{"paper":{"title":"Two-finger selection theory in the Saffman-Taylor problem","license":"","headline":"","cross_cats":["chao-dyn","cond-mat.mtrl-sci","nlin.CD","nlin.PS","patt-sol"],"primary_cat":"cond-mat.stat-mech","authors_text":"F.X. Magdaleno, J. Casademunt","submitted_at":"1999-09-15T13:26:24Z","abstract_excerpt":"We find that solvability theory selects a set of stationary solutions of the Saffman-Taylor problem with coexistence of two \\it unequal \\rm fingers advancing with the same velocity but with different relative widths $\\lambda_1$ and $\\lambda_2$ and different tip positions. For vanishingly small dimensionless surface tension $d_0$, an infinite discrete set of values of the total filling fraction $\\lambda = \\lambda_1 + \\lambda_2$ and of the relative individual finger width $p=\\lambda_1/\\lambda_2$ are selected out of a two-parameter continuous degeneracy. They scale as $\\lambda-1/2 \\sim d_0^{2/3}$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/9909225","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"}