DOI: 10.1119/1.1842734. Diffusion in a half-space: From Lord Kelvin to path integrals

Diffusion in a half-space: From Lord Kelvin to path integrals

10.1119/1.1842734

Crossref journal-article

American Association of Physics Teachers (AAPT)

American Journal of Physics (3)

Abstract

Many important transport phenomena are described by simple mathematical models rooted in the diffusion equation. Geometrical constraints present in such phenomena often have a global influence and manifest themselves in scaling relations and stable distribution functions. I treat a random walk confined to a half-space using several approaches: diffusion equations, lattice walks, and path integrals. Potential generalizations are discussed.

Bibliography

Slutsky, M. (2005). Diffusion in a half-space: From Lord Kelvin to path integrals. American Journal of Physics, 73(4), 308â314.

Authors 1

Michael Slutsky (first)

References 23 Referenced 19

{'key': '2023071300203518000_r1'}
10.1016/0370-1573(94)00087-J / Phys. Rep. / Kinetic roughening, stochastic growth, directed polymers and all that (1995)
10.1016/S0378-4371(02)01035-X / Physica A / Nonequilibrium dynamics in low-dimensional systems (2002)
10.1016/S0370-1573(00)00070-3 / Phys. Rep. / The random walk’s guide to anomalous diffusion: A fractional dynamics approach (2000)
{'key': '2023071300203518000_r5'}
{'key': '2023071300203518000_r6'}
{'key': '2023071300203518000_r7'}
{'key': '2023071300203518000_r8', 'first-page': '279', 'article-title': 'Synthetical solutions in the conduction of heat', 'volume': '19', 'year': '1887', 'journal-title': 'Proc. London Math. Soc.'} / Proc. London Math. Soc. / Synthetical solutions in the conduction of heat (1887)
{'key': '2023071300203518000_r9'}
{'key': '2023071300203518000_r10'}
{'key': '2023071300203518000_r11'}
{'key': '2023071300203518000_r12'}
{'key': '2023071300203518000_r13'}
{'key': '2023071300203518000_r14'}
10.1103/RevModPhys.15.1 / Rev. Mod. Phys. / Stochastic problems in physics and astronomy (1943)
10.1063/1.1696251 / J. Chem. Phys. / Proper accounting of conformations of a polymer near a surface (1965)
{'key': '2023071300203518000_r17'}
10.1103/RevModPhys.65.87 / Rev. Mod. Phys. / Surface phase-transitions in polymer systems (1993)
{'key': '2023071300203518000_r19'}
{'key': '2023071300203518000_r20'}
{'key': '2023071300203518000_r21'}
10.1021/ma00162a018 / Macromolecules / Test of renormalization-group crossover dependence—comparison with exact solution for a polymer attached to a penetrable interacting hypersurface (1986)
10.1021/ma00161a043 / Macromolecules / Polymer–polymer and polymer–surface excluded volume effects in flexible polymers attached to an interface—comparison of renormalization-group calculations with Monte Carlo and direct enumeration data (1986)

Dates

Type	When
Created	20 years, 5 months ago (March 14, 2005, 10:32 p.m.)
Deposited	2 years, 1 month ago (July 12, 2023, 8:32 p.m.)
Indexed	1 year, 1 month ago (Aug. 5, 2024, 10:40 p.m.)
Issued	20 years, 5 months ago (March 14, 2005)
Published	20 years, 5 months ago (March 14, 2005)
Published Online	20 years, 5 months ago (March 14, 2005)
Published Print	20 years, 5 months ago (April 1, 2005)

Funders 0

None

BibTeX

@article{Slutsky_2005, title={Diffusion in a half-space: From Lord Kelvin to path integrals}, volume={73}, ISSN={1943-2909}, url={http://dx.doi.org/10.1119/1.1842734}, DOI={10.1119/1.1842734}, number={4}, journal={American Journal of Physics}, publisher={American Association of Physics Teachers (AAPT)}, author={Slutsky, Michael}, year={2005}, month=mar, pages={308–314} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2024,
        8,
        6
      ]
    ],
    "date-time": "2024-08-06T02:40:17Z",
    "timestamp": 1722912017457
  },
  "reference-count": 23,
  "publisher": "American Association of Physics Teachers (AAPT)",
  "issue": "4",
  "content-domain": {
    "domain": [
      "pubs.aip.org"
    ],
    "crossmark-restriction": true
  },
  "published-print": {
    "date-parts": [
      [
        2005,
        4,
        1
      ]
    ]
  },
  "abstract": "<jats:p>Many important transport phenomena are described by simple mathematical models rooted in the diffusion equation. Geometrical constraints present in such phenomena often have a global influence and manifest themselves in scaling relations and stable distribution functions. I treat a random walk confined to a half-space using several approaches: diffusion equations, lattice walks, and path integrals. Potential generalizations are discussed.</jats:p>",
  "DOI": "10.1119/1.1842734",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2005,
        3,
        15
      ]
    ],
    "date-time": "2005-03-15T03:32:05Z",
    "timestamp": 1110857525000
  },
  "page": "308-314",
  "update-policy": "http://dx.doi.org/10.1063/aip-crossmark-policy-page",
  "source": "Crossref",
  "is-referenced-by-count": 19,
  "title": "Diffusion in a half-space: From Lord Kelvin to path integrals",
  "prefix": "10.1119",
  "volume": "73",
  "author": [
    {
      "given": "Michael",
      "family": "Slutsky",
      "sequence": "first",
      "affiliation": [
        {
          "name": "Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts\u200902139"
        }
      ]
    }
  ],
  "member": "3",
  "published-online": {
    "date-parts": [
      [
        2005,
        3,
        14
      ]
    ]
  },
  "reference": [
    {
      "key": "2023071300203518000_r1"
    },
    {
      "key": "2023071300203518000_r2",
      "doi-asserted-by": "crossref",
      "first-page": "215",
      "DOI": "10.1016/0370-1573(94)00087-J",
      "article-title": "Kinetic roughening, stochastic growth, directed polymers and all that",
      "volume": "254",
      "year": "1995",
      "journal-title": "Phys. Rep."
    },
    {
      "key": "2023071300203518000_r3",
      "doi-asserted-by": "crossref",
      "first-page": "110",
      "DOI": "10.1016/S0378-4371(02)01035-X",
      "article-title": "Nonequilibrium dynamics in low-dimensional systems",
      "volume": "313",
      "year": "2002",
      "journal-title": "Physica A"
    },
    {
      "key": "2023071300203518000_r4",
      "doi-asserted-by": "crossref",
      "first-page": "1",
      "DOI": "10.1016/S0370-1573(00)00070-3",
      "article-title": "The random walk\u2019s guide to anomalous diffusion: A fractional dynamics approach",
      "volume": "339",
      "year": "2000",
      "journal-title": "Phys. Rep."
    },
    {
      "key": "2023071300203518000_r5"
    },
    {
      "key": "2023071300203518000_r6"
    },
    {
      "key": "2023071300203518000_r7"
    },
    {
      "key": "2023071300203518000_r8",
      "first-page": "279",
      "article-title": "Synthetical solutions in the conduction of heat",
      "volume": "19",
      "year": "1887",
      "journal-title": "Proc. London Math. Soc."
    },
    {
      "key": "2023071300203518000_r9"
    },
    {
      "key": "2023071300203518000_r10"
    },
    {
      "key": "2023071300203518000_r11"
    },
    {
      "key": "2023071300203518000_r12"
    },
    {
      "key": "2023071300203518000_r13"
    },
    {
      "key": "2023071300203518000_r14"
    },
    {
      "key": "2023071300203518000_r15",
      "doi-asserted-by": "crossref",
      "first-page": "1",
      "DOI": "10.1103/RevModPhys.15.1",
      "article-title": "Stochastic problems in physics and astronomy",
      "volume": "15",
      "year": "1943",
      "journal-title": "Rev. Mod. Phys."
    },
    {
      "key": "2023071300203518000_r16",
      "doi-asserted-by": "crossref",
      "first-page": "2101",
      "DOI": "10.1063/1.1696251",
      "article-title": "Proper accounting of conformations of a polymer near a surface",
      "volume": "42",
      "year": "1965",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2023071300203518000_r17"
    },
    {
      "key": "2023071300203518000_r18",
      "doi-asserted-by": "crossref",
      "first-page": "87",
      "DOI": "10.1103/RevModPhys.65.87",
      "article-title": "Surface phase-transitions in polymer systems",
      "volume": "65",
      "year": "1993",
      "journal-title": "Rev. Mod. Phys."
    },
    {
      "key": "2023071300203518000_r19"
    },
    {
      "key": "2023071300203518000_r20"
    },
    {
      "key": "2023071300203518000_r21"
    },
    {
      "key": "2023071300203518000_r22",
      "doi-asserted-by": "crossref",
      "first-page": "2207",
      "DOI": "10.1021/ma00162a018",
      "article-title": "Test of renormalization-group crossover dependence\u2014comparison with exact solution for a polymer attached to a penetrable interacting hypersurface",
      "volume": "19",
      "year": "1986",
      "journal-title": "Macromolecules"
    },
    {
      "key": "2023071300203518000_r23",
      "doi-asserted-by": "crossref",
      "first-page": "2041",
      "DOI": "10.1021/ma00161a043",
      "article-title": "Polymer\u2013polymer and polymer\u2013surface excluded volume effects in flexible polymers attached to an interface\u2014comparison of renormalization-group calculations with Monte Carlo and direct enumeration data",
      "volume": "19",
      "year": "1986",
      "journal-title": "Macromolecules"
    }
  ],
  "container-title": "American Journal of Physics",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://pubs.aip.org/aapt/ajp/article-pdf/73/4/308/7521588/308_1_online.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "syndication"
    },
    {
      "URL": "https://pubs.aip.org/aapt/ajp/article-pdf/73/4/308/7521588/308_1_online.pdf",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2023,
        7,
        13
      ]
    ],
    "date-time": "2023-07-13T00:32:15Z",
    "timestamp": 1689208335000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://pubs.aip.org/ajp/article/73/4/308/529415/Diffusion-in-a-half-space-From-Lord-Kelvin-to-path"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        2005,
        3,
        14
      ]
    ]
  },
  "references-count": 23,
  "journal-issue": {
    "issue": "4",
    "published-online": {
      "date-parts": [
        [
          2005,
          3,
          14
        ]
      ]
    },
    "published-print": {
      "date-parts": [
        [
          2005,
          4,
          1
        ]
      ]
    }
  },
  "URL": "http://dx.doi.org/10.1119/1.1842734",
  "relation": {},
  "ISSN": [
    "0002-9505",
    "1943-2909"
  ],
  "subject": [],
  "published-other": {
    "date-parts": [
      [
        2005,
        4
      ]
    ]
  },
  "published": {
    "date-parts": [
      [
        2005,
        3,
        14
      ]
    ]
  }
}