Clustering and non-gaussian behavior in granular matter

We investigate the properties of a model of granular matter consisting of N particles on a line performing a Brownian motion. Each particle is also subject to inelastic collisions with the others. This model displays a genuine thermodynamic limit because at fixed density the mean values of the energy, and the energy dissipation, per particle for large values of N are independent of N. 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. Such a behavior is rather robust and it appears even under the Stosszahlansatz Boltzmann approximation.