Nonlinear Fokker-Planck Equations: Fundamentals and Applications

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Springer Science & Business Media, Jan 7, 2005 - Science - 408 pages
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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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Contents

Introduction
1
Fundamentals 19
18
Strongly Nonlinear FokkerPlanck Equations
31
Free Energy FokkerPlanck Equations
73
Free Energy FokkerPlanck Equations
108
Entropy FokkerPlanck Equations
213
General Nonlinear FokkerPlanck Equations 299
298
Epilogue
367
References 371
388
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