Nonlinear Fokker-Planck Equations
Nonlinear Fokker-Planck Equations
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DOI：
10.1007/b137680
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发表时间：
2005
期刊：
影响因子：
2.3
通讯作者：
T. Frank
中科院分区：
文献类型：
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作者：
T. Frank
提供了一个介绍非线性福克-普朗克方程的理论，这本书讨论了瞬态和平稳解决的基本性质，强调通过自洽方程，线性稳定性分析，和李亚普诺夫的直接方法的平稳解决的稳定性分析。还讨论了朗之万方程和相关函数。非线性福克-普朗克方程处理各种现象，如相变、系统的多稳定性、同步、异常扩散、截止解、行波解和幂律解的出现。给出了量子统计、广义热力学和线性非平衡热力学的非线性Fokker-Planck视角。理论概念尽可能用简单的例子加以说明。本书还回顾了凝聚态物理、多孔介质和液晶物理、加速器物理、神经物理、社会科学、人口动力学和计算物理等领域的几个应用。
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.