Noise Sustained Patterns

Fluctuations And Nonlinearities

By: Markus Loecher

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Hardcover | 8 December 2003

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Hardcover
252 Pages

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23.5 x 15.88 x 1.91

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This book investigates the impact of noise upon the emergence and sustenance of patterns. "Patterns" loosely refers to coherent spatial structures, including fronts, as well as temporal patterns. The crucial role of nonlinearities is highlighted and expanded upon in the context of dynamical system frameworks. The author's familiarity with chaos theory, statistical physics and nonlinear science is reflected in the highly interdisciplinary character of the text. Model equations and experiments taken from fluid dynamics, semiconductor devices, biophysics and statistical mechanics complement theoretical concepts. It should be of great value to researchers and graduate students who desire a quick introduction to the subject. Excursions into emerging fields such as traffic flow simulations and game theory serve to broaden the scope and to encourage the exploration of sundry topics.

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.,." provides a good summary of the current literature on the impact of noise upon the emergence ad sustenance of patterns."

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You Can Find This Book In

Non-Fiction Mathematics Applied Mathematics Chaos Theory Science Physics Classical Mathematics Wave Mechanics including Vibration & Acoustics Engineering & Technology Other Technologies & Applied Sciences Booktopia Publisher Services World Scientific Publishing

Nonlinear Science Fluid Mechanics Applied Physics Biophysics

Preface	p. vii
Acknowledgements	p. ix
Introduction	p. 1
Stability theory revisited	p. 1
Noise and metastability	p. 1
Linear stability analysis	p. 6
Instabilities and nonlinear events in everyday life	p. 11
Arms race	p. 11
Distribution of wealth	p. 13
Front nucleation and propagation	p. 14
Supply chain dynamics	p. 16
A hodgepodge of mechanical instabilities	p. 21
Postscript	p. 24
Essentials	p. 25
Probabilistic and information theoretic measures	p. 25
Matrix manipulations	p. 27
Circulant matrices	p. 37
Singular value decomposition	p. 39
Delay-differential equations	p. 40
The fluctuation-dissipation theorem	p. 43
The Fokker-Planck equation	p. 45
Numerical techniques for the simulation of stochastic equations	p. 47
Experimental aspects of generating noise	p. 50
Complex integration	p. 52
Noise Induced Temporal Phenomena	p. 59
Escape from metastable states	p. 59
Stochastic resonance in bistable systems	p. 61
Double-well potential	p. 63
Two state theory	p. 68
The diode resonator	p. 71
The logistic map	p. 74
Postscript	p. 76
Adding Spatial Dimensions	p. 77
Spatiotemporal stochastic resonance	p. 77
Array enhancement	p. 78
Global vs. local dynamics	p. 83
Kink nucleation in a [phi superscript 4] model	p. 85
Kink nucleation in the experiment	p. 91
Decay rates and kink speeds	p. 92
Coupled maps	p. 95
Doubly stochastic resonance	p. 99
Spatial patterns	p. 102
Parametric surface waves	p. 105
Noise induced bistability of Faraday waves	p. 107
Granular flow	p. 109
Intermittent pattern switching	p. 115
Postscript	p. 117
Stochastic Transport Phenomena	p. 119
Noise-sustained structures in convectively unstable media	p. 119
The Ginzburg-Landau equation	p. 122
Unidirectionally coupled diode resonators	p. 124
Coupled maps	p. 127
Noise sustained front transmission	p. 129
Propagation failure in cardiac tissue	p. 137
Information theoretic measures revisited: ROC curves	p. 141
Theory	p. 147
The continuum limit	p. 148
Kink Brownian motion	p. 149
The Peierls-Nabarro potential	p. 151
Noise enhanced wave propagation	p. 152
Monostable noise enhanced propagation	p. 160
Stochastic ratchets and Brownian motors	p. 162
Postscript	p. 164
Sundry Topics	p. 167
Minority game	p. 167
The thermal minority game	p. 171
Traffic dynamics	p. 177
Time-continuous model	p. 178
Discrete time dynamics	p. 183
Dithering	p. 187
Noise in neural networks	p. 192
Afterthoughts	p. 197
Normal Matrices	p. 203
Integrating Colored-Noise, Coupled SDEs	p. 205
Exploiting symmetries of coupled differential equations	p. 207
Coupled Duffing oscillators	p. 210
Numerical Implementation of the FFT	p. 213
Absolute and Convective Instabilities	p. 217
Bibliography	p. 221
Index	p. 237
Table of Contents provided by Rittenhouse. All Rights Reserved.

Noise Sustained Patterns

Fluctuations And Nonlinearities

At a Glance

Hardcover

Industry Reviews

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