GENERIC formalism of a Vlasov-Fokker-Planck equation and connection to large-deviation principles
نویسندگان
چکیده
In this paper we discuss the connections between a Vlasov-Fokker-Planck equation and an underlying microscopic particle system, and we interpret those connections in the context of the GENERIC framework (Öttinger 2005). This interpretation provides (a) a variational formulation for GENERIC systems, (b) insight into the origin of this variational formulation, and (c) an explanation of the origins of the conditions that GENERIC places on its constitutive elements, notably the so-called degeneracy or non-interaction conditions. This work shows how the general connection between large-deviation principles on one hand and gradient-flow structures on the other hand extends to non-reversible particle systems.
منابع مشابه
On Long Time Asymptotics of the Vlasov-fokker-planck Equation and of the Vlasov-poisson-fokker-planck System with Coulombic and Newtonian Potentials
We prove that the solution of the Vlasov-Fokker-Planck equation converges to the unique stationary solution with same mass as time tends to infinity. The same result holds in the repulsive coulombic case for the Vlasov-Poisson-Fokker-Planck system; the newtonian attractive case is also studied. We establish positive and negative answers to the question of existence of a stationary solution for ...
متن کاملLecture notes Particle systems, large-deviation and variational approaches to generalised gradient flows
In 1998, Jordan-Kinderleher-Otto [JKO98] proved a remarkable result that the diffusion equation can be seen as a gradient flow of the Boltzmann entropy with respect to the Wasserstein distance. This result has sparked off a large body of research in the field of partial differential equations and others in the last two decades. Many evolution equations have been proved to have a Wasserstein gra...
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 کاملPseudo-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.
متن کاملSmoothing Effect for the Non-linear Vlasov-poisson-fokker-planck System
We study a smoothing effect of a non-linear degenerate parabolic problem, the Vlasov-Poisson-Fokker-Planck system, in three dimensions. We prove that a solution gives rise actually to very smooth macroscopic density and force field for positive time. This is obtained by analyzing the effect of the Fokker-Planck kernel on the force term in the Vlasov equation and using classical convolution ineq...
متن کامل