{
  "annotation_id": "0c346075-d9ee-4b9a-a1bc-607739f4892d",
  "date_created": "2026-03-02T18:00:29.391000Z",
  "date_modified": "2026-03-02T18:00:29.391000Z",
  "file_hash": "0b892eecb01afa313092504ca43a1f3c8052db1bb22c3d6a714e035e54c20af8",
  "private": false,
  "record": {
    "abstract": "Recent experiments by Kudrolli, Pier and Gollub on surface waves,\nparametrically excited by two-frequency forcing, show a transition from a small\nhexagonal standing wave pattern to a triangular ``superlattice\u0027\u0027 pattern. We\nshow that generically the hexagons and the superlattice wave patterns bifurcate\nsimultaneously from the flat surface state as the forcing amplitude is\nincreased, and that the experimentally-observed transition can be described by\nconsidering a low-dimensional bifurcation problem. A number of predictions come\nout of this general analysis.",
    "arxiv_id": "patt-sol/9710004",
    "authors": [
      "Mary Silber",
      "Michael R. E. Proctor"
    ],
    "categories": [
      "patt-sol",
      "nlin.PS"
    ],
    "doi": "10.1103/PhysRevLett.81.2450",
    "title": "Nonlinear Competition Between Small and Large Hexagonal Patterns",
    "url": "https://arxiv.org/abs/patt-sol/9710004"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b1cd5cc0-8df8-4d4a-8b91-98066a82536f",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}