Title: Maximally dense packings of two-dimensional convex and concave noncircular particles

Author (Talk): Steven Atkinson, Princeton University

Abstract:

Dense packings of hard particles have important applications in many fields, including condensed matter physics, discrete geometry and cell biology. In this work, we employ a stochastic search implementation of the Torquato-Jiao Adaptive-Shrinking-Cell (ASC) optimization scheme [Nature, 460, 876 (2009)] to find maximally dense particle packings in 2-dimensional Euclidean space. We verify the robustness of this packing protocol by successfully reproducing the known putative optimal packings of congruent copies of regular pentagons and octagons, then employ it to suggest dense packing arrangements of some nontrivial shapes. In particular, we find that the densest packings of certain curved triangles are periodic with a four-particle basis, and we find that the densest periodic packings of certain moon-like shapes possess no inherent symmetries. Our work adds to the growing evidence that particle shape can be used as a tuning parameter to achieve a diversity of packing structures.