{
  "annotation_id": "1ba0f10b-3bc6-4d60-8af8-3ff4bbbf4191",
  "date_created": "2026-03-02T18:00:29.400000Z",
  "date_modified": "2026-03-02T18:00:29.400000Z",
  "file_hash": "707935558b92dda9c1f71705dac53aae704a7f62afee2ae1badb3ec01c5bbf95",
  "private": false,
  "record": {
    "abstract": "The Cross-Newell equations for hexagons and triangles are derived for general\nreal gradient systems, and are found to be in flux-divergence form. Specific\nexamples of complex governing equations that give rise to hexagons and\ntriangles and which have Lyapunov functionals are also considered, and explicit\nforms of the Cross-Newell equations are found in these cases. The general\nnongradient case is also discussed; in contrast with the gradient case, the\nequations are not flux-divergent. In all cases, the phase stability boundaries\nand modes of instability for general distorted hexagons and triangles can be\nrecovered from the Cross-Newell equations.",
    "arxiv_id": "patt-sol/9910004",
    "authors": [
      "Rebecca B. Hoyle"
    ],
    "categories": [
      "patt-sol",
      "nlin.PS"
    ],
    "doi": "10.1103/PhysRevE.61.2506",
    "title": "Cross-Newell equations for hexagons and triangles",
    "url": "https://arxiv.org/abs/patt-sol/9910004"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "873f725e-136a-4a47-8fab-2752dce6af0f",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}