On the calculation of self-diffusion in vertically agitated granular beds

We present self-diffusion calculations derived from discrete element simulations of an idealized granular material under gravity, which is energized through vertical, sinusoidal oscillations of a plane rigid floor. The bed of particles is agitated to a degree so that computed steady-state profiles of granular temperature and solids fraction are consistent with kinetic theory predictions. The average self-diffusivity for the entire assembly, computed both from the velocity autocorrelation function and the mean-square displacement, is found to compare well with an analytic expression taken from kinetic theory.