in Valparaiso and graduates as a Teacher of Mathematics and Physics in He begins his academics career at Universidad de Chile, Valparaiso, in 196:3, as assistant of Experimental Physics. He then becomes assistant to the Theoretical Mechanics and Electromagnetism courses. Between 1967 and 1976, he becomes Professor of Electrodynamics and Theoretical Mechanics in that institution. In 1966, he enters the Universidad Catolica de Valparaiso, where he lived. worked. studied. suffered and died on May 25, He worked for that institution nearly :30 years. His academic career in this institution, his lifetime university, can be summed up in a few lines: 19GD-19i:3. Assistant Professor; , Associate Professor; and from that date on. Professor. In 1971, he enters the University of Pittsburg where he graduates as Master of Science (Ph.\ sics) in Throughout his academic career, he published several papers and essays. His early interest in field theory led him to write several papers about Classic Electrodynamics. among which, "Acotaciones sobre Relatividad Especial" (" Notes on Special Relativity" ). (197:)). a text wich was required in special relativity courses intended for undergraduate students of {'niversidad Catolica de Valparaiso Physics Institute of the College of Basic Sciences and ;\lathematics. From the eighties on, he starts a new line of inquiry, fluids, which resulted in the publications of "Aproximacion al Tratamiento Teorico de la Turbulencia: Ecuaciones de Reynolds y de la Energia" (" Approach to Theoretical Treatment of Turbulence: Reynolds and Energy Equations"). "All1ilisis de Estabilidad de la Teoria de Mezclas para la Sedimentacion de Pariculas con Difusion" (" Analysis of Stability of the Compounds Theory for the Sedimentation of Particles with Diffusion"), "Estudio de Estabilidad en Conveccion Termosalina" ("Study of Stability in Thermosaline Convection") where the stability of this double diffusion phenomenon is studied and the neutral stability curves of thermosaline convection and the separation of saline concentrations strata by well-defined interfaces are shown. It is worth noticing that with these works. Walter opens a research line on the Physics of Fluids and Complex Systems at the lntitute of Physics. Another of his explicit constributions to academic life was his concern for the teaching and training of young researchers in the line of fluids physics acting as commitee chair of many graduate thesis written by students pursuing their Master in Sciences in Physics. As a result of this and his research projects, he presented numerous papers at Conferences and published them in national and international journals. ix

10 x In 1987, following a suggestion made by Prof. Enrique Tirapegui, Walter Zeller, along with the Department of Physics of the Faculty of Physics and Mathematics of the llniversidad de Chile and the Center for Non-Linear Physics and Complex Systems of Santiago. organizes for the Universidad Cat6lica de Valparaiso and, in particular, for its Intitute of Physics. onf' of the major events related to non-linear physics, the III International Workshop on Instabilitif'S and Non-equilibrium Structures, where the most distinguished researchers haw prf'sf'ntecl their works. He could organize until the VI Workshop and was co-editor of the procf'edings of such scientific meetings. Whoever knew Walter will have to agree that he was a kind, refined. modest man. whosf' brilliant, elevated conversation and generosity accompanied him in every step lh' took in life. This led him to occupy the most varied and important institutional positions at the \"ni\'ersidad Cat6lica de Valparaiso, such as Dean of the College Basic Sciences ( and I')" 1-I')8G). General Director of Research ( ), Academic Vice-Rector ( ),1I1e1 Director of the International Affairs Office ( ). Besides, he was a member of collntl",,, on- ilnd off-university study committees, such as Member of the Committee for Science and Technology of the Council of Rectors of Chilean Universities ( ). We would like to conclude with a quote of Walter himself: "Teamwork and tllf' legan' of past history have been essential in the development of projects, programs and adi\'ities in the ("niversity. The achievements are often a product of these associations in common tasks and an individual alone can hardly claim credit for them". Let these few words be a testimony of what he left in this university and in the national scif'ntific community. Let his legacy be the emphais on those "common tasks" which he left lis as a mission. Valparaiso, May 1998.Javier l\iartinez Rolando Tiemann Carlos Worner

11 ACKNOWLEDGEMENTS The organizers of the Workshop thank Academia Chilena de Ciencias for supporting this meeting since its beginning in They are also indebted to the three Institutions which act directly in the realization of the Workshop: Instituto de Fisica of the Universidad Cat6lica de Valparaiso where the meeting takes place, Facultad de Ciencias Fisicas y Matematicas of the Universidad de Chile and Centro de Fisica No Lineal y Sistemas Complejos de Santiago (CFNL). Many young physicists have helped us in the every day tasks of the organization and in the preparation of the book: special credit should be given to Drs. Hector Calisto, Enrique Cerda and Rene Rojas. The sessions of our Workshop have taken place every two years without interruptions for more than ten years. This has been possible since our institutional sponsors have maintained the continuity of their effort. They are: - CLAF (Centro Latinoamericano de Fisica). - CONICYT (Comision Nacional de Investigacion Cientifica y Tecnologica de Chile). - Departamento Tecnico de Investigacion y de Relaciones Internacionales de la Universidad de Chile. - Fundacion Andes (Chile). - Ministere Fran<,ais des Affaires Etrangeres. UNESCO. The effort of the chilean private sector deserves special credit: the Centro de Fisica No Lineal y Sistemas Complejos of Santiago (CFNL) which is with Kluwer Academic Publishers at the origin of this Series exists essentially due to the support of CHILGENER S. A. and the LUI\SIC Group. Last but not least the interest and constant encouragement of Kluwer is gratefully acknowledged. Xl

12 PREFACE The review lectures and articles presented here correspond to an actualized version of the two courses and of the invited conferences presented in the sixth session of the International Workshop on Instabilities and Nonequilibrium Structures which took place in Universidad Cat6lica de Valparaiso, Chile, in December The authors have recently revised their contributions and we thank them for their collaboration. Part I contains the lectures given by M. E. Brachet on Classical Turbulence Theory and by M. San Miguel and R. Toral on Stochastic Effects in Physical Systems. In Part II we present a selection of conferences on new aspects of pattern selection and defects dynamics and we end with two articles in the fascinating subject of granular matter. Finally in Part III we have included the articles related to statistical mechanics, stochastic and chaotic behavior, both classical and quantum.