  Via event-driven molecular dynamics simulations we study kinetics of
clustering in assemblies of inelastic particles in various space dimensions. We
consider two models, viz., the ballistic aggregation model (BAM) and the freely
cooling granular gas model (GGM), for each of which we quantify the time
dependence of kinetic energy and average mass of clusters (that form due to
inelastic collisions). These quantities, for both the models, exhibit power-law
behavior, at least in the long time limit. For the BAM, corresponding exponents
exhibit strong dimension dependence and follow a hyperscaling relation. In
addition, in the high packing fraction limit the behavior of these quantities
become consistent with a scaling theory that predicts an inverse relation
between energy and mass. On the other hand, in the case of the GGM we do not
find any evidence for such a picture. In this case, even though the energy
decay, irrespective of packing fraction, matches quantitatively with that for
the high packing fraction picture of the BAM, it is inversely proportional to
the growth of mass only in one dimension, and the growth appears to be rather
insensitive to the choice of the dimension, unlike the BAM.

Statistical Mechanics