  The diffusion and flow of amorphous materials, such as glasses and granular
materials, has resisted a simple microscopic description, analogous to defect
theories for crystals. Early models were based on either gas-like inelastic
collisions or crystal-like vacancy diffusion, but here we propose a cooperative
mechanism for dense random-packing dynamics, based on diffusing ``spots'' of
interstitial free volume. Simulations with the Spot Model can efficiently
generate realistic flowing packings, and yet the model is simple enough for
mathematical analysis. Starting from a non-local stochastic differential
equation, we derive continuum equations for tracer diffusion, given the
dynamics of free volume (spots). Throughout the paper, we apply the model to
granular drainage in a silo, and we also briefly discuss glassy relaxation. We
conclude by discussing the prospects of spot-based multiscale modeling and
simulation of amorphous materials.
