with Painter, B; Dutt, M; Behringer, RP, *Energy dissipation and clustering for a cooling granular material on a substrate*,
Physica D: Nonlinear Phenomena, vol. 175 no. 1-2
(2003),
pp. 43-68 [doi] .
**Abstract:**

*We experimentally study the dynamics of a cooling two-dimensional granular system of steel spheres moving radially inward on an aluminum substrate. We find that the cooling process in this system differs significantly from model calculations that include realistic restitutional losses and rolling (hence, weak) friction. A likely explanation for the experimental observations is the fact that particles typically slide on the substrate for some time after each collision, losing energy rapidly. Using results from an MD simulation as a reference point, we consider detailed experimental results for the cooling of systems of spheres on a substrate as a function of the system size, N. For systems with more than N=300 particles, we find that final spatial configurations consist primarily of dense central clusters, and that the velocity distributions, which have an exponential character, are only weakly dependent on system size. Thus, there is a critical system size above which a majority of particles come to rest in a densely packed lattice. We also find evidence of a spatial ordering size scale in the cooled state that is much smaller than the system size. Velocity distributions in the cooling system are nearly Maxwell-Boltzmann (MB)-like at early times, but show significant differences from a MB distribution after particles have undergone a moderate number of collisions. © 2002 Published by Elsevier B.V.*