{"paper":{"title":"A Model Problem for Nematic-Isotropic Transitions with Highly Disparate Elastic Constants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dmitry Golovaty, Michael Novack, Peter Sternberg, Raghavendra Venkatraman","submitted_at":"2018-11-30T02:38:56Z","abstract_excerpt":"We analyze a model problem based on highly disparate elastic constants that we propose in order to understand corners and cusps that form on the boundary between the nematic and isotropic phases in a liquid crystal. For a bounded planar domain $\\Omega$ we investigate the $\\varepsilon \\to 0$ asymptotics of the variational problem \\[\\inf \\frac{1}{2}\\int_\\Omega \\left( \\frac{1}{\\varepsilon} W(u)+\\varepsilon |\\nabla u|^2 + L_\\varepsilon(\\mathrm{div}\\, u)^2 \\right) \\,dx\\] within various parameter regimes for $L_\\varepsilon > 0.$ Here $u:\\Omega\\to\\mathbb{R}^2$ and $W$ is a potential vanishing on the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.12586","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"}