Dynamical collision network in granular gases

J. Ignacio Alvarez-Hamelin, Andrea Puglisi
2007 Physical Review E  
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.
more » ... 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 with the average number of collisions experienced by a particle. During the final non-homogeneous regime a growing fraction of collisions is concentrated in small, almost closed, 'communities' of particles: k_max is no more linear in and the distribution of shells becomes extremely large developing a power-law tail k^-3 for high shell indexes. We propose the k-shell decomposition as a quantitative characterization of Molecular Chaos violation.
doi:10.1103/physreve.75.051302 pmid:17677049 fatcat:fczus2szffenlfzcmkc3trozae