Minimal relaxation law for compaction of tapped granular matter

Granular systems can compact under the influence of sufficiently strong, successive tapping. Recent experimental,investigations show that the packing fraction obeys a very slow relaxation to a final, dense packing fraction that is basically proportional to the inverse of the logarithm of the tap number or time. We provide a simple macromechanical argument that explains this inverse logarithmic relaxation in time in all functional details. By considering the asymptotic limits of the resulting relaxation law, we show that the relaxational dynamics of the compaction process can be interpreted as a combination of a biased void diffusion for short times and a collective reorganization for large times. [S1063-651X(99)02611-2].