The Spot Model for random-packing dynamics

Abstract

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.