{
  "id": "1307.4242",
  "version": "v1",
  "published": "2013-07-16T11:28:09.000Z",
  "updated": "2013-07-16T11:28:09.000Z",
  "title": "Intersections of moving fractal sets",
  "authors": [
    "Indrek Mandre",
    "Jaan Kalda"
  ],
  "doi": "10.1209/0295-5075/103/10012",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "Intersection of a random fractal or self-affine set with a linear manifold or another fractal set is studied, assuming that one of the sets is in a translational motion with respect to the other. It is shown that the mass of such an intersection is a self-affine function of the relative position of the two sets. The corresponding Hurst exponent h is a function of the scaling exponents of the intersecting sets. A generic expression for h is provided, and its proof is offered for two cases --- intersection of a self-affine curve with a line, and of two fractal sets. The analytical results are tested using Monte-Carlo simulations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-16T11:28:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "moving fractal sets",
      "intersection",
      "translational motion",
      "linear manifold",
      "self-affine set"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.4242M"
    }
  }
}