This is an advanced textbook on the subject of turbulence, and is suitable for engineers, physical scientists and applied mathematicians. The aim of the book is to bridge the gap between the elementary accounts of turbulence found in undergraduate texts, and the more rigorous monographs on the subject. Throughout, the book combines the maximum of physical insight with the minimum of mathematical detail. Chapters 1 to 5 may be appropriate as background material for an advanced undergraduate or introductory postgraduate course on turbulence, while chapters 6 to 10 may be suitable as background material for an advanced postgraduate course on turbulence, or act as a reference source for professional researchers. This second edition covers a decade of advancement in the field, streamlining the original content while updating the sections where the subject has moved on. The expanded content includes large-scale dynamics, stratified & rotating turbulence, the increased power of direct numerical simulation, two-dimensional turbulence, Magnetohydrodynamics, and turbulence in the core of the Earth

The discipline of nonlinear dynamics has developed explosively in all areas of physics. This comprehensive primer summarizes the main developments in the mathematical theory of dynamical systems, chaos, pattern formation and complexity. An introduction to mathematical concepts and techniques is given in the first part of the book, before being applied to stellar, interstellar, galactic and large scale complex phenomena in the Universe. Regev demonstrates the possible application of ideas including strange attractors, Poincare sections, fractals, bifurcations, and complex spatial patterns, to specific astrophysical problems. This self-contained text will appeal to a broad audience of astrophysicists and astronomers who wish to understand and apply modern dynamical approaches to the problems they are working on. It provides researchers and graduate students with the investigative tools they need to fully explore chaotic and complex phenomena.

The process of "self-organization" reveals itself in the inanimate worlds of crystals and seashells, but, as Len Fisher shows, it is also evident in living organisms, from fish to ants to human beings. Understanding the "swarm intelligence" inherent in groups can help us do everything from throw a better party to start a fad to make our interactions with others more powerful. humorous and enlightening, The Perfect Swarm demonstrates how complexity arises from nature's simple rules and how we can use their awesome power to untangle the frustrating complexities of life in our ever more chaotic world.

The discipline of nonlinear dynamics has developed explosively in all areas of physics. This comprehensive primer summarizes the main developments in the mathematical theory of dynamical systems, chaos, pattern formation and complexity. An introduction to mathematical concepts and techniques is given in the first part of the book, before being applied to stellar, interstellar, galactic and large scale complex phenomena in the Universe. Regev demonstrates the possible application of ideas including strange attractors, Poincare sections, fractals, bifurcations, and complex spatial patterns, to specific astrophysical problems. This self-contained text will appeal to a broad audience of astrophysicists and astronomers who wish to understand and apply modern dynamical approaches to the problems they are working on. It provides researchers and graduate students with the investigative tools they need to fully explore chaotic and complex phenomena.

This textbook on the theory of nonlinear dynamical systems for nonmathematical advanced undergraduate or graduate students is also a reference book for researchers in the physical and social sciences. It provides a comprehensive introduction including linear systems, stability theory of nonlinear systems, bifurcation theory, chaotic dynamics. Discussion of the measure--theoretic approach to dynamical systems and the relation between deterministic systems and stochastic processes is featured. There are a hundred exercises and an associated website provides a software program, computer exercises and answers to selected book exercises.

This book describes advances in the application of chaos theory to classical scattering and nonequilibrium statistical mechanics generally, and to transport by deterministic diffusion in particular. The author presents the basic tools of dynamical systems theory, such as dynamical instability, topological analysis, periodic-orbit methods, Liouvillian dynamics, dynamical randomness and large-deviation formalism. These tools are applied to chaotic scattering and to transport in systems near equilibrium and maintained out of equilibrium. Chaotic Scattering is illustrated with disk scatterers and with examples of unimolecular chemical reactions and then generalized to transport in spatially extended systems. This book will be bought by researchers interested in chaos, dynamical systems, chaotic scattering, and statistical mechanics in theoretical, computational and mathematical physics and also in theoretical chemistry.

This book presents leading-edge research on artificial life, cellular automata, chaos theory, cognition, complexity theory, synchronisation, fractals, genetic algorithms, information systems, metaphors, neural networks, non-linear dynamics, parallel computation and synergetics. The unifying feature of this research is the tie to chaos and complexity.

The previous edition of this text was the first to provide a quantitative introduction to chaos and nonlinear dynamics at the undergraduate level. It was widely praised for the clarity of writing and for the unique and effective way in which the authors presented the basic ideas. These same qualities characterize this revised and expanded second edition. Interest in chaotic dynamics has grown explosively in recent years. Applications to practically every scientific field have had a far-reaching impact. As in the first edition, the authors present all the main features of chaotic dynamics using the damped, driven pendulum as the primary model. This second edition includes additional material on the analysis and characterization of chaotic data, and applications of chaos. This new edition of Chaotic Dynamics can be used as a text for courses on chaos for physics and engineering students at the second- and third-year level.

This is a graduate text surveying both the theoretical and experimental aspects of chaotic behaviour. Over the course of the past two decades it has been discovered that relatively simple, deterministic, nonlinear mathematical models that describe dynamic phenomena in various physical, chemical, biological and other systems yield solutions which are aperiodic and depend very sensitively on the initial conditions. This phenomenon is known as deterministic chaos. The authors present chaos as a model of many seemingly random processes in nature. Basic notions from the theory of dynamical systems and bifurcation theory, together with the properties of chaotic solutions, are then described and are illustrated by examples. A review of the numerical methods used both in studies of mathematical models and in the interpretation of experimental data is also provided.

This book develops deterministic chaos and fractals from the standpoint of iterated maps, but the method of analysis and choice of emphasis make it very different from all other books in the field. It is written to provide the reader with an introduction to more recent developments, such as weak universality, multifractals, and shadowing, as well as to older subjects like universal critical exponents, devil's staircases and the Farey tree. The book is written especially for those who want clear answers to the following sorts of question: How can a deterministic trajectory be unpredictable? How can one compute nonperiodic chaotic trajectories with controlled precision? Can a deterministic trajectory be random? What are multifractals and where do they come from? What is turbulence and what has it to do with chaos and multifractals? And, finally, why is it not merely convenient, but also necessary, to study classes of iterated maps instead of differential equations when one wants predictions that are applicable to computation and experiment? Throughout the book the author uses a fully discrete method, a 'theoretical computer arithmetic', because finite (but not fixed) precision is a fact of life that cannot be avoided in computation or in experiment. This approach leads to a more general formulation in terms of symbolic dynamics and to the idea of weak universality. The author explains why continuum analysis, computer simulations, and experiments form three entirely distinct approaches to chaos theory. In the end, the connection is made with Turing's ideas of computable numbers and it is explained why the continuum approach leads to predictions that are not necessarily realized incomputations or in nature, whereas the discrete approach yields all possible histograms that can be observed or computed. This algorithmic approach to chaos, dynamics and fractals will be of great interest to graduate students, research workers and advanced undergraduates in physics, engineering and other sciences with an interest in nonlinear science.

This book presents new international research on artificial life, cellular automata, chaos theory, cognition, complexity theory, synchronisation, fractals, genetic algorithms, information systems, metaphors, neural networks, non-linear dynamics, parallel computation and synergetics. The unifying feature of this research is the tie to chaos and complexity.

This book, the first in the Cambridge Nonlinear Science Series, presents the fundamentals of chaos theory in conservative systems, providing a systematic study of the theory of transitional states of physical systems which lie between deterministic and chaotic behaviour. The authors' treatment of transitions to chaos, the theory of stochastic layers and webs, and the numerous applications of this theory, particularly to pattern symmetry, will make the book of importance to scientists from many disciplines.The authors have been meticulous in providing a detailed presentation of the material, enabling the reader to learn the necessary computational methods and to apply them in other problems. The inclusion of a significant amount of computer graphics is also an important aid to understanding. The final section of the book contains a fascinating collection of patterns in art and living nature. The book will be of interest to graduate students and researchers in physics and mathematics who are interested in problems of chaos, irreversibility, statistical mechanics and theories of spatial patterns and symmetries. The perhaps unconventional links between chaos theory and other topics make the book particularly interesting.

This 1989 book is about chaos, fractals and complex dynamics, and is addressed to all people who have some familiarity with computers and enjoy using them. The mathematics has been kept simple, with few formulae, yet the reader is introduced to and can learn about an area of current scientific research which was scarcely possible before the availability of computers. The introduction is achieved through the extensive use of computer graphics. The book is divided into two main parts: in the first the most interesting problems are described, with, in each case, a solution in the form of a computer program. A large number of exercises enable the reader to undertake his or her own experimental work. In the second part, example programs are given for specific machines and operating systems; details refer to MS-DOC and Turbo-Pascal, UNIX 4.2 BSD with Berkley Pascal and C. Other implementations of the graphics routines are given for Apple Macintosh, Apple IIE and IIGS and Atari ST.

This 1989 book is about chaos, fractals and complex dynamics, and is addressed to all people who have some familiarity with computers and enjoy using them. The mathematics has been kept simple, with few formulae, yet the reader is introduced to and can learn about an area of current scientific research which was scarcely possible before the availability of computers. The introduction is achieved through the extensive use of computer graphics. The book is divided into two main parts: in the first the most interesting problems are described, with, in each case, a solution in the form of a computer program. A large number of exercises enable the reader to undertake his or her own experimental work. In the second part, example programs are given for specific machines and operating systems; details refer to MS-DOC and Turbo-Pascal, UNIX 4.2 BSD with Berkley Pascal and C. Other implementations of the graphics routines are given for Apple Macintosh, Apple IIE and IIGS and Atari ST.

An accessible account of systems that display a chaotic time evolution, which although determinative, reveals features more characteristic of a statistical technique known as time series analysis.

This book presents leading-edge research on artificial life, cellular automata, chaos theory, cognition, complexity theory, synchronisation, fractals, genetic algorithms, information systems, metaphors, neural networks, non-linear dynamics, parallel computation and synergetics. The unifying feature of this research is the tie to chaos and complexity.

Part of the Princeton Aeronautical Paperback series designed to bring to students and research engineers outstanding portions of the twelve-volume High Speed Aerodynamics and Jet Propulsion series. These books have been prepared by direct reproduction of the text from the original series and no attempt has been made to provide introductory material or to eliminate cross reference to other portions of the original volumes. Originally published in 1960. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

From its original meaning as a gaping void, or the emptiness that precedes the whole of creation, chaos has taken on the exclusive meaning of confusion, pandemonium and mayhem. This definition has become the overarching word to describe any challenge to the established order; be it railway strikes or political dissent, any unexpected event is routinely described in the media and popular parlance as 'chaos'. In his incisive new study, Stuart Walton argues that this is a pitifully one-dimensional view of the world, as he looks to many of the great social, political, artistic and philosophical advances that have emerged from periods of disorder and from the refusal to think within the standard paradigms. Exploring this worldview, Walton contends that we are superstitious about states of affairs in which anything could happen because we have been taught to prefer the imposition of rules in every aspect of our lives, from our diets to our romances. Indeed, in An Excursion through Chaos he demonstrates how it is these very restrictions that are responsible for the alienation that has characterised postwar society, a state of disengagement that could have been avoided if we had taken a less fearful attitude towards the unravelling of order.

Almost every scientist has heard of catastrophe theory and knows that there has been a considerable amount of controversy surrounding it. Yet comparatively few know anything more about it than they may have read in an article written for the general public. The aim of this book is to make it possible for anyone with a comparatively modest background in mathematics - no more than is usually included in a first year university course for students not specialising in the subject - to understand the theory well enough to follow the arguments in papers in which it is used and, if the occasion arises, to use it. Over half the book is devoted to applications, partly because it is not possible yet for the mathematician applying catastrophe theory to separate the analysis from the original problem. Most of these examples are drawn from the biological sciences, partly because they are more easily understandable and partly because they give a better illustration of the distinctive nature of catastrophe theory. This controversial and intriguing book will find applications as a text and guide to theoretical biologists, and scientists generally who wish to learn more of a novel theory.

Almost every scientist has heard of catastrophe theory and knows that there has been a considerable amount of controversy surrounding it. Yet comparatively few know anything more about it than they may have read in an article written for the general public. The aim of this book is to make it possible for anyone with a comparatively modest background in mathematics - no more than is usually included in a first year university course for students not specialising in the subject - to understand the theory well enough to follow the arguments in papers in which it is used and, if the occasion arises, to use it. Over half the book is devoted to applications, partly because it is not possible yet for the mathematician applying catastrophe theory to separate the analysis from the original problem. Most of these examples are drawn from the biological sciences, partly because they are more easily understandable and partly because they give a better illustration of the distinctive nature of catastrophe theory. This controversial and intriguing book will find applications as a text and guide to theoretical biologists, and scientists generally who wish to learn more of a novel theory.

The editors (of the Universite et Institut National des Sciences Appliquees de Rouen, France) present six chapters exploring the application of chaos theory to such topics as the topological characterisation of attractors and the reconstruction of equations of motion from data. Specific topics include the development of a method of modelling called NARMAX (non-linear autoregressive moving average models with exogenous outputs), a summary of the work of the Centre of Applied Dynamics and Optimisation at the U. of Western Australia), time delayed feedback systems, and global modelling applications to biological data and secure communication.

This volume sets out the basic applied mathematical and numerical methods of chaotic dynamics and illustrates the wide range of phenomena, inside and outside the laboratory, that can be treated as chaotic processes.

Originally published in 1986.

The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Covering one of the fastest growing areas of applied mathematics, Nonlinear Dynamics and Chaos: Second Edition, is a fully updated edition of this highly respected text. Covering a breadth of topics, ranging from the basic concepts to applications in the physical sciences, the book is highly illustrated and written in a clear and comprehensible style.

• Provides a self-contained introduction to the theory and applications of nonlinear dynamics and chaos.

• Introduces the concepts of instabilities, bifurcations, and catastrophes.

• Each idea is carefully explained and supported by examples.

• Features many applications to a wide variety of scientific fields.

• Includes an illustrated glossary of geometrical dynamics.

• Features a supplementary bibliography of further reading.

• Assumes minimal background knowledge.

Mathematical symmetry and chaos come together to form striking, beautiful colour images throughout this impressive work, which addresses how the dynamics of complexity can produce familiar universal patterns. The book, a richly illustrated blend of mathematics and art, was widely hailed in publications as diverse as the New York Review of Books, Scientific American, and Science when first published in 1992. This much-anticipated second edition features many new illustrations and addresses the progress made in the mathematics and science underlying symmetric chaos in recent years; for example, the classifications of attractor symmetries and methods for determining the symmetries of higher dimensional analogues of images in the book. In particular, the concept of patterns on average and their occurrence in the Faraday fluid dynamics experiment is described in a revised introductory chapter. The ideas addressed in this book have been featured at various conferences on intersections between art and mathematics, including the annual Bridges conference, and in lectures to art students at the University of Houston.

In this volume are collected notes of lectures delivered at the First In ternational Research Institute of the Mathematical Society of Japan. This conference, held at Tohoku University in July 1993, was devoted to geometry and global analysis. Subsequent to the conference, in answer to popular de mand from the participants, it was decided to publish the notes of the survey lectures. Written by the lecturers themselves, all experts in their respective fields, these notes are here presented in a single volume. It is hoped that they will provide a vivid account of the current research, from the introduc tory level up to and including the most recent results, and will indicate the direction to be taken by future researeh. This compilation begins with Jean-Pierre Bourguignon's notes entitled "An Introduction to Geometric Variational Problems," illustrating the gen eral framework of the field with many examples and providing the reader with a broad view of the current research. Following this, Kenji Fukaya's notes on "Geometry of Gauge Fields" are concerned with gauge theory and its applications to low-dimensional topology, without delving too deeply into technical detail. Special emphasis is placed on explaining the ideas of infi nite dimensional geometry that, in the literature, are often hidden behind rigorous formulations or technical arguments."