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 thé Voronoïtesselation of monosize packings of discs deviate from those of a totally random mosaic. Here, we describe a mosaic obtained from thé radical tesselation of a two-size mixture of dises at différent packing fractions. Two kinds of packings are considered, experimental (dises moving on an air table) and numerical. The déviations are even more striking, particularly at large packing fraction where neither Aboav's nor Lewis' law hold ; moreover, some distributions, such as thé distribution of thé number of sides of thé cells, or distribution of thé 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, thé mosaics obtained from those packings obey approximately thé laws of random mosaics but this is not so for their metric properties, which are still largely affected by steric exclusion.