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

Author: Kalmykov Yuri P,Coffey William T

Publisher: World Scientific

ISBN: 9813222018

Category: Science

Page: 928

View: 2301

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.

The Langevin Equation

With Applications to Stochastic Problems in Physics, Chemistry, and Electrical Engineering

Author: William Coffey,Yu. P. Kalmykov,J. T. Waldron

Publisher: World Scientific

ISBN: 9812384626

Category: Science

Page: 678

View: 366

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.

The Langevin Equation

With Applications to Stochastic Problems in Physics, Chemistry and Electrical Engineering

Author: William T Coffey,Yuri P Kalmykov

Publisher: World Scientific

ISBN: 981448380X

Category: Science

Page: 852

View: 5640

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

A Modern Approach to Functional Integration

Author: John R. Klauder

Publisher: Springer Science & Business Media

ISBN: 0817647910

Category: Mathematics

Page: 282

View: 9324

This text takes advantage of recent developments in the theory of path integration and attempts to make a major paradigm shift in how the art of functional integration is practiced. The techniques developed in the work will prove valuable to graduate students and researchers in physics, chemistry, mathematical physics, and applied mathematics who find it necessary to deal with solutions to wave equations, both quantum and beyond. A Modern Approach to Functional Integration offers insight into a number of contemporary research topics, which may lead to improved methods and results that cannot be found elsewhere in the textbook literature. Exercises are included in most chapters, making the book suitable for a one-semester graduate course on functional integration.

Moderne Physik

Author: Paul A. Tipler,Ralph A. Llewellyn

Publisher: De Gruyter Oldenbourg

ISBN: 9783486582758

Category: Science

Page: 963

View: 4091

Endlich liegt die anschauliche und fundierte Einführung zur Modernen Physik von Paul A. Tipler und Ralph A. Llewellyn in der deutschen Übersetzung vor. Eine umfassende Einführung in die Relativitätstheorie, die Quantenmechanik und die statistische Physik wird im ersten Teil des Buches gegeben. Die wichtigsten Arbeitsgebiete der modernen Physik - Festkörperphysik, Kern- und Teilchenphysik sowie die Kosmologie und Astrophysik - werden in der zweiten Hälfte des Buches behandelt. Zu weiteren zahlreichen Spezialgebieten gibt es Ergänzungen im Internet beim Verlag der amerikanischen Originalausgabe, die eine Vertiefung des Stoffes ermöglichen. Mit ca. 700 Übungsaufgaben eignet sich das Buch hervorragend zum Selbststudium sowie zur Begleitung einer entsprechenden Vorlesung. Die Übersetzung des Werkes übernahm Dr. Anna Schleitzer. Die Bearbeitung und Anpassung an Anforderungen deutscher Hochschulen wurde von Prof. Dr. G. Czycholl, Prof. Dr. W. Dreybrodt, Prof. Dr. C. Noack und Prof. Dr. U. Strohbusch durchgeführt. Dieses Team gewährleistet auch für die deutsche Fassung die wissenschaftliche Exaktheit und Stringenz des Originals.

Stochastic Integrals

An Introduction

Author: Heinrich von Weizsäcker

Publisher: Springer-Verlag

ISBN: 3663139239

Category: Mathematics

Page: 332

View: 5411

New Technical Books

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Engineering

Page: N.A

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Selbstorganisation chemischer Strukturen

Arbeiten von Friedlieb Ferdinand Runge, Raphael Eduard Liesegang, Boris Pavlovich Belousov und Anatol Markovich Zhabotinsky

Author: Uwe Niedersen

Publisher: N.A

ISBN: N.A

Category: Chemical structure

Page: 112

View: 871

Grundbegriffe der Wahrscheinlichkeitsrechnung

Author: A. Kolomogoroff

Publisher: Springer-Verlag

ISBN: 3642498884

Category: Mathematics

Page: 62

View: 4248

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

Books in Print

Author: N.A

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

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Books in print is the major source of information on books currently published and in print in the United States. The database provides the record of forthcoming books, books in-print, and books out-of-print.

Algorithmen - Eine Einführung

Author: Thomas H. Cormen,Charles E. Leiserson,Ronald Rivest,Clifford Stein

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110522012

Category: Computers

Page: 1339

View: 3230

Der "Cormen" bietet eine umfassende und vielseitige Einführung in das moderne Studium von Algorithmen. Es stellt viele Algorithmen Schritt für Schritt vor, behandelt sie detailliert und macht deren Entwurf und deren Analyse allen Leserschichten zugänglich. Sorgfältige Erklärungen zur notwendigen Mathematik helfen, die Analyse der Algorithmen zu verstehen. Den Autoren ist es dabei geglückt, Erklärungen elementar zu halten, ohne auf Tiefe oder mathematische Exaktheit zu verzichten. Jedes der weitgehend eigenständig gestalteten Kapitel stellt einen Algorithmus, eine Entwurfstechnik, ein Anwendungsgebiet oder ein verwandtes Thema vor. Algorithmen werden beschrieben und in Pseudocode entworfen, der für jeden lesbar sein sollte, der schon selbst ein wenig programmiert hat. Zahlreiche Abbildungen verdeutlichen, wie die Algorithmen arbeiten. Ebenfalls angesprochen werden Belange der Implementierung und andere technische Fragen, wobei, da Effizienz als Entwurfskriterium betont wird, die Ausführungen eine sorgfältige Analyse der Laufzeiten der Programme mit ein schließen. Über 1000 Übungen und Problemstellungen und ein umfangreiches Quellen- und Literaturverzeichnis komplettieren das Lehrbuch, dass durch das ganze Studium, aber auch noch danach als mathematisches Nachschlagewerk oder als technisches Handbuch nützlich ist. Für die dritte Auflage wurde das gesamte Buch aktualisiert. Die Änderungen sind vielfältig und umfassen insbesondere neue Kapitel, überarbeiteten Pseudocode, didaktische Verbesserungen und einen lebhafteren Schreibstil. So wurden etwa - neue Kapitel zu van-Emde-Boas-Bäume und mehrfädigen (engl.: multithreaded) Algorithmen aufgenommen, - das Kapitel zu Rekursionsgleichungen überarbeitet, sodass es nunmehr die Teile-und-Beherrsche-Methode besser abdeckt, - die Betrachtungen zu dynamischer Programmierung und Greedy-Algorithmen überarbeitet; Memoisation und der Begriff des Teilproblem-Graphen als eine Möglichkeit, die Laufzeit eines auf dynamischer Programmierung beruhender Algorithmus zu verstehen, werden eingeführt. - 100 neue Übungsaufgaben und 28 neue Problemstellungen ergänzt. Umfangreiches Dozentenmaterial (auf englisch) ist über die Website des US-Verlags verfügbar.

Physics Briefs

Physikalische Berichte

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Physics

Page: N.A

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The 15th International Conference on Biomedical Engineering

ICBME 2013, 4th to 7th December 2013, Singapore

Author: James Goh

Publisher: Springer Science & Business Media

ISBN: 3319029134

Category: Technology & Engineering

Page: 968

View: 6557

This volume presents the processing of the 15th ICMBE held from 4th to 7th December 2013, Singapore. Biomedical engineering is applied in most aspects of our healthcare ecosystem. From electronic health records to diagnostic tools to therapeutic, rehabilitative and regenerative treatments, the work of biomedical engineers is evident. Biomedical engineers work at the intersection of engineering, life sciences and healthcare. The engineers would use principles from applied science including mechanical, electrical, chemical and computer engineering together with physical sciences including physics, chemistry and mathematics to apply them to biology and medicine. Applying such concepts to the human body is very much the same concepts that go into building and programming a machine. The goal is to better understand, replace or fix a target system to ultimately improve the quality of healthcare. With this understanding, the conference proceedings offer a single platform for individuals and organizations working in the biomedical engineering related field to gather and network with each other in so doing create the catalyst for future development of biomedical engineering in Asia.

Elementare Wahrscheinlichkeitstheorie und stochastische Prozesse

Author: Kai L. Chung

Publisher: Springer-Verlag

ISBN: 3642670334

Category: Mathematics

Page: 346

View: 5429

Aus den Besprechungen: "Unter den zahlreichen Einführungen in die Wahrscheinlichkeitsrechnung bildet dieses Buch eine erfreuliche Ausnahme. Der Stil einer lebendigen Vorlesung ist über Niederschrift und Übersetzung hinweg erhalten geblieben. In jedes Kapitel wird sehr anschaulich eingeführt. Sinn und Nützlichkeit der mathematischen Formulierungen werden den Lesern nahegebracht. Die wichtigsten Zusammenhänge sind als mathematische Sätze klar formuliert." #FREQUENZ#1

Äther und Relativitäts-Theorie

Rede Gehalten am 5. Mai 1920 an der Reichs-Universität zu Leiden

Author: A. Einstein

Publisher: Springer-Verlag

ISBN: 3642507468

Category: Science

Page: N.A

View: 704

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

Sobolev Spaces on Domains

Author: Victor I. Burenkov

Publisher: Springer-Verlag

ISBN: 3663113744

Category: Mathematics

Page: 312

View: 5001

Kristallmodelle

Symmetriemodelle der 32 Kristallklassen zum Selbstbau

Author: Rüdiger Borchardt,Siegfried Turowski

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3486844989

Category: Science

Page: 44

View: 1255

32 Modellbaubögen ermöglichen, Kristalle sämtlicher Klassen selbst zusammenzubauen. Eine kurze Einführung, eine übersichtliche Tabelle der 32 Kristallklassen sowie ein Lernkartensystem komplettieren das Heft. "Kristallmodelle" ist im Set mit weiteren Titeln zum Sonderpreis erhältlich (s. S. 28f.)