Jürgen Parisi

Stefan C. Müller

This book presents the general concepts of self-organized spatio-temporal ordering processes. These concepts are demonstrated via prototypical examples of recent advances in materials science. Particular emphasis is on nano scale soft matter in physics, chemistry, biology and biomedicine. The questions addressed embrace a broad spectrum of complex nonlinear phenomena, ranging from self-assembling near the thermodynamical equilibrium to dissipative structure formation far from equilibrium. Their mutual interplay gives rise to increasing degrees of hierarchical order. Analogues are pointed out, differences characterized and efforts are made to reveal common features in the mechanistic description of those phenomena.

Principles and Prototypical Examples of Recent Advances

Bottom-Up Self-Organization in Supramolecular Soft Matter

Kinko Tsuji

This richly illustrated book explores the fascinating and ubiquitous occurrence of spirals and vortices in human culture and in nature. Spiral forms have been used as elements in the arts for thousands of years, whereas their role in nature and science – from DNA and sea shells to galaxies – is still a topic of investigation in numerous fields. Following an introduction to the cultural history of spiral forms, the book presents contributions from leading experts, who describe the origins, mechanisms and dynamics of spirals and vortices in their special fields. As a whole the book provides a valuable source of information, while also taking the reader on an aesthetic and scientific journey through the world of spiral forms.

In Culture, Nature, and Science

Spirals and Vortices

Friedrich H. Busse

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.

Stefan C. Müller

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