The Langevin Equation

Author: William T Coffey
Publisher: World Scientific
ISBN: 981448380X
Format: PDF, ePub, Docs
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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. Contents:Historical Background and Introductory ConceptsLangevin Equations and Methods of SolutionBrownian Motion of a Free Particle and a Harmonic OscillatorRotational Brownian Motion About a Fixed Axis in N-Fold Cosine PotentialsBrownian Motion in a Tilted Periodic Potential: Application to the Josephson Tunnelling JunctionTranslational Brownian Motion in a Double-Well PotentialNon-inertial Rotational Diffusion in Axially Symmetric External Potentials: Applications to Orientational Relaxation of Molecules in Fluids and Liquid CrystalsAnisotropic Non-inertial Rotational Diffusion in an External Potential: Application to Linear and Nonlinear Dielectric Relaxation and the Dynamic Kerr EffectBrownian Motion of Classical Spins: Application to Magnetization Relaxation in SuperparamagnetsInertial Effects in Rotational and Translational Brownian Motion for a Single Degree of FreedomInertial Effects in Rotational Diffusion in Space: Application to Orientational Relaxation in Molecular Liquids and FerrofluidsAnomalous Diffusion and Relaxation Readership: Advanced undergraduates, postgraduates, academics and researchers in statistical physics, condensed matter physics and magnetism, chemical physics, theoretical chemistry and applied mathematics. Keywords:Brownian Motion;Historical Development;Analogy with Financial Systems;Translational and Rotational Diffusion;Stochastic Differential Equations;Langevin Equation;Fokker–Planck Equation;Characteristic Times of Relaxation Processes;Escape Rate Theory;Kramers Turnover Problem;Matrix Continued Fraction Solution of Evolution Equtions;Kerr Effect;Microwave (Debye) and Far-Infrared (Poley) Absorption;Dielectric Relaxation in Liquids and Nematic Liquid Crystals;Classical Spins;Superparamagnetism;Néel-Brown Model;Dynamic Magnetic Hysteresis;Switching Fields;Stoner-Wohlfarth Astroids;Ferromagnetic Resonance;Ferrofluids;Josephson Effect;Ring Laser;Magnetic Resonance Imaging;Stochastic Resonance;Anomalous Diffusion;Continuous Time Random Walk;Fractional Langevin Equation;Fractional Fokker–Planck EquationKey Features:This volume is the third edition of the first elementary book on the Langevin equation method for the solution of problems involving the translational and rotational Brownian motion in a potential with particular emphasis on modern applications in the natural sciences, electrical engineering, etc.It has been extensively enlarged to cover in a reasonably succinct manner using a synergetic approach a number of new topics such as anomalous diffusion, continuous time random walks, stochastic resonance, superparamagnetism, magnetic resonance imaging, etc. which are of major current interest in view of the large number of disparate systems which exhibit these phenomenaThe book is written in a manner such that all the material should be accessible to an advanced undergraduate or beginning graduate studentReviews: “This book is devoted to a detailed presentation of Langevin's idea and does this almost perfectly. Successive topics considered in this book are presented in a detailed manner giving the general impression that this book is a comprehensive compendium of knowledge. This book should be a very valuable addition to libraries of many experienced scientists and also beginners (e.g., students) presenting solutions of many stochastic phenomena.” Zentralblatt MATH Reviews of the First and Second Editions: “I found this book a valuable addition to my library. It will be of interest to researchers and advanced students and the material could be used as the text for a course for advanced undergraduates and graduate students.” Irwin Oppenheim MIT “This enlarged and updated second edition of the book: 'The Langevin equation presents an extremely useful source for the practitioners of stochastic processes and its applications to physics, chemistry, engineering and biological physics, both for the experts and the beginners. It gives a valuable survey of solvable paradigms that rule many diverse stochastic phenomena. As such, it belongs onto the desk of all engaged in doing research and teaching in this area.” Peter Hanggi University of Augsburg “This is a timely update of the theory and applications of the Langevin equation, which skillfully combines the elementary approaches with most recent developments such as anomalous diffusion and fractional kinetics. Both experts and beginners will benefit from this well-written textbook.” Joseph Klafter Tel Aviv University

The Langevin Equation

Author: William Coffey
Publisher: World Scientific
ISBN: 9814355674
Format: PDF, Docs
Download Now
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.

Langevin Equation The With Applications To Stochastic Problems In Physics Chemistry And Electrical Engineering Fourth Edition

Author: Kalmykov Yuri P
Publisher: World Scientific
ISBN: 9813222018
Format: PDF
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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.

Theory and Applications of Stochastic Processes

Author: Zeev Schuss
Publisher: Springer Science & Business Media
ISBN: 1441916059
Format: PDF, ePub, Docs
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Stochastic processes and diffusion theory are the mathematical underpinnings of many scientific disciplines, including statistical physics, physical chemistry, molecular biophysics, communications theory and many more. Many books, reviews and research articles have been published on this topic, from the purely mathematical to the most practical. This book offers an analytical approach to stochastic processes that are most common in the physical and life sciences, as well as in optimal control and in the theory of filltering of signals from noisy measurements. Its aim is to make probability theory in function space readily accessible to scientists trained in the traditional methods of applied mathematics, such as integral, ordinary, and partial differential equations and asymptotic methods, rather than in probability and measure theory.

Stochastic Dynamics of Crystal Defects

Author: Thomas D Swinburne
Publisher: Springer
ISBN: 3319200194
Format: PDF, Mobi
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This thesis is concerned with establishing a rigorous, modern theory of the stochastic and dissipative forces on crystal defects, which remain poorly understood despite their importance in any temperature dependent micro-structural process such as the ductile to brittle transition or irradiation damage. The author first uses novel molecular dynamics simulations to parameterise an efficient, stochastic and discrete dislocation model that allows access to experimental time and length scales. Simulated trajectories are in excellent agreement with experiment. The author also applies modern methods of multiscale analysis to extract novel bounds on the transport properties of these many body systems. Despite their successes in coarse graining, existing theories are found unable to explain stochastic defect dynamics. To resolve this, the author defines crystal defects through projection operators, without any recourse to elasticity. By rigorous dimensional reduction, explicit analytical forms are derived for the stochastic forces acting on crystal defects, allowing new quantitative insight into the role of thermal fluctuations in crystal plasticity.

Stochastische dynamische Systeme

Author: Josef Honerkamp
Publisher:
ISBN: 9783527279456
Format: PDF, Docs
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Stochastic dynamic systems - often simply called 2complex2 systems are characterized through a) many degrees of freedom and b) being far away from a state of equilibrium. Description and modeling of such systems via stochastic processes play an increasingly important role in applications-oriented research in physics, chemistry, biology and meteorology. This book, based on lectures given in graduate courses in physics, provides the mathematical basis necessary for a comprehensive treatment of complex systems. Besides introducing the concepts, the author discusses numerical methods to simulate stochastic processes and to fit observed processes to stochastic models.

Books in Print

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