{"paper":{"title":"Maximally dense packings of two-dimensional convex and concave noncircular particles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.soft"],"primary_cat":"cond-mat.stat-mech","authors_text":"Salvatore Torquato, Steven Atkinson, Yang Jiao","submitted_at":"2014-05-01T18:26:01Z","abstract_excerpt":"Dense packings of hard particles have important applications in many fields, including condensed matter physics, discrete geometry and cell biology. In this paper, we employ a stochastic search implementation of the Torquato-Jiao Adaptive-Shrinking-Cell optimization scheme [Nature 460, 876 (2009)] to find maximally dense particle packings in d-dimensional Euclidean space $\\mathbb{R}^d$. While the original implementation was designed to study spheres and convex polyhedra in $d\\ge3$, our implementation focuses on $d=2$ and extends the algorithm to include both concave polygons and certain convex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0245","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}