Experimental study of radical tesselations of assemblies of discs with size distribution

Abstract

We had previously shown that topological and metric properties of 2d mosaics obtained from the Voronoitesselation of monosize packings of discs deviate from those of a totally random mosaic. Here, we describe a mosaic obtained from the radical tesselation of a two-size mixture of dises at different packing fractions. Two kinds of packings are considered, experimental (dises moving on an air table) and numerical. The deviations are even more striking, particularly at large packing fraction where neither Aboav's nor Lewis' law hold ; moreover, some distributions, such as the distribution of the number of sides of the cells, or distribution of the cell area, are split into two parts, each of them related to one species of dises. Finally, we consider polydisperse packings : as to their topological properties, the mosaics obtained from those packings obey approximately the laws of random mosaics but this is not so for their metric properties, which are still largely affected by steric exclusion.