{
  "id": "1403.6642",
  "version": "v2",
  "published": "2014-03-26T12:02:01.000Z",
  "updated": "2014-12-27T07:16:30.000Z",
  "title": "Escape Dynamics of Many Hard Disks",
  "authors": [
    "Tooru Taniguchi",
    "Hiroki Murata",
    "Shin-ichi Sawada"
  ],
  "comment": "14 pages, 11 figures",
  "journal": "Phys. Rev. E 90, 052923 (2014)",
  "doi": "10.1103/PhysRevE.90.052923",
  "categories": [
    "cond-mat.stat-mech",
    "nlin.CD"
  ],
  "abstract": "Many-particle effects in escapes of hard disks from a square box via a hole are discussed in a viewpoint of dynamical systems. Starting from $N$ disks in the box at the initial time, we calculate the probability $P_{n}(t)$ for at least $n$ disks to remain inside the box at time $t$ for $n=1,2,\\cdots,N$. At early times the probabilities $P_{n}(t)$, $n=2,3,\\cdots,N-1$, are described by superpositions of exponential decay functions. On the other hand, after a long time the probability $P_{n}(t)$ shows a power-law decay $\\sim t^{-2n}$ for $n\\neq 1$, in contrast to the fact that it decays with a different power law $\\sim t^{-n}$ for cases without any disk-disk collision. Chaotic or non-chaotic properties of the escape systems are discussed by the dynamics of a finite time largest Lyapunov exponent, whose decay properties are related with those of the probability $P_{n}(t)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-26T12:02:01.000Z",
      "abstract": "Many-particle effects in escapes of hard disks from a square box via a hole are discussed in a viewpoint of dynamical systems. Starting from $N$ disks in the box at the initial time, we calculate the probability $P_{n}(t)$ for at least $n$ disks to remain inside the box at time $t$ for $n=1,2,\\cdots,N$. At early times the probabilities $P_{n}(t)$, $n=2,3,\\cdots,N-1$ are described by superpositions of exponential decay functions. On the other hand, after a long time the probability $P_{n}(t)$ decays in power $\\sim t^{-2n}$ for $n\\neq 1$, in contrast to the fact that it decays in a different power $\\sim t^{-n}$ for the case without any disk-disk collision. Chaotic and non-chaotic properties of the escape systems are discussed by the dynamics of finite time largest Lyapunov exponents, whose decay properties are related with those of the probability $P_{n}(t)$.",
      "comment": "12 pages, 11 figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-12-27T07:16:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05.45.Jn",
      "05.60.Cd",
      "45.50.Jf"
    ],
    "keywords": [
      "hard disks",
      "escape dynamics",
      "finite time largest lyapunov exponents",
      "probability",
      "exponential decay functions"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review E",
      "year": 2014,
      "month": "Nov",
      "volume": 90,
      "number": 5,
      "pages": "052923"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014PhRvE..90e2923T"
    }
  }
}