  We perform extensive MD simulations of two-dimensional systems of hard disks,
focusing on the \emph{on}-collision statistical properties. We analyze the
distribution functions of velocity, free flight time and free path length for
packing fractions ranging from the fluid to the solid phase. The behaviors of
the mean free flight time and path length between subsequent collisions are
found to drastically change in the coexistence phase. We show that single
particle dynamical properties behave analogously in collisional and continuous
time representations, exhibiting apparent crossovers between the fluid and the
solid phase. We find that, both in collisional and continuous time
representation, the mean square displacement, velocity autocorrelation
functions, intermediate scattering functions and self part of the van Hove
function (propagator), closely reproduce the same behavior exhibited by the
corresponding quantities in granular media, colloids and supercooled liquids
close to the glass or jamming transition.
