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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.
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 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.
1m Rahml'll der Technisch-Wissenschaftlichen Veranstaltungen de;
Berliner Bezirksvereins Deutscher Ingenieure wurde im]'riihjahr
1938 ge meinsam mit dem AuBeninstitut der Technischen Hochschule
Berlin und dem FachausschuB fiir Larmminderung des VDI eine
Vortragsreihe iiber: "Schallabwehr im Bau- und Maschinenwesen"
veranstaltet. Die groB ' Zahl der Teilnehmer lieB das Interesse an
den behandelten Gegem;tanden erkennen. AuBerdem wurde vielfach del'
Wunsch geauBert, das Material, welches in den Vortragen an dem
Horer doch schnell voriiberzog, zum Nachschlagen zur Verfiigung zu
haben, um einzelne FaIle der SchaIl abwehr innerhalb des eigenen
Wirkungskreises mit Erfolg angreifen zu konnen. Da z. B. keine
moderne deutsche Zusammenfassung auf diesem fiir dic Gesundheit
eines sehr groBen Teiles der Bevolkerung ungemein wichtigen Gebiet
vorhanden iHt, habe ich es mit groBziigiger Unterstiit zung des
Verlages iibernommen, die einzelnen Vortrage gegeneinander ab
zustimmen, Wichtiges, was in der beschrankten Zeit des Vortrages au
gelassen werden muBte, einzufiigen, weiterfiihrende Literatur
anzugeben und eine Formelsammlung anzufiigen, die dem auf dem
Gebiet del' Schallabwehr tatigen Ingenieur die Bearbeitung
bestimmter Aufgaben erleichtern solI. Damit die Zusammenstellung
ihre Aufgabe als Nach t-lchlagewerk besser erfiillen kann, ist ein
ausfiihrliches Inhalts- lind Saeh verzeichnis eingefiigt. Ich
hoffe, daB damit, wenn auch nicht etwas Voll kommenes, so doch fUr
den praktischen Gebrauch Niitzliches entstanden ist. Das Buch soil
nicht allein eine kurze Einfiihrung in dies Sonder gebiet sein,
sondern soll dem Praktiker zeigen, welche Allfgaben bereit ' gelOst
sind, wo noch besondere Schwierigkeiten zu erwarten und wiC' }1
inzelfalle gemeistert sind."
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