Ground-state structure and dynamics in a toy model for granular compaction

TL;DR

This paper introduces a toy model simulating granular compaction dynamics, highlighting how grain shape influences static structures and low-temperature behavior in granular systems.

Contribution

The paper presents a novel stochastic model for granular compaction that incorporates grain shape effects through a parameter, revealing distinct behaviors for rational and irrational values.

Findings

Different ground state structures for rational and irrational shape parameters.

Distinct dynamical behaviors observed at low temperatures based on shape parameter.

Model provides insights into the role of grain anisotropy in granular compaction.

Abstract

We report on a toy model for the glassy compaction dynamics of granular systems, introduced and investigated in collaboration with Anita Mehta and Peter Stadler. A stochastic dynamics is defined on a column of grains. Grains are anisotropic and possess a discrete orientational degree of freedom. Gravity induces long-range directional interactions down the column. The key control parameter of the model, $\epsilon$, is a representation of granular shape. Rational and irrational values of $\epsilon$ correspond to very different kinds of behavior, both in statics (structure of ground states) and in low-temperature dynamics (retrieval of ground states).