  Motivated by recent experiments reporting non-Gaussian velocity distributions
in driven dilute granular materials, we study by numerical simulation the
properties of inelastic gases as functions of the coefficient of restitution
$\eta$ and concentration $\phi$ with various heating mechanisms. We show that
there are marked, qualitative differences in the behavior for uniform heating
(as is frequently assumed theoretically) and for particle systems driven at the
boundaries of the container (as is frequently done in experiments). In general,
we find Gaussian velocity distributions for uniform heating and non-Gaussian
velocity distributions for boundary heating. Furthermore, we demonstrate that
the form of the observed velocity distribution is governed primarily by the
coefficient of restitution $\eta$ and $q=N_H/N_C$, the ratio between the
average number of heatings and the average number of collisions in the gas. The
differences in distributions we find between uniform and boundary heating can
then be understood as different limits of $q$, for $q \gg 1$ and $q \lesssim 1$
respectively. Moreover, we demonstrate that very similar behavior is found for
a simple model of a gas of inelastic particles with no spatial degrees of
freedom.
