Granular clustering self-consistent analysis for general coefficients of restitution

We study the equilibrium behavior of one-dimensional granular clusters and one-particle granular gases for a variety of velocity dependent coefficients of restitution $r$. We obtain equations describing of the long time behavior for the cluster's pressure, r.m.s. velocity and granular inter-spacing. We show that for extremely long times, clusters with velocity dependent coefficients of restitution are unstable and dissolve into homogeneous, quasi-elastic gases, but clusters with velocity independent $r$ are permanent. This is in accordance with hydrodynamic studies pointing to the transient nature of density instabilities for granular gases with velocity dependent $r$.