%0 Journal Article %1 ignacio %A Alvarez-Hamelin, J. Ignacio %A Puglisi, A. %D 2007 %J Physical Review E %K cooling granular network puglisi %P 051302 %T The dynamical collision network in granular gases. %U http://link.aps.org/abstract/PRE/v75/e051302 %V 75 %X We address the problem of recollisions in cooling granular gases. To this aim, we dynamically construct the interaction network in a granular gas, using the sequence of collisions collected in an 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 non-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 state the $k$-shell structure evolves as in a growing network with fixed numberof vertices and randomly added links: the shell distribution isstrongly peaked around the most populated shell, which has an index$k_max 0.9 d \rangle$ with $d \rangle$ theaverage number of collisions experienced by a particle. During thefinal non-homogeneous state a growing fraction of collisions isconcentrated in small, almost closed, communities of particles:$k_\max$ is no more linear in $d \rangle$ and thedistribution of shells becomes extremely large developing a power-lawtail $k^-3$ for high shell indexes. We conclude proposing asimple algorithm to build a correlated random network that reproduces,with few essential ingredients, the whole observed phenomenology,including the $t^-1$ energy decay. It consists of two kinds ofcollisions/links: single random collisions with any other particle andlong chains of recollisions with only previously encounteredparticles. The algorithm disregards the exact spatial arrangement ofclusters, suggesting that the observed string-like structures are notessential to determine the statistics of recollisions and the energydecay.

@article{ignacio, abstract = {We address the problem of recollisions in cooling granular gases. To this aim, we dynamically construct the interaction network in a granular gas, using the sequence of collisions collected in an 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 non-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 state the $k$-shell structure evolves as in a growing network with fixed numberof vertices and randomly added links: the shell distribution isstrongly peaked around the most populated shell, which has an index$k_{max} \sim 0.9 \langle d \rangle$ with $\langle d \rangle$ theaverage number of collisions experienced by a particle. During thefinal non-homogeneous state a growing fraction of collisions isconcentrated in small, almost closed, {\em communities} of particles:$k_{\max}$ is no more linear in $\langle d \rangle$ and thedistribution of shells becomes extremely large developing a power-lawtail $\sim k^{-3}$ for high shell indexes. We conclude proposing asimple algorithm to build a correlated random network that reproduces,with few essential ingredients, the whole observed phenomenology,including the $t^{-1}$ energy decay. It consists of two kinds ofcollisions/links: single random collisions with any other particle andlong chains of recollisions with only previously encounteredparticles. The algorithm disregards the exact spatial arrangement ofclusters, suggesting that the observed string-like structures are notessential to determine the statistics of recollisions and the energydecay. }, added-at = {2007-05-09T16:41:23.000+0200}, author = {Alvarez-Hamelin, J. Ignacio and Puglisi, A.}, biburl = {https://www.bibsonomy.org/bibtex/214c8c3c243caa0bd3e3acfc579f2db13/andreapuglisi}, interhash = {163878cb88c653a61d87de104b65bcdb}, intrahash = {14c8c3c243caa0bd3e3acfc579f2db13}, journal = {Physical Review E}, keywords = {cooling granular network puglisi}, pages = 051302, timestamp = {2007-05-09T16:41:23.000+0200}, title = {The dynamical collision network in granular gases.}, url = {http://link.aps.org/abstract/PRE/v75/e051302}, volume = 75, year = 2007 }