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 <d> with <d> 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 <d> 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.
Description
[cond-mat/0609341] The dynamical collision network in granular gases
%0 Generic
%1 alvarezhamelin-2006
%A Alvarez-Hamelin, Jose Ignacio
%A Puglisi, Andrea
%D 2006
%K kcore granular models statistics model physics simulation imported network
%T The dynamical collision network in granular gases
%U http://www.citebase.org/abstract?id=oai:arXiv.org:cond-mat/0609341
%X 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 <d> with <d> 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 <d> 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.
@misc{alvarezhamelin-2006,
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 <d> with <d> 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 <d> 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.},
added-at = {2006-12-18T20:10:08.000+0100},
author = {Alvarez-Hamelin, Jose Ignacio and Puglisi, Andrea},
biburl = {https://www.bibsonomy.org/bibtex/24d8844a74d4a378c21ae7fdf939d2ed3/andreab},
description = {[cond-mat/0609341] The dynamical collision network in granular gases},
interhash = {670d605d3ef75b5395848f86a91ad202},
intrahash = {4d8844a74d4a378c21ae7fdf939d2ed3},
keywords = {kcore granular models statistics model physics simulation imported network},
timestamp = {2006-12-18T20:10:08.000+0100},
title = {The dynamical collision network in granular gases},
url = {http://www.citebase.org/abstract?id=oai:arXiv.org:cond-mat/0609341},
year = 2006
}