Exact results for the jammed state of binary mixtures of superdisks on the plane

By analytical and numerical methods we investigate the late stage deposition of binary mixtures of oriented “superdisks” on a plane. Superdisks are objects bounded by Lamé curves |x|2p+|y|2p=1|x|2p+|y|2p=1, where deformation parameter pp controls their size and shape. For deposition of single-type superdisks, the maximum packing and jamming densities are known to be nonanalytic at p=0.5p=0.5. For binary mixtures of superdisks, we discover that nonanalyticities form a locus of points separating “phase diagram” of shape combinations into regions with different excluded-area constructions. An analytical expression for this phase boundary and exact constructions of the excluded-areas are presented. The corresponding saturation coverages are obtained by extensive numerical Monte Carlo simulations.