{
  "id": "2208.04020",
  "version": "v1",
  "published": "2022-08-08T10:01:32.000Z",
  "updated": "2022-08-08T10:01:32.000Z",
  "title": "Dynamic scaling and stochastic fractal in nucleation and growth processes",
  "authors": [
    "Amit Lahiri",
    "Md. Kamrul Hassan",
    "Bernd Blasius",
    "Jürgen Kurths"
  ],
  "comment": "10 pages, 8 captioned figures",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.other",
    "cond-mat.soft"
  ],
  "abstract": "A class of nucleation and growth models of a stable phase (S-phase) is investigated for various different growth velocities. It is shown that for growth velocities $v\\sim s(t)/t$ and $v\\sim x/\\tau(x)$, where $s(t)$ and $\\tau$ are the mean domain size of the metastable phase (M-phase) and the mean nucleation time respectively, the M-phase decays following a power law. Furthermore, snapshots at different time $t$ are taken to collect data for the distribution function $c(x,t)$ of the domain size $x$ of M-phase are found to obey dynamic scaling. Using the idea of data-collapse we show that each snapshot is a self-similar fractal. However, for $v={\\rm const.}$ like in the classical Kolmogorov-Johnson-Mehl-Avrami (KJMA) model and for $v\\sim 1/t$ the decay of the M-phase are exponential and they are not accompanied by dynamic scaling. We find a perfect agreement between numerical simulation and analytical results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-08T10:01:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dynamic scaling",
      "stochastic fractal",
      "growth processes",
      "growth velocities",
      "mean nucleation time"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}