The classical Fokker–Planck equation is a linear parabolic equation which describes the time evolution of the probability distribution of a stochastic process defined on a Euclidean space. Corresponding to a stochastic process, there often exists a free energy functional which is defined on the space of probability distributions and is a linear combination of a potential and an entropy. In rece...

Stochastic reaction-diffusion equations are a popular modelling approach for studying interacting populations in a heterogeneous environment under the influence of environmental fluctuations. Although the theoretical basis of alternative models such as Fokker-Planck diffusion is not less convincing, movement of populations is most commonly modelled using the diffusion law due to Fick. An intere...

A general expression for the correlation time of the decay of the magnetization of an assembly of singledomain noninteracting ferromagnetic particles is given in terms of the inverse of the Fokker-Planck operator. The results of Moro and Nordio @G. Moro and P. L. Nordio, Mol. Phys. 56, 255 ~1985!#, given in the context of dielectric relaxation, are recovered when the Fokker-Planck operator is a...

After a recent work on spectral properties and dispersion relations of the linearized classical Fokker-Planck-Landau operator 8], we establish in this paper analogous results for two more realistic collision operators: The rst one is the Fokker-Planck-Landau collision operator obtained by relativistic calculations of binary interactions , and the second is a collision operator (of Fokker-Planck...

We review recent analytical and computational results for macroscopic-microscopic beadspring models that arise from the kinetic theory of dilute solutions of incompressible polymeric fluids with noninteracting polymer chains, involving the coupling of the unsteady Navier– Stokes system in a bounded domain Ω ⊂ Rd, d = 2 or 3, with an elastic extra-stress tensor as right-hand side in the momentum...

In recent work, Chow, Huang, Li and Zhou [6] introduced the study of Fokker-Planck equations for a free energy function defined on a finite graph. When N ≥ 2 is the number of vertices of the graph, they show that the corresponding FokkerPlanck equation is a system of N nonlinear ordinary differential equations defined on a Riemannian manifold of probability distributions. The different choices ...

This paper is concerned with the analysis and implementation of spectral Galerkin methods for a class of Fokker–Planck equations that arises from the kinetic theory of dilute polymers. A relevant feature of the class of equations under consideration from the viewpoint of mathematical analysis and numerical approximation is the presence of an unbounded drift coefficient, involving a smooth conve...

In this article we derive Fokker Planck equation for incompressible fluid and investigate its properties