Dynamics of a one-dimensional granular gas with a stochastic coefficient of restitution

Recently, we have modelled inelastic collisions of one-dimensional rods [1,2] by the absorption of translational energy Etr through internal degrees of freedom, in particular elastic vibrations. We arrived at a stochastic description of collision processes, characterised by a stochastic coefficient of restitution ε. In this paper, we construct an analytic approximation for the transition probability Etr→Etr′=(1−ε2)Etr. This allows us to perform much longer simulations of large, strongly inelastic granular systems and study relaxation to the true equilibrium state. If the internal vibrations are undamped, equilibrium is characterised by propagating sound waves. In the case of damping, the system develops towards a final state which consists of one big cluster, containing all particles at rest.