DOI: 10.1063/1.347600. Improved bounds on the effective conductivity of high-contrast suspensions

Improved bounds on the effective conductivity of high-contrast suspensions

10.1063/1.347600

Crossref journal-article

AIP Publishing

Journal of Applied Physics (317)

Abstract

Conventional upper and lower bounds on the effective conductivity σe of two-phase composite media diverge from one another in the infinite-contrast limits (α=∞ or 0). We have derived a generally nontrivial upper bound on σe for suspensions of identical spheres when the spheres are superconducting, i.e., the upper bound does not necessarily become infinite in the limit α→∞. Similarly, a generally nontrivial lower bound on σe is derived for the aforementioned suspension when the spheres are perfect insulators, i.e., the lower bound does not necessarily vanish in the limit α→0. The bounds are computed for two models: simple cubic arrays and random arrays of spheres.

Bibliography

Torquato, S., & Rubinstein, J. (1991). Improved bounds on the effective conductivity of high-contrast suspensions. Journal of Applied Physics, 69(10), 7118â7125.

Authors 2

S. Torquato (first)
J. Rubinstein (additional)

References 20 Referenced 12

10.1063/1.1728579 / J. Appl. Phys. (1962)
10.1007/BF02748596 / Nuovo Cimento (1965)
10.1063/1.329386 / J. Appl. Phys. (1981)
{'key': '2024020413373708700_r4', 'first-page': '3790', 'volume': '58', 'year': '1980', 'journal-title': 'J. Appl. Phys.'} / J. Appl. Phys. (1980)
10.1063/1.346276 / J. Appl. Phys. (1990)
10.1063/1.348708 / J. Appl. Phys. (1991)
10.1017/S0022112067001326 / J. Fluid Mech. (1967)
10.1063/1.454474 / J. Chem. Phys. (1988)
10.1063/1.456655 / J. Chem. Phys. (1989)
10.1017/S0022112089002211 / J. Fluid Mech. (1989)
{'key': '2024020413373708700_r9'}
10.1063/1.450727 / J. Chem. Phys. (1986)
10.1088/0305-4470/23/3/005 / J. Phys. A (1990)
10.1103/PhysRevA.41.2059 / Phys. Rev. A (1990)
10.1098/rspa.1978.0031 / Proc. R. Soc. London A (1978)
{'key': '2024020413373708700_r13', 'first-page': '378', 'volume': '43', 'year': '1978', 'journal-title': 'Phys. Rep.'} / Phys. Rep. (1978)
{'key': '2024020413373708700_r14', 'first-page': '6248', 'volume': '33', 'year': '1986', 'journal-title': 'Phys. Rev. B'} / Phys. Rev. B (1986)
10.1115/1.3119494 / Appl. Mech. Rev. (1991)
{'key': '2024020413373708700_r15', 'first-page': '347', 'volume': '164', 'year': '1990', 'journal-title': 'Physica A'} / Physica A (1990)
10.1103/PhysRevA.27.1053 / Phys. Rev. A (1983)

Dates

Type	When
Created	23 years, 1 month ago (July 26, 2002, 8:25 a.m.)
Deposited	1 year, 6 months ago (Feb. 4, 2024, 8:37 a.m.)
Indexed	1 year, 6 months ago (Feb. 7, 2024, 10:12 a.m.)
Issued	34 years, 3 months ago (May 15, 1991)
Published	34 years, 3 months ago (May 15, 1991)
Published Print	34 years, 3 months ago (May 15, 1991)

Funders 0

None

BibTeX

@article{Torquato_1991, title={Improved bounds on the effective conductivity of high-contrast suspensions}, volume={69}, ISSN={1089-7550}, url={http://dx.doi.org/10.1063/1.347600}, DOI={10.1063/1.347600}, number={10}, journal={Journal of Applied Physics}, publisher={AIP Publishing}, author={Torquato, S. and Rubinstein, J.}, year={1991}, month=may, pages={7118–7125} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2024,
        2,
        7
      ]
    ],
    "date-time": "2024-02-07T15:12:52Z",
    "timestamp": 1707318772711
  },
  "reference-count": 20,
  "publisher": "AIP Publishing",
  "issue": "10",
  "content-domain": {
    "domain": [
      "pubs.aip.org"
    ],
    "crossmark-restriction": true
  },
  "published-print": {
    "date-parts": [
      [
        1991,
        5,
        15
      ]
    ]
  },
  "abstract": "<jats:p>Conventional upper and lower bounds on the effective conductivity \u03c3e of two-phase composite media diverge from one another in the infinite-contrast limits (\u03b1=\u221e or 0). We have derived a generally nontrivial upper bound on \u03c3e for suspensions of identical spheres when the spheres are superconducting, i.e., the upper bound does not necessarily become infinite in the limit \u03b1\u2192\u221e. Similarly, a generally nontrivial lower bound on \u03c3e is derived for the aforementioned suspension when the spheres are perfect insulators, i.e., the lower bound does not necessarily vanish in the limit \u03b1\u21920. The bounds are computed for two models: simple cubic arrays and random arrays of spheres.</jats:p>",
  "DOI": "10.1063/1.347600",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2002,
        7,
        26
      ]
    ],
    "date-time": "2002-07-26T12:25:09Z",
    "timestamp": 1027686309000
  },
  "page": "7118-7125",
  "update-policy": "http://dx.doi.org/10.1063/aip-crossmark-policy-page",
  "source": "Crossref",
  "is-referenced-by-count": 12,
  "title": "Improved bounds on the effective conductivity of high-contrast suspensions",
  "prefix": "10.1063",
  "volume": "69",
  "author": [
    {
      "given": "S.",
      "family": "Torquato",
      "sequence": "first",
      "affiliation": [
        {
          "name": "Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012"
        }
      ]
    },
    {
      "given": "J.",
      "family": "Rubinstein",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Department of Mathematics, Technion-Israel Institute of Technology, 32000 Haifa, Israel"
        }
      ]
    }
  ],
  "member": "317",
  "reference": [
    {
      "key": "2024020413373708700_r1",
      "doi-asserted-by": "crossref",
      "first-page": "3125",
      "DOI": "10.1063/1.1728579",
      "volume": "33",
      "year": "1962",
      "journal-title": "J. Appl. Phys."
    },
    {
      "key": "2024020413373708700_r2",
      "doi-asserted-by": "crossref",
      "first-page": "771",
      "DOI": "10.1007/BF02748596",
      "volume": "38",
      "year": "1965",
      "journal-title": "Nuovo Cimento"
    },
    {
      "key": "2024020413373708700_r3",
      "doi-asserted-by": "crossref",
      "first-page": "5294",
      "DOI": "10.1063/1.329386",
      "volume": "52",
      "year": "1981",
      "journal-title": "J. Appl. Phys."
    },
    {
      "key": "2024020413373708700_r4",
      "first-page": "3790",
      "volume": "58",
      "year": "1980",
      "journal-title": "J. Appl. Phys."
    },
    {
      "key": "2024020413373708700_r5",
      "doi-asserted-by": "crossref",
      "first-page": "3892",
      "DOI": "10.1063/1.346276",
      "volume": "68",
      "year": "1990",
      "journal-title": "J. Appl. Phys."
    },
    {
      "key": "2024020413373708700_r5a",
      "doi-asserted-by": "crossref",
      "first-page": "2280",
      "DOI": "10.1063/1.348708",
      "volume": "69",
      "year": "1991",
      "journal-title": "J. Appl. Phys."
    },
    {
      "key": "2024020413373708700_r6",
      "doi-asserted-by": "crossref",
      "first-page": "97",
      "DOI": "10.1017/S0022112067001326",
      "volume": "30",
      "year": "1967",
      "journal-title": "J. Fluid Mech."
    },
    {
      "key": "2024020413373708700_r7",
      "doi-asserted-by": "crossref",
      "first-page": "6372",
      "DOI": "10.1063/1.454474",
      "volume": "88",
      "year": "1988",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020413373708700_r7a",
      "doi-asserted-by": "crossref",
      "first-page": "1644",
      "DOI": "10.1063/1.456655",
      "volume": "90",
      "year": "1989",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020413373708700_r8",
      "doi-asserted-by": "crossref",
      "first-page": "25",
      "DOI": "10.1017/S0022112089002211",
      "volume": "206",
      "year": "1989",
      "journal-title": "J. Fluid Mech."
    },
    {
      "key": "2024020413373708700_r9"
    },
    {
      "key": "2024020413373708700_r10",
      "doi-asserted-by": "crossref",
      "first-page": "6345",
      "DOI": "10.1063/1.450727",
      "volume": "84",
      "year": "1986",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020413373708700_r11",
      "doi-asserted-by": "crossref",
      "first-page": "L103",
      "DOI": "10.1088/0305-4470/23/3/005",
      "volume": "23",
      "year": "1990",
      "journal-title": "J. Phys. A"
    },
    {
      "key": "2024020413373708700_r11a",
      "doi-asserted-by": "crossref",
      "first-page": "2059",
      "DOI": "10.1103/PhysRevA.41.2059",
      "volume": "41",
      "year": "1990",
      "journal-title": "Phys. Rev. A"
    },
    {
      "key": "2024020413373708700_r12",
      "doi-asserted-by": "crossref",
      "first-page": "45",
      "DOI": "10.1098/rspa.1978.0031",
      "volume": "359",
      "year": "1978",
      "journal-title": "Proc. R. Soc. London A"
    },
    {
      "key": "2024020413373708700_r13",
      "first-page": "378",
      "volume": "43",
      "year": "1978",
      "journal-title": "Phys. Rep."
    },
    {
      "key": "2024020413373708700_r14",
      "first-page": "6248",
      "volume": "33",
      "year": "1986",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024020413373708700_r14a",
      "doi-asserted-by": "crossref",
      "first-page": "37",
      "DOI": "10.1115/1.3119494",
      "volume": "44",
      "year": "1991",
      "journal-title": "Appl. Mech. Rev."
    },
    {
      "key": "2024020413373708700_r15",
      "first-page": "347",
      "volume": "164",
      "year": "1990",
      "journal-title": "Physica A"
    },
    {
      "key": "2024020413373708700_r16",
      "doi-asserted-by": "crossref",
      "first-page": "1053",
      "DOI": "10.1103/PhysRevA.27.1053",
      "volume": "27",
      "year": "1983",
      "journal-title": "Phys. Rev. A"
    }
  ],
  "container-title": "Journal of Applied Physics",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://pubs.aip.org/aip/jap/article-pdf/69/10/7118/18642955/7118_1_online.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "syndication"
    },
    {
      "URL": "https://pubs.aip.org/aip/jap/article-pdf/69/10/7118/18642955/7118_1_online.pdf",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2024,
        2,
        4
      ]
    ],
    "date-time": "2024-02-04T13:37:47Z",
    "timestamp": 1707053867000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://pubs.aip.org/jap/article/69/10/7118/19981/Improved-bounds-on-the-effective-conductivity-of"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1991,
        5,
        15
      ]
    ]
  },
  "references-count": 20,
  "journal-issue": {
    "issue": "10",
    "published-print": {
      "date-parts": [
        [
          1991,
          5,
          15
        ]
      ]
    }
  },
  "URL": "http://dx.doi.org/10.1063/1.347600",
  "relation": {},
  "ISSN": [
    "0021-8979",
    "1089-7550"
  ],
  "subject": [],
  "published-other": {
    "date-parts": [
      [
        1991,
        5,
        15
      ]
    ]
  },
  "published": {
    "date-parts": [
      [
        1991,
        5,
        15
      ]
    ]
  }
}