Patterns and Interfaces in Dissipative Dynamics

ISBN-13: 9783031295782 / Angielski

Len Pismen

Opis

Spontaneous pattern formation in nonlinear dissipative systems far from equilibrium occurs in a variety of settings in nature and technology, and has applications ranging from nonlinear optics through solid and fluid mechanics, physical chemistry and chemical engineering to biology. This book explores the forefront of current research, describing in-depth the analytical methods that elucidate the complex evolution of nonlinear dissipative systems.

Spis treści

Dynamics, Stability and Bifurcations.- Fronts and Interfaces.- Systems with Separated Scales.- Amplitude Equations for Patterns.- Amplitude Equations for Waves.- Media with Internal Orientation. - Dynamic of active gels

0 Introduction

The notion of active (in addition to dissipative) systems will be introduced. The preliminary discussion of field variables will be amended by adding internal orientation variables.

1 Dynamics, Stability and Bifurcations

A section describing bifurcations to ordered states will be added. Active (antidissipative) systems will be discussed explicitly. The section 'Deterministic Chaos' will be excluded.

2 Fronts and Interfaces

3 Systems with Separated Scales

4 Amplitude Equations for Patterns

5 Amplitude Equations for Waves

The material of Chapters. 2-5 will remain more or less intact but corrected where necessary. Some elementary topics may be excluded.

6 Media with Internal Orientation

A new Chapter discussing dynamics of liquids and soft solids with internal orientation. Motion of defects, emphasizing similarities/distinctions to/from dynamics of defects in patterns. Turbulent patterns. Interfaces of oriented media.

7 Dynamic of Active Gels

A new Chapter dedicated to biophysical applications of the theory of active oriented media to motion of cells, tissues, and biomorphic materials.

O autorze

Len Pismen is Emeritus Professor of Fluid Mechanics at the Technion – Israel Institute of Technology. He has worked in various areas of applied physics and published over 200 papers. His earlier books include Vortices in Nonlinear Fields (1999), Patterns and Interfaces in Dissipative Dynamics (first edition, 2006), a textbook Working with Dynamical Systems (2021) and general audience books The Swings of Science (2018), Morphogenesis Deconstructed (2020), and Active Matter within and around us (2021). The latter two books appear in Springer's Frontiers Collection.

Blurb

Spontaneous pattern formation in nonlinear dissipative systems far from equilibrium is a paradigmatic case of emergent behaviour associated with complex systems. It is encountered in a great variety of settings, both in nature and technology, and has numerous applications ranging from nonlinear optics through solid and fluid mechanics, physical chemistry and chemical engineering to biology.

This book is a first-hand account by one of the leading players in this field, which gives in-depth descriptions of analytical methods elucidating the complex evolution of nonlinear dissipative systems, and brings the reader to the forefront of current research.

Since the publication of the first edition, applications of the theory of nonlinear dynamics have been substantially extended to the novel area of active systems, largely motivated by problems of biophysics and biomorphic technology. These problems typically involve media with internal orientation. This new edition incorporates a chapter discussing dynamics of liquids and soft solids with internal orientation, including special features of their instabilities and motion of topological defects, which form the background for various applications to the motion of cells, tissues, and activated soft materials. The contents of the first edition have also been substantially reworked, improving graphics, emphasizing more complex secondary instabilities, and dropping some material pertaining to dynamical systems. 

This book caters for graduate students and young researchers from many pertinent areas including applied mathematics, physical chemistry, chemical engineering and biophysics, as well as the seasoned scientist in search of a modern source of reference.