{
  "annotation_id": "771131ae-3a29-40a9-9967-aad3c4ac3a86",
  "date_created": "2026-03-02T18:00:46.800000Z",
  "date_modified": "2026-03-02T18:00:46.800000Z",
  "file_hash": "f7a4a90936257f3c56289f279ada4aa6c00c44bf72772e53e0ffcbce4a002dc1",
  "private": false,
  "record": {
    "abstract": "In this work we estimate rates of the linear transient growth of the\nperturbations of cellular flames governed by the Sivashinsky equation. The\npossibility and significance of such a growth was indicated ear- lier in both\ncomputational and analytical investigations. Numerical investigation of the\nnorm of the resolvent of the linear operator asso- ciated with the Sivashinsky\nequation linearized in a neighbourhood of the steady coalescent pole solution\nwas undertaken. The results are presented in the form of the pseudospectra and\nthe lower bound of possible transient amplification. This amplification is\nstrong enough to make the round-off errors visible in the numerical simulations\nin the form of small cusps appearing on the flame surface randomly in time.\nPerformance of available numerical approaches was compared to each other and\nthe results are checked versus directly calculated norms of the evolution\noperator.",
    "arxiv_id": "physics/0312095",
    "authors": [
      "V. Karlin"
    ],
    "categories": [
      "physics.flu-dyn",
      "physics.comp-ph",
      "physics.gen-ph"
    ],
    "title": "Estimation of the linear transient growth of perturbations of cellular   flames",
    "url": "https://arxiv.org/abs/physics/0312095"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "0d9e2f4a-fba4-4f36-aec0-2e465e373439",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}