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Slow dynamics under gravity: a nonlinear diffusion model

Author

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  • Arenzon, Jeferson J.
  • Levin, Yan
  • Sellitto, Mauro

Abstract

We present an analytical and numerical study of a nonlinear diffusion model which describes density relaxation of densely 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.

Suggested Citation

  • Arenzon, Jeferson J. & Levin, Yan & Sellitto, Mauro, 2003. "Slow dynamics under gravity: a nonlinear diffusion model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 325(3), pages 371-395.
    • Handle: RePEc:eee:phsmap:v:325:y:2003:i:3:p:371-395
    DOI: 10.1016/S0378-4371(03)00251-6
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    Cited by:

    1. Hashan, Mahamudul & Jahan, Labiba Nusrat & Tareq-Uz-Zaman, & Imtiaz, Syed & Hossain, M. Enamul, 2020. "Modelling of fluid flow through porous media using memory approach: A review," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 643-673.

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