{
  "annotation_id": "f320e8af-c47e-48d1-b82e-d62d8a6d4df5",
  "date_created": "2026-03-02T18:00:28.664000Z",
  "date_modified": "2026-03-02T18:00:28.664000Z",
  "file_hash": "48078d93eaaa5f0d2219ad1f4ceb6aec95ce6f751110739580241a0fe318b82b",
  "private": false,
  "record": {
    "abstract": "We study the exact non-singular zero-surface tension solutions of the\nSaffman-Taylor problem for all times. We show that all moving logarithmic\nsingularities a_k(t) in the complex plane \\omega = e^{i\\phi}, where \\phi is the\nstream function, are repelled from the origin, attracted to the unit circle and\neventually coalesce. This pole evolution describes essentially all the\ndynamical features of viscous fingering in the Hele-Shaw cell observed by\nSaffman and Taylor [Proc. R. Soc. A 245, 312 (1958)], namely tip-splitting,\nmulti-finger competition, inverse cascade, and subsequent formation of a single\nSaffman-Taylor finger.",
    "arxiv_id": "patt-sol/9902007",
    "authors": [
      "Mark Mineev-Weinstein",
      "Oleg Kupervasser"
    ],
    "categories": [
      "patt-sol",
      "nlin.CD",
      "nlin.PS"
    ],
    "doi": "10.1023/A:1018620302081",
    "journal_ref": "On 82nd Statistical Mechanics Meeting, Rutgers University,\n  December 10-12, 1999. Journal of Statistical Physics,Volume 99, Numbers 3-4,\n  May, P.1057-1065 (2000)",
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Laplacian Growth I: Finger Competition and Formation of a Single   Saffman-Taylor Finger without Surface Tension: An Exact Result",
    "url": "https://arxiv.org/abs/patt-sol/9902007"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "34ede173-0e1a-4e66-ad12-5e793effbf91",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}