The Fokker-Planck Equation - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Fokker-Planck Equation write by Hannes Risken. This book was released on 2012-12-06. The Fokker-Planck Equation available in PDF, EPUB and Kindle. 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.
Nonlinear Fokker-Planck Equations
Nonlinear Fokker-Planck Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonlinear Fokker-Planck Equations write by T.D. Frank. This book was released on 2005-01-07. Nonlinear Fokker-Planck Equations available in PDF, EPUB and Kindle. 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.
Asymptotic Methods for the Fokker-Planck Equation and the Exit Problem in Applications
Asymptotic Methods for the Fokker-Planck Equation and the Exit Problem in Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Asymptotic Methods for the Fokker-Planck Equation and the Exit Problem in Applications write by Johan Grasman. This book was released on 1999-03-08. Asymptotic Methods for the Fokker-Planck Equation and the Exit Problem in Applications available in PDF, EPUB and Kindle. 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.
The Fokker-Planck Equation for Stochastic Dynamical Systems and Its Explicit Steady State Solutions
The Fokker-Planck Equation for Stochastic Dynamical Systems and Its Explicit Steady State Solutions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Fokker-Planck Equation for Stochastic Dynamical Systems and Its Explicit Steady State Solutions write by Christian Soize. This book was released on 1994. The Fokker-Planck Equation for Stochastic Dynamical Systems and Its Explicit Steady State Solutions available in PDF, EPUB and Kindle. 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?
Langevin And Fokker-planck Equations And Their Generalizations: Descriptions And Solutions
Langevin And Fokker-planck Equations And Their Generalizations: Descriptions And Solutions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Langevin And Fokker-planck Equations And Their Generalizations: Descriptions And Solutions write by Sau Fa Kwok. This book was released on 2018-03-07. Langevin And Fokker-planck Equations And Their Generalizations: Descriptions And Solutions available in PDF, EPUB and Kindle. 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.
