Force Relaxation in the q-model for Granular Media
arXiv:cond-mat/0110230 · doi:10.1023/A:1020442026840
Abstract
We study the relaxation of force distributions in the q-model, assuming a uniform q-distribution. We show that "diffusion of correlations" makes this relaxation very slow. On a d-dimensional lattice, the asymptotic state is approached as a diffusion process in d-1 dimensions. Therefore the relaxation goes as the inverse square root of depth for d=2, and the inverse depth for d=3. Furthermore, we derive asymptotic modes of decay, along which an arbitrary short--range correlated initial distribution will decay towards the stationary state.
16 pages, LaTex, 5 figures