{"paper":{"title":"Unexpected validity of Schottky's conjecture for two-stage field emitters: a response via Schwarz-Christoffel transformation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.mes-hall","authors_text":"Caio M. C. de Castilho, Edgar Marcelino, Thiago A. de Assis","submitted_at":"2017-04-13T22:03:52Z","abstract_excerpt":"The electric field in the vicinity of the top of an emitter with a profile consisting of a triangular protrusion on an infinite line is analytically obtained when this system is under an external uniform electric field. The same problem is also studied when the profile features a two-stage system, consisting of a triangular protrusion centered on the top of a rectangular one on a line. These problems are approached by using a Schwarz-Christoffel conformal mapping, and the validity of Schottky's conjecture (SC) is discussed. The authors provide an analytical proof of SC when the dimensions of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.04284","kind":"arxiv","version":3},"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"}