Overview
- First textbook that deals with the nonlinear Fokker-Planck equations
Part of the book series: Springer Series in Synergetics (SSSYN)
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Table of contents(8 chapters)
About this book
Providing an introduction to the theory of nonlinear Fokker-Planck equations, this book discusses fundamental properties of transient and stationary solutions, emphasizing the stability analysis of stationary solutions by means of self-consistency equations, linear stability analysis, and Lyapunov's direct method. Also treated are Langevin equations and correlation functions. Nonlinear Fokker-Planck Equations addresses various phenomena such as phase transitions, multistability of systems, synchronization, anomalous diffusion, cut-off solutions, travelling-wave solutions and the emergence of power law solutions. A nonlinear Fokker-Planck perspective to quantum statistics, generalized thermodynamics, and linear nonequilibrium thermodynamics is given. Theoretical concepts are illustrated where possible by simple examples. The book also reviews several applications in the fields of condensed matter physics, the physics of porous media and liquid crystals, accelerator physics, neurophysics, social sciences, population dynamics, and computational physics.
Reviews
From the reviews of the first edition:
"The author discusses the theory and application of nonlinear Fokker-Planck equations to the description of the nonlinear dynamics of many-body systems … . The principles and concepts of the theory are carefully exposited, along with simple examples and a very large list of references, illustrating the wide applicability to natural phenomena occurring in fields as diverse as physics, mathematics, biology, neurophysics, psychology, social sciences and population dynamics. The book will be very useful for researchers and graduate students interested or working in these areas." (Vitor R. Vieira, Mathematical Reviews, Issue 2006 h)
"The book focuses on common fundamental physical mechanisms present in diverse research fields. … The book may be a resource of mathematical problems in a field with diverse applications: each chapter gives an outline of examples and applications of various partial differential equations and an approach towards equilibrium of their solutions (H-theorems). A concept of negative stochastic feedback, with biological motivations, may be found interesting." (Piotr Garbaczewski, Zentralblatt MATH, Vol. 1071, 2005)
Authors and Affiliations
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Institut für Theoretische Physik, Universität Münster, Münster, Germany
Till Daniel Frank
Bibliographic Information
Book Title: Nonlinear Fokker-Planck Equations
Book Subtitle: Fundamentals and Applications
Authors: Till Daniel Frank
Series Title: Springer Series in Synergetics
DOI: https://doi.org/10.1007/b137680
Publisher: Springer Berlin, Heidelberg
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2005
Hardcover ISBN: 978-3-540-21264-5Published: 07 January 2005
Softcover ISBN: 978-3-642-05954-4Published: 19 October 2010
eBook ISBN: 978-3-540-26477-4Published: 08 December 2005
Series ISSN: 0172-7389
Series E-ISSN: 2198-333X
Edition Number: 1
Number of Pages: XII, 408
Topics: Quantum Physics, Complex Systems, Probability Theory and Stochastic Processes, Mathematical Methods in Physics, Thermodynamics, Statistical Physics and Dynamical Systems