{"paper":{"title":"Conformal map and harmonic measure of the Bunimovich stadium","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.CV"],"primary_cat":"math.NA","authors_text":"Vipin Kerala Varma","submitted_at":"2014-10-18T09:45:13Z","abstract_excerpt":"We consider the conformal mapping of the Bunimovich stadium, a region enclosed by a Jordan curve with four smooth corners, primarily in the context of a particle undergoing Brownian motion within its closed geometry with Dirichlet boundary conditions. A Chebyshev weighting of the solutions of Symm's integral equation is employed to give a numerical conformal map of the region onto the canonical domain of the unit disk in the complex plane. As a measure of the accuracy of the transformation, the domes' harmonic measure evaluated at the centre of the stadium is thereby extracted and is compared "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.4932","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"}