Phenomenological glass model for vibratory granular compaction

A model for weakly excited granular media is derived by combining the free volume argument of Nowak et al. [Phys. Rev. E 57, 1971 (1998)] and the phenomenological model for supercooled liquids of Adam and Gibbs [J. Chem. Phys. 43, 139 (1965)]. This is made possible by relating the granular excitation parameter $\Gamma ,$ defined as the peak acceleration of the driving pulse scaled by gravity, to a temperaturelike parameter $\eta \left(\Gamma \right).\mathrm{}$ The resulting master equation is formally identical to that of Bouchaud’s trap model for glasses [J. Phys. I 2, 1705 (1992)]. Analytic and simulation results are shown to compare favorably with a range of known experimental behavior. This includes the logarithmic densification and power spectrum of fluctuations under constant $\eta ,$ the annealing curve when $\eta$ is varied cyclically in time, and memory effects observed for a discontinuous shift in $\eta .$ Finally, we discuss the physical interpretation of the model parameters and suggest further experiments for this class of systems.