The Fokker-Planck equation
methods of solution and applications
| Autor | |
| Quelle | Sonstige Datenquellen |
| ISBN | 978-3-540-61530-9 |
| Lieferbarkeit | lieferbar |
| Katalogisat | Basiskatalogisat |
| Verlag | Springer Berlin |
| Erscheinungsdatum | 17.09.1996 |
Beschreibung (Kurztext)
The Fokker-Planck equation deals with those fluctuations of systems which stem from many tiny disturbances, each of which changes the variable of the system in an unpredictable way. In this book, the methods of solution are applied to the statistics of a simple laser model and to Brownian motion in potentials. Such Brownian motion is important in solid state physics, chemical physics and electrical circuit theory. In this second edition, some misprints have been corrected and a supplement is included, containing a short review of new material together with some recent references.
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 einzigartige Kombination zwischen mathematischen Ableitungen und physikalischen Anwendungsbeispielen.
Beschreibung (Langtext)
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.