Related papers: Particle approximation of the BGK equation
This paper proposes a novel reaction-diffusion system approximation tailored for singular diffusion problems, typified by the fast diffusion equation. While such approximation methods have been successfully applied to degenerate parabolic…
We introduce a global thermostat on Kac's 1D model for the velocities of particles in a space-homogeneous gas subjected to binary collisions, also interacting with a (local) Maxwellian thermostat. The global thermostat rescales the…
In this work, we investigate a system of interacting particles governed by a set of stochastic differential equations. Our main goal is to rigorously demonstrate that the empirical measure associated with the particle system converges…
We investigate the behavior in $N$ of the $N$--particle entropy functional for Kac's stochastic model of Boltzmann dynamics, and its relation to the entropy function for solutions of Kac's one dimensional nonlinear model Boltzmann equation.…
Stochastic thermodynamics provides an important framework to explore small physical systems where thermal fluctuations are inevitable. In the studies of stochastic thermodynamics, some thermodynamic quantities, such as the trajectory work,…
We consider a system of particles which interact through a jump process. The jump intensities are functions of the proximity rank of the particles, a type of interaction referred to as topological in the literature. Such interactions have…
We study stochastic particle systems on a complete graph and derive effective mean-field rate equations in the limit of diverging system size, which are also known from cluster aggregation models. We establish the propagation of chaos under…
The grand canonical density functional theory for inhomogeneous systems of interacting bosons is developed in the effective action approach. The Legendre transform of the generating functional for Green's functions is used to define the…
We investigate numerically a recent BGK-type model for a multi-component mixture of monatomic gases, undergoing a reversible bimolecular chemical reaction. The model replaces each collisional term of the Boltzmann equation with a relaxation…
A new direct integration method is established to construct the solutions of the stationary BBGKY hierarchy, assuming the usual form of the equilibrium correlation functions, for infinite classical systems of particles interacting via a…
We consider the long time behavior of heterogeneously interacting diffusive particle systems and their large population limit. The interaction is of mean field type with weights characterized by an underlying graphon. The limit is given by…
Several approximations are made to study the microcanonical formalism that are valid in the thermodynamics limit. Usually it is assumed that: 1)Stirling approximation can be used to evaluate the number of microstates; 2) the surface entropy…
We study a system of diffusing point particles in which any triplet of particles reacts and is removed from the system when the relative proximity of the constituent particles satisfies a predefined condition. Proximity-based reaction…
We discuss a simple model of particles hopping in one dimension with attractive interactions. Taking a hydrodynamic limit in which the interaction strength increases with the system size, we observe the formation of multiple clusters of…
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 study the nonequlibrium state of heat conduction in a one-dimensional system of hard point particles of unequal masses interacting through elastic collisions. A BBGKY-type formulation is presented and some exact results are obtained from…
We propose a collision-oriented particle system to approximate a class of Landau-type equations. This particle system is formally derived from a particle system with random collisions in the grazing regime, and happens to be a special…
This paper is concerned with a fluid-particle system given by the incompressible Navier-Stokes equations coupled with the Vlasov(-Fokker-Planck) equation through a drag force. Such a model arises naturally in the study of aerosols, sprays,…
We experimentally investigate the statistical behaviour of a model two-dimensional granular system undergoing stationary sedimentation. Buoyant cylindrical particles are rotated in liquid-filled drum, thus confined in a harmonic centripetal…
We study a lattice-gas model of penetrable particles on a square-lattice substrate with same-site and nearest-neighbor interactions. Penetrability implies that the number of particles occupying a single lattice site is unlimited and the…