{
  "annotation_id": "5d7376b1-3428-422d-b2e1-9251813bf2f9",
  "date_created": "2026-03-02T18:00:29.402000Z",
  "date_modified": "2026-03-02T18:00:29.402000Z",
  "file_hash": "9573b041fbe94fc59f9637d99526059a8c22df33d537611a8bf4abdfaf2e5762",
  "private": false,
  "record": {
    "abstract": "The general form of the amplitude equations for a hexagonal pattern including\nspatial terms is discussed. At the lowest order we obtain the phase equation\nfor such patterns. The general expression of the diffusion coefficients is\ngiven and the contributions of the new spatial terms are analysed in this\npaper. From these coefficients the phase stability regions in a hexagonal\npattern are determined. In the case of Benard-Marangoni instability our results\nagree qualitatively with numerical simulations performed recently.",
    "arxiv_id": "patt-sol/9805007",
    "authors": [
      "B. Echebarria",
      "C. Perez-Garcia"
    ],
    "categories": [
      "patt-sol",
      "nlin.PS"
    ],
    "doi": "10.1209/epl/i1998-00315-2",
    "title": "Phase instabilities in hexagonal patterns",
    "url": "https://arxiv.org/abs/patt-sol/9805007"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "b7da4738-14b1-4a70-a238-504a3c3973fe",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}