Correlation between Voronoi volumes in disc packings

¹ Max-Planck-Institut für Dynamik und Selbstorganisation - Bunsenstr. 10, D-37073 Göttingen, Germany, EU
² Center for Nonlinear Dynamics and Department of Physics, University of Texas at Austin Austin, TX 78712, USA

^a songchuan.zhao@ds.mpg.de
^b matthias.schroeter@ds.mpg.de

Received: 9 September 2011
Accepted: 20 December 2011

Abstract

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