Partially Ordered Systems

With Examples from Physics, Chemistry, and Materials Science

By: Daniel Walgraef, D. Walgraef

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Hardcover | 13 December 1996

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324 Pages

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23.39 x 15.6 x 1.91

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Spatio-temporal patterns appear almost everywhere in nature, and their description and understanding still raise important and basic questions. However, if one looks back 20 or 30 years, definite progress has been made in the modeling of insta bilities, analysis of the dynamics in their vicinity, pattern formation and stability, quantitative experimental and numerical analysis of patterns, and so on. Universal behaviors of complex systems close to instabilities have been determined, leading to the wide interdisciplinarity of a field that is now referred to as nonlinear science or science of complexity, and in which initial concepts of dissipative structures or synergetics are deeply rooted. In pioneering domains related to hydrodynamics or chemical instabilities, the interactions between experimentalists and theoreticians, sometimes on a daily basis, have been a key to progress. Everyone in the field praises the role played by the interactions and permanent feedbacks between ex perimental, numerical, and analytical studies in the achievements obtained during these years. Many aspects of convective patterns in normal fluids, binary mixtures or liquid crystals are now understood and described in this framework. The generic pres ence of defects in extended systems is now well established and has induced new developments in the physics of laser with large Fresnel numbers. Last but not least, almost 40 years after his celebrated paper, Turing structures have finally been ob tained in real-life chemical reactors, triggering anew intense activity in the field of reaction-diffusion systems.

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Preface
Introduction	p. 1
Instabilities and Patterns in Hydrodynamical Systems	p. 15
Instabilities and Patterns in Reaction-Diffusion Systems	p. 25
Generic Aspects of Pattern-Forming Instabilities	p. 37
The Hopf Bifurcation and Related Spatio-Temporal Patterns	p. 65
The Turing Instability and Associated Spatial Structures	p. 87
Defects and Defect Bifurcations	p. 107
The Effect of External Fields	p. 127
Fronts	p. 169
Pattern Formation: Generic versus Nongeneric Aspects	p. 189
Microstructures in Irradiated Materials	p. 197
Plastic Instabilities	p. 231
Afterword	p. 241
Appendices	p. 245
Index	p. 303
Table of Contents provided by Blackwell. All Rights Reserved.

Partially Ordered Systems

With Examples from Physics, Chemistry, and Materials Science

At a Glance

Hardcover

Shipping

How to return your order

Defective items

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