The Fokker-Planck Operator as an Asymptotic Limit in Anisotropic Media
نویسندگان
چکیده
We derive the Fokker-Planck operator describing a highly forward peaked scattering process in the linear transport equation, in anisotropic media, as a formal asymptotic limit of the exact integral operator. The resulting operator, being both con-vective and diiusive in angle and energy variables, reduces the degenerate nature of the Fokker-Planck system compared to the isotropic media case where the corresponding limit is only convective in energy and diiusive in angle.
منابع مشابه
Operator-stable Lévy motions and renormalizing the chaotic dynamics of microbes in anisotropic porous media
Self-motile particles, such as microbes, that can preferentially orient their microscale movement are embedded in a multiscale anisotropic porous medium. Such an environment is consistent with most natural geological systems. The preferential directional orientation and position of the self-motile particles at the microscale is accounted for with an operator-stable Lévy process. The anisotropy ...
متن کاملA class of asymptotic-preserving schemes for the Fokker-Planck-Landau equation
We present a class of asymptotic-preserving (AP) schemes for the nonhomogeneous Fokker–Planck–Landau (nFPL) equation. Filbet and Jin [16] designed a class of AP schemes for the classical Boltzmann equation, by penalization with the BGK operator, so they become efficient in the fluid dynamic regime. We generalize their idea to the nFPL equation, with a different penalization operator, the Fokker...
متن کاملOscillatory Survival Probability and Eigenvalues of the Non-Self-Adjoint Fokker-Planck Operator
We demonstrate the oscillatory decay of the survival probability of the stochastic dynamics dxε = a(xε) dt+ √ 2ε b(xε) dw, which is activated by small noise over the boundary of the domain of attraction D of a stable focus of the drift a(x). The boundary ∂D of the domain is an unstable limit cycle of a(x). The oscillations are explained by a singular perturbation expansion of the spectrum of th...
متن کاملThe Lévy-Fokker-Planck equation: Φ-entropies and convergence to equilibrium
In this paper, we study a Fokker-Planck equation of the form ut = I[u] + div(xu) where the operator I, which is usually the Laplacian, is replaced here with a general Lévy operator. We prove by the entropy production method the exponential decay in time of the solution to the only steady state of the associated stationnary equation.
متن کاملNumerical 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...
متن کامل