Screen LibraryThe dynamics of patterns /
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?...
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| Main Authors: | |
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| Corporate Authors: | |
| Group Author: | ; |
| Published: |
World Scientific Pub. Co.,
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| Publisher Address: | Singapore : |
| Publication Dates: | 2000. |
| Literature type: | eBook |
| Language: | English |
| Subjects: | |
| Online Access: |
http://www.worldscientific.com/worldscibooks/10.1142/4207#t=toc |
| Summary: |
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. |
| Carrier Form: | 1 online resource (xii,324pages) : illustrations |
| Bibliography: | Includes bibliographical references (pages 309-319) and index. |
| ISBN: | 9789812813350 |
| CLC: | O4 |
| Contents: |
ch. 1. Patterns: prelude to a dynamical description -- ch. 2. Linear stage of pattern formation -- ch. 3. Model equations. 3.1. Swift-Hohenberg equation. 3.2. Newell-Whitehead-Segel equation. 3.3. Coupled amplitude equations. 3.4. Phase equations -- ch. 4. The Ginzburg-Landau Equation. 4.1. The dissipative Ginzburg-Landau equation. 4.2. Nerve membrane excitation and the CGL equation. 4.3. Optical dynamics and the CGL equation. 4.4. Simple patterns in the CGL equation. 4.5. Phase equations revisited. 4.6. Gallery of phenomena -- ch. 5. 'Crystal' formation -- ch. 6. Quasicrystals. 6.1. Octagons, decagons, and dodecagons. 6.2. A generalized Swift-Hohenberg model. 6.3. The 'turbulent' crystal -- ch. 7. Breaking of order. 7.1. A simple model for domain walls. 7.2. Topological defects. 7.3. The birth of penta-hepta defects. 7.4. Dislocations and domain walls in Faraday ripples. ch. 8. Localized patterns. 8.1. Bistable media. 8.2. Dynamical disorder of structures. 8.3. Particle interaction. 8.4. Chaotic scattering -- ch. 9. Spirals. 9.1. Active spirals. 9.2. Passive spirals -- ch. 10. Patterns in oscillating soap films. 10.1. Introduction. 10.2. Observations. 10.3. Models for vorticity generation -- ch. 11. Patterns in colonies of microorganisms. 11.1. Dictyostelium Discoideum. 11.2. Esherichia coli. 11.3. Bacillus subtilis -- ch. 12. Spatial disorder. 12.1. Introductory remarks. 12.2. Characteristics of space series. 12.3. The Grassberger-Procaccia algorithm. 12.4. Qualitative description of developing disorder. 12.5. Dynamical dimension of defect-mediated turbulence -- ch. 13. Patterns in chaotic media. 13.1. Introductory remarks. 13.2. Chaotic synchronization. 13.3. Coexistence of regular patterns and chaos. 13.4. Coarse grain spatio-temporal patterns. 13.5. Coherent patterns on a chaotic checkerboard -- ch. 14. Epilogue: living matter and dynamic forms. 14.1. Hallucinations. 14.2. Spatio-temporal patterns and information processing. |