Download or read book Fokker Planck Solution of the Theis Equation written by Mahmut Sercan Ceyhan and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The Fokker-Planck-Equation (FPE) methodology proposed by Kavvas (2003) was applied to the transient state confined groundwater flow under the initial and boundary conditions leading to the Theis problem (Theis, 1935). Towards that goal, the differential form of the Theis equation was converted to an ordinary differential equation (ODE) by using the non-dimensionalizing symmetry transformations determined from the symmetry analysis. The resulting ODE and the transformed initial and boundary conditions formed an end value problem in the symmetry space. The backward form of the Master Key Equation provided by Kavvas (2003) was used in order to write the FPE, which describes the evolution of the probability density function of the state variable for this system. Numerical solutions of the FPE was obtained with a hybrid, higher order numerical scheme that uses the explicit Lax-Wendroff Scheme with a Flux Limiter for the advective terms and the implicit Crank-Nicholson scheme for the dispersive terms. This hybrid scheme, combined with the appropriate discretization of the solution domain, made it possible to obtain a solution without numerical dispersion. The results of the FPE methodology were compared with the Monte-Carlo solutions of the analytical Theis solution. The comparison shows a good match in terms of the ensemble mean, variance, and probability density functions in general. The FPE methodology overestimated the ensemble variance in the close vicinity of the well.

Download or read book Langevin And Fokker planck Equations And Their Generalizations Descriptions And Solutions written by Sau Fa Kwok and published by World Scientific. This book was released on 2018-03-07 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book The Fokker Planck Equation written by Hannes Risken and published by . This book was released on 1984-05-01 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Fokker Planck Equation written by Hannes Risken and published by . This book was released on 1996-09-17 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Analysis of the Langevin Equation with Random Damping by the Fokker Planck Equation written by J. A. Young and published by . This book was released on 1963 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Fokker Planck Kolmogorov Equations written by Vladimir I. Bogachev and published by American Mathematical Society. This book was released on 2022-02-10 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book On the Solution of the Fokker Planck Equation for Multi dimensional Nonlinear Mechanical Systems written by Wolfram Martens and published by . This book was released on 2014-02-07 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Variational Formulation of the Fokker Planck Equation written by Richard Jordan and published by . This book was released on 1996 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "The Fokker-Planck equation, or forward Kolmogorov equation, describes the evolution of the probability density for a stochastic process associated with an Ito stochastic differential equation. It pertains to a wide variety of time-dependent systems in which randomness plays a role. In this paper, we are concerned with Fokker-Planck equations for which the drift term is given by the gradient of a potential. For a broad class of potentials, we construct a time-discrete, iterative variational scheme whose solutions converge to the solution of the Fokker-Planck equation. The major novelty of this iterative scheme is that the time step is governed by the Wasserstein metric on probability measures. This formulation enables us to reveal an appealing, and previously unexplored, relationship between the Fokker-Planck equation and the associated free energy functional. Namely we demonstrate that the dynamics may be regarded as a gradient flux, or a steepest descent, for the free energy with respect to the Wasserstein metric."

Download or read book Generalized Function Solutions to the Fokker Planck Equation written by Edward Bruce Parlette and published by . This book was released on 1985 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Simulation of the Fokker Planck Equation by Random Walks of Test Particles in Velocity Space with Application to Magnetic Mirror Systems written by Gerald W. Englert and published by . This book was released on 1970 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Weak Solutions to a Fractional Fokker Planck Equation Via Splitting and Wasserstein Gradient Flow written by Malcolm Bowles and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Numerical Solution of the Fokker Planck Equation with Applications to Control Theory written by Richard H. Wiggins and published by . This book was released on 1973 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Identification of the Drift Coefficient of a Fokker Planck Equation from the Moment Discretization of Its Stationary Solution written by Gabriele Inglese and published by . This book was released on 1995 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Free Energy and the Fokker Planck Equation written by Richard Jordan and published by . This book was released on 1996 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "We establish a new and intriguing connection between the Fokker-Planck equation with gradient drift term and an associated free energy functional. Namely, we demonstrate that such a Fokker-Planck equation may be interpreted as a gradient flux, or a steepest descent, of a free energy functional with respect to a certain metric. This is accomplished through the construction of a time-discrete iterative variational scheme whose solutions converge to the solution of the Fokker-Planck equation. The time step in this scheme is governed by the Wasserstein metric on probability measures."

Download or read book The Numerical Solution to the Fokker Planck Equation in N dimensions Using the Finite Element Method written by Maamar Benkraouda and published by . This book was released on 1998 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis deals with the numerical solution of the Fokker-Planck equation in n-dimensional space using the method of finite element with n-simplex elements. The numerical code is validated through numerous examples. Finally the method is used in investigating the problem of cooling atoms and ions using laser light.

Download or read book Solution of a Stationary Fokker Planck Equation written by Tore Leversen and published by . This book was released on 1971 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Solution of the Fokker Planck Equation with Boundary Conditions by Feynman Kac Integration written by Marc Decamps and published by . This book was released on 2003 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: