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 the long-time behavior for the cluster's pressure, rms velocity, and granular interspacing. We show that for extremely long times, clusters with velocity-dependent coefficients of restitution are unstable and dissolve into homogeneous, quasielastic 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.