Clustering and Non-Gaussian Behavior in Granular Matter

We investigate the properties of a model of granular matter consisting of $N$ Brownian particles on a line, subject to inelastic mutual collisions. This model displays a genuine thermodynamic limit for the mean values of the energy, and the energy dissipation. When the typical relaxation time $\ensuremath{\tau}$ associated with the Brownian process is small compared with the mean collision time ${\ensuremath{\tau}}_{c}$ the spatial density is nearly homogeneous and the velocity probability distribution is Gaussian. In the opposite limit $\ensuremath{\tau}\ensuremath{\gg}{\ensuremath{\tau}}_{c}$ one has strong spatial clustering, with a fractal distribution of particles, and the velocity probability distribution strongly deviates from the Gaussian one.