  We study a layer of grains atop a plate which oscillates sinusoidally in the
direction of gravity, using three-dimensional, time-dependent numerical
solutions of continuum equations to Navier-Stokes order as well as hard-sphere
molecular dynamics simulations. For high accelerational amplitudes of the
plate, the layer exhibits a steady-state "density inversion" in which a
high-density portion of the layer is supported by a lower-density portion. At
low accelerational amplitudes, the layer exhibits oscillatory time dependence
that is strongly correlated to the motion of the plate. We show that continuum
simulations yield results consistent with molecular dynamics results in both
regimes.
