The Langevin Equation
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The Langevin Equation
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Author : William Coffey
language : en
Publisher: World Scientific
Release Date : 2004
The Langevin Equation written by William Coffey and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Science categories.
This volume is the second edition of the first-ever elementary book on the Langevin equation method for the solution of problems involving the Brownian motion in a potential, with emphasis on modern applications in the natural sciences, electrical engineering and so on. It has been substantially enlarged to cover in a succinct manner a number of new topics, such as anomalous diffusion, continuous time random walks, stochastic resonance etc, which are of major current interest in view of the large number of disparate physical systems exhibiting these phenomena. The book has been written in such a way that all the material should be accessible to an advanced undergraduate or beginning graduate student. It draws together, in a coherent fashion, a variety of results which have hitherto been available only in the form of research papers or scattered review articles. Contents: Historical Background and Introductory Concepts; Langevin Equations and Methods of Solution; Brownian Motion of a Free Particle and a Harmonic Oscillator; Two-Dimensional Rotational Brownian Motion in N -Fold Cosine Potentials; Brownian Motion in a Tilted Cosine Potential: Application to the Josephson Tunnelling Junction; Translational Brownian Motion in a Double-Well Potential; Three-Dimensional Rotational Brownian Motion in an External Potential: Application to the Theory of Dielectric and Magnetic Relaxation; Rotational Brownian Motion in Axially Symmetric Potentials: Matrix Continued Fraction Solutions; Rotational Brownian Motion in Non-Axially Symmetric Potentials; Inertial Langevin Equations: Application to Orientational Relaxation in Liquids; Anomalous Diffusion. Readership: Advanced undergraduates, graduate students, academics and researchers in statistical physics, condensed matter physics and magnetism, the physics of fluids, theoretical chemistry and applied mathematics.
The Langevin Equation
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Author : William Coffey
language : en
Publisher: World Scientific
Release Date : 1996
The Langevin Equation written by William Coffey and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
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.
Langevin Equation The With Applications To Stochastic Problems In Physics Chemistry And Electrical Engineering Fourth Edition
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Author : Kalmykov Yuri P
language : en
Publisher: World Scientific
Release Date : 2017-03-22
Langevin Equation The With Applications To Stochastic Problems In Physics Chemistry And Electrical Engineering Fourth Edition written by Kalmykov Yuri P and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-22 with Science categories.
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.
Langevin Equation The With Applications To Stochastic Problems In Physics Chemistry And Electrical Engineering 3rd Edition
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Author : Yuri P Kalmykov
language : en
Publisher: World Scientific
Release Date : 2012-07-31
Langevin Equation The With Applications To Stochastic Problems In Physics Chemistry And Electrical Engineering 3rd Edition written by Yuri P Kalmykov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-31 with Science categories.
This volume is the third edition of the first-ever elementary book on the Langevin equation method for the solution of problems involving the translational and rotational Brownian motion of particles and spins in a potential highlighting modern applications in physics, chemistry, electrical engineering, and so on. In order to improve the presentation, to accommodate all the new developments, and to appeal to the specialized interests of the various communities involved, the book has been extensively rewritten and a very large amount of new material has been added. This has been done in order to present a comprehensive overview of the subject emphasizing via a synergetic approach that seemingly unrelated physical problems involving random noise may be described using virtually identical mathematical methods in the spirit of the founders of the subject, viz., Einstein, Langevin, Smoluchowski, Kramers, etc. The book has been written in such a way that all the material should be accessible both to an advanced researcher and a beginning graduate student. It draws together, in a coherent fashion, a variety of results which have hitherto been available only in the form of scattered research papers and review articles.
Langevin Equation The With Applications In Physics Chemistry And Electrical Engineering
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Author : William T Coffey
language : en
Publisher: World Scientific
Release Date : 1996-07-03
Langevin Equation The With Applications In Physics Chemistry And Electrical Engineering written by William T Coffey and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-07-03 with Science categories.
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.
Langevin And Fokker Planck Equations And Their Generalizations Descriptions And Solutions
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Author : Kwok Sau Fa
language : en
Publisher: World Scientific
Release Date : 2018-03-06
Langevin And Fokker Planck Equations And Their Generalizations Descriptions And Solutions written by Kwok Sau Fa and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-06 with Science categories.
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
Analysis Of The Langevin Equation With Random Damping By The Fokker Planck Equation
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Author : J. A. Young
language : en
Publisher:
Release Date : 1963
Analysis Of The Langevin Equation With Random Damping By The Fokker Planck Equation written by J. A. Young and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with Fokker-Planck equation categories.
The Langevin And Generalised Langevin Approach To The Dynamics Of Atomic Polymeric And Colloidal Systems
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Author : Ian Snook
language : en
Publisher: Elsevier
Release Date : 2006-12-11
The Langevin And Generalised Langevin Approach To The Dynamics Of Atomic Polymeric And Colloidal Systems written by Ian Snook and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-11 with Science categories.
The Langevin and Generalised Langevin Approach To The Dynamics Of Atomic, Polymeric And Colloidal Systems is concerned with the description of aspects of the theory and use of so-called random processes to describe the properties of atomic, polymeric and colloidal systems in terms of the dynamics of the particles in the system. It provides derivations of the basic equations, the development of numerical schemes to solve them on computers and gives illustrations of application to typical systems.Extensive appendices are given to enable the reader to carry out computations to illustrate many of the points made in the main body of the book. * Starts from fundamental equations* Gives up-to-date illustration of the application of these techniques to typical systems of interest* Contains extensive appendices including derivations, equations to be used in practice and elementary computer codes
The Langevin Equation
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Author : Yuri P. Kalmykov
language : en
Publisher: World Scientific Publishing Company
Release Date : 2017
The Langevin Equation written by Yuri P. Kalmykov and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Brownian motion processes categories.
This book offers to the reader a self-contained treatment and systematic exposition of the real-valued theory of a nonabsolute integral on measure spaces. It is an introductory textbook to HenstockKurzweil type integrals defined on abstract spaces. It co
A Langevin Equation Description Of Dynamic Nuclear Deformation
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Author : Neil Lucien Roeth
language : en
Publisher:
Release Date : 1992
A Langevin Equation Description Of Dynamic Nuclear Deformation written by Neil Lucien Roeth and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with categories.