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Slow dynamics under gravity: a nonlinear diffusion model

Jeferson J. Arenzon·Yan Levin·Mauro Sellitto
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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.

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Jeferson J. Arenzon, Yan Levin, Mauro Sellitto. 2003-01-23. Slow dynamics under gravity: a nonlinear diffusion model. https://doi.org/10.1016/s0378-4371(03)00251-6

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