{
  "id": "cond-mat/0309196",
  "version": "v1",
  "published": "2003-09-08T17:35:25.000Z",
  "updated": "2003-09-08T17:35:25.000Z",
  "title": "Testing the Collective Properties of Small-World Networks through Roughness Scaling",
  "authors": [
    "B. Kozma",
    "M. B. Hastings",
    "G. Korniss"
  ],
  "comment": "4 pages, 3 figures",
  "journal": "Phys. Rev. Lett. 92, 108701 (2004).",
  "doi": "10.1103/PhysRevLett.92.108701",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.dis-nn"
  ],
  "abstract": "Motivated by a fundamental synchronization problem in scalable parallel computing and by a recent criterion for ``mean-field'' synchronizability in interacting systems, we study the Edwards-Wilkinson model on two variations of a small-worldnetwork. In the first version each site has exactly one random link of strength $p$, while in the second one each site on average has $p$ links of unit strength. We construct a perturbative description for the width of the stationary-state surface (a measure of synchronization), in the weak- and sparse-coupling limits, respectively, and verify the results by performing exact numerical diagonalization. The width remains finite in both cases, but exhibits anomalous scaling with $p$ in the latter for $d\\leq 2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-09-08T17:35:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "small-world networks",
      "collective properties",
      "roughness scaling",
      "width remains finite",
      "fundamental synchronization problem"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. Lett."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}