Nonlinear Fokker-Planck Equations: Fundamentals and Applications / Edition 1

by T.D. Frank

Overview

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.

Product Details

ISBN-13:	9783540212645
Publisher:	Springer Berlin Heidelberg
Publication date:	02/24/2005
Series:	Springer Series in Synergetics
Edition description:	2005
Pages:	408
Product dimensions:	6.10(w) x 9.25(h) x 0.04(d)

Table of Contents

Fundamentals.- Strongly Nonlinear Fokker-Planck Equations.- Free Energy Fokker-Planck Equations.- Free Energy Fokker-Planck Equations with Boltzmann Statistics.- Entropy Fokker-Planck Equations.- General Nonlinear Fokker-Planck Equations.- Epilogue.

Editorial 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 shastic feedback, with biological motivations, may be found interesting." (Piotr Garbaczewski, Zentralblatt MATH, Vol. 1071, 2005)

From the Publisher