Download or read book Instabilities and Fronts in Extended Systems written by Pierre Collet and published by Princeton University Press. This book was released on 2014-07-14 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: The physics of extended systems is a topic of great interest for the experimentalist and the theoretician alike. There exists a large literature on this subject in which solutions, bifurcations, fronts, and the dynamical stability of these objects are discussed. To the uninitiated reader, the theoretical methods that lead to the various results often seem somewhat ad hoc, and it is not clear how to generalize them to the nextthat is, not yet solvedproblem. In an introduction to the subject of instabilities in spatially infinite systems, Pierre Collet and Jean-Pierre Eckmann aim to give a systematic account of these methods, and to work out the relevant features that make them operational. The book examines in detail a number of model equations from physics. The mathematical developments of the subject are based on bifurcation theory and on the theory of invariant manifolds. These are combined to give a coherent description of several problems in which instabilities occur, notably the Eckhaus instability and the formation of fronts in the Swift-Hohenberg equation. These phenomena can appear only in infinite systems, and this book breaks new ground as a systematic account of the mathematics connected with infinite space domains. Originally published in 1990. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Download or read book Perspectives In Mathematical Sciences written by Yisong Yang and published by World Scientific. This book was released on 2010-01-18 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical sciences have been playing an increasingly important role in modern society. They are in high demand for investigating complex problems in physical science, environmental and geophysical sciences, materials science, life science and chemical sciences.This is a review volume on some timely and interesting topics in applied mathematical sciences. It surveys new developments and presents some future research directions in these topics. The chapters are written by experts in these fields, with a wide audience in mind and hence will be accessible to graduate students, junior researchers and other professionals who are interested in the subjects. The contributions of Professor Youzhong Guo, a leading expert in these areas, will be celebrated. His life and academic achievements are highlighted in the Preface and Postscript of the book. The underlying theme that binds the various chapters seamlessly is a set of dedicated ideas and techniques from partial differential equations and dynamical systems.
Download or read book PDE Dynamics written by Christian Kuehn and published by SIAM. This book was released on 2019-04-10 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of the myriad methods for applying dynamical systems techniques to PDEs and highlights the impact of PDE methods on dynamical systems. Also included are many nonlinear evolution equations, which have been benchmark models across the sciences, and examples and techniques to strengthen preparation for research. PDE Dynamics: An Introduction is intended for senior undergraduate students, beginning graduate students, and researchers in applied mathematics, theoretical physics, and adjacent disciplines. Structured as a textbook or seminar reference, it can be used in courses titled Dynamics of PDEs, PDEs 2, Dynamical Systems 2, Evolution Equations, or Infinite-Dimensional Dynamics.
Download or read book Nonlinear Dynamics Materials Theory and Experiments written by Mustapha Tlidi and published by Springer. This book was released on 2015-11-14 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents recent advances, new ideas and novel techniques related to the field of nonlinear dynamics, including localized pattern formation, self-organization and chaos. Various natural systems ranging from nonlinear optics to mechanics, fluids and magnetic are considered. The aim of this book is to gather specialists from these various fields of research to promote cross-fertilization and transfer of knowledge between these active research areas. In particular, nonlinear optics and laser physics constitute an important part in this issue due to the potential applications for all-optical control of light, optical storage, and information processing. Other possible applications include the generation of ultra-short pulses using all-fiber cavities.
Download or read book ICIAM 91 written by Robert E. O'Malley and published by SIAM. This book was released on 1992-01-01 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings -- Computer Arithmetic, Algebra, OOP.
Download or read book Ergodic Theory Analysis and Efficient Simulation of Dynamical Systems written by Bernold Fiedler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 816 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting very recent results in a major research area, this book is addressed to experts and non-experts in the mathematical community alike. The applied issues range from crystallization and dendrite growth to quantum chaos, conveying their significance far into the neighboring disciplines of science.
Download or read book Instabilities and Nonequilibrium Structures V written by E. Tirapegui and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Lectures on Dynamical Systems Structural Stability and Their Applications written by Kotik K. Lee and published by World Scientific. This book was released on 1992 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: The communication of knowledge on nonlinear dynamical systems, between the mathematicians working on the analytic approach and the scientists working mostly on the applications and numerical simulations has been less than ideal. This volume hopes to bridge the gap between books written on the subject by mathematicians and those written by scientists. The second objective of this volume is to draw attention to the need for cross-fertilization of knowledge between the physical and biological scientists. The third aim is to provide the reader with a personal guide on the study of global nonlinear dynamical systems.
Download or read book Thermo hydraulic Instabilities written by J-M. Buchlin and published by . This book was released on 2007 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Discrete and Continuous Dynamical Systems written by and published by . This book was released on 2007 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Proceedings of the European Conference on Complex Systems 2012 written by Thomas Gilbert and published by Springer Science & Business Media. This book was released on 2013-08-15 with total page 1030 pages. Available in PDF, EPUB and Kindle. Book excerpt: The European Conference on Complex Systems, held under the patronage of the Complex Systems Society, is an annual event that has become the leading European conference devoted to complexity science. ECCS'12, its ninth edition, took place in Brussels, during the first week of September 2012. It gathered about 650 scholars representing a wide range of topics relating to complex systems research, with emphasis on interdisciplinary approaches. More specifically, the following tracks were covered: 1. Foundations of Complex Systems 2. Complexity, Information and Computation 3. Prediction, Policy and Planning, Environment 4. Biological Complexity 5. Interacting Populations, Collective Behavior 6. Social Systems, Economics and Finance This book contains a selection of the contributions presented at the conference and its satellite meetings. Its contents reflect the extent, diversity and richness of research areas in the field, both fundamental and applied.
Download or read book Proceedings written by and published by . This book was released on 2004 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Local Bifurcations Center Manifolds and Normal Forms in Infinite Dimensional Dynamical Systems written by Mariana Haragus and published by Springer Science & Business Media. This book was released on 2010-11-23 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: An extension of different lectures given by the authors, Local Bifurcations, Center Manifolds, and Normal Forms in Infinite Dimensional Dynamical Systems provides the reader with a comprehensive overview of these topics. Starting with the simplest bifurcation problems arising for ordinary differential equations in one- and two-dimensions, this book describes several tools from the theory of infinite dimensional dynamical systems, allowing the reader to treat more complicated bifurcation problems, such as bifurcations arising in partial differential equations. Attention is restricted to the study of local bifurcations with a focus upon the center manifold reduction and the normal form theory; two methods that have been widely used during the last decades. Through use of step-by-step examples and exercises, a number of possible applications are illustrated, and allow the less familiar reader to use this reduction method by checking some clear assumptions. Written by recognised experts in the field of center manifold and normal form theory this book provides a much-needed graduate level text on bifurcation theory, center manifolds and normal form theory. It will appeal to graduate students and researchers working in dynamical system theory.
Download or read book Nonlinear Optical Cavity Dynamics written by Philippe Grelu and published by John Wiley & Sons. This book was released on 2015-12-14 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: By recirculating light in a nonlinear propagation medium, the nonlinear optical cavity allows for countless options of light transformation and manipulation. In passive media, optical bistability and frequency conversion are central figures. In active media, laser light can be generated with versatile underlying dynamics. Emphasizing on ultrafast dynamics, the vital arena for the information technology, the soliton is a common conceptual keyword, thriving into its modern developments with the closely related denominations of dissipative solitons and cavity solitons. Recent technological breakthroughs in optical cavities, from micro-resonators to ultra-long fiber cavities, have entitled the exploration of nonlinear optical dynamics over unprecedented spatial and temporal orders of magnitude. By gathering key contributions by renowned experts, this book aims at bridging the gap between recent research topics with a view to foster cross-fertilization between research areas and stimulating creative optical engineering design.
Download or read book From Finite to Infinite Dimensional Dynamical Systems written by James Robinson and published by Springer Science & Business Media. This book was released on 2001-05-31 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the NATO Advanced Study Institute, Cambridge, UK, 21 August-1 September 1995
Download or read book Mathematical Reviews written by and published by . This book was released on 2006 with total page 860 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Methods In Equivariant Bifurcations And Dynamical Systems written by Pascal Chossat and published by World Scientific Publishing Company. This book was released on 2000-02-28 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable book presents a comprehensive introduction to bifurcation theory in the presence of symmetry, an applied mathematical topic which has developed considerably over the past twenty years and has been very successful in analysing and predicting pattern formation and other critical phenomena in most areas of science where nonlinear models are involved, like fluid flow instabilities, chemical waves, elasticity and population dynamics.The book has two aims. One is to expound the mathematical methods of equivariant bifurcation theory. Beyond the classical bifurcation tools, such as center manifold and normal form reductions, the presence of symmetry requires the introduction of the algebraic and geometric formalism of Lie group theory and transformation group methods. For the first time, all these methods in equivariant bifurcations are presented in a coherent and self-consistent way in a book.The other aim is to present the most recent ideas and results in this theory, in relation to applications. This includes bifurcations of relative equilibria and relative periodic orbits for compact and noncompact group actions, heteroclinic cycles and forced symmetry-breaking perturbations. Although not all recent contributions could be included and a choice had to be made, a rather complete description of these new developments is provided. At the end of every chapter, exercises are offered to the reader.
