Related papers: A particle method for the multispecies Landau equa…
We develop novel asymptotic-preserving (AP) deterministic particle methods for collisional plasma models, including both Landau--Fokker--Planck and Dougherty collision operators, under hydrodynamic scaling. Our schemes treat the non-stiff…
We investigate the gravitational effect on Landau levels. We show that the familiar infinite Landau degeneracy of the energy levels of a quantum particle moving inside a uniform and constant magnetic field is removed by the interaction of…
The global-in-time existence of weak solutions to a spatially homogeneous multispecies Fokker-Planck-Landau system for plasmas in the three-dimensional whole space is shown. The Fokker-Planck-Landau system is a simplification of the Landau…
Dissipative particle dynamics (DPD) and multi-particle collision (MPC) dynamics are powerful tools to study mesoscale hydrodynamic phenomena accompanied by thermal fluctuations. To understand the advantages of these types of mesoscale…
When applying Hamiltonian operator splitting methods for the time integration of multi-species Vlasov-Maxwell-Landau systems, the reliable and efficient numerical approximation of the Landau equation represents a fundamental component of…
This research note documents new developments regarding finite-element discretizations of the relativistic Beliaev-Budker Coulomb collision operator and the nonrelativistic Landau operator. Where energy conservation in a finite-element…
Kinetic equations model the position-velocity distribution of particles subject to transport and collision effects. Under a diffusive scaling, these combined effects converge to a diffusion equation for the position density in the limit of…
This paper presents a unified gas-kinetic wave-particle (UGKWP) method for simulating multiscale binary-species gas mixtures. Benefiting from direct modeling in a discretized space, the UGKWP method enables the automatic decomposition of…
The dynamics of thermally fluctuating conserved order parameters are described by stochastic conservation laws. Thermal equilibrium in such systems requires the dissipative and stochastic components of the flux to be related by detailed…
The relaxation of a weakly collisional plasma, which is of fundamental interest to laboratory and astrophysical plasmas, can be described by the Boltzmann-Poisson equations with the Lenard-Bernstein collision operator. We perform a…
We study the Landau equation for a mixture of two species in the whole space, with initial condition of one species near a vacuum and the other near a Maxwellian equilibrium state. For the linearized level, without any smoothness assumption…
The Dougherty model Fokker-Planck operator is extended to describe nonlinear full-f collisions between multiple species in plasmas. Simple relations for cross-species interactions are developed which obey conservation laws, and reproduce…
We provide the first and rigorous confirmations of the hypotheses by Ludwig Boltzmann in his seminal paper \cite{Boltzmann} within the context of the Landau equation in the presence of a harmonic potential. We prove that (i) Each {\it…
We consider in this paper random batch interacting particle methods for solving the Poisson-Nernst-Planck (PNP) equations, and thus the Poisson-Boltzmann (PB) equation as the equilibrium, in the external unbounded domain. To justify the…
We consider a system of N classical particles, interacting via a smooth, short- range potential, in a weak-coupling regime. This means that N tends to infinity when the interaction is suitably rescaled. The j-particle marginals, which obey…
We derive a class of multi-species aggregation-diffusion systems from stochastic interacting particle systems via relative entropy method with quantitative bounds. We show an algebraic $L^1$-convergence result using moderately interacting…
In the smoothed particle dynamics (SPH) method, the characteristics of a target particle are interpolated based on the information from its neighboring particles. Consequently, a uniform initial distribution of particles significantly…
Within the framework of the hypothesis offered by authors about complex-valued nature of physical quantities, the effect of the Landau damping has been explored with assumption that not only frequency can be a small imaginary component but…
We present new results building on the conservative deterministic spectral method for the space homogeneous Boltzmann equation developed by Gamba and Tharkabhushaman. This approach is a two-step process that acts on the weak form of the…
We consider the Vlasov-Poisson-Landau system, a classical model for a dilute collisional plasma interacting through Coulombic collisions and with its self-consistent electrostatic field. We establish global stability and well-posedness near…