{"paper":{"title":"Energy Driven Pattern Formation in Planar Dipole-Dipole Systems in the Presence of Weak Noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.PS"],"primary_cat":"cond-mat.soft","authors_text":"Andrew J. Bernoff, Jaron Kent-Dobias","submitted_at":"2014-06-14T16:00:27Z","abstract_excerpt":"We study pattern formation in planar fluid systems driven by intermolecular cohesion (which manifests as a line tension) and dipole-dipole repulsion which are observed in physical systems including ferrofluids in Hele-Shaw cells and Langmuir layers. When the dipolar repulsion is sufficiently strong, domains undergo forked branching reminiscent of viscous fingering. A known difficulty with these models is that the energy associated with dipole-dipole interactions is singular at small distances. Following previous work, we demonstrate how to ameliorate this singularity and show that in the macro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3749","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"}