  We report numerical simulations of strongly vibrated granular materials
designed to mimic recent experiments performed both in presence [1] or absence
[2] of gravity. We show that a model with impact velocity dependent restitution
coefficient is necessary to bring the simulations into agreement with
experiments. We measure the scaling exponents of the granular temperature,
collision frequency, impulse and pressure with the vibrating piston velocity.
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. In absence of gravity, a loose cluster
appears near the upper wall, opposite the piston, and acts as a buffer for
fastest particles leading to unexpected non-extensive scaling exponents ;
whereas in presence of gravity, the cluster bounces as a single inelastic body.
All these results differ significantly from classical inelastic hard sphere
kinetic theory and previous simulations, both based on a constant restitution
coefficient.
