Instabilities and Nonequilibrium Structures II: Dynamical Systems and Instabilities

308 Pages·1989·11.716 MB·English

by  André Avez (auth.), Enrique Tirapegui, Danilo Villarroel (eds.)

Instabilities and Nonequilibrium Structures II
Mathematics and Its Applications
Managing Editor:
M. HAZEWINKEL
Centre for Mathematics and Computer Science, Amsterdam, The Netherlands
Editorial Board:
F. CALOGERO, Universitii degli Studi di Roma, Italy
Yu. I. MANIN, Steklov Institute ofM athematics, Moscow, U.S.S.R.
A. H. G. RINNOOY KAN, Erasmus University, Rotterdam, The Netherlands
G.-C. ROT A, M.l.T., Cambridge, Mass., U.S A.
Volume 50
Instabilities and
Nonequilibrium Structures II
Dynamical Systems and Instabilities
edited by
Enrique Tirapegui
Facultad de Ciencias Ffsicas y Matemdticas.
Universidad de Chile. Santiago. Chile
and
Danilo Villarroel
Facultad de Ciencias. Universidad Tecnica Federico Santa Marfa.
Valparaiso. Chile
KLUWER ACADEMIC PUBLISHERS
DORDRECHT / BOSTON / LONDON
Library of Congress Cataloging in Publication Data
Instabilities and nonequilibrium structures II : dynamical systems and
instabilities I edited by Enrique Tirapegui and Danilo Villarroel.
p. cm. -- (Mathematics and its applications: 50)
"A selection of the seminars given at the Second International
Workshop on Instabilities and Nonequilibrium Structures in
Valparaiso, Chile, in December 1987 ... organized by Facultad de
Ciencias Fisicas y Matematicas of Universidad de Chile and by
Universldad Tecnica Federico Santa Maria"--Foreword.
Inc ludes index.
1. Fluid dynamics--Congresses. 2. Stochastic processes-
-Congresses. 3. Stabil ity--Congresses. I. Tirapegui. EnriQue.
II. Villarroel, D. III. International Workshop on Instabilities and
Nonequilibrium Structures (2nd 1987 Valparaiso, Chile)
IV. Universidad de Chile. Facultad de Ciencias Fisicas y
Matematicas. V. Un;versidad Tecnica Federico Santa Marla.
VI. Title: Instabilities and nonequilibrium structures 2.
VII. Series: Mathematics and its applications (Kluwer Academic
Publishers) ; 50.
OA911.1522 1989
532' .05--dc20 89-15408
ISBN-I3: 978-94-010-7535-0 e-ISBN-I3: 978-94-009-2305-8
DOl: 10.1007/978-94-009-2305-8
Published by Kluwer Academic Publishers,
P.O. Box 17, 3300 AA Dordrecht, The Netherlands.
Kluwer Academic Publishers incorporates
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D. Reidel, Martinus Nijhoff, Dr W. Junk and MTP Press.
Sold and distributed in the U.S.A. and Canada
by Kluwer Academic Publishers,
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In all other countries, sold and distributed
by Kluwer Academic Publishers Group,
P.O. Box 322, 3300 AH Dordrecht, The Netherlands.
printed on acid free paper
All Rights Reserved
© 1989 by Kluwer Academic Publishers
Softcover reprint of the hardcover 15t edition 1989
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.
TABLE OF CONTENTS
vii
FOREWORD
ix
LIST OF SPONSORS OF THE WORKSHOP
ix
LIST OF SUPPORTERS OF THE WORKSHOP
PREFACE I
PART I. DYNAMICAL SYSTEMS AND STATISTICAL MECHANICS 3
ERGODIC THEORY AND SOBOLEV SPACES
A. Avez 5
ABSOLUTELY CONTINUOUS INVARIANT MEASURE FOR EXPANDING
PICK MAPS OF THE INTERVAL EXCEPT AT A MARGINAL FIXED
POINT
P. Collet and P. Ferrero 27
TRANSPORT OF PASSIVE SCALARS: KAM SURFACES AND DIFFUSION
IN THREE-DIMENSIONAL LIOUVILLIAN MAPS
N. Feingold, L.P. Kadanoff and O. Piro 37
PERIODIC ORBITS OF MAPS ON THE DISK WITH ZERO ENTROPY
J.N. Gambaudo and C. Tresser 53
PERIODICALLY AND RAND ONLY NODULATED NON LINEAR PROCESSES
N. Kiwi, B. Hess, M. Narkus and J. Rossler 67
THE GAP ROAD TO CHAOS AND ITS MAIN CHARACTERISTICS
N.C. de Sousa Vieira and C. Tsallis 75
POTTS NODEL AND AUTOMATA NETWORKS
E. Goles 89
CELLULAR-AUTOMATA FLUIDS
G. Vichniac 97
CYLINDER DISTRIBUTION OF THERNODYNANIC LINIT ON BETRE
LATTICES
S. Nartinez 117
vi TABLE OF CONTENTS
RIGOROUS RESULTS ABOUT DETAILED BALANCE AND CRITICAL
SLOWING DOWN
A. Verbeure 131
QUANTUM CHAOS
T. Dittrich and R. Graham 145
REDUCTION OF QUANTUM NOISE IN ATOMIC SYSTEMS
M. Orszag 163
PART II. INSTABILITIES IN NONEQUILIBRIUM SYSTEMS 169
DIRECT SIMULATION OF TWO-DIMENSIONAL TURBULENCE
M.E. Brachet 171
TRANSITION TO TURBULENCE IN OPEN FLOWS. A "metaphoric"
approach
Y. Pomeau 181
THE ROLE OF TOPOLOGICAL DEFECTS IN SUBCRITICAL BIFURCATIONS
P. Cou11et, L. Gil and D. Repaux 189
VORTEX VARIATIONS
F. Lund, A. Reisenegger and C. Rojas 207
OSCILLATORY INSTABILITIES IN BENARD-MARANGONI CONVECTION
IN A FLUID BOUNDED ABOVE BY A FREE ~URFACE
R.D. Benguria and M.C. Depassier 221
PARAMETRIC INSTABILITIES
O. Thua1, S. Douady and S. Fauve 227
SPATIO-TEMPORAL RADIATION PATTERN OF A HIGH ENERGY ELECTRON
D. Villarroe1 239
STABILITY OF TAYLOR-COUETTE FLOW WITH RADIAL HEATING
P.D. Weidman and M.E. Ali 255
FLOW FIELD EFFECTS ON DYNAMICAL INSTABILITIES
D. Wa1graef 269
INSTABILITIES IN NON-AUTONOMOUS SYSTEMS
M. San Miguel 285
POLYNOMIAL APPROXIMATIONS FOR NONEQUILIBRIUM POTENTIALS
NEAR INSTABILITIES
~Desca1zi and E. Tirapegui 297
SUBJECT INDEX 307
FOREWORD
We present here a selection of the seminars given at the Second
International Workshop on Instabilities and Nonequilibrium Structures
in Valparaiso, Chile, in December 1987. The Workshop was organized
by Facultad de Ciencias Fisicas y Matematicas of Universidad de Chile
and by Universidad Tecnica Federico Santa Maria where it took place.
This periodic meeting takes place every two years in Chile and
aims to contribute to the efforts of Latin America towards the
development of scientific research. This development is certainly
a necessary condition for progress in our countries and we thank
our lecturers 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 also our sponsors and supporters for their valuable
help, and most especially the Scientific Cooperation Program of France,
UNESCO, Ministerio de Educaci6n of Chile and Fundaci6n Andes. We
are grateful to Professor Michiel Hazewinkel for including this book
in his series and to Dr. David Larner of Kluwer for his continuous
interest and support to this project.
E. Tirapegui
D. Villarroel
vii
LIST OF SPONSORS OF THE WORKSHOP
Academia Chilena de Ciencias
Academia de Ciencias de America Latina
Academia de Ciencias Exactas, Fisicas y Naturales de Argentina
Facultad de Ciencias Fisicas y Matematicas de la Universidad de
Chile
Universidad Tecnica Federico Santa Maria
Ministere Francais des Affaires Etrangeres
UNESCO
Fundaci6n Andes (Chile)
Ministerio de Educaci6n (Chile)
Departamento Tecnico de Investigaci6n y de Relaciones
Internacionales de la Universidad de Chile
Universidad de Santiago de Chile
Sociedad Chilena de Fisica
LIST OF SUPPORTERS OF THE WORKSHOP
Nestle Chile S.A.
Embotelladora Williamson, Coca-Cola-Chile.
ix
PREFACE
The articles we present here are devoted to the study of macroscopic
systems both from a mathematical and a phenomenological point of
view.
In Part I we have included works which emphasize the mathematical
aspects of the subject, namely the theory of dynamical systems and
statistical mechanics. The last articles study the notion of quantum
chaos and the problem of the reduction of quantum noise in atomic
physics.
In Part II the works are of much more phenomenological nature
and explore new developments in some fundamental open questions. The
first articles treat the old problem of the transition to turbulence.
Next we include works on the role of topological defects in phase
transitions and articles on instabilities and pattern formation.
Finally the last works study the role of fluctuations in nonequilibrium
systems.
PART I
DYNAMICAL SYSTEMS
AND
STATISTICAL
MECHANICS