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Chemical Oscillations, Waves, and Turbulence

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Chemical Oscillations, Waves, and Turbulence Cover

 

Synopses & Reviews

Publisher Comments:

This highly respected, frequently cited book addresses two exciting fields: pattern formation and synchronization of oscillators. It systematically develops the dynamics of many-oscillator systems of dissipative type, with special emphasis on oscillating reaction-diffusion systems. The author applies the reductive perturbation method and the phase description method to the onset of collective rhythms, the formation of wave patterns, and diffusion-induced chemical turbulence.

This two-part treatment starts with a section on methods, defining and exploring the reductive perturbation method — oscillators versus fields of oscillators, the Stuart-Landau equation, onset of oscillations in distributed systems, and the Ginzburg-Landau equations. It further examines methods of phase description, including systems of weakly coupled oscillators, one-oscillator problems, nonlinear phase diffusion equations, and representation by the Floquet eigenvectors.

Additional methods include systematic perturbation expansion, generalization of the nonlinear phase diffusion equation, and the dynamics of both slowly varying wavefronts and slowly phase-modulated periodic waves. The second part illustrates applications, from mutual entrainment to chemical waves and chemical turbulence. The text concludes with a pair of convenient appendixes.

Book News Annotation:

Kuramoto (Kyoto U.) describes a few asymptotic methods that can be used to analyze the dynamics of self-oscillating fields of the reactive-diffusion type and some related systems, and surveys some applications of them. The original, published by Springer-Verlag in 1984, is here slightly corrected. Annotation (c)2003 Book News, Inc., Portland, OR (booknews.com)

Synopsis:

A fundamental and frequently cited book provides asymptotic methods applicable to the dynamics of self-oscillating fields of the reaction-diffusion type. Graduate level. 40 figures. 1984 edition.

Synopsis:

A fundamental and frequently cited book in two very exciting fields: pattern formation and synchronization of oscillators. Provides asymptotic methods that can be applied to the dynamics of self-oscillating fields of the reaction-diffusion type and of some related systems. Graduate level. Contents: 1. Introduction. 2. Reductive Perturbation Method. 3. Method of Phase Description I. 4. Method of Phase Description II. 5. Mutual Entrainment. 6. Chemical Waves. 7. Chemical Turbulence. Appendix. References. Subject Index. Unabridged republication of the edition originally published by Springer-Verlag, New York, 1984. 40 Figures.

Synopsis:

A fundamental and frequently cited book in two very exciting fields: pattern formation and synchronization of oscillators. Provides asymptotic methods that can be applied to the dynamics of self-oscillating fields of the reaction-diffusion type and of some related systems. Graduate level. 40 figures.

Table of Contents

1. Introduction

    Part I Methods

    2. Reductive Perturbation Method

      2.1 Oscillators Versus Fields of Oscillators

      2.2 The Stuart-Landau Equation

      2.3 Onset of Oscillations in Distributed Systems

      2.4 The Ginzburg-Landau Equation

    3. Method of Phase Description I

      3.1 Systems of Weakly Coupled Oscillators

      3.2 One-Oscillator Problem

      3.3 Nonlinear Phase Diffusion Equation

      3.4 Representation by the Floquet Eigenvectors

      3.5 Case of the Ginzburg-Landau Equation

    4. Method of Phase Description II

      4.1 Systematic Perturbation Expansion

      4.2 Generalization of the Nonlinear Phase Diffusion Equation

      4.3 Dynamics of Slowly Varying Wavefronts

      4.4 Dynamics of Slowly Phase-Modulated Periodic Waves

    Part II Applications

    5. Mutual Entrainment

      5.1 Synchronization as a Mode of Self-Organization

      5.2 Phase Description of Entrainment

        5.2.1 One Oscillator Subject to Periodic Force

        5.2.2 A Pair of Oscillators with Different Frequencies

        5.2.3 Many Oscillators with Frequency Distribution

      5.3 Calculation of ? for a Simple Model

      5.4 Soluble Many-Oscillator Model Showing Synchronization-Desynchronization Transitions

      5.5 Oscillators Subject to Fluctuating Forces

        5.5.1 One Oscillator Subject to Stochastic Forces

        5.5.2 A Pair of Oscillators Subject to Stochastic Forces

        5.5.3 Many Oscillators Which are Statistically Identical

      5.6 Statistical Model Showing Synchronization-Desynchronization Transitions

      5.7 Bifurcation of Collective Oscillations

    6. Chemical Waves

      6.1 Synchronization in Distributed Systems

      6.2 Some Properties of the Nonlinear Phase Diffusion Equation

      6.3 Development of a Single Target Pattern

      6.4 Development of Multiple Target Patterns

      6.5 Phase Singularity and Breakdown of the Phase Description

      6.6 Rotating Wave Solution of the Ginzburg-Landau Equation

    7 Chemical Turbulence

      7.1 Universal Diffusion-Induced Turbulence

      7.2 Phase Turbulence Equation

      7.3 Wavefront Instability

      7.4 Phase Turbulence

      7.5 Amplitude Turbulence

      7.6 Turbulence Caused by Phase Singularities

  Appendix

  A. Plane Wave Solutions of the Ginzburg-Landau Equation

  B. The Hopf Bifurication for the Brusselator

  References

  Subject Index

Product Details

ISBN:
9780486428819
Author:
Kuramoto, Y.
Publisher:
Dover Publications
Author:
Kuramoto, Yoshiki
Author:
Chemistry
Location:
Mineola, N.Y.
Subject:
Chemistry - General
Subject:
Dynamics
Subject:
Waves & Wave Mechanics
Subject:
Chemistry - Physical & Theoretical
Subject:
System Theory
Subject:
Self-organizing systems
Subject:
Oscillating chemical reactions.
Subject:
Chemistry | Physical Chemistry
Edition Number:
Dover ed.
Edition Description:
Trade Paper
Series:
Dover Books on Chemistry
Series Volume:
no. 7-4936
Publication Date:
20030831
Binding:
TRADE PAPER
Language:
English
Illustrations:
41 Figs.
Pages:
176
Dimensions:
9.25 x 6.13 in 0.54 lb

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Related Subjects

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Chemical Oscillations, Waves, and Turbulence New Trade Paper
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$18.95 In Stock
Product details 176 pages Dover Publications - English 9780486428819 Reviews:
"Synopsis" by ,
A fundamental and frequently cited book provides asymptotic methods applicable to the dynamics of self-oscillating fields of the reaction-diffusion type. Graduate level. 40 figures. 1984 edition.
"Synopsis" by ,
A fundamental and frequently cited book in two very exciting fields: pattern formation and synchronization of oscillators. Provides asymptotic methods that can be applied to the dynamics of self-oscillating fields of the reaction-diffusion type and of some related systems. Graduate level. Contents: 1. Introduction. 2. Reductive Perturbation Method. 3. Method of Phase Description I. 4. Method of Phase Description II. 5. Mutual Entrainment. 6. Chemical Waves. 7. Chemical Turbulence. Appendix. References. Subject Index. Unabridged republication of the edition originally published by Springer-Verlag, New York, 1984. 40 Figures.

"Synopsis" by ,
A fundamental and frequently cited book in two very exciting fields: pattern formation and synchronization of oscillators. Provides asymptotic methods that can be applied to the dynamics of self-oscillating fields of the reaction-diffusion type and of some related systems. Graduate level. 40 figures.
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