Slow dynamics under gravity: a nonlinear diffusion model

Details Slow dynamics under gravity: a nonlinear diffusion model Slow dynamics under gravity: a nonlinear diffusion model

2003-01-23

arxiv.org/abs/cond-mat/0301454v1

2003 Physica A 325 371-395

Physics

Condensed Matter

Soft Condensed Matter

14 pages, submitted to Physica A

Scientific paper

10.1016/S0378-4371(03)00251-6

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.

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