In recent works it has been demonstrated that using an appropriate rescaling, linear Boltzmann-type equations give rise to a scalar fractional diffusion equation in the limit of a small mean free path. The equilibrium distributions are typically heavy-tailed distributions, but also classical Gaussian equilibrium distributions allow for this phenomena if combined with a degenerate collision freq...

We consider a system of hard spheres in thermal equilibrium. Using Lanford's result about the convergence of the solutions of the BBGKY hierarchy to the solutions of the Boltzmann hierarchy, we show that in the low-density limit (Boltzmann-Grad limit): (i) the total time correlation function is governed by the linearized Boltzmann equation (proved to be valid for short times), (ii) the self tim...

We develop a kinetic theory for point vortices in two-dimensional hydrodynamics. Using standard projection operator techniques, we derive a Fokker-Planck equation describing the relaxation of a "test" vortex in a bath of "field" vortices at statistical equilibrium. The relaxation is due to the combined effect of a diffusion and a drift. The drift is shown to be responsible for the organization ...

In this paper we develop the two-equation model for solute transport and adsorption in a two-region model of a mechanically and chemically heterogeneous porous medium. The closure problem is derived and the coefficients in both the oneand two-equation models are determined on the basis of the Darcy-scale parameters. Numerical experiments are carried out for a stratified system at the aquifer sc...

We obtain equilibration rates for a one-dimensional nonlocal Fokker–Planck equation with time-dependent diffusion coefficient and drift, modeling the relaxation of large swarm robots, feeling each other in terms their distance, towards steady profile characterized by uniform spreading over finite interval line. The result follows combining entropy methods quantifying decay solution its quasi-st...