{"paper":{"title":"Asymptotic shape of isolated magnetic domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CA","math.MP"],"primary_cat":"math.AP","authors_text":"Dominik Stantejsky, Hans Kn\\\"upfer","submitted_at":"2022-01-07T10:14:01Z","abstract_excerpt":"We investigate the energy of an isolated magnetized domain $\\Omega \\subset \\mathbb{R}^n$ for $n=2,3$. In non-dimensionalized variables, the energy given by $$ \\mathcal{E}(\\Omega) \\ = \\ \\int_{\\mathbb{R}^n} |\\nabla \\chi_{\\Omega}| \\ dx + \\int_{\\mathbb{R}^n} |\\nabla h_\\Omega|^2 \\ dx $$ penalizes the interfacial area of the domain as well as the energy of the corresponding magnetostatic field. Here, the magnetostatic potential $h_\\Omega$ is determined by $\\Delta h_\\Omega = \\partial_1 \\chi_\\Omega$, corresponding to uniform magnetization within the domain. We consider the macroscopic regime $|\\Omega|"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2201.02384","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2201.02384/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}