Slow dynamics under gravity: a nonlinear diffusion model

TL;DR

This paper introduces a nonlinear diffusion model for density relaxation in granular materials under gravity, predicting a jamming transition and capturing history-dependent behaviors like memory effects and dynamical heterogeneities.

Contribution

It provides an analytical and numerical framework linking density relaxation, jamming transition, and history-dependent phenomena in granular systems.

Findings

Predicts a jamming transition between fluid and glassy phases.

Shows divergence of relaxation time near the transition.

Captures history-dependent effects such as memory and hysteresis.

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.