{
  "tag": "N39YK7",
  "kind": "model",
  "slug": "hard-disk-model",
  "name": "Hard-disk model",
  "area": "foundations/models-of-computation",
  "level": "intro",
  "summary": "Physical model of particles as hard circles moving in a box, colliding elastically with each other and the walls.",
  "prereqs": [
    "priority-queue"
  ],
  "sources": [
    {
      "book": "isbn:9780321573513",
      "title": "Robert Sedgewick and Kevin Wayne, Algorithms, fourth edition",
      "locator": "Chapter 6, Section 6.1 (event-driven simulation, the classes Particle and CollisionSystem)"
    },
    {
      "url": "https://algs4.cs.princeton.edu/61event/",
      "locator": "Section 6.1, Event-driven simulation, on the booksite of Sedgewick and Wayne"
    },
    {
      "paper": "doi:10.1016/0021-9991(91)90222-7",
      "title": "Boris D. Lubachevsky, How to simulate billiards and similar systems, Journal of Computational Physics 94(2) (1991)",
      "locator": "pp. 255 to 283 (abstract, the O(log N) cost per event with sectors)"
    },
    {
      "paper": "B. J. Alder and T. E. Wainwright, Phase transition for a hard sphere system, Journal of Chemical Physics 27 (1957)",
      "locator": "pp. 1208 to 1209"
    },
    {
      "paper": "B. J. Alder and T. E. Wainwright, Studies in molecular dynamics. I. General method, Journal of Chemical Physics 31 (1959)",
      "locator": "page 459 onward (the method of predicting the next collision)"
    },
    {
      "paper": "B. J. Alder and T. E. Wainwright, Phase transition in elastic disks, Physical Review 127 (1962)",
      "locator": "page 359 onward"
    },
    {
      "paper": "doi:10.1063/1.1699114",
      "title": "Nicholas Metropolis, Arianna W. Rosenbluth, Marshall N. Rosenbluth, Augusta H. Teller and Edward Teller, Equation of state calculations by fast computing machines, Journal of Chemical Physics 21 (1953)",
      "locator": "pp. 1087 to 1092 (the method, applied to rigid disks in two dimensions)"
    },
    {
      "paper": "Etienne P. Bernard, Werner Krauth and David B. Wilson, Event-chain Monte Carlo algorithms for hard-sphere systems, Physical Review E 80 (2009)",
      "locator": "article 056704"
    },
    {
      "paper": "Etienne P. Bernard and Werner Krauth, Two-step melting in two dimensions: first-order liquid-hexatic transition, Physical Review Letters 107 (2011)",
      "locator": "article 155704"
    }
  ],
  "see_also": [
    "event-driven-simulation",
    "collision-prediction-and-resolution",
    "priority-queue",
    "binary-heap",
    "lazy-deletion",
    "spatial-hashing",
    "molecular-dynamics",
    "metropolis-hastings"
  ],
  "url": "https://algorithm.tamnd.com/hard-disk-model/",
  "path": "nodes/foundations/models-of-computation/hard-disk-model",
  "status": {
    "slug": "hard-disk-model",
    "h": {
      "level": 0,
      "max": 3,
      "label": "H0",
      "name": "no proof",
      "next": [
        "add a proof in proofs/ (06.5)"
      ]
    },
    "l": {
      "level": 0,
      "max": 4,
      "label": "L0",
      "name": "no Lean part",
      "next": [
        "name a Lean module in the lean field (07)"
      ]
    },
    "i": {},
    "v": {
      "level": 0,
      "max": 3,
      "label": "V0",
      "name": "none",
      "next": [
        "add viz/scene.ts or a figure (10)"
      ]
    },
    "w": {
      "level": 4,
      "max": 5,
      "label": "W4",
      "name": "complete",
      "next": [
        "a review of the text: no review record reviews/N39YK7/text.yaml"
      ]
    }
  },
  "scene": false
}