{
  "annotation_id": "8705b1ce-9552-42d3-80a2-0b377b2242b0",
  "date_created": "2026-03-02T18:00:28.607000Z",
  "date_modified": "2026-03-02T18:00:28.607000Z",
  "file_hash": "2eb58cc0fb863fdff652c2578de93de741e8da3d04baf78b3d01fa7a8ded9afa",
  "private": false,
  "record": {
    "abstract": "Pattern formation in parametric surface waves is studied in the limit of weak\nviscous dissipation. A set of quasi-potential equations (QPEs) is introduced\nthat admits a closed representation in terms of surface variables alone. A\nmultiscale expansion of the QPEs reveals the importance of triad resonant\ninteractions, and the saturating effect of the driving force leading to a\ngradient amplitude equation. Minimization of the associated Lyapunov function\nyields standing wave patterns of square symmetry for capillary waves, and\nhexagonal patterns and a sequence of quasi-patterns for mixed capillary-gravity\nwaves. Numerical integration of the QPEs reveals a quasi-pattern of eight-fold\nsymmetry in the range of parameters predicted by the multiscale expansion.",
    "arxiv_id": "patt-sol/9603005",
    "authors": [
      "Wenbin Zhang",
      "Jorge Vinals"
    ],
    "categories": [
      "patt-sol",
      "nlin.PS"
    ],
    "doi": "10.1103/PhysRevE.53.R4283",
    "journal_ref": "Phys. Rev. E 53, R4283 (1996)",
    "title": "Square Patterns and Quasi-patterns in Weakly Damped Faraday Waves",
    "url": "https://arxiv.org/abs/patt-sol/9603005"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f42a86aa-d058-416e-890a-366ecd7d45c9",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}