Time-Dependent Continuum and Molecular Dynamics Simulations of Density Inversion in Shaken Granular Layers

We investigate density inversion in vertically oscillated granular layers using continuum and molecular dynamics simulations. Layers of grains atop a plate that is shaken sinusoidally in the direction of gravity will leave the plate at some time in the cycle if the maximum acceleration of the plate $a_{max}$ exceeds the acceleration of gravity $g$. For some values of shaking frequency $f$ and accelerational amplitude $a_{max}$, a small region near the plate displays time-dependence in response to the sinusoidal shaking, while the bulk of the layer reaches a steady-state. In certain cases, the system exhibits a ``density inversion'' in which a low density granular gas supports a higher density layer of grains. We use three-dimensional simulations of time-dependent continuum equations as well as molecular dynamics simulations to study both the time-dependent and the steady-state regions of the flow.