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Exact results for the jammed state of binary mixtures of superdisks on the plane. (English) Zbl 1400.82338

Summary: 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 \(| x |^{2 p} + | y |^{2 p} = 1\), where deformation parameter \(p\) controls their size and shape. For deposition of single-type superdisks, the maximum packing and jamming densities are known to be nonanalytic at \(p = 0.5\). 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.

MSC:

82D80 Statistical mechanics of nanostructures and nanoparticles
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