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One service mathematics has rendered the 'Ht moi, ...* Ii j'avait
so comment en revenir, je ny _ais point aile':' human race. It has
put common sense back Jules Verne where it belongs, on the topmost
shelf neJll to the dusty canister labelled 'discarded non- The
series is diwrgent; therefore we may be sense' . * ble to do
something with it. Eric T. Bell O. H eniside Mathematics is a tool
for thought. A highly necessary tool in a world where both feedback
and non- linearities abound. Similarly, alI kinds of parts of
mathematics serve as tools for other parts and for other sciences.
Applying a simple rewriting rule to the quote on the right above
one finds such statements as: 'One service topology has rendered
mathematical physics ...'; 'One service logic has rendered com-
puter science ...'; 'One service category theory has rendered
mathematics ...'. All arguably true. And all statements obtainable
this way form part of the raison d't!tre of this series.
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, math ematical 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. PART I STATISTICAL MECHANICS AND RELATED TOPICS
NONEQUILIBRIUM POTENTIALS FOR PERIOD DOUBLING R. Graham and A. Hamm
Fachbereich Physik, Universitiit Gesamthochschule Essen D4300 Essen
1 Germany ABSTRACT. In this lecture we consider the influence of
weak stochastic perturbations on period doubling using
nonequilibrium potentials, a concept which is explained in section
1 and formulated for the case of maps in section 2. In section 3
nonequilibrium potentials are considered for the family of
quadratic maps (a) at the Feigenbaum 'attractor' with Gaussian
noise, (b) for more general non Gaussian noise, and (c) for the
case of a strange repeller. Our discussion will be informal. A more
detailed account of this and related material can be found in our
papers [1-3] and in the reviews [4, 5], where further references to
related work are also given. 1.
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.
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.
It is with great emotion that we present here this volume dedicated
to the memory of Bernard Jouvet, Docteur es Sciences, Directeur des
Recher- ches at the Centre National pour la Recherche Scientifique.
The life and the career as a physicist of Professor Jouvet are
evoked in the following pages by Professor F. Cerulus, a friend of
long standing of Professor Jouvet. The contributions have been
written by physicists who were friends, collaborators or former
students of Professor Jouvet. I express here my gratitude for their
contributions. I wish also to thank Mrs. France Jouvet for her kind
help in the realiza- tion of this book. Without her support this
would have been impossible. I am also especially indebted to
Professor M. Flato for his constant encouragement and kind
cooperation, and to F. Langouche and D. Roekaerts for their
generous help in the preparation of this volume. E. TIRAPEGUI TABLE
OF CONTENTS FOREWORD VII BIOGRAPHICAL SKETCH XI XIX LIST OF
SELECTED SCIENTIFIC PUBLICA TIONS PART ONE: FIELD THEORY AND
QUANTIZATION C. BECCHI, A. ROUET and R. sToRA/Renormalizable
Theories with Symmetry Breaking 3 J. CALMET and A.
VISCONTI/Computing Methods in Quantum Electrodynamics 33 GERARD
CLEMENT/Classical Mechanics of Autocomposite Particles 59 s.
DEsER/Exclusion of Static Solutions in Gravity-Matter Coupling 77
D. ARNAL, J. C. COR TET, M. FLATO and D. STERNHEIMER/
Star-Products: Quantization and Representations without Operators
85 R. GASTMANs/High Energy Tests of Quantum Electrodynamics 113 L.
GOMBEROFF and E. K.
Approach your problems from the right end It isn't that they can't
see the solution. It is and begin with the answers. Then one day,
that they can't see the problem. perbaps you will find the final
question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad
in Crane Feathers' in R. Brown 'The point of a Pin'. van GuIik's
The Chinese Maze Murders. Growing specialization and
diversification have brought a host of monographs and textbooks on
increasingly specialized topics. However, the "tree" of knowledge
of mathematics and related fields does not grow only by putting
forth new branches. It also happens, quite often in fact, that
branches which were thought to be completely disparate are suddenly
seen to be related. Further, the kind and level of sophistication
of mathematics applied in various sciences has changed drastically
in recent years: measure theory is used (non-trivially) in regional
and theoretical economics; algebraic geometry interacts with
physics; the Minkowsky lemma, coding theory and the structure of
water meet one another in packing and covering theory; quantum
fields, crystal defects and mathematical programming profit from
homotopy theory; Lie algebras are relevant to filtering; and
prediction and electrical engineering can use Stein spaces. And in
addition to this there are such new emerging subdisciplines as
"experimental mathematics," "CFD," "completely integrable systems,"
"chaos, synergetics and large-scale order," which are almost
impossible to fit into the existing classification schemes. They
draw upon widely different sections of mathematics.
This book contains the lectures and a selection of the seminars gi
ven in the Fifth International Workshop on Instabilities and
Nonequilibrium Structures which took place in Santiago, Chile, in
December 1993. The Workshop was organized by Facultad de Ciencias
Fisicas y Matematicas, Universidad de Chile, Instituto de Fisica of
Universidad Cat6lica de Valparaiso and Centro de Fisica No Lineal y
Sistemas Complejos de Santiago. This volume is the first of a new
series of Kluwer on Nonlinear Phenomena and Complex Systems which
will be edited by the Centro de Fisica No Lineal y Sistemas
Complejos de Santiago. We thank Dr. David Lamer of Kluwer for his
encouragements and support for this project. ix LIST OF SPONSORS OF
THE WORKSHOP * Academia Chilena de Ciencias * Facultad de Ciencias
Fisicas y Mathematicas de la Univ. de Chile * Instituto de Fisica
de la Univ. Cat6lica de Valparaiso * Centro de FIsica No Lineal y
Sistemas Complejos de Santiago (CFNL) * CONICYT (Chile) * Ministere
Francais des Affaires Etrangeres * International Centre for
Theoretical Physics (Trieste) * UNESCO * Fundaci6n Andes (Chile) *
Departamento Tecnico de Investigaci6n y de Relaciones Internationa-
cion ales de la Universidad de Chile * IDIEM (Fac. Cs. FIs. y Mat.,
Univ. de Chile) * CHILGENER S.A.
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.
This book is intended as a fairly complete presentation of
what..'We call the discretization approach to functional integrals,
i.e. path integrals defined as limits of discretized axpressions.
In its main parts it is based 0n the original work of the authors.
We hope to have provided the readers with a rather complete and
up-to-date bibliography, and we apologize to authors whose work has
not been cited through ignorance ori our part. Our main concern has
been to present a for malism that is practical and which can be
adapted to make computations in the numerous areas where path
integrals are being increasingly used. For these reasons
applications, illustrative examples, and detailed calculations are
included. The book is partially based on lectures given by one of
us (E.T.) at the Institut de Physique Theorique of the u.c.L.
(Louvain-la-Neuve). We thank Dr. M.E. Brachet (University of Paris)
for his help in the redaction of chapter 8. We are indebted to many
of our colleagues and especially to the members of the Instituut
voor Theoretische Fysica, K.U. Leuven for their interest and
encouragement. We also thank Professor Claudio Anguita, Dean of the
Faculty of Physics and Mathematics of .the University of Chile, for
his constant support. Special thanks are due to Christine Detroije
and Lutgarde Dubois for their very fine and hard work in typing the
manuscript."
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.
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.
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, math ematical 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. PART I STATISTICAL MECHANICS AND RELATED TOPICS
NONEQUILIBRIUM POTENTIALS FOR PERIOD DOUBLING R. Graham and A. Hamm
Fachbereich Physik, Universitiit Gesamthochschule Essen D4300 Essen
1 Germany ABSTRACT. In this lecture we consider the influence of
weak stochastic perturbations on period doubling using
nonequilibrium potentials, a concept which is explained in section
1 and formulated for the case of maps in section 2. In section 3
nonequilibrium potentials are considered for the family of
quadratic maps (a) at the Feigenbaum 'attractor' with Gaussian
noise, (b) for more general non Gaussian noise, and (c) for the
case of a strange repeller. Our discussion will be informal. A more
detailed account of this and related material can be found in our
papers [1-3] and in the reviews [4, 5], where further references to
related work are also given. 1.
One service mathematics has rendered the 'Ht moi, ...* Ii j'avait
so comment en revenir, je ny _ais point aile':' human race. It has
put common sense back Jules Verne where it belongs, on the topmost
shelf neJll to the dusty canister labelled 'discarded non- The
series is diwrgent; therefore we may be sense' . * ble to do
something with it. Eric T. Bell O. H eniside Mathematics is a tool
for thought. A highly necessary tool in a world where both feedback
and non- linearities abound. Similarly, alI kinds of parts of
mathematics serve as tools for other parts and for other sciences.
Applying a simple rewriting rule to the quote on the right above
one finds such statements as: 'One service topology has rendered
mathematical physics ...'; 'One service logic has rendered com-
puter science ...'; 'One service category theory has rendered
mathematics ...'. All arguably true. And all statements obtainable
this way form part of the raison d't!tre of this series.
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.
Approach your problems from the right end It isn't that they can't
see the solution. It is and begin with the answers. Then one day,
that they can't see the problem. perbaps you will find the final
question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad
in Crane Feathers' in R. Brown 'The point of a Pin'. van GuIik's
The Chinese Maze Murders. Growing specialization and
diversification have brought a host of monographs and textbooks on
increasingly specialized topics. However, the "tree" of knowledge
of mathematics and related fields does not grow only by putting
forth new branches. It also happens, quite often in fact, that
branches which were thought to be completely disparate are suddenly
seen to be related. Further, the kind and level of sophistication
of mathematics applied in various sciences has changed drastically
in recent years: measure theory is used (non-trivially) in regional
and theoretical economics; algebraic geometry interacts with
physics; the Minkowsky lemma, coding theory and the structure of
water meet one another in packing and covering theory; quantum
fields, crystal defects and mathematical programming profit from
homotopy theory; Lie algebras are relevant to filtering; and
prediction and electrical engineering can use Stein spaces. And in
addition to this there are such new emerging subdisciplines as
"experimental mathematics," "CFD," "completely integrable systems,"
"chaos, synergetics and large-scale order," which are almost
impossible to fit into the existing classification schemes. They
draw upon widely different sections of mathematics.
This book is intended as a fairly complete presentation of
what..'We call the discretization approach to functional integrals,
i.e. path integrals defined as limits of discretized axpressions.
In its main parts it is based 0n the original work of the authors.
We hope to have provided the readers with a rather complete and
up-to-date bibliography, and we apologize to authors whose work has
not been cited through ignorance ori our part. Our main concern has
been to present a for malism that is practical and which can be
adapted to make computations in the numerous areas where path
integrals are being increasingly used. For these reasons
applications, illustrative examples, and detailed calculations are
included. The book is partially based on lectures given by one of
us (E.T.) at the Institut de Physique Theorique of the u.c.L.
(Louvain-la-Neuve). We thank Dr. M.E. Brachet (University of Paris)
for his help in the redaction of chapter 8. We are indebted to many
of our colleagues and especially to the members of the Instituut
voor Theoretische Fysica, K.U. Leuven for their interest and
encouragement. We also thank Professor Claudio Anguita, Dean of the
Faculty of Physics and Mathematics of .the University of Chile, for
his constant support. Special thanks are due to Christine Detroije
and Lutgarde Dubois for their very fine and hard work in typing the
manuscript."
It is with great emotion that we present here this volume dedicated
to the memory of Bernard Jouvet, Docteur es Sciences, Directeur des
Recher- ches at the Centre National pour la Recherche Scientifique.
The life and the career as a physicist of Professor Jouvet are
evoked in the following pages by Professor F. Cerulus, a friend of
long standing of Professor Jouvet. The contributions have been
written by physicists who were friends, collaborators or former
students of Professor Jouvet. I express here my gratitude for their
contributions. I wish also to thank Mrs. France Jouvet for her kind
help in the realiza- tion of this book. Without her support this
would have been impossible. I am also especially indebted to
Professor M. Flato for his constant encouragement and kind
cooperation, and to F. Langouche and D. Roekaerts for their
generous help in the preparation of this volume. E. TIRAPEGUI TABLE
OF CONTENTS FOREWORD VII BIOGRAPHICAL SKETCH XI XIX LIST OF
SELECTED SCIENTIFIC PUBLICA TIONS PART ONE: FIELD THEORY AND
QUANTIZATION C. BECCHI, A. ROUET and R. sToRA/Renormalizable
Theories with Symmetry Breaking 3 J. CALMET and A.
VISCONTI/Computing Methods in Quantum Electrodynamics 33 GERARD
CLEMENT/Classical Mechanics of Autocomposite Particles 59 s.
DEsER/Exclusion of Static Solutions in Gravity-Matter Coupling 77
D. ARNAL, J. C. COR TET, M. FLATO and D. STERNHEIMER/
Star-Products: Quantization and Representations without Operators
85 R. GASTMANs/High Energy Tests of Quantum Electrodynamics 113 L.
GOMBEROFF and E. K.
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