E. Tirapegui

W. Zeller

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.

Instabilities and Nonequilibrium Structures IV

Javier Martínez

Orazio Descalzi

The contents of this book correspond to Sessions VII and VIII of the International Workshop on Instabilities and Nonequilibrium Structures which took place in Viña del Mar, Chile, in December 1997 and December 1999, respectively. Part I is devoted to self-contained courses. Three courses are related to 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 refers to the bifurcations arising in attractive Bose-Einstein condensates and superfluid helium and the third course by André 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 one on diffusion limited reactions of particles with fluctuating activity and the second on the phase boundary dynamics in a one dimensional nonequilibrium lattice gas. Part II includes a selection of invited seminars at both Workshops.

Instabilities and Nonequilibrium Structures VII & VIII

Flor Langouche

Dirk Roekaerts

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.

Functional Integration and Semiclassical Expansions

This volume contains a selection of the lectures given at the Fifth International Workshop on Instabilities and Nonequilibrium Structures, held in Santiago, Chile, in December 1993. The following general subjects are covered: instabilities and pattern formation, stochastic effects in nonlinear systems, nonequilibrium statistical mechanics and granular matter. Review articles on transitions between spatio-temporal patterns and nonlinear wave equations are also included. Audience: This book should appeal to physicists and mathematicians working in the areas of nonequilibrium systems, dynamical systems, pattern formation and partial differential equations. Chemists and biologists interested in self-organization and statistical mechanics should also be interested, as well as engineers working in fluid mechanics and materials science.

Instabilities and Nonequilibrium Structures V

Danilo Villarroel

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

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