Fluctuations and Order

Author: Mark Millonas
Publisher: Springer Science & Business Media
ISBN: 1461239923
Format: PDF, ePub, Mobi
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The volume that you have before you is the result of a growing realization that fluctuations in nonequilibrium systems playa much more important role than was 1 first believed. It has become clear that in nonequilibrium systems noise plays an active, one might even say a creative, role in processes involving self-organization, pattern formation, and coherence, as well as in biological information processing, energy transduction, and functionality. Now is not the time for a comprehensive summary of these new ideas, and I am certainly not the person to attempt such a thing. Rather, this short introductory essay (and the book as a whole) is an attempt to describe where we are at present and how the viewpoint that has evolved in the last decade or so differs from those of past decades. Fluctuations arise either because of the coupling of a particular system to an ex ternal unknown or "unknowable" system or because the particular description we are using is only a coarse-grained description which on some level is an approxima tion. We describe the unpredictable and random deviations from our deterministic equations of motion as noise or fluctuations. A nonequilibrium system is one in which there is a net flow of energy. There are, as I see it, four basic levels of sophistication, or paradigms, con cerning fluctuations in nature. At the lowest level of sophistication, there is an implicit assumption that noise is negligible: the deterministic paradigm.

Physics of Fractal Operators

Author: Bruce West
Publisher: Springer Science & Business Media
ISBN: 9780387955544
Format: PDF, Kindle
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This text describes the statistcal behavior of complex systems and shows how the fractional calculus can be used to model the behavior. The discussion emphasizes physical phenomena whose evolution is best described using the fractional calculus, such as systems with long-range spatial interactions or long-time memory. The book gives general strategies for understanding wave propagation through random media, the nonlinear response of complex materials, and the fluctuations of heat transport in heterogeneous materials.

Analysis of Observed Chaotic Data

Author: Henry Abarbanel
Publisher: Springer Science & Business Media
ISBN: 1461207630
Format: PDF
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A clear and systematic treatment of time series of data, regular and chaotic, found in nonlinear systems. The text leads readers from measurements of one or more variables through the steps of building models of the source as a dynamical system, classifying the source by its dynamical characteristics, and finally predicting and controlling the dynamical system. It examines methods for separating the signal of physical interest from contamination by unwanted noise, and for investigating the phase space of the chaotic signal and its properties. The emphasis throughout is on the use of modern mathematical tools for investigating chaotic behaviour to uncover properties of physical systems, requiring knowledge of dynamical systems at the advanced undergraduate level and some knowledge of Fourier transforms and other signal processing methods.

Digital Communications Using Chaos and Nonlinear Dynamics

Author: Jia-Ming Liu
Publisher: Springer Science & Business Media
ISBN: 038729788X
Format: PDF, ePub, Docs
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This book provides a summary of the research conducted at UCLA, Stanford University, and UCSD over the last ?ve years in the area of nonlinear dyn- ics and chaos as applied to digital communications. At ?rst blush, the term “chaotic communications” seems like an oxymoron; how could something as precise and deterministic as digital communications be chaotic? But as this book will demonstrate, the application of chaos and nonlinear dynamicstocommunicationsprovidesmanypromisingnewdirectionsinareas of coding, nonlinear optical communications, and ultra-wideband commu- cations. The eleven chapters of the book summarize many of the promising new approaches that have been developed, and point the way to new research directions in this ?eld. Digital communications techniques have been continuously developed and re?ned for the past ?fty years to the point where today they form the heart of a multi-hundred billion dollar per year industry employing hundreds of thousands of people on a worldwide basis. There is a continuing need for transmission and reception of digital signals at higher and higher data rates. There are a variety of physical limits that place an upper limit on these data rates, and so the question naturally arises: are there alternative communi- tion techniques that can overcome some of these limitations? Most digital communications today is carried out using electronic devices that are essentially “linear,” and linear system theory has been used to c- tinually re?ne their performance. In many cases, inherently nonlinear devices are linearized in order to achieve a certain level of linear system performance.

Synthesis of Feedback Systems

Author: Isaac M. Horowitz
Publisher: Elsevier
ISBN: 1483267709
Format: PDF, Kindle
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Synthesis of Feedback Systems presents the feedback theory which exists in various feedback problems. This book provides techniques for the analysis and solution of these problems. The text begins with an introduction to feedback theory and exposition of problems of plant identification, representation, and analysis. Subsequent chapters are devoted to the application of the feedback point of view to any system; the principal useful properties of feedback; the feedback control system synthesis techniques; and the class of two degree-of-freedom feedback configurations and synthesis procedures appropriate for such configurations. The final chapter considers how to translate specifications from their typical original formulation, to the language appropriate for detailed design. The book is intended for engineers and graduate students of engineering design.

Complex Population Dynamics

Author: Peter Turchin
Publisher: Princeton University Press
ISBN: 1400847281
Format: PDF, Docs
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Why do organisms become extremely abundant one year and then seem to disappear a few years later? Why do population outbreaks in particular species happen more or less regularly in certain locations, but only irregularly (or never at all) in other locations? Complex population dynamics have fascinated biologists for decades. By bringing together mathematical models, statistical analyses, and field experiments, this book offers a comprehensive new synthesis of the theory of population oscillations. Peter Turchin first reviews the conceptual tools that ecologists use to investigate population oscillations, introducing population modeling and the statistical analysis of time series data. He then provides an in-depth discussion of several case studies--including the larch budmoth, southern pine beetle, red grouse, voles and lemmings, snowshoe hare, and ungulates--to develop a new analysis of the mechanisms that drive population oscillations in nature. Through such work, the author argues, ecologists can develop general laws of population dynamics that will help turn ecology into a truly quantitative and predictive science. Complex Population Dynamics integrates theoretical and empirical studies into a major new synthesis of current knowledge about population dynamics. It is also a pioneering work that sets the course for ecology's future as a predictive science.