TY - BOOK ID - 208189 TI - Nonlinear Fokker-Planck Equations : Fundamentals and Applications PY - 2005 SN - 3540264779 3540212647 3642059546 PB - Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, DB - UniCat KW - Fokker-Planck equation. KW - Stochastic differential equations. KW - Differential equations, Nonlinear. KW - Nonlinear differential equations KW - Nonlinear theories KW - Differential equations KW - Fokker-Planck equation KW - Equation, Fokker-Planck KW - Planck-Fokker equation KW - Differential equations, Partial KW - Stochastic differential equations KW - Quantum theory. KW - Distribution (Probability theory. KW - Mathematical physics. KW - Thermodynamics. KW - Statistical physics. KW - Quantum Physics. KW - Complex Systems. KW - Probability Theory and Stochastic Processes. KW - Mathematical Methods in Physics. KW - Statistical Physics and Dynamical Systems. KW - Physics KW - Mathematical statistics KW - Chemistry, Physical and theoretical KW - Dynamics KW - Mechanics KW - Heat KW - Heat-engines KW - Quantum theory KW - Physical mathematics KW - Distribution functions KW - Frequency distribution KW - Characteristic functions KW - Probabilities KW - Quantum dynamics KW - Quantum mechanics KW - Quantum physics KW - Thermodynamics KW - Statistical methods KW - Mathematics KW - Quantum physics. KW - Dynamical systems. KW - Probabilities. KW - Physics. KW - Natural philosophy KW - Philosophy, Natural KW - Physical sciences KW - Probability KW - Statistical inference KW - Combinations KW - Chance KW - Least squares KW - Risk KW - Dynamical systems KW - Kinetics KW - Mechanics, Analytic KW - Force and energy KW - Statics UR - https://www.unicat.be/uniCat?func=search&query=sysid:208189 AB - 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. ER -