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Noise In Spatially Extended Systems

Author: Jordi Garcia-Ojalvo
Publisher: Springer Science & Business Media
ISBN: 1461215366
Size: 40.74 MB
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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.

Noise In Spatially Extended Systems

Author: Jordi Garcia-Ojalvo
Publisher: Springer Science & Business Media
ISBN: 1461215366
Size: 23.42 MB
Format: PDF, ePub, Docs
View: 4118
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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.

Aspects Of Mathematical Modelling

Author: Roger J. Hosking
Publisher: Springer Science & Business Media
ISBN: 9783764385910
Size: 72.40 MB
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The construction of mathematical models is an essential scientific activity. Mathematics is associated with developments in science and engineering, but more recently mathematical modelling has been used to investigate complex systems that arise in other fields. This book demonstrates the application of mathematics to research topics in ecology and environmental science, health and medicine, phylogenetics and neural networks, theoretical chemistry, economics and management.

Physics Of Stochastic Processes

Author: Reinhard Mahnke
Publisher: John Wiley & Sons
ISBN: 3527626107
Size: 78.76 MB
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Based on lectures given by one of the authors with many years of experience in teaching stochastic processes, this textbook is unique in combining basic mathematical and physical theory with numerous simple and sophisticated examples as well as detailed calculations. In addition, applications from different fields are included so as to strengthen the background learned in the first part of the book. With its exercises at the end of each chapter (and solutions only available to lecturers) this book will benefit students and researchers at different educational levels. Solutions manual available for lecturers on www.wiley-vch.de

An Introduction To Computational Stochastic Pdes

Author: Gabriel J. Lord
Publisher: Cambridge University Press
ISBN: 0521899907
Size: 21.17 MB
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This book gives a comprehensive introduction to numerical methods and analysis of stochastic processes, random fields and stochastic differential equations, and offers graduate students and researchers powerful tools for understanding uncertainty quantification for risk analysis. Coverage includes traditional stochastic ODEs with white noise forcing, strong and weak approximation, and the multi-level Monte Carlo method. Later chapters apply the theory of random fields to the numerical solution of elliptic PDEs with correlated random data, discuss the Monte Carlo method, and introduce stochastic Galerkin finite-element methods. Finally, stochastic parabolic PDEs are developed. Assuming little previous exposure to probability and statistics, theory is developed in tandem with state-of-the-art computational methods through worked examples, exercises, theorems and proofs. The set of MATLAB codes included (and downloadable) allows readers to perform computations themselves and solve the test problems discussed. Practical examples are drawn from finance, mathematical biology, neuroscience, fluid flow modelling and materials science.

Synchronization

Author: Stefano Boccaletti
Publisher: Cambridge University Press
ISBN: 1107056268
Size: 10.48 MB
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A modern introduction to synchronization phenomena, combining the development of deep mathematical concepts with illustrative examples and practical applications.

Nonlinear Dynamics And Chaos In Agricultural Systems

Author: Kenshi Sakai
Publisher: Gulf Professional Publishing
ISBN: 9780444506467
Size: 61.78 MB
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This book provides an introduction to the analysis of chaos and chaos theory as it relates to agricultural science. With clear explanations of chaos theory and principles, the first part of the book offers some basic facts, the fundamental terminology, and the concepts of deterministic chaos. The second part of this volume contains rich applications of the theory as applied to real agricultural systems. Applications include a wide area such as alternate bearing in tree crops, weed control and tillage, nonlinear vibrations in agricultural tractors, and piglet pricing analysis. Readers will find useful tools for calculating the order, rules and theory behind complex phenomena observed in arable land.

Nonlinear Dynamics Of Chaotic And Stochastic Systems

Author: Vadim S. Anishchenko
Publisher: Springer Science & Business Media
ISBN: 3540381686
Size: 20.31 MB
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We present an improved and enlarged version of our book Nonlinear - namics of Chaotic and Stochastic Systems published by Springer in 2002. Basically, the new edition of the book corresponds to its ?rst version. While preparingthiseditionwemadesomeclari?cationsinseveralsectionsandalso corrected the misprints noticed in some formulas. Besides, three new sections have been added to Chapter 2. They are “Statistical Properties of Dynamical Chaos,” “E?ects of Synchronization in Extended Self-Sustained Oscillatory Systems,” and “Synchronization in Living Systems.” The sections indicated re?ect the most interesting results obtained by the authors after publication of the ?rst edition. We hope that the new edition of the book will be of great interest for a widesectionofreaderswhoarealreadyspecialistsorthosewhoarebeginning research in the ?elds of nonlinear oscillation and wave theory, dynamical chaos, synchronization, and stochastic process theory. Saratov, Berlin, and St. Louis V.S. Anishchenko November 2006 A.B. Neiman T.E. Vadiavasova V.V. Astakhov L. Schimansky-Geier Preface to the First Edition Thisbookisdevotedtotheclassicalbackgroundandtocontemporaryresults on nonlinear dynamics of deterministic and stochastic systems. Considerable attentionisgiventothee?ectsofnoiseonvariousregimesofdynamicsystems with noise-induced order. On the one hand, there exists a rich literature of excellent books on n- linear dynamics and chaos; on the other hand, there are many marvelous monographs and textbooks on the statistical physics of far-from-equilibrium andstochasticprocesses.Thisbookisanattempttocombinetheapproachof nonlinear dynamics based on the deterministic evolution equations with the approach of statistical physics based on stochastic or kinetic equations. One of our main aims is to show the important role of noise in the organization and properties of dynamic regimes of nonlinear dissipative systems.