Slow relaxation in granular compaction

Experimental studies show that the density of a vibrated granular material evolves from a low density initial state into a higher density final steady state. The relaxation towards the final density follows an inverse logarit hmic law. As the system approaches its final state, a growing number of bea ds have to be rearranged to enable a local density increase. A free volume argument shows that this number grows as N = rho/(1 - rho). The time scale associated with such events increases exponentially similar to e(N), and as a result a logarithmically slow approach to the final state is found rho(i nfinity) - rho(t) similar to 1/1nt. Furthermore, a one-dimensional toy mode l that captures this relaxation dynamics as well as the observed density fl uctuations is discussed. Copyright (C) 1998 Published by Elsevier Science B .V.