Force Relaxation in the q-model for Granular Media
Statistical Mechanics
2015-06-24 v1 Soft Condensed Matter
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.
Cite
@article{arxiv.cond-mat/0110230,
title = {Force Relaxation in the q-model for Granular Media},
author = {Jacco H. Snoeijer and J. M. J. van Leeuwen},
journal= {arXiv preprint arXiv:cond-mat/0110230},
year = {2015}
}
Comments
16 pages, LaTex, 5 figures