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

Author : C Soize
Publisher : World Scientific
Page : 340 pages
File Size : 43,6 Mb
Release : 1994-05-16
Category : Mathematics
ISBN : 9789814502023

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The Fokker-Planck Equation for Stochastic Dynamical Systems and Its Explicit Steady State Solutions by C Soize Pdf

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
Page : 346 pages
File Size : 44,9 Mb
Release : 1994
Category : Science
ISBN : 9810217552

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The Fokker-Planck Equation for Stochastic Dynamical Systems and Its Explicit Steady State Solutions by Christian Soize Pdf

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,Donghua Jiang
Publisher : Springer Science & Business Media
Page : 296 pages
File Size : 53,6 Mb
Release : 2004
Category : Markov processes
ISBN : 3540206116

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Mathematical Theory of Nonequilibrium Steady States by Da-Quan Jiang,Donghua Jiang Pdf

Author : Manolis Papadrakakis,George Stefanou
Publisher : Springer
Page : 306 pages
File Size : 41,7 Mb
Release : 2014-07-02
Category : Science
ISBN : 9783319063317

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Multiscale Modeling and Uncertainty Quantification of Materials and Structures by Manolis Papadrakakis,George Stefanou Pdf

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
Page : 560 pages
File Size : 48,5 Mb
Release : 2018-05-04
Category : Mathematics
ISBN : 9781351083508

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Nonlinear Dynamics and Stochastic Mechanics by Wolfgang Kliemann Pdf

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,Onno A., van Herwaarden
Publisher : Springer Science & Business Media
Page : 224 pages
File Size : 43,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662038574

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Asymptotic Methods for the Fokker-Planck Equation and the Exit Problem in Applications by Johan Grasman,Onno A., van Herwaarden Pdf

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,Daniela Mansutti,Antonello Provenzale
Publisher : Springer Nature
Page : 243 pages
File Size : 53,5 Mb
Release : 2020-03-16
Category : Science
ISBN : 9783030386696

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Mathematical Approach to Climate Change and its Impacts by Piermarco Cannarsa,Daniela Mansutti,Antonello Provenzale Pdf

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
Page : 244 pages
File Size : 41,8 Mb
Release : 2014-09-08
Category : Mathematics
ISBN : 9781400832507

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Chaotic Transitions in Deterministic and Stochastic Dynamical Systems by Emil Simiu Pdf

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 : Tim Palmer,Renate Hagedorn
Publisher : Cambridge University Press
Page : 693 pages
File Size : 47,9 Mb
Release : 2006-07-27
Category : Science
ISBN : 9781139458207

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Predictability of Weather and Climate by Tim Palmer,Renate Hagedorn Pdf

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.

Author : Yevgeny Mamontov,M. Willander
Publisher : World Scientific
Page : 322 pages
File Size : 44,6 Mb
Release : 2001
Category : Mathematics
ISBN : 9789810243852

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High-dimensional Nonlinear Diffusion Stochastic Processes by Yevgeny Mamontov,M. Willander Pdf

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 : Mircea Grigoriu
Publisher : Springer Science & Business Media
Page : 794 pages
File Size : 42,8 Mb
Release : 2002-09-24
Category : Mathematics
ISBN : 0817642420

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Stochastic Calculus by Mircea Grigoriu Pdf

Chapters 6-9 present methods for solving problems defined by equations with deterministic and/or random coefficients and deterministic and/or stochastic inputs. The Monte Carlo simulation is used extensively throughout to clarify advanced theoretical concepts and provide solutions to a broad range of stochastic problems.".

Author : Ioannis A. Kougioumtzoglou
Publisher : Springer Nature
Page : 233 pages
File Size : 44,8 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 9783031578632

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Path Integrals in Stochastic Engineering Dynamics by Ioannis A. Kougioumtzoglou Pdf

Author : Ronald E. Mickens
Publisher : World Scientific
Page : 340 pages
File Size : 43,8 Mb
Release : 1996
Category : Science
ISBN : 9789810222925

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Oscillations in Planar Dynamic Systems by Ronald E. Mickens Pdf

This book provides a concise presentation of the major techniques for determining analytic approximations to the solutions of planar oscillatory dynamic systems. These systems model many important phenomena in the sciences and engineering. In addition to the usual perturbation procedures, the book gives the details of when and how to correctly apply the method of harmonic balance for both first-order and higher-order calculations. This procedure is rarely given or discussed fully in standard textbooks. The basic philosophy of the book stresses how to initiate and complete the calculation of approximate solutions. This is done by a clear presentation of necessary background materials and by the working out of many examples.

Author : Jian-Qiao Sun
Publisher : Elsevier
Page : 426 pages
File Size : 43,5 Mb
Release : 2006-08-10
Category : Mathematics
ISBN : 0080463983

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Stochastic Dynamics and Control by Jian-Qiao Sun Pdf

This book is a result of many years of author’s research and teaching on random vibration and control. It was used as lecture notes for a graduate course. It provides a systematic review of theory of probability, stochastic processes, and stochastic calculus. The feedback control is also reviewed in the book. Random vibration analyses of SDOF, MDOF and continuous structural systems are presented in a pedagogical order. The application of the random vibration theory to reliability and fatigue analysis is also discussed. Recent research results on fatigue analysis of non-Gaussian stress processes are also presented. Classical feedback control, active damping, covariance control, optimal control, sliding control of stochastic systems, feedback control of stochastic time-delayed systems, and probability density tracking control are studied. Many control results are new in the literature and included in this book for the first time. The book serves as a reference to the engineers who design and maintain structures subject to harsh random excitations including earthquakes, sea waves, wind gusts, and aerodynamic forces, and would like to reduce the damages of structural systems due to random excitations. · Comprehensive review of probability theory, and stochastic processes · Random vibrations · Structural reliability and fatigue, Non-Gaussian fatigue · Monte Carlo methods · Stochastic calculus and engineering applications · Stochastic feedback controls and optimal controls · Stochastic sliding mode controls · Feedback control of stochastic time-delayed systems · Probability density tracking control

Author : Grigorios A. Pavliotis
Publisher : Springer
Page : 345 pages
File Size : 46,6 Mb
Release : 2014-11-19
Category : Mathematics
ISBN : 9781493913237

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Stochastic Processes and Applications by Grigorios A. Pavliotis Pdf

This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applications such as stochastic resonance, Brownian motion in periodic potentials and Brownian motors are studied and the connection between diffusion processes and time-dependent statistical mechanics is elucidated. The book contains a large number of illustrations, examples, and exercises. It will be useful for graduate-level courses on stochastic processes for students in applied mathematics, physics and engineering. Many of the topics covered in this book (reversible diffusions, convergence to equilibrium for diffusion processes, inference methods for stochastic differential equations, derivation of the generalized Langevin equation, exit time problems) cannot be easily found in textbook form and will be useful to both researchers and students interested in the applications of stochastic processes.