Shaken, not stirred: why gravel packs better than bricks

TL;DR

This paper investigates how the shape of grains, specifically jagged versus regular, affects their packing and jamming behavior under gentle shaking, revealing distinct behaviors based on the grains' geometric properties.

Contribution

It introduces a novel measure of grain shape based on void space and demonstrates how rational and irrational shapes lead to different packing and retrievability outcomes.

Findings

Regular grains achieve perfect packing but lose it under shaking.

Jagged grains only reach optimal packing and are fully retrievable.

Intermittency at the surface observed at low temperatures.

Abstract

We explore the effect of shape -- jagged vs. regular -- in the jamming limit of very gently shaken packings. Our measure of shape $\eps$ is the void space occupied by a disordered grain; we show that depending on its number-theoretic nature, two generic behaviours are obtained. Thus, regularly shaped grains (rational $\eps$) have ground states of perfect packing, which are irretrievably lost under zero-temperature shaking; the reverse is the case for jagged grains (irrational $\eps$), where the ground state is only optimally packed, but entirely retrievable. At low temperatures, we find intermittency at the surface, which has recently been seen experimentally.