Hydrodynamic Limit of a Fokker--Planck Equation Describing Fiber Lay-Down Processes

Exponential rate of convergence to equilibrium for a model describing fiber lay-down processes

This paper is devoted to the adaptation of the method developed in Dolbeault et al. [2011, 2009] to a Fokker-Planck equation for fiber lay-down which has been studied in Bonilla et al. [2007/08], Götz et al. [2007]. Exponential convergence towards a unique stationary state is proved in a norm which is equivalent to a weighted L norm. The method is based on a micro / macro decomposition which is...

Kinetic and hydrodynamic models of chemotactic aggregation

We derive general kinetic and hydrodynamic models of chemotactic aggregation that describe certain features of the morphogenesis of biological colonies (like bacteria, amoebae, endothelial cells or social insects). Starting from a stochastic model defined in terms of N coupled Langevin equations, we derive a nonlinear mean field Fokker-Planck equation governing the evolution of the distribution...

Pseudo-spectral ‎M‎atrix and Normalized Grunwald Approximation for Numerical Solution of Time Fractional Fokker-Planck Equation

This paper presents a new numerical method to solve time fractional Fokker-Planck equation. The space dimension is discretized to the Gauss-Lobatto points, then we apply pseudo-spectral successive integration matrix for this dimension. This approach shows that with less number of points, we can approximate the solution with more accuracy. The numerical results of the examples are displayed.

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...

Iterative methods for solving non linear Fokker-Planck equation