The Dynamics of Patterns

Front Cover
World Scientific, 2000 - Science - 324 pages
Spirals, vortices, crystalline lattices, and other attractive patterns are prevalent in Nature. How do such beautiful patterns appear from the initial chaos? What universal dynamical rules are responsible for their formation? What is the dynamical origin of spatial disorder in nonequilibrium media? Based on the many visual experiments in physics, hydrodynamics, chemistry, and biology, this invaluable book answers those and related intriguing questions. The mathematical models presented for the dynamical theory of pattern formation are nonlinear partial differential equations. The corresponding theory is not so accessible to a wide audience. Consequently, the authors have made every attempt to synthesize long and complex mathematical calculations to exhibit the underlying physics. The book will be useful for final year undergraduates, but is primarily aimed at graduate students, postdoctoral fellows, and others interested in the puzzling phenomena of pattern formation.
 

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Contents

Prelude to a Dynamical Description
1
Linear Stage of Pattern Formation
15
Model Equations
27
The GinzburgLandau Equation
45
Crystal Formation
63
Quasicrystals
75
Breaking of Order
87
Localized Patterns
107
Patterns in Chaotic Media
205
herein with H Abarbanel V Afraimovich I Aranson A GaponovGrekhov
213
Living matter and dynamic forms
225
Appendix A A Short Guide to Nonlinear Dynamics
239
Bifurcations
250
Chaotic Oscillations
261
Dynamical chaos and turbulence
271
Appendix B Key Experiments in Pattern Formation
279

Spirals
129
Patterns in Oscillating Soap Films
151
Patterns in Colonies of Microorganisms
173
Spatial Disorder
189
Thermal convection
292
Diffusive chemical reactions
302
A B Ezersky
309
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