Previous work has indicated that inelastic grains undergoing homogeneous cooling may be unstable, giving rise to the formation of velocity vortices, which may also lead to particle clustering. In this effort, molecular dynamics (MD) simulations are performed over a wide parameter space to determine the critical system size demarcating the stable and unstable regions. Specifically, a system of monodisperse, frictionless, inelastic hard spheres is simulated for restitution coefficients e ! 0.6 and solids fractions / 0.4. Simulations for each e, / pairing are then carried out over a range of system sizes to determine the critical dimensionless length scale L C =d (L is the system length and d is the particle diameter), above which velocity vortices appear (unstable system) and below which they are suppressed (stable system). The results show excellent agreement with the theoretical predictions obtained by Garzó [Phys. Rev. E 72, 021106 (2005)] using a linear stability analysis of kinetic-theory-based (continuum) equations that were derived from the Enskog equation. Finally, the time required for onset of the unstable behavior is also explored via MD and found to be a universal function of the ratio of L=d to L C =d.
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