{
  "id": "1608.03347",
  "version": "v1",
  "published": "2016-08-11T02:06:50.000Z",
  "updated": "2016-08-11T02:06:50.000Z",
  "title": "Static Structural Signatures of Nearly Jammed Disordered and Ordered Hard-Sphere Packings: Direct Correlation Function",
  "authors": [
    "Steven Atkinson",
    "Frank H. Stillinger",
    "Salvatore Torquato"
  ],
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.soft"
  ],
  "abstract": "Dynamical signatures are known to precede jamming in hard-particle systems, but static structural signatures have proven more elusive. The observation that compressing hard-particle packings towards jamming causes growing hyperuniformity has paved the way for the analysis of jamming as an \"inverted critical point\" in which the direct correlation function $c(r)$ diverges. We establish quantitative relationships between various singularities in $c(r)$ and the total correlation function $h(r)$ that provide a concrete means of identifying features that must be expressed in $c(r)$ if one hopes to reproduce details in the pair correlation function accurately. We also analyze systems of three-dimensional monodisperse hard-spheres of diameter $D$ as they approach ordered and disordered jammed configurations. For the latter, we use the Lubachevsky-Stillinger (LS) and Torquato-Jiao (TJ) packing algorithms, which both generate disordered packings, but can show perceptible structural differences. We identify a short-ranged scaling $c(r) \\propto -1/r$ as $r \\rightarrow 0$ and show that this, along with the developing delta function at $c(D)$, is a consequence of the growing long-rangedness in $c(r)$. Near the freezing density, we identify qualitative differences in the structure factor $S(k)$ as well as $c(r)$ between TJ- and LS-generated configurations and link them to differences in the protocols' packing dynamics. Configurations from both algorithms have structure factors that approach zero in the low-wavenumber limit as jamming is approached and are shown to exhibit a corresponding power-law decay in $c(r)$ for large $r$ as a consequence. Our work advances the notion that static signatures are exhibited by hard-particle packings as they approach jamming and underscores the utility of the direct correlation function as a means of monitoring for an incipient rigid network.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-11T02:06:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "direct correlation function",
      "static structural signatures",
      "ordered hard-sphere packings",
      "hard-particle packings",
      "structure factor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}