A ``Tetris''-like model for the Compaction of Dry Granular Media

TL;DR

This paper introduces a two-dimensional geometrical model inspired by Tetris to study granular media compaction, revealing inverse logarithmic dynamics and connecting it to spin systems with vacancies.

Contribution

It presents a novel geometrical and dynamical model for granular compaction, linking it to Ising-like spin systems and explaining logarithmic relaxation phenomena.

Findings

Inverse logarithmic compaction law observed

Model clarifies origin of slow relaxation

Mapping to spin systems provides analytical insights

Abstract

We propose a two-dimensional geometrical model, based on the concept of geometrical frustration, conceived for the study of compaction in granular media. The dynamics exhibits an interesting inverse logarithmic law that is well known from real experiments. Moreover we present a simple dynamical model of $N$ planes exchanging particles with excluded volume problems, which allows to clarify the origin of the logarithmic relaxations and the stationary density distribution. A simple mapping allows us to cast this Tetris-like model in the form of an Ising-like spin systems with vacancies.