The Langevin Equation

Author : William Coffey,Yu. P. Kalmykov,J. T. Waldron
Publisher : World Scientific
Page : 436 pages
File Size : 46,6 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 : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 51,7 Mb
Release : 2024-06-16
Category : Electronic
ISBN : 9789814485395

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The Langevin Equation by Anonim Pdf

Author : William Coffey,Yu. P. Kalmykov,J. T. Waldron
Publisher : World Scientific
Page : 706 pages
File Size : 44,6 Mb
Release : 2004
Category : Science
ISBN : 981279509X

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

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.

Author : Kalmykov Yuri P,Coffey William T
Publisher : World Scientific
Page : 928 pages
File Size : 53,7 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 : Ian Snook
Publisher : Elsevier
Page : 320 pages
File Size : 40,8 Mb
Release : 2006-12-11
Category : Science
ISBN : 008046792X

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The Langevin and Generalised Langevin Approach to the Dynamics of Atomic, Polymeric and Colloidal Systems by Ian Snook Pdf

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

Author : Kwok Sau Fa
Publisher : World Scientific
Page : 208 pages
File Size : 53,6 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 : William Coffey,Yu. P. Kalmykov
Publisher : World Scientific
Page : 850 pages
File Size : 41,5 Mb
Release : 2012
Category : Science
ISBN : 9789814355674

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

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, 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.

Author : Grigorios A. Pavliotis
Publisher : Springer
Page : 339 pages
File Size : 42,5 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 : Trifce Sandev,Živorad Tomovski
Publisher : Springer Nature
Page : 357 pages
File Size : 53,9 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 : V. Balakrishnan
Publisher : Springer
Page : 314 pages
File Size : 45,9 Mb
Release : 2021-12-05
Category : Science
ISBN : 3030622355

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Elements of Nonequilibrium Statistical Mechanics by V. Balakrishnan Pdf

This book deals with the basic principles and techniques of nonequilibrium statistical mechanics. The importance of this subject is growing rapidly in view of the advances being made, both experimentally and theoretically, in statistical physics, chemical physics, biological physics, complex systems and several other areas. The presentation of topics is quite self-contained, and the choice of topics enables the student to form a coherent picture of the subject. The approach is unique in that classical mechanical formulation takes center stage. The book is of particular interest to advanced undergraduate and graduate students in engineering departments.

Author : Jean-Louis Barrat,Jean-Pierre Hansen
Publisher : Cambridge University Press
Page : 410 pages
File Size : 54,6 Mb
Release : 2003-03-27
Category : Science
ISBN : 0521789532

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Basic Concepts for Simple and Complex Liquids by Jean-Louis Barrat,Jean-Pierre Hansen Pdf

Presenting a unified approach, this book focusses on the concepts and theoretical methods that are necessary for an understanding of the physics and chemistry of the fluid state. The authors do not attempt to cover the whole field in an encyclopedic manner. Instead, important ideas are presented in a concise and rigorous style, and illustrated with examples from both simple molecular liquids and more complex soft condensed matter systems such as polymers, colloids, and liquid crystals.

Author : David D. Nolte
Publisher : Oxford University Press
Page : 384 pages
File Size : 53,6 Mb
Release : 2018-07-12
Category : Science
ISBN : 9780192528506

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Galileo Unbound by David D. Nolte Pdf

Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once — setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.

Author : Stuart A. Rice,Aaron R. Dinner
Publisher : John Wiley & Sons
Page : 374 pages
File Size : 51,9 Mb
Release : 2012-03-27
Category : Science
ISBN : 9781118167847

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Advances in Chemical Physics, Volume 150 by Stuart A. Rice,Aaron R. Dinner Pdf

The Advances in Chemical Physics series the cutting edge of research in chemical physics The Advances in Chemical Physics series provides the chemical physics and physical chemistry fields with a forum for critical, authoritative evaluations of advances in every area of the discipline. Filled with cutting-edge research reported in a cohesive manner not found elsewhere in the literature, each volume of the Advances in Chemical Physics series presents contributions from internationally renowned chemists and serves as the perfect supplement to any advanced graduate class devoted to the study of chemical physics. This volume explores: Multidimensional Incoherent Time-Resolved Spectroscopy and Complex Kinetics (Mark A. Berg) Complex Multiconfigurational Self-Consistent Field-Based Methods to Investigate Electron-Atom/Molecule Scattering Resonances (Kousik Samanta and Danny L. Yeager) Determination of Molecular Orientational Correlations in Disordered Systems from Diffraction Data (Szilvia Pothoczki, László Temleitner, and László Pusztai) Recent Advances in Studying Mechanical Properties of DNA (Reza Vafabakhsh, Kyung Suk Lee, and Taekjip Ha) Viscoelastic Subdiffusion: Generalized Langevin Equation Approach (Igor Goychuk) Efficient and Unbiased Sampling of Biomolecular Systems in the Canonical Ensemble: A Review of Self-Guided Langevin Dynamics (Xiongwu Wu, Ana Damjanovic, and Bernard R. Brooks)

Author : Hannes Risken,Till Frank
Publisher : Springer Science & Business Media
Page : 486 pages
File Size : 55,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642615443

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The Fokker-Planck Equation by Hannes Risken,Till Frank Pdf

This is the first textbook to include the matrix continued-fraction method, which is very effective in dealing with simple Fokker-Planck equations having two variables. Other methods covered are the simulation method, the eigen-function expansion, numerical integration, and the variational method. Each solution is applied to the statistics of a simple laser model and to Brownian motion in potentials. The whole is rounded off with a supplement containing a short review of new material together with some recent references. This new study edition will prove to be very useful for graduate students in physics, chemical physics, and electrical engineering, as well as for research workers in these fields.

Author : Cyrille Rossant
Publisher : Packt Publishing Ltd
Page : 512 pages
File Size : 43,5 Mb
Release : 2014-09-25
Category : Computers
ISBN : 9781783284825

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IPython Interactive Computing and Visualization Cookbook by Cyrille Rossant Pdf

Intended to anyone interested in numerical computing and data science: students, researchers, teachers, engineers, analysts, hobbyists... Basic knowledge of Python/NumPy is recommended. Some skills in mathematics will help you understand the theory behind the computational methods.