{
  "annotation_id": "598641b5-cddc-4701-b1ca-405fd83448e9",
  "date_created": "2026-03-02T18:00:29.391000Z",
  "date_modified": "2026-03-02T18:00:29.391000Z",
  "file_hash": "ec5a2186a94b12720e04a102fca5f11976a0399e401509d88b4f9ba3202c66d2",
  "private": false,
  "record": {
    "abstract": "We present calculations of the stability of planar fronts in two mean field\nmodels of diffusion limited growth. The steady state solution for the front can\nexist for a continuous family of velocities, we show that the selected velocity\nis given by marginal stability theory. We find that naive mean field theory has\nno instability to transverse perturbations, while a threshold mean field theory\nhas such a Mullins-Sekerka instability. These results place on firm theoretical\nground the observed lack of the dendritic morphology in naive mean field theory\nand its presence in threshold models. The existence of a Mullins-Sekerka\ninstability is related to the behavior of the mean field theories in the\nzero-undercooling limit.",
    "arxiv_id": "patt-sol/9507004",
    "authors": [
      "Douglas Ridgway",
      "Herb Levine",
      "Yuhai Tu"
    ],
    "categories": [
      "patt-sol",
      "nlin.PS"
    ],
    "doi": "10.1103/PhysRevE.53.861",
    "title": "Front Stability in Mean Field Models of Diffusion Limited Growth",
    "url": "https://arxiv.org/abs/patt-sol/9507004"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "9e691095-6bb6-458c-af91-977cf723e486",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}