{"paper":{"title":"Note on the numerical solution of the scalar Helmholtz equation in a nanotorus with uniform Dirichlet boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.mes-hall","authors_text":"(2) Department of Electrical, B-4000 Li\\`ege, Belgium, Chicago, Computer Engineering, IL 60607, Michael A. Stroscio (2) ((1) D\\'epartement de Physique B5, N.D. Nguyen (1), R. Evrard (1), Universit\\'e de Li\\`ege, University of Illinois at Chicago, USA)","submitted_at":"2016-03-20T13:39:38Z","abstract_excerpt":"This note describes the solution of the Helmholtz equation inside a nanotorus with uniform Dirichlet boundary conditions. The eigenfunction symmetry is discussed and the lower-order eigenvalues and eigenfunctions are shown. The similarity with the case of a long cylinder and with that of the vibrations of a circular elastic membrane is discussed. This similarity is used to propose a classification scheme of the eigenfunctions based on three indices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06213","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"}