Length scales of clustering in granular gases

Clustering of granular gases is caused by the dissipation occurring in part icle collisions. We use the generalized dimension, a measure for the inhomo geneity of a spatial distribution of particles to characterize the structur al evolution. Furthermore, we quantify the typical length scale of the clus ters obtained by 3D simulations using the index of dispersion, a measure fo r the deviation of the particle density from a Poissonian. We then derive a n expression for the expected length scales of cluster formation from a sta bility analysis in the hydrodynamical approximation. We find a good agreeme nt between our theoretical prediction and numerical experiments.