The Fokker Planck Equation For Stochastic Dynamical Systems And Its Explicit Steady State Solutions

Author : C Soize
Publisher : World Scientific
ISBN 13 : 9814502022
Total Pages : 340 pages
Book Rating : 4.23/5 ( download)

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Download or read book The Fokker-Planck Equation for Stochastic Dynamical Systems and Its Explicit Steady State Solutions written by C Soize and published by World Scientific. This book was released on 1994-05-16 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an analysis of multidimensional nonlinear dissipative Hamiltonian dynamical systems subjected to parametric and external stochastic excitations by the Fokker-Planck equation method. The author answers three types of questions concerning this area. First, what probabilistic tools are necessary for constructing a stochastic model and deriving the FKP equation for nonlinear stochastic dynamical systems? Secondly, what are the main results concerning the existence and uniqueness of an invariant measure and its associated stationary response? Finally, what is the class of multidimensional dynamical systems that have an explicit invariant measure and what are the fundamental examples for applications? Contents:Stochastic Canonical Equation of Multidimensional Nonlinear Dissipative Hamiltonian Dynamical SystemsFundamental Examples of Nonlinear Dynamical Systems and Associated Second-Order EquationBrief Review of Probability and Random VariablesProbabilistic Tools I. Classical Stochastic ProcessesProbabilistic Tools II. Mean-Square Theory of Linear Integral Transformations and of Linear Differential EquationsProbabilistic Tools III. Diffusion Processes and Fokker-Planck EquationProbabilistic Tools IV. Stochastic Integrals and Stochastic Differential EquationsStochastic Modeling with Stochastic Differential EquationsFKP Equation for the Dissipative Hamiltonian Dynamical SystemsStationary Response of Dissipative Dynamical Systems, Existence and Uniqueness, Explicit Solution of an Invariant MeasureComplements for the Normalization Condition, Characteristic Function and Moments of the Invariant MeasureApplication I. Multidimensional Linear Oscillators Subject to External and Parametric Random ExcitationsApplication II. Multidimensional Nonlinear Oscillators with Inertial Nonlinearity Subject to External Random ExcitationsApplication III. Multidimensional Nonlinear Oscillators Subject to External and Parametric Random ExcitationsSymplectic Change of Variables in the Multidimensional Unsteady FKP Equation ReferencesIndex Readership: Applied mathematicians. keywords:Fokker–Planck Equation;Stochastic Dynamics;Diffusion Process;Stochastic Methods;Random Vibration;Random Process;Stochastic Differential Equation;Hamiltonian Dynamical System;Stochastic Process;Probabilistic Methods “This is a timely volume summarizing and unifying 30 years of search for explicit solutions of (stationary) FPE's. New articles in this area, which continue to appear, have to explain in which way they extend Soize's presentation. As such, this book is a useful reference for the random vibrations community.” Mathematics Abstracts

Author : Christian Soize
Publisher : World Scientific
ISBN 13 : 9789810217556
Total Pages : 346 pages
Book Rating : 4.52/5 ( download)

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Download or read book The Fokker-Planck Equation for Stochastic Dynamical Systems and Its Explicit Steady State Solutions written by Christian Soize and published by World Scientific. This book was released on 1994 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an analysis of multidimensional nonlinear dissipative Hamiltonian dynamical systems subjected to parametric and external stochastic excitations by the Fokker-Planck equation method.The author answers three types of questions concerning this area. First, what probabilistic tools are necessary for constructing a stochastic model and deriving the FKP equation for nonlinear stochastic dynamical systems? Secondly, what are the main results concerning the existence and uniqueness of an invariant measure and its associated stationary response? Finally, what is the class of multidimensional dynamical systems that have an explicit invariant measure and what are the fundamental examples for applications?

Author : Da-Quan Jiang
Publisher : Springer Science & Business Media
ISBN 13 : 9783540206118
Total Pages : 296 pages
Book Rating : 4.16/5 ( download)

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Download or read book Mathematical Theory of Nonequilibrium Steady States written by Da-Quan Jiang and published by Springer Science & Business Media. This book was released on 2004 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Manolis Papadrakakis
Publisher : Springer
ISBN 13 : 3319063316
Total Pages : 306 pages
Book Rating : 4.17/5 ( download)

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Download or read book Multiscale Modeling and Uncertainty Quantification of Materials and Structures written by Manolis Papadrakakis and published by Springer. This book was released on 2014-07-02 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of the IUTAM Symposium on Multiscale Modeling and Uncertainty Quantification of Materials and Structures that was held at Santorini, Greece, September 9 – 11, 2013. It consists of 20 chapters which are divided in five thematic topics: Damage and fracture, homogenization, inverse problems–identification, multiscale stochastic mechanics and stochastic dynamics. Over the last few years, the intense research activity at micro scale and nano scale reflected the need to account for disparate levels of uncertainty from various sources and across scales. As even over-refined deterministic approaches are not able to account for this issue, an efficient blending of stochastic and multiscale methodologies is required to provide a rational framework for the analysis and design of materials and structures. The purpose of this IUTAM Symposium was to promote achievements in uncertainty quantification combined with multiscale modeling and to encourage research and development in this growing field with the aim of improving the safety and reliability of engineered materials and structures. Special emphasis was placed on multiscale material modeling and simulation as well as on the multiscale analysis and uncertainty quantification of fracture mechanics of heterogeneous media. The homogenization of two-phase random media was also thoroughly examined in several presentations. Various topics of multiscale stochastic mechanics, such as identification of material models, scale coupling, modeling of random microstructures, analysis of CNT-reinforced composites and stochastic finite elements, have been analyzed and discussed. A large number of papers were finally devoted to innovative methods in stochastic dynamics.

Author : Wolfgang Kliemann
Publisher : CRC Press
ISBN 13 : 1351083503
Total Pages : 560 pages
Book Rating : 4.08/5 ( download)

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Download or read book Nonlinear Dynamics and Stochastic Mechanics written by Wolfgang Kliemann and published by CRC Press. This book was released on 2018-05-04 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: Engineering systems have played a crucial role in stimulating many of the modern developments in nonlinear and stochastic dynamics. After 20 years of rapid progress in these areas, this book provides an overview of the current state of nonlinear modeling and analysis for mechanical and structural systems. This volume is a coherent compendium written by leading experts from the United States, Canada, Western and Eastern Europe, and Australia. The 22 articles describe the background, recent developments, applications, and future directions in bifurcation theory, chaos, perturbation methods, stochastic stability, stochastic flows, random vibrations, reliability, disordered systems, earthquake engineering, and numerics. The book gives readers a sophisticated toolbox that will allow them to tackle modeling problems in mechanical systems that use stochastic and nonlinear dynamics ideas. An extensive bibliography and index ensure this volume will remain a reference standard for years to come.

Author : Johan Grasman
Publisher : Springer Science & Business Media
ISBN 13 : 3662038579
Total Pages : 224 pages
Book Rating : 4.74/5 ( download)

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Download or read book Asymptotic Methods for the Fokker-Planck Equation and the Exit Problem in Applications written by Johan Grasman and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic methods are of great importance for practical applications, especially in dealing with boundary value problems for small stochastic perturbations. This book deals with nonlinear dynamical systems perturbed by noise. It addresses problems in which noise leads to qualitative changes, escape from the attraction domain, or extinction in population dynamics. The most likely exit point and expected escape time are determined with singular perturbation methods for the corresponding Fokker-Planck equation. The authors indicate how their techniques relate to the Itô calculus applied to the Langevin equation. The book will be useful to researchers and graduate students.

Author : Piermarco Cannarsa
Publisher : Springer Nature
ISBN 13 : 3030386694
Total Pages : 243 pages
Book Rating : 4.96/5 ( download)

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Download or read book Mathematical Approach to Climate Change and its Impacts written by Piermarco Cannarsa and published by Springer Nature. This book was released on 2020-03-16 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents important recent applied mathematics research on environmental problems and impacts due to climate change. Although there are inherent difficulties in addressing phenomena that are part of such a complex system, exploration of the subject using mathematical modelling is especially suited to tackling poorly understood issues in the field. It is in this spirit that the book was conceived. It is an outcome of the International INDAM Workshop “Mathematical Approach to Climate Change Impacts – MAC2I”, held in Rome in March 2017. The workshop comprised four sessions, on Ecosystems, Hydrology, Glaciology, and Monitoring. The book includes peer-reviewed contributions on research issues discussed during each of these sessions or generated by collaborations among the specialists involved. Accurate parameter determination techniques are explained and innovative mathematical modelling approaches, presented. The book also provides useful material and mathematical problem-solving tools for doctoral programs dealing with the complexities of climate change.

Author : Emil Simiu
Publisher : Princeton University Press
ISBN 13 : 1400832500
Total Pages : 244 pages
Book Rating : 4.07/5 ( download)

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Download or read book Chaotic Transitions in Deterministic and Stochastic Dynamical Systems written by Emil Simiu and published by Princeton University Press. This book was released on 2014-09-08 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classical Melnikov method provides information on the behavior of deterministic planar systems that may exhibit transitions, i.e. escapes from and captures into preferred regions of phase space. This book develops a unified treatment of deterministic and stochastic systems that extends the applicability of the Melnikov method to physically realizable stochastic planar systems with additive, state-dependent, white, colored, or dichotomous noise. The extended Melnikov method yields the novel result that motions with transitions are chaotic regardless of whether the excitation is deterministic or stochastic. It explains the role in the occurrence of transitions of the characteristics of the system and its deterministic or stochastic excitation, and is a powerful modeling and identification tool. The book is designed primarily for readers interested in applications. The level of preparation required corresponds to the equivalent of a first-year graduate course in applied mathematics. No previous exposure to dynamical systems theory or the theory of stochastic processes is required. The theoretical prerequisites and developments are presented in the first part of the book. The second part of the book is devoted to applications, ranging from physics to mechanical engineering, naval architecture, oceanography, nonlinear control, stochastic resonance, and neurophysiology.

Author : Yevgeny Mamontov
Publisher : World Scientific
ISBN 13 : 9810243855
Total Pages : 322 pages
Book Rating : 4.52/5 ( download)

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Download or read book High-dimensional Nonlinear Diffusion Stochastic Processes written by Yevgeny Mamontov and published by World Scientific. This book was released on 2001 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first one devoted to high-dimensional (or large-scale) diffusion stochastic processes (DSPs) with nonlinear coefficients. These processes are closely associated with nonlinear Ito's stochastic ordinary differential equations (ISODEs) and with the space-discretized versions of nonlinear Ito's stochastic partial integro-differential equations. The latter models include Ito's stochastic partial differential equations (ISPDEs).The book presents the new analytical treatment which can serve as the basis of a combined, analytical-numerical approach to greater computational efficiency in engineering problems. A few examples discussed in the book include: the high-dimensional DSPs described with the ISODE systems for semiconductor circuits; the nonrandom model for stochastic resonance (and other noise-induced phenomena) in high-dimensional DSPs; the modification of the well-known stochastic-adaptive-interpolation method by means of bases of function spaces; ISPDEs as the tool to consistently model non-Markov phenomena; the ISPDE system for semiconductor devices; the corresponding classification of charge transport in macroscale, mesoscale and microscale semiconductor regions based on the wave-diffusion equation; the fully time-domain nonlinear-friction aware analytical model for the velocity covariance of particle of uniform fluid, simple or dispersed; the specific time-domain analytics for the long, non-exponential “tails” of the velocity in case of the hard-sphere fluid.These examples demonstrate not only the capabilities of the developed techniques but also emphasize the usefulness of the complex-system-related approaches to solve some problems which have not been solved with the traditional, statistical-physics methods yet. From this veiwpoint, the book can be regarded as a kind of complement to such books as “Introduction to the Physics of Complex Systems. The Mesoscopic Approach to Fluctuations, Nonlinearity and Self-Organization” by Serra, Andretta, Compiani and Zanarini, “Stochastic Dynamical Systems. Concepts, Numerical Methods, Data Analysis” and “Statistical Physics: An Advanced Approach with Applications” by Honerkamp which deal with physics of complex systems, some of the corresponding analysis methods and an innovative, stochastics-based vision of theoretical physics.To facilitate the reading by nonmathematicians, the introductory chapter outlines the basic notions and results of theory of Markov and diffusion stochastic processes without involving the measure-theoretical approach. This presentation is based on probability densities commonly used in engineering and applied sciences.

Author : Tim Palmer
Publisher : Cambridge University Press
ISBN 13 : 1139458205
Total Pages : 693 pages
Book Rating : 4.07/5 ( download)

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Download or read book Predictability of Weather and Climate written by Tim Palmer and published by Cambridge University Press. This book was released on 2006-07-27 with total page 693 pages. Available in PDF, EPUB and Kindle. Book excerpt: With contributions by leading experts, including an unpublished paper by Ed Lorenz, this book, first published in 2006, covers many topics in weather and climate predictability. It will interest those in the fields of environmental science and weather and climate forecasting, from graduate students to researchers, by examining theoretical and practical aspects of predictability.