Logarithmic density relaxation in compaction of granular materials
arXiv:cond-mat/9707237 · doi:10.1103/PhysRevE.57.829
Abstract
On the basis of physical considerations we propose a one-dimensional discrete lattice model for the density relaxation of granular materials under tapping. Solving the difference equation numerically, we find a logarithmic time-dependence of the density relaxation. This is in agreement with experimental results of Knight et al. [Phys. Rev. E 51, 3957(1995)]. The origin of this anomalous relaxation is elucidated analytically by solving the equation of its continuum version asymptotically in time.
12 pages, RevTex, 5 figures in postscript