{"paper":{"title":"Matched asymptotic expansions for twisted elastic knots: a self-contact problem with non- trivial contact topology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.class-ph","authors_text":"B. Audoly, N. Clauvelin, S. Neukirch","submitted_at":"2008-12-15T19:31:15Z","abstract_excerpt":"We derive solutions of the Kirchhoff equations for a knot tied on an infinitely long elastic rod subjected to combined tension and twist. We consider the case of simple (trefoil) and double (cinquefoil) knots; other knot topologies can be investigated similarly. The rod model is based on Hookean elasticity but is geometrically non-linear. The problem is formulated as a non-linear self-contact problem with unknown contact regions. It is solved by means of matched asymptotic expansions in the limit of a loose knot. Without any a priori assumption, we derive the topology of the contact set, which"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.2881","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"}