{
  "id": "cond-mat/0603218",
  "version": "v1",
  "published": "2006-03-08T16:45:33.000Z",
  "updated": "2006-03-08T16:45:33.000Z",
  "title": "Is it really possible to grow isotropic on-lattice diffusion-limited aggregates?",
  "authors": [
    "S. G. Alves",
    "S. C. Ferreira Jr"
  ],
  "comment": "12 pages, 8 figures",
  "journal": "J. Phys. A: Math. Gen. 39 (2006) 2843-2852",
  "doi": "10.1088/0305-4470/39/12/001",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "In a recent paper (Bogoyavlenskiy V A 2002 \\JPA \\textbf{35} 2533), an algorithm aiming to generate isotropic clusters of the on-lattice diffusion-limited aggregation (DLA) model was proposed. The procedure consists of aggregation probabilities proportional to the squared number of occupied sites ($k^2$). In the present work, we analyzed this algorithm using the noise reduced version of the DLA model and large scale simulations. In the noiseless limit, instead of isotropic patterns, a $45^\\circ$ ($30^\\circ$) rotation in the anisotropy directions of the clusters grown on square (triangular) lattices was observed. A generalized algorithm, in which the aggregation probability is proportional to $k^\\nu$, was proposed. The exponent $\\nu$ has a nonuniversal critical value $\\nu_c$, for which the patterns generated in the noiseless limit exhibit the original (axial) anisotropy for $\\nu<\\nu_c$ and the rotated one (diagonal) for $\\nu>\\nu_c$. The values $\\nu_c = 1.395\\pm0.005$ and $\\nu_c = 0.82\\pm 0.01$ were found for square and triangular lattices, respectively. Moreover, large scale simulations show that there are a nontrivial relation between noise reduction and anisotropy direction. The case $\\nu=2$ (\\bogo's rule) is an example where the patterns exhibit the axial anisotropy for small and the diagonal one for large noise reduction.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-03-08T16:45:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "grow isotropic on-lattice diffusion-limited aggregates",
      "large scale simulations",
      "anisotropy direction",
      "noise reduction",
      "aggregation probability"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2006,
      "month": "Mar",
      "volume": 39,
      "number": 12,
      "pages": 2843
    },
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006JPhA...39.2843A"
    }
  }
}