Far-from-equilibrium dynamics
著者
書誌事項
Far-from-equilibrium dynamics
（Translations of mathematical monographs, v. 209）（Iwanami series in modern mathematics）
American Mathematical Society, c2002
- タイトル別名
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非線形問題1 : パターン形成の数理
Hisenkei mondai 1 : patan keisei no suri
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注記
Originally published: Tokyo : Iwanami Shoten, 1999
Includes bibliographical references (p. 291-308) and index
内容説明・目次
内容説明
This book is devoted to the study of evolution of non equilibrium 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 non uniformity in special directions, one can see patterns separated by clearly distinguishable boundaries or interfaces. The author considers several examples of non equilibrium 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 non uniformity book.
目次
Separation and unification of scales Amplitude equations Marginal stability criterion and pattern selection Pattern formation Method of singular limit analysis Transient dynamics Future perspectives Bibliography Index.
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