Session J53: Disordered Systems: Jamming
11:15 AM–2:15 PM, Tuesday, February 28, 2012
Room: 153B
Sponsoring Unit:
GSNP
Chair: Patrick Charbonneau, Duke University
Abstract ID: BAPS.2012.MAR.J53.9
Abstract: J53.00009 : Energy decay of freely cooling granular gases in three dimensions
12:51 PM–1:03 PM
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Abstract 
Authors:
Zahera Jabeen
(Department of Physics, University of Michigan, Ann Arbor, MI 48109-1040)
Sudhir N. Pathak
(Institute of Mathematical Sciences, CIT Campus, Taramani Chennai-600 113, India)
Rajesh R.
(Institute of Mathematical Sciences, CIT Campus, Taramani Chennai-600 113, India)
Freely cooling granular gases, wherein a dilute system of macroscopic particles with uncorrelated initial velocities lose energy through inelastic collisions, have been extensively studied both as a simple model for granular systems as well as a nonequilibrium system showing nontrivial coarsening at late times. As the system cools, inelasticity induces clustering, making the system inhomogeneous. While the form of energy decay ($E(t)\sim t^{-\theta}$) in the initial homogeneous regime is well established by Haff's law ($\theta=2$), the energy decay in the clustered regime is still unresolved in higher dimensions. Within mean field theory, $\theta=2 d/(d+2)$ (where $d$ is the spatial dimension), while a correspondence to Burgers equation implies an exponent $\theta= 2/3 (d=1), d/2 (d>1)$. In one and two dimensions, the two formulae predict the same exponents. By performing extensive event driven molecular dynamics simulations, we show that in three dimensions, the energy decays asymptotically with a power $\approx 1.2$, for all coefficients of restitution $r<1$, consistent with the mean field exponent. However, we argue that the mean field arguments fail due to non local interactions between mass clusters.
To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2012.MAR.J53.9