{"paper":{"title":"A diffusion generated method for computing Dirichlet partitions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.OC","authors_text":"Braxton Osting, Dong Wang","submitted_at":"2018-02-08T01:06:57Z","abstract_excerpt":"A Dirichlet $k$-partition of a closed $d$-dimensional surface is a collection of $k$ pairwise disjoint open subsets such that the sum of their first Laplace-Beltrami-Dirichlet eigenvalues is minimal. In this paper, we develop a simple and efficient diffusion generated method to compute Dirichlet $k$-partitions for $d$-dimensional flat tori and spheres. For the $2d$ flat torus, for most values of $k=3$-9,11,12,15,16, and 20, we obtain hexagonal honeycombs. For the $3d$ flat torus and $k=2,4,8,16$, we obtain the rhombic dodecahedral honeycomb, the Weaire-Phelan honeycomb, and Kelvin's tessellati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.02682","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"}