{
  "id": "1307.6495",
  "version": "v1",
  "published": "2013-07-24T17:10:57.000Z",
  "updated": "2013-07-24T17:10:57.000Z",
  "title": "On turbulence: deciphering a renormalization flow out of an elliptic curve, II",
  "authors": [
    "Luis G. D. C. Borges"
  ],
  "comment": "10 pages, 11 figures",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "Reaching for a better understanding of turbulence, a line of investigation was followed, its main presupposition being that each scale dependent state, in a general renormalization flow, is a state that can be modeled using a class of ninth degree polynomials. These polynomials are deduced from the Weierstrass models of a certain kind of elliptic curves. As the consequences of this presupposition unfolded, leading to the numerical study of a few samples of elliptic curves, the L functions associated with these later were considered. Their bifurcation diagrams were observed and their escape rates were determined. The consistency of such an approach was put to a statistical test, measuring the rank correlation between escape rates and values taken by these L functions on the point z=1+0i. In the most significant case, the rank correlation coefficient found, r_s, was about r_s=-0.78, with an associated p-value of an order of magnitude close to the (-69) power of 10.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-07-24T17:10:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "76F20",
      "14H52"
    ],
    "keywords": [
      "elliptic curve",
      "turbulence",
      "escape rates",
      "rank correlation coefficient",
      "general renormalization flow"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1307.6495B"
    }
  }
}