Related papers: Homogeneous kinetic equations for probabilistic li…
In this paper we study Kac's 1D particle system, consisting of the velocities of $N$ particles colliding at constant rate and randomly exchanging energies. We prove uniform (in time) propagation of chaos in Wasserstein distance with…
A simplified version of a classical problem in thermodynamics -- the adiabatic piston -- is discussed in the framework of kinetic theory. We consider the limit of gases whose relaxation time is extremely fast so that the gases contained on…
This paper provides an introduction to some stochastic models of lattice gases out of equilibrium and a discussion of results of various kinds obtained in recent years. Although these models are different in their microscopic features, a…
We consider a model of a dynamical Lorentz gaz : a single particle is moving in $\mathbb{R}^d$ through an array of fixed an soft scatterers each possessing an internal degree of freedom coupled to the particle. Assuming the initial velocity…
We study the effect of reaction times on the kinetics of relaxation to stationary states and on congestion transitions in heterogeneous traffic. Heterogeneity is modeled as quenched disorders in the parameters of the car following model and…
A one-dimensional driven lattice gas with disorder in the particle hopping probabilities is considered. It has previously been shown that in the version of the model with random sequential updating, a phase transition occurs from a low…
We study the quasi-stationary evolution of systems where an energetic confinement is unable to completely retain their constituents. It is performed an extensive numerical study of a gas whose dynamics is driven by binary encounters and its…
We continue our investigation of kinetic models of a one-dimensional gas in contact with homogeneous thermal reservoirs at different temperatures. Nonlinear collisional interactions between particles are modeled by a so-called BGK dynamics…
Many physical observables can be represented as a particle spending some random time within a given domain. For a broad class of transport-dominated processes, we detail how it is possible to express the moments of the number of particle…
We use a probabilistic approach to study the rate of convergence to equilibrium for a collisionless (Knudsen) gas in dimension equal to or larger than 2. The use of a coupling between two stochastic processes allows us to extend and refine,…
We study a class of one-dimensional particle systems with true (Bird type) binary interactions, which includes Kac's model of the Boltzmann equation and nonlinear equations for the evolution of wealth distribution arising in kinetic…
A granular gas composed of inelastic hard spheres or disks in the homogeneous cooling state is considered. Some of the particles are labeled and their number density exhibits a time-independent linear profile along a given direction. As a…
The periodic Lorentz gas describes an ensemble of non-interacting point particles in a periodic array of spherical scatterers. We have recently shown that, in the limit of small scatterer density (Boltzmann-Grad limit), the macroscopic…
Systems with long range interactions present generically the formation of quasi-stationary long-lived non-equilibrium states. These states relax to Boltzmann equilibrium following a dynamics which is not well understood. In this paper we…
Different quantum Langevin equations obtained by coupling a particle to a field are examined. Instabilities or violations of causality affect the motion of a point charge linearly coupled to the electromagnetic field. In contrast, coupling…
We analyze the behavior of an isentropic gas in a narrow pipe with periodically-varying cross-sectional area. Using multiple-scale perturbation theory, we derive homogenized effective equations, which take the form of a constant-coefficient…
The non-equilibrium statistical mechanics and kinetic theory for a model of a confined quasi-two-dimensional gas of inelastic hard spheres is presented. The dynamics of the particles includes an effective mechanism to transfer the energy…
We study spatially non-homogeneous kinetic models for vehicular traffic flow. Classical formulations, as for instance the BGK equation, lead to unconditionally unstable solutions in the congested regime of traffic. We address this issue by…
We develop two further numerical tests of parton cascade models: the ideal gas equation of state and the collision frequency tests. The equation of state test checks the initial momentum distribution generator and free expansion dynamics in…
In the present paper we introduce generalized kinetic equations describing the dynamics of a system of interacting gas and photons obeying to a very general statistics. In the space homogeneous case we study the equilibrium state of the…