{"paper":{"title":"Elastic curves and surfaces under long-range forces: A geometric approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.soft"],"primary_cat":"cond-mat.stat-mech","authors_text":"G. Chacon-Acosta, J. A. Santiago, O. Gonzalez-Gaxiola","submitted_at":"2013-01-10T18:57:00Z","abstract_excerpt":"Using classical differential geometry, the problem of elastic curves and surfaces in the presence of long-range interactions $\\Phi$, is posed. Starting from a variational principle, the balance of elastic forces and the corresponding projections ${\\bf n}_i\\cdot \\nabla\\Phi$, are found. In the case of elastic surfaces, a force coupling the mean curvature with the external potential, $K\\Phi$, appears; it is also present in the shape equation along the normal principal in the case of curves. The potential $\\Phi$ contributes to the effective tension of curves and surfaces and also to the orbital to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2217","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"}