{"paper":{"title":"The $\\mathbf \\Gamma$-limit of the two-dimensional Ohta-Kawasaki energy. I. Droplet density","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mtrl-sci","math.MP","nlin.PS"],"primary_cat":"math-ph","authors_text":"Cyrill B. Muratov, Dorian Goldman, Sylvia Serfaty","submitted_at":"2011-12-31T04:34:47Z","abstract_excerpt":"This is the first in a series of two papers in which we derive a $\\Gamma$-expansion for a two-dimensional non-local Ginzburg-Landau energy with Coulomb repulsion, also known as the Ohta-Kawasaki model in connection with diblock copolymer systems. In that model, two phases appear, which interact via a nonlocal Coulomb type energy. We focus on the regime where one of the phases has very small volume fraction, thus creating small \"droplets\" of the minority phase in a \"sea\" of the majority phase. In this paper we show that an appropriate setting for $\\Gamma$-convergence in the considered parameter"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0222","kind":"arxiv","version":2},"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"}