Pattern Formation and Dynamics in Nonequilibrium Systems

Author: Michael Cross
Publisher: Cambridge University Press
ISBN: 1139480464
Format: PDF, Mobi
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Many exciting frontiers of science and engineering require understanding the spatiotemporal properties of sustained nonequilibrium systems such as fluids, plasmas, reacting and diffusing chemicals, crystals solidifying from a melt, heart muscle, and networks of excitable neurons in brains. This introductory textbook for graduate students in biology, chemistry, engineering, mathematics, and physics provides a systematic account of the basic science common to these diverse areas. This book provides a careful pedagogical motivation of key concepts, discusses why diverse nonequilibrium systems often show similar patterns and dynamics, and gives a balanced discussion of the role of experiments, simulation, and analytics. It contains numerous worked examples and over 150 exercises. This book will also interest scientists who want to learn about the experiments, simulations, and theory that explain how complex patterns form in sustained nonequilibrium systems.

Pattern Formation in Liquid Crystals

Author: Agnes Buka
Publisher: Springer Science & Business Media
ISBN: 9780387946047
Format: PDF, Kindle
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This volume bridges two topics of considerable current interest: pattern formation in nonequilibrium phenomena and physics of liquid crystals, both active and diverse areas of research. Because liquid crystals form large-scale and regular patterns under the influence of a variety of applied fields they are fruitful materials to study the spontaneous formation and evolution of ordered and disordered patterns. The chapters, each by a noted researcher in the field, briefly summarize the fundamental work done in the 1960s but concentrate on reviewing results from the recent resurgence of interest in the field as well as indicating the direction of current work.

Far from equilibrium Dynamics

Author: Yasumasa Nishiura
Publisher: American Mathematical Soc.
ISBN: 9780821826256
Format: PDF, Kindle
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This book is devoted to the study of evolution of nonequilibrium systems. Such a system usually consists of regions with different dominant scales, which coexist in the space-time where the system lives. In the case of high nonuniformity in special directions, one can see patterns separated by clearly distinguishable boundaries or interfaces. The author considers several examples of nonequilibrium systems. One of the examples describes the invasion of the solid phase into the liquid phase during the crystallization process. Another example is the transition from oxidized to reduced states in certain chemical reactions. An easily understandable example of the transition in the temporal direction is a sound beat, and the author describes typical patterns associated with this phenomenon. The main goal of the book is to present a mathematical approach to the study of highly nonuniform systems and to illustrate it with examples from physics and chemistry. The two main theories discussed are the theory of singular perturbations and the theory of dissipative systems. A set of carefully selected examples of physical and chemical systems nicely illustrates the general methods described in the book.

Pattern Formation

Author: Rebecca B. Hoyle
Publisher: Cambridge University Press
ISBN: 9780521817509
Format: PDF, Kindle
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Fully illustrated mathematical guide to pattern formation. Includes instructive exercises and examples.

Granular Patterns

Author: Igor Aranson
Publisher: OUP Oxford
ISBN: 0191560006
Format: PDF, Mobi
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This book is a systematic introduction to a new and exciting field of patterns in granular matter. Granular materials are collections of discrete macroscopic solid grains with a typical size large enough that thermal fluctuations are negligible. Despite this seeming simplicity, properties of granular materials are different from conventional solids, liquids and gases due to the dissipative and highly nonlinear nature of forces among grains. The last decade has seen an explosion of interest to nonequilibrium phenomena in granular matter among physicists, both on the experimental and theoretical side. Among these phenomena, one of the most interesting is the ability of granular matter upon mechanical excitation to form highly ordered patterns such as ripples, avalanches, or bands of segregated materials. This book presents a comprehensive review of experiments and novel theoretical concepts needed to understand the mechanisms of pattern formation in granular materials. This book is written for experienced physicists interested in this new rapidly developing field, as well as young researchers and graduate students entering this field. We hope that both experimentalists and theorists already working in the field will find it useful.

The Dynamics of Patterns

Author: M I Rabinovich
Publisher: World Scientific
ISBN: 9814494356
Format: PDF, Mobi
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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 DescriptionLinear Stage of Pattern FormationModel EquationsThe Ginzburg–Landau Equation‘Crystal’ FormationQuasicrystalsBreaking of OrderLocalized PatternsSpiralsPatterns in Oscillating Soap FilmsPatterns in Colonies of MicroorganismsSpatial DisorderPatterns in Chaotic MediaEpilogue: Living Matter and Dynamic FormsA Short Guide to Nonlinear DynamicsKey Experiments in Pattern Formation Readership: Graduate students of mathematical physics and nonlinear science. Keywords:Quasicrystals;Disordered Patterns;Defects;Spirals;Turbulence;Synchronization;Convection;Capillary Waves;Chaotic Dynamics;Biological PatternsReviews: “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.” UK Nonlinear News “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.” Mathematical Reviews

Self Organization in Nonequilibrium Systems

Author: Gregoire Nicolis
Publisher: John Wiley & Sons Incorporated
ISBN:
Format: PDF, ePub, Mobi
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Membranes, Dissipative Structures, and Evolution Edited by G. Nicolis & R. Lefever Focuses on the problem of the emergence/maintenance of biological order at successively higher levels of complexity. Covers the spatiotemporal organization of simple biochemical networks; the formation of pluricellular or macromolecular assemblies; the evolution of these structures; and the functions of specific biological structures. Volume 29 in Advances in Chemical Physics Series, I. Prigogine & Stuart A. Rice, Editors. 1975 Theory and Applications of Molecular Paramagnetism Edited by E. A. Boudreaux & L. N. Mulay Comprehensively treats the basic theory of paramagnetic phenomena from both the classical and mechanical vantages. It examines the magnetic behavior of Lanthanide and Actinide elements as well as traditional transition metals. For each class of compounds, appropriate details of descriptive and mathematical theory are given before their applications. 1976 Theory and Aapplications of Molecular Diamagnetism Edited by L. N. Mulay & E. A. Boudreaux An invaluable reference for solving chemical problems in magnetics, magnetochemistry, and related areas where magnetic data are important, such as solid-state physics and optical spectroscopy. 197