Abstract
We consider the free evolution of systems of granular particles whose dynamics is characterized by a collision rule which preserves the total momentum, but dissipates the kinetic energy. Starting from an inelastic version of a minimal model proposed by Ulam for a gas of Maxwell molecules, we introduce a new lattice model aimed at investigating the role of dynamical correlations and the onset of spatial order induced by the inelasticity of the interactions. We study, in one- and two-dimensional cases, the velocity distribution, the decay of the energy, the formation of spatial structures and topological defects. Finally, we relate our findings to other models known in other fields.
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