COLLISION PROPERTIES OF ONE-DIMENSIONAL GRANULAR PARTICLES WITH INTERNAL DEGREES OF FREEDOM

Starting from a microscopic model of interacting elastic rods, we deri ve an effective dissipative dynamics for the translational motion, whe n the internal degrees of freedom, i.e., the vibrations of the rods, a re represented by a thermalized bath. Focusing on two-particle collisi ons, we calculate the coefficient of restitution epsilon as a function of the relative length of the colliding rods, the center of mass velo city, and the degree of excitation of the internal vibrations. In gene ral, epsilon is a stochastic quantity; its distribution is interpreted as the transition probability for the Markovian jump process, which d escribes the loss of translational energy in successive two-particle c ollisions.