Length scales of clustering in granular gases

Clustering of granular gases is caused by the dissipation occurring in particle collisions. We use the generalized dimension, a measure for the inhomogeneity of a spatial distribution of particles to characterize the structural evolution. Furthermore, we quantify the typical length scale of the clusters obtained by 3D simulations using the index of dispersion, a measure for the deviation of the particle density from a Poissonian. We then derive an expression for the expected length scales of cluster formation from a stability analysis in the hydrodynamical approximation. We find a good agreement between our theoretical prediction and numerical experiments.