Langevin And Fokker Planck Equations And Their Generalizations Descriptions And Solutions

Author : Kwok Sau Fa
Publisher : World Scientific
Page : 208 pages
File Size : 41,7 Mb
Release : 2018-03-06
Category : Science
ISBN : 9789813228429

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Langevin And Fokker-planck Equations And Their Generalizations: Descriptions And Solutions by Kwok Sau Fa Pdf

This invaluable book provides a broad introduction to a rapidly growing area of nonequilibrium statistical physics. The first part of the book complements the classical book on the Langevin and Fokker–Planck equations (H. Risken, The Fokker–Planck Equation: Methods of Solution and Applications (Springer, 1996)). Some topics and methods of solutions are presented and discussed in details which are not described in Risken's book, such as the method of similarity solution, the method of characteristics, transformation of diffusion processes into the Wiener process in different prescriptions, harmonic noise and relativistic Brownian motion. Connection between the Langevin equation and Tsallis distribution is also discussed. Due to the growing interest in the research on the generalized Langevin equations, several of them are presented. They are described with some details. Recent research on the integro-differential Fokker–Planck equation derived from the continuous time random walk model shows that the topic has several aspects to be explored. This equation is worked analytically for the linear force and the generic waiting time probability distribution function. Moreover, generalized Klein-Kramers equations are also presented and discussed. They have the potential to be applied to natural systems, such as biological systems. Contents: Introduction Langevin and Fokker–Planck Equations Fokker–Planck Equation for One Variable and its Solution Fokker–Planck Equation for Several Variables Generalized Langevin Equations Continuous Time Random Walk Model Uncoupled Continuous Time Random Walk Model andits Solution Readership: Advanced undergraduate and graduate students in mathematical physics and statistical physics; biologists and chemists who are interested in nonequilibrium statistical physics. Keywords: Langevin Equation;Fokker-Planck Equation;Klein-Kramers Equation;Continuous Time Random Walk Model;Colored Noise;Tsallis Entropy;Population Growth Models;Wright Functions;Mittag-Leffler Function;Method of Similarity Solution;First Passage Time;Relativistic Brownian Motion;Fractional Derivatives;Integro-Differential Fokker-Planck EquationsReview: Key Features: This book complements Risken's book on the Langevin and Fokker-Planck equations. Some topics and methods of solutions are presented and discussed in details which are not described in Risken's book Several generalized Langevin equations are presented and discussed with some detail Integro-differential Fokker–Planck equation is derived from the uncoupled continuous time random walk model for generic waiting time probability distribution function which can be used to distinguish the differences for the initial and intermediate times with the same behavior in the long-time limit. Moreover, generalized Klein–Kramers equations are also described and discussed. To our knowledge these approaches are not found in other textbooks

Author : Trifce Sandev,Živorad Tomovski
Publisher : Springer Nature
Page : 357 pages
File Size : 54,7 Mb
Release : 2019-11-23
Category : Science
ISBN : 9783030296148

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Fractional Equations and Models by Trifce Sandev,Živorad Tomovski Pdf

Fractional equations and models play an essential part in the description of anomalous dynamics in complex systems. Recent developments in the modeling of various physical, chemical and biological systems have clearly shown that fractional calculus is not just an exotic mathematical theory, as it might have once seemed. The present book seeks to demonstrate this using various examples of equations and models with fractional and generalized operators. Intended for students and researchers in mathematics, physics, chemistry, biology and engineering, it systematically offers a wealth of useful tools for fractional calculus.

Author : Kalmykov Yuri P,Coffey William T
Publisher : World Scientific
Page : 928 pages
File Size : 51,9 Mb
Release : 2017-03-22
Category : Science
ISBN : 9789813222014

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Langevin Equation, The: With Applications To Stochastic Problems In Physics, Chemistry And Electrical Engineering (Fourth Edition) by Kalmykov Yuri P,Coffey William T Pdf

Our original objective in writing this book was to demonstrate how the concept of the equation of motion of a Brownian particle — the Langevin equation or Newtonian-like evolution equation of the random phase space variables describing the motion — first formulated by Langevin in 1908 — so making him inter alia the founder of the subject of stochastic differential equations, may be extended to solve the nonlinear problems arising from the Brownian motion in a potential. Such problems appear under various guises in many diverse applications in physics, chemistry, biology, electrical engineering, etc. However, they have been invariably treated (following the original approach of Einstein and Smoluchowski) via the Fokker–Planck equation for the evolution of the probability density function in phase space. Thus the more simple direct dynamical approach of Langevin which we use and extend here, has been virtually ignored as far as the Brownian motion in a potential is concerned. In addition two other considerations have driven us to write this new edition of The Langevin Equation. First, more than five years have elapsed since the publication of the third edition and following many suggestions and comments of our colleagues and other interested readers, it became increasingly evident to us that the book should be revised in order to give a better presentation of the contents. In particular, several chapters appearing in the third edition have been rewritten so as to provide a more direct appeal to the particular community involved and at the same time to emphasize via a synergetic approach how seemingly unrelated physical problems all involving random noise may be described using virtually identical mathematical methods. Secondly, in that period many new and exciting developments have occurred in the application of the Langevin equation to Brownian motion. Consequently, in order to accommodate all these, a very large amount of new material has been added so as to present a comprehensive overview of the subject.

Author : William Coffey,Yu. P. Kalmykov,J. T. Waldron
Publisher : World Scientific
Page : 436 pages
File Size : 42,8 Mb
Release : 1996
Category : Mathematics
ISBN : 9810216513

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The Langevin Equation by William Coffey,Yu. P. Kalmykov,J. T. Waldron Pdf

The book is suitable for a lecture course on the theory of Brownian motion, being based on final year undergraduate lectures given at Trinity College, Dublin. Topics that are discussed include: white noise; the Chapman-Kolmogorov equation ? Kramers-Moyal expansion; the Langevin equation; the Fokker-Planck equation; Brownian motion of a free particle; spectral density and the Wiener-Khintchin theorem ? Brownian motion in a potential application to the Josephson effect, ring laser gyro; Brownian motion in two dimensions; harmonic oscillators; itinerant oscillators; linear response theory; rotational Brownian motion; application to loss processes in dielectric and ferrofluids; superparamagnetism and nonlinear relaxation processes.As the first elementary book on the Langevin equation approach to Brownian motion, this volume attempts to fill in all the missing details which students find particularly hard to comprehend from the fundamental papers contained in the Dover reprint ? Selected Papers on Noise and Stochastic Processes, ed. N Wax (1954) ? together with modern applications particularly to relaxation in ferrofluids and polar dielectrics.

Author : William Coffey,Yu. P. Kalmykov
Publisher : Unknown
Page : 902 pages
File Size : 52,6 Mb
Release : 2017
Category : MATHEMATICS
ISBN : 981322200X

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The Langevin Equation by William Coffey,Yu. P. Kalmykov Pdf

"Our original objective in writing this book was to demonstrate how the concept of the equation of motion of a Brownian particle — the Langevin equation or Newtonian-like evolution equation of the random phase space variables describing the motion — first formulated by Langevin in 1908 — so making him inter alia the founder of the subject of stochastic differential equations, may be extended to solve the nonlinear problems arising from the Brownian motion in a potential. Such problems appear under various guises in many diverse applications in physics, chemistry, biology, electrical engineering, etc. However, they have been invariably treated (following the original approach of Einstein and Smoluchowski) via the Fokker–Planck equation for the evolution of the probability density function in phase space. Thus the more simple direct dynamical approach of Langevin which we use and extend here, has been virtually ignored as far as the Brownian motion in a potential is concerned. In addition two other considerations have driven us to write this new edition of The Langevin Equation. First, more than five years have elapsed since the publication of the third edition and following many suggestions and comments of our colleagues and other interested readers, it became increasingly evident to us that the book should be revised in order to give a better presentation of the contents. In particular, several chapters appearing in the third edition have been rewritten so as to provide a more direct appeal to the particular community involved and at the same time to emphasize via a synergetic approach how seemingly unrelated physical problems all involving random noise may be described using virtually identical mathematical methods. Secondly, in that period many new and exciting developments have occurred in the application of the Langevin equation to Brownian motion. Consequently, in order to accommodate all these, a very large amount of new material has been added so as to present a comprehensive overview of the subject."--Publisher's website.

Author : Johan Grasman,Onno A., van Herwaarden
Publisher : Springer Science & Business Media
Page : 224 pages
File Size : 50,7 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 : Hannes Risken
Publisher : Unknown
Page : 472 pages
File Size : 52,6 Mb
Release : 1996
Category : Electronic
ISBN : OCLC:849110996

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The Fokker-Planck Equation by Hannes Risken Pdf

Author : Vladimir I. Bogachev,Nicolai V. Krylov,Michael Röckner,Stanislav V. Shaposhnikov
Publisher : American Mathematical Society
Page : 495 pages
File Size : 46,5 Mb
Release : 2022-02-10
Category : Mathematics
ISBN : 9781470470098

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Fokker–Planck–Kolmogorov Equations by Vladimir I. Bogachev,Nicolai V. Krylov,Michael Röckner,Stanislav V. Shaposhnikov Pdf

This book gives an exposition of the principal concepts and results related to second order elliptic and parabolic equations for measures, the main examples of which are Fokker–Planck–Kolmogorov equations for stationary and transition probabilities of diffusion processes. Existence and uniqueness of solutions are studied along with existence and Sobolev regularity of their densities and upper and lower bounds for the latter. The target readership includes mathematicians and physicists whose research is related to diffusion processes as well as elliptic and parabolic equations.

Author : Anonim
Publisher : Unknown
Page : 796 pages
File Size : 50,6 Mb
Release : 2006
Category : Mathematics
ISBN : UOM:39015067268402

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Mathematical Reviews by Anonim Pdf

Author : Grigorios A. Pavliotis
Publisher : Springer
Page : 345 pages
File Size : 51,8 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.

Author : T.D. Frank
Publisher : Springer Science & Business Media
Page : 414 pages
File Size : 46,7 Mb
Release : 2005-01-07
Category : Science
ISBN : 9783540212645

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Nonlinear Fokker-Planck Equations by T.D. Frank Pdf

Centered around the natural phenomena of relaxations and fluctuations, this monograph provides readers with a solid foundation in the linear and nonlinear Fokker-Planck equations that describe the evolution of distribution functions. It emphasizes principles and notions of the theory (e.g. self-organization, stochastic feedback, free energy, and Markov processes), while also illustrating the wide applicability (e.g. collective behavior, multistability, front dynamics, and quantum particle distribution). The focus is on relaxation processes in homogeneous many-body systems describable by nonlinear Fokker-Planck equations. Also treated are Langevin equations and correlation functions. Since these phenomena are exhibited by a diverse spectrum of systems, examples and applications span the fields of physics, biology and neurophysics, mathematics, psychology, and biomechanics.

Author : Anonim
Publisher : Elsevier
Page : 3421 pages
File Size : 50,7 Mb
Release : 2018-08-21
Category : Medical
ISBN : 9780128114322

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Encyclopedia of Bioinformatics and Computational Biology by Anonim Pdf

Encyclopedia of Bioinformatics and Computational Biology: ABC of Bioinformatics, Three Volume Set combines elements of computer science, information technology, mathematics, statistics and biotechnology, providing the methodology and in silico solutions to mine biological data and processes. The book covers Theory, Topics and Applications, with a special focus on Integrative –omics and Systems Biology. The theoretical, methodological underpinnings of BCB, including phylogeny are covered, as are more current areas of focus, such as translational bioinformatics, cheminformatics, and environmental informatics. Finally, Applications provide guidance for commonly asked questions. This major reference work spans basic and cutting-edge methodologies authored by leaders in the field, providing an invaluable resource for students, scientists, professionals in research institutes, and a broad swath of researchers in biotechnology and the biomedical and pharmaceutical industries. Brings together information from computer science, information technology, mathematics, statistics and biotechnology Written and reviewed by leading experts in the field, providing a unique and authoritative resource Focuses on the main theoretical and methodological concepts before expanding on specific topics and applications Includes interactive images, multimedia tools and crosslinking to further resources and databases

Author : Simo Särkkä,Arno Solin
Publisher : Cambridge University Press
Page : 327 pages
File Size : 54,6 Mb
Release : 2019-05-02
Category : Business & Economics
ISBN : 9781316510087

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Applied Stochastic Differential Equations by Simo Särkkä,Arno Solin Pdf

With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.

Author : Norman J. Wagner,Jan Mewis
Publisher : Cambridge University Press
Page : 437 pages
File Size : 41,8 Mb
Release : 2021-04-15
Category : Science
ISBN : 9781108423038

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Theory and Applications of Colloidal Suspension Rheology by Norman J. Wagner,Jan Mewis Pdf

Essential text on the practical application and theory of colloidal suspension rheology, written by an international coalition of experts.

Author : Anonim
Publisher : Unknown
Page : 632 pages
File Size : 42,8 Mb
Release : 1989
Category : Power resources
ISBN : MINN:30000006336600

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Energy Research Abstracts by Anonim Pdf