Correlation between Voronoi volumes in disc packings

TL;DR

This study investigates how Voronoi volume correlations in binary disc packings change with packing density, revealing short-range correlations and anti-correlations that relate to dilatancy onset.

Contribution

It provides the first detailed analysis of two-point Voronoi volume correlations in binary disc packings across a range of packing fractions.

Findings

Short-ranged correlations observed throughout the density range.

Anti-correlations emerge at higher packing fractions.

Anti-correlation onset may indicate dilatancy transition.

Abstract

We measure the two-point correlation of free Voronoi volumes in binary disc packings, where the packing fraction $\phi_{\rm avg}$ ranges from 0.8175 to 0.8380. We observe short-ranged correlations over the whole range of $\phi_{\rm avg}$ and anti-correlations for $\phi_{\rm avg}>0.8277$. The spatial extent of the anti-correlation increases with $\phi_{\rm avg}$ while the position of the maximum of the anti-correlation and the extent of the positive correlation shrink with $\phi_{\rm avg}$. We conjecture that the onset of anti-correlation corresponds to dilatancy onset in this system.