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The collisional rates associated with the isotropic velocity moments$<V^{2r}>$ and the anisotropic moments $<V^{2r}V_i>$ and$<V^{2r}(V_iV_j-d^{-1}V^2\delta_{ij})>$ are exactly derived in the case of theinelastic Maxwell model as functions of the exponent $r$, the coefficient ofrestitution $\alpha$, and the dimensionality $d$. The results are applied tothe evolution of the moments in the homogeneous free cooling state. It is foundthat, at a given value of $\alpha$, not only the isotropic moments of a degreehigher than a certain value diverge but also the anisotropic moments do. Thisimplies that, while the scaled distribution function has been proven in theliterature to converge to the isotropic self-similar solution in well-definedmathematical terms, nonzero initial anisotropic moments do not decay with time.On the other hand, our results show that the ratio between an anisotropicmoment and the isotropic moment of the same degree tends to zero.

granular matter

Collisional rates for the inelastic Maxwell model: application to the  divergence of anisotropic high-order velocity moments in the homogeneous  cooling state