{"paper":{"title":"Singular Limits for Thin Film Superconductors in Strong Magnetic Fields - Maan Field Model for Thin Films","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Bernardo Galv\\~ao-Sousa, Lia Bronsard, Stan Alama","submitted_at":"2012-09-17T15:44:21Z","abstract_excerpt":"We consider singular limits of the three-dimensional Ginzburg-Landau functional for a superconductor with thin-film geometry, in a constant external magnetic field. The superconducting domain has characteristic thickness on the scale $\\eps>0$, and we consider the simultaneous limit as the thickness $\\eps\\rightarrow 0$ and the Ginzburg-Landau parameter $\\kappa\\rightarrow\\infty$. We assume that the applied field is strong (on the order of $\\eps^{-1}$ in magnitude) in its components tangential to the film domain, and of order $\\log\\kappa$ in its dependence on $\\kappa$. We prove that the Ginzburg-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.3696","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"}