DOI: 10.1098/rspa.1982.0056. The surface statistics of a granular aggregate

The surface statistics of a granular aggregate

10.1098/rspa.1982.0056

Crossref journal-article

The Royal Society

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences (175)

Abstract

The problem of the surface fluctuations in a settled granular material is posed. A simple model is given which describes the process by which a particle settles and comes to rest on the existing surface of the packing and from this a set of Langevin equations for the Fourier modes of the surface are derived. These equations imply that the Fourier amplitudes behave like the velocities of a set of independent Brownian particles. We show that this results in logarithmically divergent surface fluctuations if the flux of particles onto the surface is random, the divergence being removed by a more accurate description of the settling material, for example by having the granules fall through a sieve.

Bibliography

The surface statistics of a granular aggregate. (1982). Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 381(1780), 17â31.

Authors 0

None

References 4 Referenced 1,336

Chandrasekhar S. 1943 Rev. mod.Phys. 15 1. (10.1103/RevModPhys.15.1)
Edwards S. F. 1976 Molecular fluids (eds. R. Balian and G. Weill). New York: Gordon and Breach.
Reif F. 1965 Statistical and thermal physics ch. 15. New York: McGraw-Hill.
Resibois P. & De Leener M. 1978 Classical kinetic theory of fluids. Wiley.

Dates

Type	When
Created	18 years, 8 months ago (Dec. 15, 2006, 5:20 p.m.)
Deposited	4 years, 6 months ago (Feb. 21, 2021, 2:25 a.m.)
Indexed	2 weeks, 3 days ago (Aug. 6, 2025, 8:57 a.m.)
Issued	43 years, 3 months ago (May 8, 1982)
Published	43 years, 3 months ago (May 8, 1982)
Published Online	28 years, 7 months ago (Jan. 1, 1997)
Published Print	43 years, 3 months ago (May 8, 1982)

Funders 0

None

BibTeX

@article{1982, volume={381}, ISSN={0080-4630}, url={http://dx.doi.org/10.1098/rspa.1982.0056}, DOI={10.1098/rspa.1982.0056}, number={1780}, journal={Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences}, publisher={The Royal Society}, year={1982}, month=may, pages={17–31} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        8,
        6
      ]
    ],
    "date-time": "2025-08-06T12:57:54Z",
    "timestamp": 1754485074399
  },
  "reference-count": 4,
  "publisher": "The Royal Society",
  "issue": "1780",
  "license": [
    {
      "start": {
        "date-parts": [
          [
            1982,
            5,
            8
          ]
        ],
        "date-time": "1982-05-08T00:00:00Z",
        "timestamp": 389664000000
      },
      "content-version": "tdm",
      "delay-in-days": 0,
      "URL": "https://royalsociety.org/journals/ethics-policies/data-sharing-mining/"
    }
  ],
  "content-domain": {
    "domain": [],
    "crossmark-restriction": false
  },
  "published-print": {
    "date-parts": [
      [
        1982,
        5,
        8
      ]
    ]
  },
  "abstract": "<jats:p>The problem of the surface fluctuations in a settled granular material is posed. A simple model is given which describes the process by which a particle settles and comes to rest on the existing surface of the packing and from this a set of Langevin equations for the Fourier modes of the surface are derived. These equations imply that the Fourier amplitudes behave like the velocities of a set of independent Brownian particles. We show that this results in logarithmically divergent surface fluctuations if the flux of particles onto the surface is random, the divergence being removed by a more accurate description of the settling material, for example by having the granules fall through a sieve.</jats:p>",
  "DOI": "10.1098/rspa.1982.0056",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2006,
        12,
        15
      ]
    ],
    "date-time": "2006-12-15T22:20:43Z",
    "timestamp": 1166221243000
  },
  "page": "17-31",
  "source": "Crossref",
  "is-referenced-by-count": 1336,
  "title": "The surface statistics of a granular aggregate",
  "prefix": "10.1098",
  "volume": "381",
  "member": "175",
  "published-online": {
    "date-parts": [
      [
        1997,
        1
      ]
    ]
  },
  "reference": [
    {
      "key": "p_1",
      "doi-asserted-by": "crossref",
      "unstructured": "Chandrasekhar S. 1943 Rev. mod.Phys. 15 1.",
      "DOI": "10.1103/RevModPhys.15.1"
    },
    {
      "key": "p_2",
      "unstructured": "Edwards S. F. 1976 Molecular fluids (eds. R. Balian and G. Weill). New York: Gordon and Breach."
    },
    {
      "key": "p_3",
      "unstructured": "Reif F. 1965 Statistical and thermal physics ch. 15. New York: McGraw-Hill."
    },
    {
      "key": "p_4",
      "unstructured": "Resibois P. & De Leener M. 1978 Classical kinetic theory of fluids. Wiley."
    }
  ],
  "container-title": "Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.1982.0056",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "text-mining"
    },
    {
      "URL": "https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.1982.0056",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2021,
        2,
        21
      ]
    ],
    "date-time": "2021-02-21T07:25:33Z",
    "timestamp": 1613892333000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://royalsocietypublishing.org/doi/10.1098/rspa.1982.0056"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1982,
        5,
        8
      ]
    ]
  },
  "references-count": 4,
  "journal-issue": {
    "issue": "1780",
    "published-print": {
      "date-parts": [
        [
          1982,
          5,
          8
        ]
      ]
    }
  },
  "alternative-id": [
    "10.1098/rspa.1982.0056"
  ],
  "URL": "http://dx.doi.org/10.1098/rspa.1982.0056",
  "relation": {},
  "ISSN": [
    "0080-4630"
  ],
  "subject": [],
  "container-title-short": "Proc. R. Soc. Lond. A",
  "published": {
    "date-parts": [
      [
        1982,
        5,
        8
      ]
    ]
  }
}