Nonlinear dynamics and pattern formation in the natural environment

著者

• Doelman, A.
• Harten, Aart van

書誌事項

Nonlinear dynamics and pattern formation in the natural environment

A. Doelman and A. Van Harten (editors)

（Pitman research notes in mathematics series, 335）

Longman , Copublished in the U.S. with J. Wiley, 1995

注記

Includes bibliographical references

内容説明・目次

内容説明

This Research Note aims to provide an insight into recent developments in the theory of pattern formation. In the last decade there has been considerable progress in this field, both from a theoretical and a practical point of view. Recent mathematical developments concern the study of the nonlinear stability of systems at near-critical conditions by an appropriate system of modulation equations. The complexity of the original problem can be reduced drastically by this approximation. Moreover, it provides unifying point of view for a wide range of problems. New applications of the theory arise in a multitude of scientific areas such as hydrodynamics, reaction-diffusion problems, oceanography, meteorology, combustion, geophysical and biological morphodynamics and semi-conductors. This book is intended to show the interactions between the mathematical theory of nonlinear dynamics and the study of pattern generating phenomena in the natural environment. There is an intimate relationship between new insights in the mathematical aspects of nonlinear pattern formation and the comprehension of such phenomena. Therefore there are two partly overlapping main themes: one in which the emphasis is on generally applicable mathematical theories and techniques and one in which the phenomenology of pattern evolution in various areas is discussed. The book comprises 19 contributions by experts in the field. Although the emphasis changes considerably from paper to paper, in each contribution the same two themes are present; all the authors have aimed to achieve a suitable balance between the mathematical theory and the physical phenomena. Contents:

目次

Nonlinear evolution of cellular flame instabilities On the justification of the Ginzburg-Landau approximation Bifurcations far from criticality in fluid systems Self-organization and chaotic advection in quasi-2D confined flows Surface tension driven cellular flows in small aspect ratio horizontally square boxes Pattern formation in systems on spatially periodic domains Solitary wave interactions with external forces Breaking the dimension of a steady wave: some examples Remarks on the use and misuse of the GinzburgnLandau equation The mean flows driven by sandbar instabilities Dynamical systems, temporal vs. spatio-temporal chaos, and climate Interaction of modes with disparate scales in Rayleigh-Benard convection A new approach to sideband-instabilities using the principle of reduced instability Pattern formation in activator-inhibitor systems Instabilities in two-layer channel flows A personal sample of patterns in biology Invitation to river morphodynamics Periodic orbits in singularly-perturbed systems Dynamics of large-scale bed forms in coastal seas

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詳細情報

• NII書誌ID(NCID): BA26304514
• ISBN:
  • 0582273714
• LCCN: 95009094
• 出版国コード: uk
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Harlow, Essex, England,New York
• ページ数/冊数: 331 p.
• 大きさ: 25 cm
• 件名:
  • LCSH : Differential equations, Nonlinear -- Congresses
  • LCSH : Fluid dynamics -- Congresses
  • LCSH : Nonlinear theories -- Congresses
  • LCSH : Pattern perception -- Congresses
  • LCSH : Self-organizing systems -- Congresses
• 親書誌ID:
  • BA00276264