The dynamical collision network in granular gases.Report as inadecuate

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1 FIUBA - Facultad de Ingeniería 2 CONICET - CONICET Argentinian Council of Scientific and Technological Research 3 DF-LS - Dipartimento di Fisica

Abstract : 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 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.

Keywords : Granular Systems Kinetic and transport theory of gases Networks k-cores

Author: José Ignacio Alvarez-Hamelin - Andrea Puglisi -



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