Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Nonlinear Fokker-Planck Equations PDF full book. Access full book title Nonlinear Fokker-Planck Equations by T.D. Frank. Download full books in PDF and EPUB format.
Author: T.D. Frank Publisher: Springer Science & Business Media ISBN: 3540212647 Category : Science Languages : en Pages : 414
Book Description
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.
Author: T.D. Frank Publisher: Springer Science & Business Media ISBN: 3540212647 Category : Science Languages : en Pages : 414
Book Description
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.
Author: T.D. Frank Publisher: Springer Science & Business Media ISBN: 3540264779 Category : Science Languages : en Pages : 415
Book Description
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.
Author: Christian Soize Publisher: World Scientific ISBN: 9789810217556 Category : Science Languages : en Pages : 346
Book Description
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?
Author: Hannes Risken Publisher: Springer Science & Business Media ISBN: 3642615449 Category : Mathematics Languages : en Pages : 486
Book Description
This is the first textbook to include the matrix continued-fraction method, which is very effective in dealing with simple Fokker-Planck equations having two variables. Other methods covered are the simulation method, the eigen-function expansion, numerical integration, and the variational method. Each solution is applied to the statistics of a simple laser model and to Brownian motion in potentials. The whole is rounded off with a supplement containing a short review of new material together with some recent references. This new study edition will prove to be very useful for graduate students in physics, chemical physics, and electrical engineering, as well as for research workers in these fields.
Author: Johan Grasman Publisher: Springer Science & Business Media ISBN: 9783540644354 Category : Mathematics Languages : en Pages : 242
Book Description
Asymptotic methods are of great importance for practical applications, especially in dealing with boundary value problems for small stochastic perturbations. This book deals with nonlinear dynamical systems perturbed by noise. It addresses problems in which noise leads to qualitative changes, escape from the attraction domain, or extinction in population dynamics. The most likely exit point and expected escape time are determined with singular perturbation methods for the corresponding Fokker-Planck equation. The authors indicate how their techniques relate to the Itô calculus applied to the Langevin equation. The book will be useful to researchers and graduate students.
Author: Vladimir I. Bogachev Publisher: American Mathematical Soc. ISBN: 1470425580 Category : Mathematics Languages : en Pages : 495
Book Description
This book gives an exposition of the principal concepts and results related to second order elliptic and parabolic equations for measures, the main examples of which are Fokker-Planck-Kolmogorov equations for stationary and transition probabilities of diffusion processes. Existence and uniqueness of solutions are studied along with existence and Sobolev regularity of their densities and upper and lower bounds for the latter. The target readership includes mathematicians and physicists whose research is related to diffusion processes as well as elliptic and parabolic equations.
Author: Sau Fa Kwok Publisher: World Scientific ISBN: 9813228423 Category : Science Languages : en Pages : 208
Book Description
This invaluable book provides a broad introduction to a rapidly growing area of nonequilibrium statistical physics. The first part of the book complements the classical book on the Langevin and Fokker-Planck equations (H. Risken, The Fokker-Planck Equation: Methods of Solution and Applications (Springer, 1996)). Some topics and methods of solutions are presented and discussed in details which are not described in Risken's book, such as the method of similarity solution, the method of characteristics, transformation of diffusion processes into the Wiener process in different prescriptions, harmonic noise and relativistic Brownian motion. Connection between the Langevin equation and Tsallis distribution is also discussed.Due to the growing interest in the research on the generalized Langevin equations, several of them are presented. They are described with some details.Recent research on the integro-differential Fokker-Planck equation derived from the continuous time random walk model shows that the topic has several aspects to be explored. This equation is worked analytically for the linear force and the generic waiting time probability distribution function. Moreover, generalized Klein-Kramers equations are also presented and discussed. They have the potential to be applied to natural systems, such as biological systems.
Author: T.D. Frank
Author: T.D. Frank
Author: T.D. Frank
Author: Viorel Barbu
Author: Christian Soize
Author: Hannes Risken
Author: Johan Grasman
Author: 
Author: Vladimir I. Bogachev
Author: Dennis C. Frezzo
Author: Sau Fa Kwok