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This book is an introduction to the application of nonlinear dynamics to problems of stability, chaos and turbulence arising in continuous media and their connection to dynamical systems. With an emphasis on the understanding of basic concepts, it should be of interest to nearly any science-oriented undergraduate and potentially to anyone who wants to learn about recent advances in the field of applied nonlinear dynamics. Technicalities are, however, not completely avoided. They are instead explained as simply as possible using heuristic arguments and specific worked examples.

This book is an introduction to the application of nonlinear dynamics to problems of stability, chaos and turbulence arising in continuous media and their connection to dynamical systems. With an emphasis on the understanding of basic concepts, it should be of interest to nearly any science-oriented undergraduate and potentially to anyone who wants to learn about recent advances in the field of applied nonlinear dynamics. Technicalities are, however, not completely avoided. They are instead explained as simply as possible using heuristic arguments and specific worked examples.

Offers an introduction to a wide body of knowledge on nonlinear dynamics and chaos. This book emphasises the understanding of basic concepts and the nontrivial character of nonlinear response, contrasting it with the intuitively simple linear response. It explains the theoretical framework using pedagogical examples from fluid dynamics.

Cellular automata are fully discrete dynamical systems with dynamical variables defined at the nodes of a lattice and taking values in a finite set. Application of a local transition rule at each lattice site generates the dynamics. The interpretation of systems with a large number of degrees of freedom in terms of lattice gases has received considerable attention recently due to the many applications of this approach, e.g. for simulating fluid flows under nearly realistic conditions, for modeling complex microscopic natural phenomena such as diffusion-reaction or catalysis, and for analysis...

This book presents five sets of pedagogical lectures by internationally respected researchers on nonlinear instabilities and the transition to turbulence in hydrodynamics. The book begins with a general introduction to hydrodynamics covering fluid properties, flow measurement, dimensional analysis and turbulence. Chapter two reviews the special characteristics of instabilities in open flows. Chapter three presents mathematical tools for multiscale analysis and asymptotic matching applied to the dynamics of fronts and localized nonlinear states. Chapter four gives a detailed review of pattern...