{
  "annotation_id": "67e6623f-4f73-4e3d-9a90-95556814161c",
  "date_created": "2026-03-02T18:00:52.816000Z",
  "date_modified": "2026-03-02T18:00:52.816000Z",
  "file_hash": "3440bfd1056df90216776478db5ac6ec05935dd3aad57b267fa2c060dd209659",
  "private": false,
  "record": {
    "abstract": "In this brief report, the group velocity of the eigen-modes in sonic crystals\nis derived, and shown to equal the averaged energy velocity of the eigen-modes.\nHow the group velocity can be used to describe acoustic energy flows in sonic\ncrystals is discussed.",
    "arxiv_id": "physics/0411060",
    "authors": [
      "Zhen Ye"
    ],
    "categories": [
      "physics.class-ph",
      "physics.gen-ph"
    ],
    "title": "Group velocity of the acoustic eigen-modes in sonic crystals",
    "url": "https://arxiv.org/abs/physics/0411060"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f51f78e6-6b29-4e2c-a574-0da3980db2d3",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}