{"paper":{"title":"An Energy-Minimization Finite-Element Approach for the Frank-Oseen Model of Nematic Liquid Crystals: Continuum and Discrete Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"D. B. Emerson, J. H. Adler, S. P. MacLachlan, T. J. Atherton","submitted_at":"2014-02-13T21:40:43Z","abstract_excerpt":"This paper outlines an energy-minimization finite-element approach to the computational modeling of equilibrium configurations for nematic liquid crystals under free elastic effects. The method targets minimization of the system free energy based on the Frank-Oseen free-energy model. Solutions to the intermediate discretized free elastic linearizations are shown to exist generally and are unique under certain assumptions. This requires proving continuity, coercivity, and weak coercivity for the accompanying appropriate bilinear forms within a mixed finite-element framework. Error analysis demo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3310","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"}