Author: P Cvitanovic

Publisher: CRC Press

ISBN: 9780852742600

Category: Science

Page: 648

View: 4378

Nature provides many examples of physical systems that are described by deterministic equations of motion, but that nevertheless exhibit nonpredictable behavior. The detailed description of turbulent motions remains perhaps the outstanding unsolved problem of classical physics. In recent years, however, a new theory has been formulated that succeeds in making quantitative predictions describing certain transitions to turbulence. Its significance lies in its possible application to large classes (often very dissimilar) of nonlinear systems. Since the publication of Universality in Chaos in 1984, progress has continued to be made in our understanding of nonlinear dynamical systems and chaos. This second edition extends the collection of articles to cover recent developments in the field, including the use of statistical mechanics techniques in the study of strange sets arising in dynamics. It concentrates on the universal aspects of chaotic motions, the qualitative and quantitative predictions that apply to large classes of physical systems. Much like the previous edition, this book will be an indispensable reference for researchers and graduate students interested in chaotic dynamics in the physical, biological, and mathematical sciences as well as engineering.
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With Applications to Physics, Biology, Chemistry, and Engineering, Second Edition

Author: Steven H. Strogatz

Publisher: CRC Press

ISBN: 0429680155

Category: Mathematics

Page: 404

View: 7011

This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.
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With Applications in Science and Engineering

Author: Saber N. Elaydi

Publisher: CRC Press

ISBN: 1584885920

Category: Mathematics

Page: 440

View: 2333

While maintaining the lucidity of the first edition, Discrete Chaos, Second Edition: With Applications in Science and Engineering now includes many recent results on global stability, bifurcation, chaos, and fractals. The first five chapters provide the most comprehensive material on discrete dynamical systems, including trace-determinant stability, bifurcation analysis, and the detailed analysis of the center manifold theory. This edition also covers L-systems and the periodic structure of the bulbs in the Mandelbrot set as well as new applications in biology, chemistry, and physics. The principal improvements to this book are the additions of PHASER software on an accompanying CD-ROM and the MapleTM and Mathematica® code available for download online. Incorporating numerous new topics and technology not found in similar texts, Discrete Chaos, Second Edition presents a thorough, up-to-date treatment of the theory and applications of discrete dynamical systems.
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Author: Hao Bailin,Zheng Wei-mou

Publisher: World Scientific

ISBN: 9813236442

Category: Science

Page: 520

View: 2095

Symbolic dynamics is a coarse-grained description of dynamics. It has been a long-studied chapter of the mathematical theory of dynamical systems, but its abstract formulation has kept many practitioners of physical sciences and engineering from appreciating its simplicity, beauty, and power. At the same time, symbolic dynamics provides almost the only rigorous way to understand global systematics of periodic and, especially, chaotic motion in dynamical systems. In a sense, everyone who enters the field of chaotic dynamics should begin with the study of symbolic dynamics. However, this has not been an easy task for non-mathematicians. On one hand, the method of symbolic dynamics has been developed to such an extent that it may well become a practical tool in studying chaotic dynamics, both on computers and in laboratories. On the other hand, most of the existing literature on symbolic dynamics is mathematics-oriented. This book is an attempt at partially filling up this apparent gap by emphasizing the applied aspects of symbolic dynamics without mathematical rigor. Contents: Preface to the Second Edition Preface to the First Edition Introduction Symbolic Dynamics of Unimodal Maps Maps with Multiple Critical Points Symbolic Dynamics of Circle Maps Symbolic Dynamics of Two-Dimensional Maps Application to Ordinary Differential Equations Counting the Number of Periodic Orbits Symbolic Dynamics and Grammatical Complexity Symbolic Dynamics and Knot Theory Appendix References Index Readership: Researchers and students interested in chaotic dynamics. Keywords: Symbolic Dynamics;ChaosReview: Key Features: No previous knowledge of dynamical systems theory is required in order to read this book The revisions concern mainly the application to ordinary differential equations via constructing two-dimensional symbolic dynamics of the corresponding Poincare maps
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An Introduction for Scientists and Engineers

Author: Robert C. Hilborn,Amanda and Lisa Cross Professor of Physics Robert Hilborn

Publisher: Oxford University Press on Demand

ISBN: 9780198507239

Category: Mathematics

Page: 650

View: 7466

This is a comprehensive introduction to the exciting scientific field of nonlinear dynamics for students, scientists, and engineers, and requires only minimal prerequisites in physics and mathematics. The book treats all the important areas in the field and provides an extensive and up-to-date bibliography of applications in all fields of science, social science, economics, and even the arts.
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Author: N.A

Publisher: N.A

ISBN: N.A

Category: Sociology

Page: N.A

View: 2977

International journal for the application of formal methods to history.
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Author: Denny Gulick

Publisher: CRC Press

ISBN: 1584885173

Category: Mathematics

Page: 387

View: 614

Now with an extensive introduction to fractal geometry Revised and updated, Encounters with Chaos and Fractals, Second Edition provides an accessible introduction to chaotic dynamics and fractal geometry for readers with a calculus background. It incorporates important mathematical concepts associated with these areas and backs up the definitions and results with motivation, examples, and applications. Laying the groundwork for later chapters, the text begins with examples of mathematical behavior exhibited by chaotic systems, first in one dimension and then in two and three dimensions. Focusing on fractal geometry, the author goes on to introduce famous infinitely complicated fractals. He analyzes them and explains how to obtain computer renditions of them. The book concludes with the famous Julia sets and the Mandelbrot set. With more than enough material for a one-semester course, this book gives readers an appreciation of the beauty and diversity of applications of chaotic dynamics and fractal geometry. It shows how these subjects continue to grow within mathematics and in many other disciplines.
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Author: Robert T. Hudspeth

Publisher: World Scientific Publishing Company Incorporated

ISBN: N.A

Category: Science

Page: 932

View: 9824

This book focuses on: (1) the physics of the fundamental dynamics of fluids and of semi-immersed Lagrangian solid bodies that are responding to wave-induced loads; (2) the scaling of dimensional equations and boundary value problems in order to determine a small dimensionless parameter e that may be applied to linearize the equations and the boundary value problems so as to obtain a linear system; (3) the replacement of differential and integral calculus with algebraic equations that require only algebraic substitutions instead of differentiations and integrations; and (4) the importance of comparing numerical and analytical computations with data from laboratories and/or nature.
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eine Wissenschaftsphilosophie der nachmodernen Physik

Author: Jan Cornelius Schmidt

Publisher: De Gruyter

ISBN: N.A

Category: Philosophy

Page: 459

View: 5789

Review text: "Es gibt Bücher, die durch ihre unprätentiöse, stille und sorgfältige Vorgehensweise auf den ersten Blick über die Sensation hinwegtäuschen, die sie bloßlegen und zur Diskussion anbieten. So ein Buch ist die "Wissenschaftphilosophie? von Jan C. Schmidt, die über die "Instabilität in Natur und Wissenschaft? handelt."Günter Altner in: Naturwissenschaftliche Rundschau 9/2009.
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Author: Fritz Haake

Publisher: Springer Science & Business Media

ISBN: 3642054285

Category: Science

Page: 576

View: 8346

This classic text provides an excellent introduction to a new and rapidly developing field of research. Now well established as a textbook in this rapidly developing field of research, the new edition is much enlarged and covers a host of new results.
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Author: Nicholas Tufillaro,Tyler Abbott

Publisher: Addison Wesley Publishing Company

ISBN: N.A

Category: Chaotic behavior in systems.

Page: 420

View: 1096

This essential handbook provides the theoretical and experimental tools necessary to begin researching the nonlinear behavior of mechanical, electrical, optical, and other systems. The book describes several nonlinear systems which are realized by desktop experiments, such as an apparatus showing chaotic string vibrations, an LRC circuit displaying strange scrolling patterns, and a bouncing ball machine illustrating the period doubling route to chaos. Fractal measures, periodic orbit extraction, and symbolic analysis are applied to unravel the chaotic motions of these systems. The simplicity of the examples makes this an excellent book for undergraduate and graduate-level physics and mathematics courses, new courses in dynamical systems, and experimental laboratories.
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Geschichte, Theorie, Flut

Author: James Gleick

Publisher: Redline Wirtschaft

ISBN: 3864142245

Category: Science

Page: 500

View: 5231

Blut, Treibstoff, Lebensprinzip - in seinem furiosen Buch erzählt Bestsellerautor James Gleick, wie die Information zum Kernstück unserer heutigen Zivilisation wurde. Beginnend bei den Wörtern, den "sprechenden" Trommeln in Afrika, über das Morsealphabet und bis hin zur Internetrevolution beleuchtet er, wie die Übermittlung von Informationen die Gesellschaften prägten und veränderten. Gleick erläutert die Theorien, die sich mit dem Codieren und Decodieren, der Übermittlung von Inhalten und dem Verbreiten der Myriaden von Botschaften beschäftigen. Er stellt die bekannten und unbekannten Pioniere der Informationsgesellschaft vor: Claude Shannon, Norbert Wiener, Ada Byron, Alan Turing und andere. Er bietet dem Leser neue Einblicke in die Mechanismen des Informationsaustausches. So lernt dieser etwa die sich selbst replizierende Meme kennen, die "DNA" der Informationen. Sein Buch ermöglicht ein neues Verständnis von Musik, Quantenmechanik - und eine gänzlich neue Sicht auf die faszinierende Welt der Informationen.
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Eine moderne Einführung in die Sprache des Web

Author: Marijn Haverbeke

Publisher: dpunkt.verlag

ISBN: 3864911915

Category: Computers

Page: 240

View: 9638

Das Buch ist eine Einführung in JavaScript, die sich auf gute Programmiertechniken konzentriert. Der Autor lehrt den Leser, wie man die Eleganz und Präzision von JavaScript nutzt, um browserbasierte Anwendungen zu schreiben. Das Buch beginnt mit den Grundlagen der Programmierung - Variablen, Kontrollstrukturen, Funktionen und Datenstrukturen -, dann geht es auf komplexere Themen ein, wie die funktionale und objektorientierte Programmierung, reguläre Ausdrücke und Browser-Events. Unterstützt von verständlichen Beispielen wird der Leser rasch die Sprache des Web fließend 'sprechen' können.
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Author: Yuval Noah Harari

Publisher: DVA

ISBN: 364110498X

Category: History

Page: 528

View: 8868

Krone der Schöpfung? Vor 100 000 Jahren war der Homo sapiens noch ein unbedeutendes Tier, das unauffällig in einem abgelegenen Winkel des afrikanischen Kontinents lebte. Unsere Vorfahren teilten sich den Planeten mit mindestens fünf weiteren menschlichen Spezies, und die Rolle, die sie im Ökosystem spielten, war nicht größer als die von Gorillas, Libellen oder Quallen. Vor 70 000 Jahren dann vollzog sich ein mysteriöser und rascher Wandel mit dem Homo sapiens, und es war vor allem die Beschaffenheit seines Gehirns, die ihn zum Herren des Planeten und zum Schrecken des Ökosystems werden ließ. Bis heute hat sich diese Vorherrschaft stetig zugespitzt: Der Mensch hat die Fähigkeit zu schöpferischem und zu zerstörerischem Handeln wie kein anderes Lebewesen. Anschaulich, unterhaltsam und stellenweise hochkomisch zeichnet Yuval Harari die Geschichte des Menschen nach und zeigt alle großen, aber auch alle ambivalenten Momente unserer Menschwerdung.
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