{
  "annotation_id": "934a54a5-df0b-4532-8037-24ce6e43f7c5",
  "date_created": "2026-03-02T18:01:07.026000Z",
  "date_modified": "2026-03-02T18:01:07.026000Z",
  "file_hash": "758d0c1f159e9268c0255021958207296cce10c2a02300eefd017a0ec3452a27",
  "private": false,
  "record": {
    "abstract": "For real world systems, nonuniform medium is ubiquitous. Therefore, we\ninvestigate the diffusion-limited-aggregation process on a two dimensional\ndirected small-world network instead of regular lattice. The network structure\nis established by rewiring connections on the two dimensional directed lattice.\nThose rewired edges are controlled by two parameters $\\theta$ and $m$, which\ncharacterize the spatial length and the density of the long-range connections,\nrespectively. Simulations show that there exists a maximum value of the fractal\ndimension when $\\theta$ equals zero. Interestingly, we find that the symmetry\nof the aggregation pattern is broken when rewired connections are long enough,\nwhich may be an explanation for the formation of asymmetrical fractal in\nnature. Then, we perform multifractal analysis on the patterns further.",
    "arxiv_id": "physics/0602178",
    "authors": [
      "Jie Ren",
      "Wen-Xu Wang",
      "Gang Yan",
      "Bing-Hong Wang"
    ],
    "categories": [
      "physics.comp-ph",
      "physics.atm-clus"
    ],
    "title": "Diffusion-limited-aggregation on a directed small world network",
    "url": "https://arxiv.org/abs/physics/0602178"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "bbb63d19-e017-4ad8-ba59-83f764e7430f",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}