Nonlinear Fokker Planck Equations
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Nonlinear Fokker Planck Equations
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Author : T.D. Frank
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-01-07
Nonlinear Fokker Planck Equations written by T.D. Frank and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-07 with Science categories.
Centered around the natural phenomena of relaxations and fluctuations, this monograph provides readers with a solid foundation in the linear and nonlinear Fokker-Planck equations that describe the evolution of distribution functions. It emphasizes principles and notions of the theory (e.g. self-organization, stochastic feedback, free energy, and Markov processes), while also illustrating the wide applicability (e.g. collective behavior, multistability, front dynamics, and quantum particle distribution). The focus is on relaxation processes in homogeneous many-body systems describable by nonlinear Fokker-Planck equations. Also treated are Langevin equations and correlation functions. Since these phenomena are exhibited by a diverse spectrum of systems, examples and applications span the fields of physics, biology and neurophysics, mathematics, psychology, and biomechanics.
Nonlinear Fokker Planck Flows And Their Probabilistic Counterparts
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Author : Viorel Barbu
language : en
Publisher: Springer Nature
Release Date :
Nonlinear Fokker Planck Flows And Their Probabilistic Counterparts written by Viorel Barbu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Nonlinear Fokker Planck Equations
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Author : T.D. Frank
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-08
Nonlinear Fokker Planck Equations written by T.D. Frank and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-08 with Science categories.
Centered around the natural phenomena of relaxations and fluctuations, this monograph provides readers with a solid foundation in the linear and nonlinear Fokker-Planck equations that describe the evolution of distribution functions. It emphasizes principles and notions of the theory (e.g. self-organization, stochastic feedback, free energy, and Markov processes), while also illustrating the wide applicability (e.g. collective behavior, multistability, front dynamics, and quantum particle distribution). The focus is on relaxation processes in homogeneous many-body systems describable by nonlinear Fokker-Planck equations. Also treated are Langevin equations and correlation functions. Since these phenomena are exhibited by a diverse spectrum of systems, examples and applications span the fields of physics, biology and neurophysics, mathematics, psychology, and biomechanics.
Stochastic Properties Of Human Motor Control Nonlinear Fokker Planck Equations
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Author : Till Daniel Frank
language : en
Publisher:
Release Date : 2001
Stochastic Properties Of Human Motor Control Nonlinear Fokker Planck Equations written by Till Daniel Frank and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with categories.
Coalescing Particle Systems And Applications To Nonlinear Fokker Planck Equations
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Author : Gleb Zhelezov
language : en
Publisher:
Release Date : 2017
Coalescing Particle Systems And Applications To Nonlinear Fokker Planck Equations written by Gleb Zhelezov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with categories.
We study a stochastic particle system with a logarithmically-singular inter-particle interaction potential which allows for inelastic particle collisions. We relate the squared Bessel process to the evolution of localized clusters of particles, and develop a numerical method capable of detecting collisions of many point particles without the use of pairwise computations, or very refined adaptive timestepping. We show that when the system is in an appropriate parameter regime, the hydrodynamic limit of the empirical mass density of the system is a solution to a nonlinear Fokker-Planck equation, such as the Patlak-Keller-Segel (PKS) model, or its multispecies variant. We then show that the presented numerical method is well-suited for the simulation of the formation of finite-time singularities in the PKS, as well as PKS pre- and post-blow-up dynamics. Additionally, we present numerical evidence that blow-up with an increasing total second moment in the two species Keller-Segel system occurs with a linearly increasing second moment in one component, and a linearly decreasing second moment in the other component.
The Fokker Planck Equation For Stochastic Dynamical Systems And Its Explicit Steady State Solutions
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Author : Christian Soize
language : en
Publisher: World Scientific
Release Date : 1994
The Fokker Planck Equation For Stochastic Dynamical Systems And Its Explicit Steady State Solutions written by Christian Soize and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Science categories.
This is an analysis of multidimensional nonlinear dissipative Hamiltonian dynamical systems subjected to parametric and external stochastic excitations by the Fokker-Planck equation method.The author answers three types of questions concerning this area. First, what probabilistic tools are necessary for constructing a stochastic model and deriving the FKP equation for nonlinear stochastic dynamical systems? Secondly, what are the main results concerning the existence and uniqueness of an invariant measure and its associated stationary response? Finally, what is the class of multidimensional dynamical systems that have an explicit invariant measure and what are the fundamental examples for applications?
Noise In Nonlinear Dynamical Systems Volume 1 Theory Of Continuous Fokker Planck Systems
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Author : Frank Moss
language : en
Publisher: Cambridge University Press
Release Date : 1989-04-06
Noise In Nonlinear Dynamical Systems Volume 1 Theory Of Continuous Fokker Planck Systems written by Frank Moss and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-04-06 with Mathematics categories.
Vol. 1.
Uniqueness And Regularity Of Weak Solutions Of The Nonlinear Fokker Planck Equation
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Author : Tamir Tassa
language : en
Publisher:
Release Date : 1993
Uniqueness And Regularity Of Weak Solutions Of The Nonlinear Fokker Planck Equation written by Tamir Tassa and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.
On The Solution Of The Fokker Planck Equation For Multi Dimensional Nonlinear Mechanical Systems
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Author : Wolfram Martens
language : en
Publisher:
Release Date : 2014-02-07
On The Solution Of The Fokker Planck Equation For Multi Dimensional Nonlinear Mechanical Systems written by Wolfram Martens and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02-07 with categories.
Semigroup Approach To Nonlinear Diffusion Equations
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Author : Viorel Barbu
language : en
Publisher: World Scientific
Release Date : 2021-09-23
Semigroup Approach To Nonlinear Diffusion Equations written by Viorel Barbu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-23 with Mathematics categories.
This book is concerned with functional methods (nonlinear semigroups of contractions, nonlinear m-accretive operators and variational techniques) in the theory of nonlinear partial differential equations of elliptic and parabolic type. In particular, applications to the existence theory of nonlinear parabolic equations, nonlinear Fokker-Planck equations, phase transition and free boundary problems are presented in details. Emphasis is put on functional methods in partial differential equations (PDE) and less on specific results.