{
  "annotation_id": "5cc4f105-5b9b-4daa-8711-7801244979e5",
  "date_created": "2026-03-02T18:00:29.161000Z",
  "date_modified": "2026-03-02T18:00:29.161000Z",
  "file_hash": "af99318444902c70b63baf07a78fc6abaeea1ffdf26a32cf14a97d286cffe41d",
  "private": false,
  "record": {
    "abstract": "I argue that ``good\u0027\u0027 mathematical models of spatio-temporal dynamics in\ntwo-dimensions require non-local operators in the nonlinear terms.\nConsequently, the often used Swift-Hohenberg equation requires modification as\nit is purely local. My aim here is to provoke more critical examination of the\nrationale for using the Swift-Hohenberg equations as a reliable model of the\nspatial pattern evolution in specific physical systems.",
    "arxiv_id": "patt-sol/9412002",
    "authors": [
      "A. J. Roberts"
    ],
    "categories": [
      "patt-sol",
      "nlin.PS"
    ],
    "title": "The Swift-Hohenberg Equation Requires Non-Local Modifications to Model   Spatial Pattern Evolution of Physical Problems",
    "url": "https://arxiv.org/abs/patt-sol/9412002"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "5cd6ffa3-1f9a-487a-ad81-2f934db2f0d7",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}