Evolution of Spontaneous Structures in Dissipative Continuous Systems

ISBN-13: 9783642084553 / Angielski / Miękka / 2011 / 586 str.

Friedrich H. Busse; Stefan C. Muller

Opis

In the decades the of the formation of structures past subject spontaneous in far from has into a branch of - systems equilibrium major physics grown search with ties to It has become evident that strong neighboring disciplines. a diverse of can be understood within a common mat- phenomena range matical framework which has been called nonlinear of continuous dynamics This name the close to the field of nonlinear systems. emphasizes relationship of with few of freedom which has evolved into a dynamics systems degrees mature in the recent features mathematically subject past. Many dynamical of continuous be described reduction few can a to a systems actually through of freedom and of the latter of continue to degrees properties type systems of continuous the inspire study systems. The of this book is to demonstrate the numerous goal through examples that exist for the of nonlinear the opportunities study phenomena through tools of mathematical and use of common analyses dynamical interpretations. Instead of overview of the a providing comprehensive rapidly evolving field, the contributors to this book are to communicate to a wide scientific trying audience the of what have learnt about the formation of essence they spon- neous structures in continuous and about the dissipative systems competition between order and chaos that characterizes these It is that systems. hoped the book will be even to those scientists whose not helpful are disciplines the authors.

Recenzje

 From the reviews:

"Overall, the book is a remarkable achievement, bringing together as it does so many of the strands ofresearch in so many different fields of physics and mathematics, and managing to present a digestible mixture of experiment and theory in almost every article." (UK Nonlinear News, 2001)

Spis treści

Mathematical Tools for Pattern Formation.- Formation of Dynamical Structures in Axisymmetric Fluid Systems.- Pattern Formation in Binary Fluid Convection and in Systems with Throughflow.- Dynamical Structures in Open Fluid Systems.- Theoretical and Experimental Investigations of the Faraday Instability.- Pattern Formation in an Inhomogeneous Environment.- Electrically Driven Instabilities in Smectic Liquid Crystal Films.- Electrohydrodynamic Convection in Nematics.- Dynamics of Patterns of Chemical Reactions on Surfaces.- Convection and Pattern Formation Induced by Autocatalytic Chemical Reactions.- Formation of Spatio-Temporal Structures in Semiconductors.- Formation of Patterns in Granular Materials.- Spontaneous Generation of Magnetic Fields in the Laboratory.- From Single Cells to a Multicellular Organism: The Development of the Social Amoebae Dictyostelium Discoideum.

Blurb

This collection of articles forms a cohesive text on the rapidly evolving field of nonlinear dynamics of continous systems. It addresses researchers but it can also be used as a text for graduate work. The authors demonstrate through numerous examples the use of common tools of mathematical analyses and dynamical interpretations for the study of nonlinear phenomena. Instead of providing a comprehensive overview of the rapidly evolving field, the contributors treat the essence of what is known about the formation of spontaneous structures in dissipative continuous systems and about the competition between order and chaos that characterizes those systems. The topics discussed in this volume range from mathematical foundations to interpretations of concrete phenomena in fluids, chemical reactions, structure forming processes in semiconductors and even biological organisms.