Phenomenological glass model for vibratory granular compaction

A model for weakly excited granular media is derived by combining the free volume argument of Nowak ct nl. [Phys. Rev. E 57, 1971 (1998)] and the phen omenologicaI model for supercooled liquids of Adam and Gibbs [J. Chem. Phys . 43, 139 (1965)]. This is made possible by relating the granular excitatio n parameter Gamma, defined as the peak acceleration of the driving pulse sc aled by gravity, to a temperaturelike parameter eta(Gamma) The resulting ma ster equation is formally identical to that of Bouchaud's trap model for gl asses [J. Phys. I 2, 1705 (1992)]. Analytic and simulation results are show n to compare favorably with a range of known experimental behavior. This in cludes the logarithmic densification and power spectrum of fluctuations und er 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 fur ther experiments far this class of systems.