{
  "annotation_id": "c3a6cb7b-0a4c-4e03-bf12-6f81602db728",
  "date_created": "2026-03-02T18:00:28.836000Z",
  "date_modified": "2026-03-02T18:00:28.836000Z",
  "file_hash": "79bcd5c6d2a71da894e072abbc699f8b5a08ba3b8689e7408b98239e430b3859",
  "private": false,
  "record": {
    "abstract": "The dynamics of transient patterns formed by front propagation in extended\nnonequilibrium systems is considered. Under certain circumstances, the state\nleft behind a front propagating into an unstable homogeneous state can be an\nunstable periodic pattern. It is found by a numerical solution of a model of\nthe Fr\\\u0027eedericksz transition in nematic liquid crystals that the mechanism of\ndecay of such periodic unstable states is the propagation of a second front\nwhich replaces the unstable pattern by a another unstable periodic state with\nlarger wavelength. The speed of this second front and the periodicity of the\nnew state are analytically calculated with a generalization of the marginal\nstability formalism suited to the study of front propagation into periodic\nunstable states. PACS: 47.20.Ky, 03.40.Kf, 47.54.+r",
    "arxiv_id": "patt-sol/9312001",
    "authors": [
      "R. Montagne",
      "A. Amengual",
      "E. Hernandez-Garcia",
      "M. San Miguel"
    ],
    "categories": [
      "patt-sol",
      "nlin.PS"
    ],
    "doi": "10.1103/PhysRevE.50.377",
    "journal_ref": "Physical Review E 50, 377-385 (1994)",
    "title": "Multiple Front Propagation into Unstable States",
    "url": "https://arxiv.org/abs/patt-sol/9312001"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "2b1ec494-d98d-4a13-b028-e4fd16a903fa",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}