{
  "slug": "discrete-grains-model",
  "term": "Discrete-grains model",
  "aliases": [
    "rectangular-grain model"
  ],
  "definition": "The discrete-grains model represents a magnetic recording medium as a tiling of grains drawn from a finite set of shapes.",
  "note": "A common tileset uses 1 x 1, 1 x 2, 2 x 1 and 2 x 2 rectangles. Grain proportions alone do not specify a distribution over complete tilings. [sampling]\n\nIn the reviewed raster-write model, a grain takes the polarity of the last bit written to it. Multiple bit locations within one grain therefore do not provide independent stored values. [detector]\n\nGeometric model tiles are different from lithographically fabricated magnetic islands in bit-patterned media. [bpm]",
  "status": "research",
  "advantages": [],
  "limitations": [],
  "related": [
    "bit-patterned-media",
    "smr",
    "areal-density"
  ],
  "supersedes": [],
  "supersededBy": [],
  "firstSeen": null,
  "lastSeen": null,
  "updated": "2026-10-20",
  "provenance": [
    "Scope: the cited rectangular-grain research models, not a manufacturing process or a specification for current HDDs.",
    "Source review only. No detector, sampling algorithm or physical medium was reproduced."
  ],
  "citations": [
    {
      "id": "sampling",
      "title": "Das and Kashyap. MCMC Methods for Drawing Random Samples from the Discrete-Grains Model of a Magnetic Medium; sections I, III-VI.",
      "url": "https://ece.iisc.ac.in/~nkashyap/Papers/discrete_grains_mcmc.final-2col.pdf",
      "accessed": "2026-10-20"
    },
    {
      "id": "detector",
      "title": "Carosino et al. Iterative Detection and Decoding for the Four-Rectangular-Grain TDMR Model. arXiv:1309.7518v1 (2013), sections II-IV.",
      "url": "https://arxiv.org/pdf/1309.7518v1",
      "accessed": "2026-10-20"
    },
    {
      "id": "bpm",
      "title": "Albrecht et al. Bit Patterned Magnetic Recording: Theory, Media Fabrication, and Recording Performance. arXiv:1503.06664v1 (2015), section I.",
      "url": "https://arxiv.org/pdf/1503.06664v1",
      "accessed": "2026-10-20"
    }
  ]
}