Kinetics models of inelastic gases

In the present paper we review some recent progresses in the study of the dynamics of cooling granular gases, obtained using idealized models to address different issues of their kinetics. The inelastic Maxwell gas is studied as an introductory mean field model that has the major advantage of being exactly resoluble in the case of scalar velocities, showing an asymptotic velocity distribution with power law tails \v\(-4). More realistic models can be obtained placing the same process on a spatial lattice. Two regimes are observed: an uncorrelated transient followed by a dynamical stage characterized by correlations in the velocity field in the form of shocks and vortices. The lattice models, in one and two dimensions, account for different numerical measurements: some of them agree with the already known results, while others have never been efficiently measured and shed light on the deviation from homogeneity. In particular in the velocity-correlated regime the computation of structure factors gives indication of a dynamics similar to that of a diffusion process on large scales with a more complex behavior at shorter scales.