Non-Linear Dynamics Near and Far from Equilibrium

Non-Linear Dynamics Near and Far from Equilibrium PDF

Author: J.K. Bhattacharjee

Publisher: Springer Science & Business Media

Published: 2007-12-27

Total Pages: 300

ISBN-13: 1402053886

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This text gives a detailed account of various techniques that are used in the study of dynamics of continuous systems, near as well as far from equilibrium. The analytic methods covered include diagrammatic perturbation theory, various forms of the renormalization group, and self-consistent mode coupling.

Nonlinear Dynamics and Chaos

Nonlinear Dynamics and Chaos PDF

Author: Steven H. Strogatz

Publisher: CRC Press

Published: 2018-05-04

Total Pages: 532

ISBN-13: 0429961111

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This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.

Nonlinear Dynamics of Chaotic and Stochastic Systems

Nonlinear Dynamics of Chaotic and Stochastic Systems PDF

Author: Vadim S. Anishchenko

Publisher: Springer Science & Business Media

Published: 2007-07-20

Total Pages: 463

ISBN-13: 3540381686

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We present an improved and enlarged version of our book Nonlinear - namics of Chaotic and Stochastic Systems published by Springer in 2002. Basically, the new edition of the book corresponds to its ?rst version. While preparingthiseditionwemadesomeclari?cationsinseveralsectionsandalso corrected the misprints noticed in some formulas. Besides, three new sections have been added to Chapter 2. They are “Statistical Properties of Dynamical Chaos,” “E?ects of Synchronization in Extended Self-Sustained Oscillatory Systems,” and “Synchronization in Living Systems.” The sections indicated re?ect the most interesting results obtained by the authors after publication of the ?rst edition. We hope that the new edition of the book will be of great interest for a widesectionofreaderswhoarealreadyspecialistsorthosewhoarebeginning research in the ?elds of nonlinear oscillation and wave theory, dynamical chaos, synchronization, and stochastic process theory. Saratov, Berlin, and St. Louis V.S. Anishchenko November 2006 A.B. Neiman T.E. Vadiavasova V.V. Astakhov L. Schimansky-Geier Preface to the First Edition Thisbookisdevotedtotheclassicalbackgroundandtocontemporaryresults on nonlinear dynamics of deterministic and stochastic systems. Considerable attentionisgiventothee?ectsofnoiseonvariousregimesofdynamicsystems with noise-induced order. On the one hand, there exists a rich literature of excellent books on n- linear dynamics and chaos; on the other hand, there are many marvelous monographs and textbooks on the statistical physics of far-from-equilibrium andstochasticprocesses.Thisbookisanattempttocombinetheapproachof nonlinear dynamics based on the deterministic evolution equations with the approach of statistical physics based on stochastic or kinetic equations. One of our main aims is to show the important role of noise in the organization and properties of dynamic regimes of nonlinear dissipative systems.

Nonlinear Dynamics

Nonlinear Dynamics PDF

Author: H.G Solari

Publisher: Routledge

Published: 2019-01-22

Total Pages: 369

ISBN-13: 1351428306

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Nonlinear Dynamics: A Two-Way Trip from Physics to Math provides readers with the mathematical tools of nonlinear dynamics to tackle problems in all areas of physics. The selection of topics emphasizes bifurcation theory and topological analysis of dynamical systems. The book includes real-life problems and experiments as well as exercises and work

Far-from-equilibrium Dynamics

Far-from-equilibrium Dynamics PDF

Author: Yasumasa Nishiura

Publisher: American Mathematical Soc.

Published: 2002

Total Pages: 340

ISBN-13: 9780821826256

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This book is devoted to the study of evolution of nonequilibrium systems. Such a system usually consists of regions with different dominant scales, which coexist in the space-time where the system lives. In the case of high nonuniformity in special direction, one can see patterns separated by clearly distinguishable boundaries or interfaces. The author considers several examples of nonequilibrium systems. One of the examples describes the invasion of the solid phase into the liquidphase during the crystallization process. Another example is the transition from oxidized to reduced states in certain chemical reactions. An easily understandable example of the transition in the temporal direction is a sound beat, and the author describes typical patterns associated with thisphenomenon. The main goal of the book is to present a mathematical approach to the study of highly nonuniform systems and to illustrate it with examples from physics and chemistry. The two main theories discussed are the theory of singular perturbations and the theory of dissipative systems. A set of carefully selected examples of physical and chemical systems nicely illustrates the general methods described in the book.

Nonequilibrium Physics at Short Time Scales

Nonequilibrium Physics at Short Time Scales PDF

Author: Klaus Morawetz

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 499

ISBN-13: 3662089904

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This introductory level text addresses the broad range of nonequilibrium phenomena observed at short time scales. It focuses on the important questions of correlations and memory effects in dense interacting systems. Experiments on very short time scales are characterized, in particular, by strong correlations far from equilibrium, by nonlinear dynamics, and by the related phenomena of turbulence and chaos. The impressive successes of experiments using pulsed lasers to study the properties of matter and of the new methods of analysis of the early phases of heavy ion reactions have necessitated a review of the available many-body theoretical methods. The aim of this book is thus to provide an introduction to the experimental and theoretical methods that help us to understand the behaviour of such systems when disturbed on very short time scales.

Galileo Unbound

Galileo Unbound PDF

Author: David D. Nolte

Publisher: Oxford University Press

Published: 2018-07-12

Total Pages: 384

ISBN-13: 0192528505

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Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once — setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.

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