Slow dynamics under gravity: a nonlinear diffusion model
Abstract
We present an analytical and numerical study of a nonlinear diffusion model which describes density relaxation of loosely packed particles under gravity and weak random (thermal) vibration, and compare the results with Monte Carlo simulations of a lattice gas under gravity. The dynamical equation can be thought of as a local density functional theory for a class of lattice gases used to model slow relaxation of glassy and granular materials. The theory predicts a jamming transition line between a low density fluid phase and a high density glassy regime, characterized by diverging relaxation time and logarithmic or power-law compaction according to the specific form of the diffusion coefficient. In particular, we show that the model exhibits history dependent properties, such as quasi reversible-irreversible cycle and memory effects -- as observed in recent experiments, and dynamical heterogeneities.
Cite
@article{arxiv.cond-mat/0301454,
title = {Slow dynamics under gravity: a nonlinear diffusion model},
author = {Jeferson J. Arenzon and Yan Levin and Mauro Sellitto},
journal= {arXiv preprint arXiv:cond-mat/0301454},
year = {2009}
}
Comments
14 pages, submitted to Physica A