Nonlinear Dynamics and Pattern Formation in the Natural Environment

A Doelman, A Van Harten (Autoren)

Buch | Hardcover

344 Seiten

1995
CRC Press (Verlag)
978-0-582-27371-9 (ISBN)

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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:

A. Van Harten, A. Doelman

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 GinzburgñLandau 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

Erscheint lt. Verlag	27.10.1995
Reihe/Serie	Chapman & Hall/CRC Research Notes in Mathematics Series
Verlagsort	London
Sprache	englisch
Maße	174 x 246 mm
Gewicht	566 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
ISBN-10	0-582-27371-4 / 0582273714
ISBN-13	978-0-582-27371-9 / 9780582273719
Zustand	Neuware