{
  "annotation_id": "9646c6b6-94e2-4ff8-8426-29e101e623e5",
  "date_created": "2026-03-02T18:00:28.860000Z",
  "date_modified": "2026-03-02T18:00:28.860000Z",
  "file_hash": "289a8e59763e9235bc09127628d7ae0130f4902c694d132fcf8664f4dac342f0",
  "private": false,
  "record": {
    "abstract": "We present a systematic nonlinear theory of pattern selection for parametric\nsurface waves (Faraday waves), not restricted to fluids of low viscosity. A\nstanding wave amplitude equation is derived from the Navier-Stokes equations\nthat is of gradient form. The associated Lyapunov function is calculated for\ndifferent regular patterns to determine the selected pattern near threshold.\nFor fluids of large viscosity, the selected wave pattern consists of parallel\nstripes. At lower viscosity, patterns of square symmetry are obtained in the\ncapillary regime (large frequencies). At lower frequencies (the mixed\ngravity-capillary regime), a sequence of six-fold (hexagonal), eight-fold, ...\npatterns are predicted. The regions of stability of the various patterns are in\nquantitative agreement with recent experiments conducted in large aspect ratio\nsystems.",
    "arxiv_id": "patt-sol/9702002",
    "authors": [
      "Peilong Chen",
      "Jorge Vinals"
    ],
    "categories": [
      "patt-sol",
      "nlin.PS"
    ],
    "doi": "10.1103/PhysRevLett.79.2670",
    "journal_ref": "Phys. Rev. Lett. 79, 2670 (1997).",
    "title": "Amplitude equations and pattern selection in Faraday waves",
    "url": "https://arxiv.org/abs/patt-sol/9702002"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "00799861-671e-4ab3-aadd-829216421e63",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}