Role of voids in granular convection

We study the dynamics of voids in granular convection. First, we associate the formation of voids with the onset of convection, and thereby develop predictions for convective onset as a function of system parameters. Second, we use a stochastic approach to examine the role of void penetration in fully developed granular convection. We find that the vertical flow field should depend on the hyperbolic cosine of the horizontal coordinate and on a mixed linear-exponential function of the vertical coordinate. We present both lattice-based and particle-dynamic numerical simulations to validate this analysis, and provide several testable predictions.