Slow dynamics under gravity: a nonlinear diffusion model

✍ Scribed by Jeferson J. Arenzon; Yan Levin; Mauro Sellitto

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 364 KB
• Volume: 325
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/s0378-4371(03)00251-6

✦ Synopsis

We present an analytical and numerical study of a nonlinear di usion 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 uid phase and a high-density glassy regime, characterized by diverging relaxation time and logarithmic or power-law compaction according to the speciÿc form of the di usion coe cient. In particular, we show that the model exhibits history-dependent properties, such as quasi-reversible-irreversible cycle and memory e ects-as observed in recent experiments, and dynamical heterogeneities.