  We study the stability, the clustering and the phase-diagram of free cooling
granular gases. The systems consist of mono-disperse particles with additional
non-contact (long-range) interactions, and are simulated here by the
event-driven molecular dynamics algorithm with discrete (short-range shoulders
or wells) potentials (in both 2D and 3D). Astonishingly good agreement is found
with a mean field theory, where only the energy dissipation term is modified to
account for both repulsive or attractive non-contact interactions. Attractive
potentials enhance cooling and structure formation (clustering), whereas
repulsive potentials reduce it, as intuition suggests. The system evolution is
controlled by a single parameter: the non-contact potential strength scaled by
the fluctuation kinetic energy (granular temperature). When this is small, as
expected, the classical homogeneous cooling state is found. However, if the
effective dissipation is strong enough, structure formation proceeds, before
(in the repulsive case) non-contact forces get strong enough to undo the
clustering (due to the ongoing dissipation of granular temperature). For both
repulsive and attractive potentials, in the homogeneous regime, the cooling
shows a universal behaviour when the (inverse) control parameter is used as
evolution variable instead of time. The transition to a non-homogeneous regime,
as predicted by stability analysis, is affected by both dissipation and
potential strength. This can be cast into a phase diagram where the system
changes with time, which leaves open many challenges for future research.
