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Author : Jordi Garcia-Ojalvo
Release : 1999-06-01
Genre :
Kind : eBook
Book Rating : 370/5 ( reviews)
Book Synopsis Noise in Spatially Extended Systems by : Jordi Garcia-Ojalvo
Download or read book Noise in Spatially Extended Systems written by Jordi Garcia-Ojalvo. This book was released on 1999-06-01. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jordi Garcia-Ojalvo
Release : 2012-12-06
Genre : Science
Kind : eBook
Book Rating : 366/5 ( reviews)
Book Synopsis Noise in Spatially Extended Systems by : Jordi Garcia-Ojalvo
Download or read book Noise in Spatially Extended Systems written by Jordi Garcia-Ojalvo. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: Intended for graduates and researchers in physics, chemistry, biology, and applied mathematics, this book provides an up-to-date introduction to current research in fluctuations in spatially extended systems. It covers the theory of stochastic partial differential equations and gives an overview of the effects of external noise on dynamical systems with spatial degrees of freedom. Starting with a general introduction to noise-induced phenomena in dynamical systems, the text moves on to an extensive discussion of analytical and numerical tools needed to gain information from stochastic partial differential equations. It then turns to particular problems described by stochastic PDEs, covering a wide part of the rich phenomenology of spatially extended systems, such as nonequilibrium phase transitions, domain growth, pattern formation, and front propagation. The only prerequisite is a minimal background knowledge of the Langevin and Fokker-Planck equations.
Author : Martin Gassel
Release : 2009
Genre :
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Influence of Noise, Variability, and Time-delayed Feedback on Spatially Extended Systems by : Martin Gassel
Download or read book Influence of Noise, Variability, and Time-delayed Feedback on Spatially Extended Systems written by Martin Gassel. This book was released on 2009. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Erik Glatt
Release : 2008
Genre :
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Pattern Formation in Spatially Extended Systems by : Erik Glatt
Download or read book Pattern Formation in Spatially Extended Systems written by Erik Glatt. This book was released on 2008. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Kevin B. Wood
Release : 2007
Genre :
Kind : eBook
Book Rating : 020/5 ( reviews)
Book Synopsis Nonequilibrium Phase Transitions to Collective Behavior in Stochastic Spatially Extended Systems by : Kevin B. Wood
Download or read book Nonequilibrium Phase Transitions to Collective Behavior in Stochastic Spatially Extended Systems written by Kevin B. Wood. This book was released on 2007. Available in PDF, EPUB and Kindle. Book excerpt: We explore nonequilibrium collective behavior in large, spatially extended stochastic systems. In Part I, we present a model of discrete, active, noisy phase oscillators sufficiently simple to be characterized in complete detail in a host of diverse settings. In Chapter 2, we introduce the model and detail its utility for the study of both continuous and discontinuous phase transitions to macroscopic oscillations. In Chapter 3 we analyze a locally coupled version of the model undergoing a continuous transition and provide strong evidence that the inherently nonequilibrium system shows qualitative and quantitative characteristics of a known class of equilibrium phase transitions. Chapter 4 offers an analysis of the discrete model in the face of quenched transition rate disorder, where synchronization still occurs and depends on the degree of disorder in the population. The final chapter of Part I, Chapter 5, details the microscopic underpinnings of synchronization above threshold, including the counterintuitive relationship between time-averaged frequency and the mean field oscillations. The second part of the dissertation begins with an introduction to generic relaxational models with field-dependent kinetic coeffcients, highlighting in particular the role of this class of models in the study of noise-induced phase transitions. Using these systems as prototypical models of noise-induced phenomena in spatially extended systems, we offer a comprehensive study of static pattern formation in Chapter 7, while Chapter 8 provides a numerical study of coherent oscillatory dynamics induced purely by noise. Finally, Chapter 9 details an analytical framework for studying the dynamics of these systems which is capable of approximately describing both static and time-dependent phases associated with the nonequilibrium transitions in these relaxational models.
