Related papers: Interacting particle systems with long range inter…
The goal of this paper is to describe the various kinetic equations which arise from scaling limits of interacting particle systems. We provide a formalism which allows us to determine the kinetic equation for a given interaction potential…
A system of interacting Brownian particles subject to short-range repulsive potentials is considered. A continuum description in the form of a nonlinear diffusion equation is derived systematically in the dilute limit using the method of…
Long-range interacting systems exhibit unusual physical properties not shared by systems with short-range interactions. Understanding the dynamical and statistical effects of long-range interactions yields insights into a host of physical…
Fokker-Planck equations are extensively employed in various scientific fields as they characterise the behaviour of stochastic systems at the level of probability density functions. Although broadly used, they allow for analytical treatment…
We study a class of interacting particle systems in which $n$ signed particles move on the real line. At close range particles with the same sign repel and particles with opposite sign attract each other. The repulsion and attraction are…
In this paper, we construct a type of interacting particle systems to approximate a class of stochastic different equations whose coefficients depend on the conditional probability distributions of the processes given partial observations.…
We consider a class of particle systems which appear in various applications such as approximation theory, plasticity, potential theory and space-filling designs. The positions of the particles on the real line are described as a global…
We introduce a model of long-range interacting particles evolving under a stochastic Monte Carlo dynamics, in which possible increase or decrease in the values of the dynamical variables is accepted with preassigned probabilities. For…
We prove the existence of weak solutions of a class of multi-species cross-diffusion systems as well as the propagation of chaos result by means of nonlocal approximation of the nonlinear diffusion terms, coupling methods and compactness…
We describe the macroscopic behaviour of a particle system with long-range interactions. We describe conditions on the interaction strength in dependency of the distance of the particles, such that the scaling limit of the particle system…
This paper investigates the long time dynamics of interacting particle systems subject to singular interactions. We consider a microscopic system of $N$ interacting point particles, where the time evolution of the joint distribution…
The dynamical properties and diffusive behavior of a collection of mutually interacting particles are numerically investigated for two types of long-range interparticle interactions: Coulomb-electrostatic and dipole-electrodynamic. It is…
We develop a kinetic theory of systems with long-range interactions taking collective effects and spatial inhomogeneity into account. Starting from the Klimontovich equation and using a quasilinear approximation, we derive a…
A linear Boltzmann equation is derived in the Boltzmann-Grad scaling for the deterministic dynamics of many interacting particles with random initial data. We study a Rayleigh gas where a tagged particle is undergoing hard-sphere collisions…
We provide a rigorous justification of the linearized Boltzmann- and Landau equations from interacting particle systems with long-range interaction. The result shows that the fluctuations of Hamiltonian $N$- particle systems governed by…
In this paper we consider an interacting particle system modeled as a system of $N$ stochastic differential equations driven by Brownian motions with a drift term including a confining potential acting on each particle, and an interaction…
We propose a local, O(N) molecular dynamics algorithm for the simulation of charged systems. The long ranged Coulomb potential is generated by a propagating electric field that obeys modified Maxwell equations. On coupling the…
We investigate the dynamics of two interacting diffusing particles in an infinite effectively one dimensional system; the particles interact through a step-like potential of width b and height phi_0 and are allowed to pass one another. By…
We study the convergence of the empirical distribution associated with a system of interacting kinetic particles subject to independent Brownian forcing in a finite horizon setting, using some recent progress on kinetic non-linear partial…
We present a new approach to the dynamics of interacting particles with reaction and diffusion. Starting from the underlying discrete stochastic jump process we derive a general field theory describing the dynamics of the density field,…