Correlation between Voronoi volumes in disc packings

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

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