Fluctuations and Order

Author: Mark Millonas
Publisher: Springer Science & Business Media
ISBN: 1461239923
Format: PDF, Kindle
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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.

Analysis of Observed Chaotic Data

Author: Henry Abarbanel
Publisher: Springer Science & Business Media
ISBN: 1461207630
Format: PDF, Kindle
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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.

Physics of Fractal Operators

Author: Bruce West
Publisher: Springer Science & Business Media
ISBN: 9780387955544
Format: PDF, ePub, Mobi
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This text describes how fractal phenomena, both deterministic and random, change over time, using the fractional calculus. The intent is to identify those characteristics of complex physical phenomena that require fractional derivatives or fractional integrals to describe how the process changes over time. The discussion emphasizes the properties of physical phenomena whose evolution is best described using the fractional calculus, such as systems with long-range spatial interactions or long-time memory. In many cases, classic analytic function theory cannot serve for modeling complex phenomena; "Physics of Fractal Operators" shows how classes of less familiar functions, such as fractals, can serve as useful models in such cases. Because fractal functions, such as the Weierstrass function (long known not to have a derivative), do in fact have fractional derivatives, they can be cast as solutions to fractional differential equations. The traditional techniques for solving differential equations, including Fourier and Laplace transforms as well as Green's functions, can be generalized to fractional derivatives. Physics of Fractal Operators addresses a general strategy for understanding wave propagation through random media, the nonlinear response of complex materials, and the fluctuations of various forms of transport in heterogeneous materials. This strategy builds on traditional approaches and explains why the historical techniques fail as phenomena become more and more complicated.

Digital Communications Using Chaos and Nonlinear Dynamics

Author: Jia-Ming Liu
Publisher: Springer Science & Business Media
ISBN: 038729788X
Format: PDF, 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.

Books in Print

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Books in print is the major source of information on books currently published and in print in the United States. The database provides the record of forthcoming books, books in-print, and books out-of-print.

Applications of Nonlinear Programming to Optimization and Control

Author: H. E. Rauch
Publisher: Elsevier
ISBN: 1483148394
Format: PDF, Mobi
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Applications of Nonlinear Programming to Optimization and Control is a collection of papers presented at the Fourth International Federation of Automatic Control Workshop by the same title, held in San Francisco, California on June 20-21, 1983. This workshop aims to exchange information on the applications of optimization and nonlinear programming techniques to real-life control problems, to investigate ideas that arise from these exchanges, and to look for advances in nonlinear programming that are useful in solving control problems. This book is divided into 16 chapters. It covers a wide range of related topics, starting with computer-aided-design of practical control systems, continuing through advanced work on quasi-Newton methods and gradient restoration algorithms. Other chapters provide specific examples, which apply these methods to representative problems. The remaining chapters present examples, including trajectory optimization, optimal design of a structure for a satellite, identification of hovercraft characteristics, determination of optimal electricity generation, and optimal automatic transmission for road vehicles. This book is of value to computer scientists and mathematicians.