  We explore the consequences of the excluded volume interaction of hard
spheres at high densities and present a theory for excited granular materials.
We first demonstrate that, in the presence of gravity, the granular density
crosses over from Boltzmann to Fermi statistics, when temperature is decreased
in the weak excitation limit. Comparisons of numerical simulations with our
predictions concerning the scaling behavior of temperature with agitation
frequency, gravity and particle-diameter show satisfying agreement. Next,
within the framework of the Enskog theory of hard spheres, we interpret this
crossover as a 'condensation' of hard spheres from the dilute gas-state to a
high density solid-like state. In the high density, low temperature limit
Enskog theory fails because it predicts densities larger than the closed packed
density below a certain temperature. We show how to extend the range of
applicability of the Enskoq theory to arbitrarily low temperatures by
constructing a physical solution: all particles that are situated in regions
with densities larger than a certain maximum density are assumed to be
'condensed.'
