Warenkorb
€ 0,00 0 Buch dabei,
portofrei
The Fokker-Planck Equation als Buch
PORTO-
FREI

The Fokker-Planck Equation

Methods of Solution and Applications. 'Springer Series in Synergetics'. 2nd ed. 1996. Sprache: Englisch.
Buch (kartoniert)
Ihr 10% Rabatt bei Hugendubel.de
 
14% Rabatt sichern mit Gutscheincode: VALENTIN14
 

Dieser Band ist zum Standardwerk über das Fachgebiet der Fokker-Planck Gleichung geworden. Unentbehrlich für Studenten und Wissenschaftler, die sich mit statistischer Physik und der Rolle der Fluktuationen beschäftigen, präsentiert das Buch eine einz … weiterlesen
Buch

74,99 *

inkl. MwSt.
Portofrei
Sofort lieferbar
The Fokker-Planck Equation als Buch

Produktdetails

Titel: The Fokker-Planck Equation
Autor/en: Till Frank, Hannes Risken

ISBN: 354061530X
EAN: 9783540615309
Methods of Solution and Applications.
'Springer Series in Synergetics'.
2nd ed. 1996.
Sprache: Englisch.
Springer, Berlin

17. September 1996 - kartoniert - 472 Seiten

Beschreibung

One of the central problems synergetics is concerned with consists in the study of macroscopic qualitative changes of systems belonging to various disciplines such as physics, chemistry, or electrical engineering. When such transitions from one state to another take place, fluctuations, i.e., random processes, may play an im portant role. Over the past decades it has turned out that the Fokker-Planck equation pro vides a powerful tool with which the effects of fluctuations close to transition points can be adequately treated and that the approaches based on the Fokker Planck equation are superior to other approaches, e.g., based on Langevin equa tions. Quite generally, the Fokker-Planck equation plays an important role in problems which involve noise, e.g., in electrical circuits. For these reasons I am sure that this book will find a broad audience. It pro vides the reader with a sound basis for the study of the Fokker-Planck equation and gives an excellent survey of the methods of its solution. The author of this book, Hannes Risken, has made substantial contributions to the development and application of such methods, e.g., to laser physics, diffusion in periodic potentials, and other problems. Therefore this book is written by an experienced practitioner, who has had in mind explicit applications to important problems in the natural sciences and electrical engineering.

Inhaltsverzeichnis

'1. Introduction.- 1.1 Brownian Motion.- 1.1.1 Deterministic Differential Equation.- 1.1.2 Stochastic Differential Equation.- 1.1.3 Equation of Motion for the Distribution Function.- 1.2 Fokker-Planck Equation.- 1.2.1 Fokker-Planck Equation for One Variable.- 1.2.2 Fokker-Planck Equation for N Variables.- 1.2.3 How Does a Fokker-Planck Equation Arise?.- 1.2.4 Purpose of the Fokker-Planck Equation.- 1.2.5 Solutions of the Fokker-Planck Equation.- 1.2.6 Kramers and Smoluchowski Equations.- 1.2.7 Generalizations of the Fokker-Planck Equation.- 1.3 Boltzmann Equation.- 1.4 Master Equation.- 2. Probability Theory.- 2.1 Random Variable and Probability Density.- 2.2 Characteristic Function and Cumulants.- 2.3 Generalization to Several Random Variables.- 2.3.1 Conditional Probability Density.- 2.3.2 Cross Correlation.- 2.3.3 Gaussian Distribution.- 2.4 Time-Dependent Random Variables.- 2.4.1 Classification of Stochastic Processes.- 2.4.2 Chapman-Kolmogorov Equation.- 2.4.3 Wiener-Khintchine Theorem.- 2.5 Several Time-Dependent Random Variables.- 3. Langevin Equations.- 3.1 Langevin Equation for Brownian Motion.- 3.1.1 Mean-Squared Displacement.- 3.1.2 Three-Dimensional Case.- 3.1.3 Calculation of the Stationary Velocity Distribution Function.- 3.2 Ornstein-Uhlenbeck Process.- 3.2.1 Calculation of Moments.- 3.2.2 Correlation Function.- 3.2.3 Solution by Fourier Transformation.- 3.3 Nonlinear Langevin Equation, One Variable.- 3.3.1 Example.- 3.3.2 Kramers-Moyal Expansion Coefficients.- 3.3.3 Itô's and Stratonovich's Definitions.- 3.4 Nonlinear Langevin Equations, Several Variables.- 3.4.1 Determination of the Langevin Equation from Drift and Diffusion Coefficients.- 3.4.2 Transformation of Variables.- 3.4.3 How to Obtain Drift and Diffusion Coefficients for Systems.- 3.5 Markov Property.- 3.6 Solutions of the Langevin Equation by Computer Simulation.- 4. Fokker-Planck Equation.- 4.1 Kramers-Moyal Forward Expansion.- 4.1.1 Formal Solution.- 4.2 Kramers-Moyal Backward Expansion.- 4.2.1 Formal Solution.- 4.2.2 Equivalence of the Solutions of the Forward and Backward Equations.- 4.3 Pawula Theorem.- 4.4 Fokker-Planck Equation for One Variable.- 4.4.1 Transition Probability Density for Small Times.- 4.4.2 Path Integral Solutions.- 4.5 Generation and Recombination Processes.- 4.6 Application of Truncated Kramers-Moyal Expansions.- 4.7 Fokker-Planck Equation for N Variables.- 4.7.1 Probability Current.- 4.7.2 Joint Probability Distribution.- 4.7.3 Transition Probability Density for Small Times.- 4.8 Examples for Fokker-Planck Equations with Several Variables.- 4.8.1 Three-Dimensional Brownian Motion without Position Variable.- 4.8.2 One-Dimensional Brownian Motion in a Potential.- 4.8.3 Three-Dimensional Brownian Motion in an External Force.- 4.8.4 Brownian Motion of Two Interacting Particles in an External Potential.- 4.9 Transformation of Variables.- 4.10 Covariant Form of the Fokker-Planck Equation.- 5. Fokker-Planck Equation for One Variable; Methods of Solution.- 5.1 Normalization.- 5.2 Stationary Solution.- 5.3 Ornstein-Uhlenbeck Process.- 5.4 Eigenfunction Expansion.- 5.5 Examples.- 5.5.1 Parabolic Potential.- 5.5.2 Inverted Parabolic Potential.- 5.5.3 Infinite Square Well for the Schrüdinger Potential.- 5.5.4 V-Shaped Potential for the Fokker-Planck Equation.- 5.6 Jump Conditions.- 5.7 A Bistable Model Potential.- 5.8 Eigenfunctions and Eigenvalues of Inverted Potentials.- 5.9 Approximate and Numerical Methods for Determining Eigenvalues and Eigenfunctions.- 5.9.1 Variational Method.- 5.9.2 Numerical Integration.- 5.9.3 Expansion into a Complete Set.- 5.10 Diffusion Over a Barrier.- 5.10.1 Kramers' Escape Rate.- 5.10.2 Bistable and Metastable Potential.- 6. Fokker-Planck Equation for Several Variables; Methods of Solution.- 6.1 Approach of the Solutions to a Limit Solution.- 6.2 Expansion into a Biorthogonal Set.- 6.3 Transformation of th

Mehr aus dieser Reihe

zurück
Dissipative Solitons in Reaction Diffusion Systems
Buch (gebunden)
von Andreas Liehr
Dissipative Solitons in Reaction Diffusion Systems
Buch (kartoniert)
von Andreas Liehr
Asymptotic Approaches in Nonlinear Dynamics
Buch (kartoniert)
von Igor V. Andriano…
Synergetics of Measurement, Prediction and Control
Buch (kartoniert)
von Igor Grabec, Wol…
Principles of Brain Functioning
Buch (kartoniert)
von Hermann Haken
vor
Servicehotline
089 - 70 80 99 47

Mo. - Fr. 8.00 - 20.00 Uhr
Sa. 10.00 - 20.00 Uhr
Filialhotline
089 - 30 75 75 75

Mo. - Sa. 9.00 - 20.00 Uhr
Bleiben Sie in Kontakt:
Sicher & bequem bezahlen:
akzeptierte Zahlungsarten: Überweisung, offene Rechnung,
Visa, Master Card, American Express, Paypal
Zustellung durch:
* Alle Preise verstehen sich inkl. der gesetzlichen MwSt. Informationen über den Versand und anfallende Versandkosten finden Sie hier.
** Deutschsprachige eBooks und Bücher dürfen aufgrund der in Deutschland geltenden Buchpreisbindung und/oder Vorgaben von Verlagen nicht rabattiert werden. Soweit von uns deutschsprachige eBooks und Bücher günstiger angezeigt werden, wurde bei diesen kürzlich von den Verlagen der Preis gesenkt oder die Buchpreisbindung wurde für diese Titel inzwischen aufgehoben. Angaben zu Preisnachlässen beziehen sich auf den dargestellten Vergleichspreis.