{"paper":{"title":"A Ginzburg-Landau type problem for highly anisotropic nematic liquid crystals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dmitry Golovaty, Peter Sternberg, Raghavendra Venkatraman","submitted_at":"2017-12-01T21:12:51Z","abstract_excerpt":"We carry out an asymptotic analysis of a thin nematic liquid crystal in which one elastic constant dominates over the others, namely \\begin{align} \\label{energyab} \\inf E_\\varepsilon(u)\\quad\\mbox{where}\\quad E_\\varepsilon(u) := \\frac{1}{2}\\int_\\Omega \\left\\{\\varepsilon\\,|\\nabla u|^2 + \\frac{1}{\\varepsilon} \\,(|u|^2 - 1)^2 + L \\,(\\mathrm{div}\\,u)^2\\right\\} \\,dx. \\end{align} Here $u: \\Omega \\to \\mathbb R^2$ is a vector field, $0 < \\varepsilon \\ll 1 $ is a small parameter, and $L > 0$ is a fixed constant, independent of $\\varepsilon$. We derive the $\\Gamma$-limit $E_0$, which is a sum of a bulk t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00493","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"}