We simulate direct-drive CH target implosions with square laser pulses by a one-dimensional Fokker-Planck solver combined with a hydrodynamic code, and compare the results with those simulated by the flux-limited Spitzer-Härm model. We find that the electron thermal flux inhibition is time dependent, resulting in longer density scale length, larger laser absorption, and smaller growth of Raylei...

The Fokker–Planck equation with diffusion coefficient quadratic in space variable, linear drift coefficient, and nonlocal nonlinearity term is considered in the framework of a model of analysis of asset returns at financial markets. For special cases of such a Fokker– Planck equation we describe a construction of exact solution of the Cauchy problem. In the general case, we construct the leadin...

In recent years, several fractional generalizations of the usual Kramers-Fokker-Planck equation have been presented. Using an idea of Fogedby [H., we show how these equations are related to Langevin equations via the procedure of subor-dination. Introduction. – Some 70 years ago, Kramers [1] considered the motion of a Brownian particle subject to a space-dependent force F(x) per unit mass. His ...

A supersymmetric method for the construction of so-called conditionally exactly solvable quantum systems is reviewed and extended to classical stochastic dynamical systems characterized by a Fokker-Planck equation with drift. A class of drift-potentials on the real line as well as on the half line is constructed for which the associated Fokker-Planck equation can be solved exactly. Explicit dri...

Abstract: Given a probability measure, we consider the diffusion flows of probability measures associated with the partial differential equation (PDE) of Fokker–Planck. Our flows of the probability measures are defined as the solution of the Fokker–Planck equation for the same strictly convex potential, which means that the flows have the same equilibrium. Then, we shall investigate the time de...

We present the first post core collapse models of initially rotating star clusters, using the numerical solution of an orbit-averaged 2D Fokker-Planck equation. Based on the code developed by Einsel & Spurzem (1999), we have improved the speed and the stability and included the steady three-body binary heating source. We have confirmed that rotating clusters, whether they are in a tidal field o...

We exactly solve a Fokker-Planck equation by determining its eigenvalues and eigenfunctions: we construct nonlinear second-order differential operators which act as raising and lowering operators, generating ladder spectra for the odd- and even-parity states. The ladders are staggered: the odd-even separation differs from even-odd. The Fokker-Planck equation corresponds, in the limit of weak da...

The kinetics of fluctuations and switching of polarization in ferroelectrics, described by the Landau–Ginzburg Hamiltonian, is considered, based on a multi–dimensional Fokker–Planck equation. It describes the time evolution of the probability distribution function over the polarization field configurations in presence of a time–dependent external field. The Fokker–Planck equation in the Fourier...

It is well known that the analysis of the large-time asymptotics of Fokker-Planck type equations by the entropy method is closely related to proving the validity of convex Sobolev inequalities. Here we highlight this connection from an applied PDE point of view. In our unified presentation of the theory we present new results to the following topics: an elementary derivation of Bakry-Emery type...

We consider operators of Kramers-Fokker-Planck type in the semi-classical limit such that the exponent of the associated Maxwellian is a Morse function with two local minima and a saddle point. Under suitable additional assumptions we establish the complete asymptotics of the exponentially small splitting between the first two eigenvalues. Résumé On considère des opérateurs du type de Kramers-F...