Universal properties of Voronoi tessellations of hard discs

Abstract

The authors describe a 2D mosaic obtained by the Voronoi tessellation of a monosize assembly of discs at different packing fractions. The experimental device (hard discs moving on an air table) produces, for every packing fraction, a succession of mosaics in statistical equilibrium, which constitutes a statistical ensemble. This ensemble is large enough for fluctuations from the most probable distributions to be negligible. They use the maximum entropy principle to get the distribution of the polygons in 2D mosaics generated from an assembly of hard discs. Steric exclusion yields an extra conservation law, which is sufficient to give a good agreement with the experimental data. A similar behaviour in the six-fold parameter seems to hold for other mosaics.