Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2006-09-14
Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 75, 5 (02/05/2007) 051302
Physics
Condensed Matter
Statistical Mechanics
Scientific paper
10.1103/PhysRevE.75.051302
We dynamically construct the interaction network in a granular gas, using the sequence of collisions collected in an MD event driven simulation of inelastic hard disks from time 0 till time t. The network is decomposed into its k-core structure: particles in a core of index k have collided at least k times with other particles in the same core. The difference between cores k+1 and k is the so-called k-shell, and the set of all shells is a complete and on-overlapping decomposition of the system. Because of energy dissipation, the gas cools down: its initial spatially homogeneous dynamics, characterized by the Haff law, i.e. a t^{-2} energy decay, is unstable towards a strongly inhomogeneous phase with clusters and vortices, where energy decays as t^{-1}. The clear transition between those two phases appears in the evolution of the k-shells structure in the collision network. In the homogeneous regime the k-shell structure evolves as in a growing network with fixed number of vertices and randomly added links: the shell distribution is strongly peaked around the most populated shell, which has an index k_{max} ~ 0.9
Alvarez-Hamelin José Ignacio
Puglisi Andrea
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