{"paper":{"title":"Minimal Model for the Topology of the Critical State in Hard Superconductors","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.supr-con","authors_text":"A. Bad\\'ia, C. L\\'opez","submitted_at":"2003-07-01T11:04:01Z","abstract_excerpt":"The critical state problem in type-II superconductivity is described theoretically by a direct optimization method, which allows a straightforward treatment for non idealized geometries.\n  Based on Faraday's law and the principle of minimum entropy production, the magnetic history is built up just by a constrained minimization of the field changes along the process. Constraints are in the form $\\vec{J}\\in\\Delta$, with $\\vec{J}$ the electric current density and $\\Delta$ some bounded set. This incorporates the vortex pinning and interaction phenomena and may be used for the modelling of anisotro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0307018","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"}