Temperature of a granular gas with regard to the stochastic nature of particle interactions

The decay of temperature of a force-free granular gas in the homogeneous cooling state depends on the specific model for particle interaction. For the case of rough spheres, in recent experimental and theoretical work, the coefficient of restitution was characterized as a fluctuating quantity. We show that for such particles, the decay of temperature with time follows the law $T\sim t^{- {50}/{29}}$ which deviates from Haff's law, T ~ t−2, obtained for gases of particles interacting via a constant coefficient of restitution also from $T\sim t^{-{5}/{3}}$ obtained for gases of viscoelastic particles. Our results are obtained from kinetic theory and are in very good agreement with Monte Carlo simulations