Item description for Nonlinear Fokker-Planck Equations: Fundamentals and Applications (Springer Series in Synergetics) by Till D. Frank...
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.
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Est. Packaging Dimensions: Length: 9.4" Width: 6" Height: 1" Weight: 1.15 lbs.
Release Date Feb 24, 2005
ISBN 3540212647 ISBN13 9783540212645
Availability 71 units. Availability accurate as of Oct 25, 2016 08:07.
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Reviews - What do customers think about Nonlinear Fokker-Planck Equations: Fundamentals and Applications (Springer Series in Synergetics)?
Not carefully thought out! Apr 6, 2006
This book is riddled with very serious mistakes, as are many of the papers it refers to. There is no such thing as a 'nonlinear Markov process'. There is no such thing as a 'nonlinear Fokker-Planck equation' for a conditional probability. A conditional probability with initial state memory is nonMarkovian. A conditional probability with initial state memory is not guaranteed to obey a Chapman-Kolmogorov equation and usually doesn't. A Chapman-Kolmogorov equation is a necessary but not sufficient condition for a Markov process. A Fokker-Planck equation with memory of an initial state in its drift and/or diffusion coefficients does not generate a Markov process. A nonlinear diffusion equation does not define any stochastic process at all, in fact a diffusion equation for a 1-point density defines no stochastic process at all. A 1-point density cannot be used to identify/define a stochastic process, both scaling Markov processes and strongly nonMarkov processes like fractional Brownian motion have exactly the same 1-point density, with widely differing conditional densities. For detailed explanations see cond-mat/0701589.