  We report numerical simulations of strongly vibrated granular materials
designed to mimic recent experiments performed both in presence or absence of
gravity. The coefficient of restitution used here depends on the impact
velocity by taking into account both the viscoelastic and plastic deformations
of particles, occurring at low and high velocities respectively. We show that
this model with impact velocity dependent restitution coefficient reproduce
results that agree with experiments. We measure the scaling exponents of the
granular temperature, collision frequency, impulse, and pressure with the
vibrating piston velocity as the particle number increases. As the system
changes from a homogeneous gas state at low density to a clustered state at
high density, these exponents are all found to decrease continuously with the
particle number. All these results differ significantly from classical
inelastic hard sphere kinetic theory and previous simulations, both based on a
constant restitution coefficient.
