Marginal scaling scenario and analytic results for a glassy compaction model

TL;DR

This paper analyzes a diffusion-deposition model for glassy dynamics in granular systems, revealing asymptotic behaviors like Vogel-Fulcher dependence and inverse logarithmic decay, with broad experimental agreement.

Contribution

It introduces a marginal scaling approach that provides exact asymptotic results for glassy compaction, highlighting its generic applicability to glassy systems.

Findings

Vogel-Fulcher dependence of rates on density

Inverse logarithmic decay of densities

Exponential distribution of decay times

Abstract

A diffusion-deposition model for glassy dynamics in compacting granular systems is treated by time scaling and by a method that provides the exact asymptotic (long time) behavior. The results include Vogel-Fulcher dependence of rates on density, inverse logarithmic time decay of densities, exponential distribution of decay times and broadening of noise spectrum. These are all in broad agreement with experiments. The main characteristics result from a marginal rescaling in time of the control parameter (density); this is argued to be generic for glassy systems.