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 $\tau$ associated with the Brownian process is small compared with the mean collision time ${\tau }_c$ the spatial density is nearly homogeneous and the velocity probability distribution is Gaussian. In the opposite limit $\tau \gg {\tau }_c$ one has strong spatial clustering, with a fractal distribution of particles, and the velocity probability distribution strongly deviates from the Gaussian one.