Consequences of using different pair-correlation funtions on the stability properties of the Homogeneous Cooling State for a monodisperse system of near-elastic disks

We show the differences in the stability properties of the Homogeneous Cooling State (HCS) of a two-dimensional monodisperse collection of rigid and near-elastic disks, obtained by using different formulae for the pair-correlation function.For an equation of state that takes into account the crystallization and ordering of the particles (and the respective pressure drop), the critical wavelength of the heat conduction mode is considerably modified in the transition zone, involving a bifurcation and an additional mode of instability. The theoretical predictions, using the improved equation of state are confirmed by numerical simulations. Nevertheless, some open questions remain.