相关论文: Nonlinear $\delta f$ Method for Beam-Beam Simulati…

While accurate simulations of dense gas flows far from the equilibrium can be achieved by Direct Simulation adapted to the Enskog equation, the significant computational demand required for collisions appears as a major constraint. In order…

Molecular dynamics simulations, with full Coulomb interaction and self-consistent field emission, are used to examine mutual space-charge interactions between beams originating from several emitter areas, in a planar infinite diode. The…

We present a new algorithm which is named the Dynamical Functional Particle Method, DFPM. It is based on the idea of formulating a finite dimensional damped dynamical system whose stationary points are the solution to the original…

Motivated by recent work on approximation of diffusion equations by deterministic interacting particle systems, we develop a nonlocal approximation for a range of linear and nonlinear diffusion equations and prove convergence of the method…

A challenging and fundamental research problem is the better understanding and control of the turbulent transport of heat in present-day tokamak fusion experiments. Recent developments in numerical methods along with enormous gains in…

We propose a novel approach for modeling chemical reactions within the particle-based Fokker-Planck framework for gas flow simulations which conserves mass, momentum, and energy while retaining the performance advantages of the…

Undulator radiation from synchrotron light sources must be transported down a beamline from the source to the sample. A partially coherent photon beam may be represented in phase space using a Wigner function, and its transport may use some…

An FFT-based algorithm is developed to simulate the propagation of elastic waves in heterogeneous $d$-dimensional rectangular shape domains. The method allows one to prescribe the displacement as a function of time in a subregion of the…

We propose a discrete lattice version of the Fokker-Planck kinetic equation along lines similar to the Lattice-Boltzmann scheme. Our work extends an earlier one-dimensional formulation to arbitrary spatial dimension $D$. A generalized…

We obtain equilibration rates for a one-dimensional nonlocal Fokker-Planck equation with time-dependent diffusion coefficient and drift, modeling the relaxation of a large swarm of robots, feeling each other in terms of their distance,…

The equilibrium distribution function determines macroscopic observables in statistical physics. While conventional methods correct equilibrium distributions in weakly nonlinear or near-integrable systems, they fail in strongly nonlinear…

We study a Fokker-Planck equation modelling the firing rates of two interacting populations of neurons. This model arises in computational neuroscience when considering, for example, bistable visual perception problems and is based on a…

In this work, we present a new diagrammatic method for computing the effective Hamiltonian of driven nonlinear oscillators. At the heart of our method is a self-consistent perturbation expansion developed in phase space, which establishes a…

Consider the linear Boltzmann equation of radiative transfer in a half-space, with constant scattering coefficient $\sigma$. Assume that, on the boundary of the half-space, the radiation intensity satisfies the Lambert (i.e. diffuse)…

Nonlinear damping of parallel propagating Alfv\'en waves in high-$\beta$ plasma is considered. Trapping of thermal ions and Coulomb collisions are taken into account. Saturated damping rate is calculated. Applications are made for cosmic…

We present a generalized, data-driven collisional operator for one-component plasmas, learned from molecular dynamics simulations, to extend the collisional kinetic model beyond the weakly coupled regime. The proposed operator features an…

The diffusion process near low order synchro-betatron resonances driven by beam-beam interactions at a crossing angle is investigated. Macroscopic observables such as beam emittance, lifetime and beam profiles are calculated. These are…

We present a nonlinear optical platform to emulate a nonlinear \textit{L\'{e}vy waveguide} that supports the pulse propagation governed by a generalized fractional nonlinear Schr\"{o}dinger equation (FNLSE). Our approach distinguishes…

We demonstrate that a nonthermal distribution of particles described by a kappa distribution can be accurately approximated by a weighted sum of Maxwell-Boltzmann distributions. We apply this method to modeling collision processes in…

To simulate plasma phenomena, large-scale computational resources have been employed in developing high-precision and high-resolution plasma simulations. One of the main obstacles in plasma simulations is the requirement of computational…