In this paper we study under which circumstances there exists a general change of gross variables that transforms any Fokker-Planck equation into another of the Ornstein-Uhlenbeck class that, therefore, has an exact solution. We find that any Fokker-Planck equation will be exactly solvable by means of a change of gross variables if and only if the curvature tensor and the torsion tensor associa...

Wave propagation is studied in a sufficiently anisotropic random medium where backscattering along one direction can be neglected. A Fokker-Planck equation, the solution to which would provide a complete statistical description of such directed waves, is derived. The Fokker-Planck equation is mapped onto an su(1,1) ferromagnet and its symmetries are identified. Using the symmetries, asymptotic ...

We derive the generalized Fokker-Planck equation associated with a Langevin equation driven by arbitrary additive white noise. We apply our result to study the distribution of symmetric and asymmetric Lévy flights in an infinitely deep potential well. The fractional Fokker-Planck equation for Lévy flights is derived and solved analytically in the steady state. It is shown that Lévy flights are ...

We consider a polymeric fluid model, consisting of the incompressible Navier-Stokes equations coupled to a non-symmetric Fokker-Planck equation. First, steady states and exponential convergence to them in relative entropy are proved for the linear Fokker-Planck equation in the Hookean case. The FENE model is also addressed proving the existence of stationary states and the convergence towards t...

We address the objective of the generation of finite magnetic flux out of unbiased thermal current fluctuations in a collection of identical mesoscopic cylinders which are coupled via mutual inductances. The influence of thermal Nyquist fluctuations are described in terms of a set of Langevin equations or a corresponding Fokker–Planck equation, respectively. In the limit of infinitely many cons...

This paper is concerned with scaling limits in kinetic semiconductor models. For the classical Vlasov-Poisson-Fokker-Planck equation and its quantum mechanical counterpart, the Wigner-Poisson-Fokker-Planck equation, three distinguished scaling regimes are presented. Using Hilbert and Chapman-Enskog expansions, we derive two drift-diiusion type approximations. The test case of a n + ?n?n + diode...

A new algorithm for nonconvex optimization by means of a so-called Fokker-Planck Learning Machine is proposed in this paper. This is done by considering the Fokker-Planck (FP) equation related to continuous simulated annealing, which has been proven to convergence to the global optimum under certain conditions. An approximate solution to the FP equation is sought by parametrizing the transition...

This paper is concerned with scaling limits in kinetic semiconductor models. For the classical Vlasov-Poisson-Fokker-Planck equation and its quantum mechanical counterpart, the Wigner-Poisson-Fokker-Planck equation, three distinguished scaling regimes are presented. Using Hilbert and Chapman-Enskog expansions, we derive two drift-diffusion type approximations. The test case of a n+−n−n+ diode r...

The gyrokinetic linearized exact Fokker-Planck collision operator is obtained in a form suitable for plasma gyrokinetic equations, for arbitrary mass ratio. The linearized Fokker-Planck operator includes both the test-particle and field-particle contributions, and automatically conserves particles, momentum, and energy, while ensuring non-negative entropy production. Finite gyroradius effects i...

abstract We present fast numerical algorithms to solve the non linear Fokker-Planck-Landau equation in 3-D velocity space. The discretization of the collision operator preserves the properties required by the physical nature of the Fokker-Planck-Landau equation, such as the conservation of mass, momentum and energy, the decay of the entropy, and the fact that the steady states are Maxwellians. ...