Table Of ContentInstabilities 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.
