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THE DYNAMICS OF PATTERNS
by M I Rabinovich (University of California, San Diego), A B Ezersky (Russian Academy of Sciences) & P D Weidman (University of Colorado)
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.
Contents:
- Patterns: Prelude to a Dynamical Description
- Linear Stage of
Pattern Formation
- Model Equations
- The Ginzburg-Landau Equation
- 'Crystal' Formation
- Quasicrystals
- Breaking of Order
- Localized Patterns
- Spirals
- Patterns in Oscillating Soap Films
- Patterns in Colonies of Microorganisms
- Spatial Disorder
- Patterns in Chaotic Media
- Epilogue: Living Matter and Dynamic Forms
- A Short Guide to Nonlinear Dynamics
- Key Experiments in Pattern Formation
Readership: Graduate students of mathematical physics and nonlinear science.
"This beautifully illustrated book brings together a remarkable array of pattern-forming phenomena ... The authors have assembled an impressive collection of striking photographs and computer-generated images, and the book would be worth buying for this alone ... the Appendix describing key experiments is a highlight. Here the authors outline the historical development of experiments in parametrically-excited patterns, thermal convection and diffusive chemical reactions."
"This book contains a very impressive account of key ideas and results in nonlinear dynamics and an equally excellent description of important experiments in pattern formation ... readers can gain quite comprehensive knowledge about all possible patterns and their mathematical theories by reading a single chapter, coupled with Appendix I."
| 336pp |
Pub. date: Nov 2000 |
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* Special price applies only to individuals purchasing online and cannot be used in conjunction with any other offers.
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