Instabilities and Nonequilibrium Structures VII & VIII PDF
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Instabilities and Nonequilibrium Structures VII & VIII 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 of Mathematical Modeling, Universidad de Chile, Santiago, Chile) Advisory Editorial Board Marc Etienne Brachet (Ecole Normale Superieure, Paris, France) Pierre Collet (Ecole Poly technique, Paris, France) Pierre Coullet (lnstitut 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. Instabilities and Nonequilibrium Structures VII & VIII Edited by Orazio Descalzi Facultad de Ingenierfa, Universidad de los Andes, Santiago, Chile Javier Martinez lnstituto de Fisica, Universidad Cat6lica de Valparaiso, Valparaiso, Chile and Enrique Tirapegui Facultad de Ciencias Fisicas y Matemdticas, Universidad de Chile, Santiago, Chile KLUWER ACADEMIC PUBLISHERS DORDRECHT I BOSTON I LONDON A c.I.P. Catalogue record for this book is available from the Library of Congress. ISBN 978-94-015-6994-1 ISBN 978-1-4020-2149-7 (eBook) DOI 10.1007/978-1-4020-2149-7 Published by Kluwer Academic Publishers. P.O. Box 17. 3300 AA Dordrecht, The Netherlands. Sold and distributed in North, Central and South America by Kluwer Academic Publishers, IOJ Philip Drive, Norwell, MA 02061, U.S.A. In all other countries, sold and distributed by Kluwer Academic Publishers, P.O. Box 322, 3300 AH Dordrecht, The Netherlands. Printed on acid-free paper All Rights Reserved © 2004 Kluwer Academic Publishers Softcover reprint of the hardcover I st edition 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. v TABLE OF CONTENTS Foreword ...................................................................................................................................... VII Preface ........................................................................................................................................ . Part I. Courses Diffusion-limited reactions of particles with fluctuating activity. O. Benichou, M. Moreau and G. Oshanin ....................................................................... 5 Classical Dynamics of Excitations of Bose Condensates in Anisotropic Traps. R. Graham ......................................................................................................................... 23 Bifurcations in Attractive Bose-Einstein Condensates and Superfluid Helium. C. Huepe, C. Nore and M. E. Brachet .............................................................................. 43 Phase boundary dynamics in a one-dimensional non-equilibrium lattice gas. G. Oshanin, J. De Coninck, M. Moreau and S. F. Burlatsky .......................................... 69 Conventional Bose-Einstein condensation. A. Verbeure ...................................................................................................................... 109 Part II. Invited Conferences and Seminars On the topographic rectification of ocean fluctuations. A. Alvarez, E. Hernandez-Garcia and 1. Tintore ............................................................. 133 Dynamics of conical singularities: S type d-cones. V. Apablaza and F. Melo ................................................................................................. 141 Nonlinear Dynamic Analysis of Scalp EEG Epileptic Signals. S. A. Blanco, J. Creso, A. Figliola, R. Quian Quiroga and O. A. Rosso ......................... 149 A theorem on wave packets. M. Castagnino and J. Guer6n 159 The Kolmogorov-Lax-Phillips Systems as Branch Systems of the Reichembach Model. M. Castagnino, S. Iguri, E. Gunzig and A. Ord6nez ....................................................... 169 Computing the quantum Boltzmann equation from a Kossakowski-Lindblad generator. A. K. Chattah and M. O. Caceres ..................................................................................... 183 A Combined Density Functional and Semiclassical Approach to Describe Atomic/Ionic Radii. M. C. Donnamaria .................................. ..................... ......................... ............................ 197 Boundary-Forced Spatial Chaos. V. M. Eguiluz, E. Hernandez-Garcia and O. Piro ............................................................ 205 Chaotic toy model of mobile beds in natural channels. P. M. Jacovkis, W. E. Legnani and O. A. Rosso ............................................................. 213 Chaotic motion and the classical-quantum border. A. M. Kowalski and A. N. Proto ...................................................................................... 219 VI Thermodynamic behavior of a stain. V. A. Kuz .......................................................................................................................... 237 Approach to equilibrium for quantum systems with continuous spectrum. R. Laura ............................................................................................................................ 255 Linear Marangoni problem in a diluted polymer. J. Martinez-Mardones, M. Vega and W. Zeller ............................................................... 267 On some localized solutions of coupled Ginzburg-Landau equations. R. Montagne and E. Hernandez-Garcia ........................................................................... 273 Stable-Unstable Transitions in Viscous Fingering. S. Obernauer and M. Rosen ............................................................................................. 281 Force distribution in two dimensional sandpile. M. Olivares, J. N. Roux and F. Melo ............................................................................... 297 Time-periodic forcing of Turing patterns in the Brusselator model. B. Pena and C. Perez-Garcia ............................................................................................ 305 Realizations of the random representations of the Navier-Stokes equations by ordinary differential equations. D. L. Rapoport .................................................................................................................. 313 Characterization of the Dynamical Evolution of Electroencephalogram Time Series. O. A. Rosso, S. A. Blanco and A. Figliola ...................................................................... 333 Exact results in trapping reactions for mobile particles and a single trap. A. Sanchez, M. A. Rodriguez and H. S. Wio .................................................................. 339 Vortex-dipole surface wave interactions in deep water. F. Vivanco and F.Melo ..................................................................................................... 345 Non linear dynamics, pattern formation and materials science. D. Walgraef ...................................................................................................................... 355 New results for diffusion-limited reactions within a stochastic model. H. S. Wio, M. A. Rodriguez and A. Sanchez .................................................................. 371 Subject Index ..................................................................................................................................... 385 Author Index ..................................................................................................................................... 387 vii FOREWORD The contents of this book correspond to Sessions VII and VIII of the International Workshop on Instabilities and Nonequilibrium Structures which took place in Vifia del Mar, Chile, in December 1997 and December 1999, respectively. We were not able to publish this book before and we apologize for this fact to the authors and participants of the meeting. We have made an effort to actualize the courses and articles which have been reviewed by the authors. Both Workshops were organized by Facultad de Ciencias Fisicas y Matematicas, Universidad de Chile, Instituto de Fisica of Universidad Cat61ica de Valparaiso and Centro de Fisica No Lineal y Sistemas Complejos de Santiago. We are glad to acknowledge here the support of the Facultad de Ingenieria of Universidad de los Andes of Santiago which also be from now on one of the organizing Institutions of future Workshops. Enrique Tirapegui PREFACE This book is divided in two parts. In Part I we have collected the courses given in Sessions VII and VIII of the Workshop and in Part II we include a selection of the invited Conferences and Seminars presented at both meetings. Three courses are related to the very important new developments in Bose-Einstein condensation: the first one by Robert Graham studies the classical dynamics of excitations of Bose condensates in anisotropic traps, the second by Marc Etienne Brachet is devoted to the bifurcations arising in attractive Bose-Einstein condensates and superfluid helium and the third course by Andre Verbeure is a pedagogical introduction to the subject with special emphasis on first principles and rigorous results. Part I is completed by two courses given by Michel Moreau: the first on diffusion limited reactions of particles with fluctuating activity and the second on the phase boundary dynamics in a one dimensional nonequilibrium lattice gas. The articles presented in Part II refer to a variety of subjects, both experimental and theoretical, of current interest in Nonlinear Physics. Santiago, Marzo 2003 Orazio Descalzi Javier Martinez Enrique Tirapegui (Eds.) PART I Courses Diffusion-limited reactions of particles with fluctuating activity by O. Benichou*, M. Moreau** and G. Oshanin** * Physique de la Matiere Condensee, College de France, 11 pI. Marcelin Berthelot, 75005 Paris, France ** Physique Theorique des liquides, Universite Pierre et Marie Curie, 75252 Paris Cedex 05, France Abstract We study a diffusion-limited reaction, which consists in the annihilation of some species A by another species B. However, the B particles can only destroy A if they are in an activated form, whereas they also have an inert form which leaves B unchanged. Each form has a stochastic lifetime following an exponential law. We compute the reaction probability of a particle B, and deduce the kinetics of the reaction. It is shown that in one or two dimensions these fluctuations do not change the reaction kinetics, which differs from the ordinary, mean-field kinetics, as it is the case when there are no fluctuations. In three dimensions, the effective reaction constant, including the fluctuations, is computed. We prove that it is an increasing function of the relaxation frequency of the fluctuations. 5 O. Descalzi et al. (eds.), Instabilities and Nonequi/ibrium Structures VII & VIII, 5-22. © 2004 Kluwer Academic Publishers.
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