Higher Order Averaging of Linear Fokker-Planck Equations with Periodic Forcing

Iterative methods for solving non linear Fokker-Planck equation

How accurate are the nonlinear chemical Fokker-Planck and chemical Langevin equations?

The chemical Fokker-Planck equation and the corresponding chemical Langevin equation are commonly used approximations of the chemical master equation. These equations are derived from an uncontrolled, second-order truncation of the Kramers-Moyal expansion of the chemical master equation and hence their accuracy remains to be clarified. We use the system-size expansion to show that chemical Fokk...

Numerical Studies and Simulation of the Lower Hybrid Waves Current Drive by using Fokker – Planck Equation in NSST and HT-7 Tokamaks

Recent experiments on the spherical tokamak have discovered the conditions to create a powerful plasma and ensure easy shaping and amplification of stability, high bootstrap current and confinement energy. The spherical tours (ST) fusion energy development path is complementary to the tokamak burning plasma experiment such as NSTX and higher toroidal beta regimes and improves the design of a po...

Fokker–Planck equation with fractional coordinate derivatives

Using the generalized Kolmogorov-Feller equation with long-range interaction, we obtain kinetic equations with fractional derivatives with respect to coordinates. The method of successive approximations with the averaging with respect to fast variable is used. The main assumption is that the correlator of probability densities of particles to make a step has a power-law dependence. As a result,...

Entropy Methods, PDEs, Functional Inequalities, and Applications

S (in alphabetic order by speaker surname) Anton Arnold (TU Wien) Entropy method for hypocoercive Fokker-Planck equations with linear drift In the last 15 years the entropy method became an invaluable tool for analyzing the large-time behavior (in particular the convergence to a steady state) for wide classes of PDEs: starting from linear FokkerPlanck equations, to various dissipative kinetic m...