Asymptotic Expansion of the Elastic Far-Field of a Crystalline Defect View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2022-07-22

AUTHORS

Julian Braun, Thomas Hudson, Christoph Ortner

ABSTRACT

Lattice defects in crystalline materials create long-range elastic fields which can be modelled on the atomistic scale using an infinite system of discrete nonlinear force balance equations. Starting with these equations, this work rigorously derives a novel far-field expansion of these fields. The expansion is computable and is expressed as a sum of continuum correctors and discrete multipole terms which decay with increasing algebraic rate as the order of the expansion increases. Truncating the expansion leaves a remainder describing the defect core structure, which is localised in the sense that it decays with an algebraic rate corresponding to the order at which the truncation occurred. More... »

PAGES

1437-1490

References to SciGraph publications

  • 2016-09-28. Existence and convergence of solutions of the boundary value problem in atomistic and continuum nonlinear elasticity theory in CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
  • 2020-09-15. Thermodynamic Limit of the Transition Rate of a Crystalline Defect in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 1966. Multiple Integrals in the Calculus of Variations in NONE
  • 2016-06-22. Analysis of Boundary Conditions for Crystal Defect Atomistic Simulations in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 2006-09-13. Cauchy–Born Rule and the Stability of Crystalline Solids: Static Problems in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00205-022-01810-3

    DOI

    http://dx.doi.org/10.1007/s00205-022-01810-3

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1149653059


    Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
    Incoming Citations Browse incoming citations for this publication using opencitations.net

    JSON-LD is the canonical representation for SciGraph data.

    TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

    [
      {
        "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
        "about": [
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Mathematical Sciences", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Pure Mathematics", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Department of Mathematics, Heriot-Watt University, EH14 4AS, Edinburgh, UK", 
              "id": "http://www.grid.ac/institutes/grid.9531.e", 
              "name": [
                "Department of Mathematics, Heriot-Watt University, EH14 4AS, Edinburgh, UK"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Braun", 
            "givenName": "Julian", 
            "id": "sg:person.013262144421.35", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013262144421.35"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Mathematics Institute, University of Warwick, CV4 7AL, Coventry, UK", 
              "id": "http://www.grid.ac/institutes/grid.7372.1", 
              "name": [
                "Mathematics Institute, University of Warwick, CV4 7AL, Coventry, UK"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Hudson", 
            "givenName": "Thomas", 
            "id": "sg:person.011106364171.68", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011106364171.68"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Department of Mathematics, University of British Columbia, 1984 Mathematics Road, V6T 1Z2, Vancouver, BC, Canada", 
              "id": "http://www.grid.ac/institutes/grid.17091.3e", 
              "name": [
                "Department of Mathematics, University of British Columbia, 1984 Mathematics Road, V6T 1Z2, Vancouver, BC, Canada"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Ortner", 
            "givenName": "Christoph", 
            "id": "sg:person.0605542270.52", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0605542270.52"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/s00205-020-01568-6", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1130863389", 
              "https://doi.org/10.1007/s00205-020-01568-6"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00205-016-1019-6", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1010292279", 
              "https://doi.org/10.1007/s00205-016-1019-6"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00205-006-0031-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1046362835", 
              "https://doi.org/10.1007/s00205-006-0031-7"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00526-016-1048-x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1026345878", 
              "https://doi.org/10.1007/s00526-016-1048-x"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-540-69952-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1043166905", 
              "https://doi.org/10.1007/978-3-540-69952-1"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2022-07-22", 
        "datePublishedReg": "2022-07-22", 
        "description": "Lattice defects in crystalline materials create long-range elastic fields which can be modelled on the atomistic scale using an infinite system of discrete nonlinear force balance equations. Starting with these equations, this work rigorously derives a novel far-field expansion of these fields. The expansion is computable and is expressed as a sum of continuum correctors and discrete multipole terms which decay with increasing algebraic rate as the order of the expansion increases. Truncating the expansion leaves a remainder describing the defect core structure, which is localised in the sense that it decays with an algebraic rate corresponding to the order at which the truncation occurred.", 
        "genre": "article", 
        "id": "sg:pub.10.1007/s00205-022-01810-3", 
        "isAccessibleForFree": true, 
        "isFundedItemOf": [
          {
            "id": "sg:grant.7611592", 
            "type": "MonetaryGrant"
          }
        ], 
        "isPartOf": [
          {
            "id": "sg:journal.1047617", 
            "issn": [
              "0003-9527", 
              "1432-0673"
            ], 
            "name": "Archive for Rational Mechanics and Analysis", 
            "publisher": "Springer Nature", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "3", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "245"
          }
        ], 
        "keywords": [
          "algebraic rate", 
          "force balance equation", 
          "defect core structures", 
          "far-field expansion", 
          "long-range elastic fields", 
          "infinite system", 
          "asymptotic expansion", 
          "balance equations", 
          "multipole terms", 
          "elastic fields", 
          "far field", 
          "equations", 
          "lattice defects", 
          "atomistic scale", 
          "expansion increases", 
          "field", 
          "expansion", 
          "corrector", 
          "sum", 
          "truncation", 
          "crystalline defects", 
          "crystalline materials", 
          "order", 
          "core structure", 
          "terms", 
          "sense", 
          "system", 
          "structure", 
          "work", 
          "scale", 
          "defects", 
          "materials", 
          "rate", 
          "remainder", 
          "increase"
        ], 
        "name": "Asymptotic Expansion of the Elastic Far-Field of a Crystalline Defect", 
        "pagination": "1437-1490", 
        "productId": [
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1149653059"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/s00205-022-01810-3"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/s00205-022-01810-3", 
          "https://app.dimensions.ai/details/publication/pub.1149653059"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2022-11-24T21:08", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-springernature-scigraph/baseset/20221124/entities/gbq_results/article/article_927.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://doi.org/10.1007/s00205-022-01810-3"
      }
    ]
     

    Download the RDF metadata as:  json-ld nt turtle xml License info

    HOW TO GET THIS DATA PROGRAMMATICALLY:

    JSON-LD is a popular format for linked data which is fully compatible with JSON.

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s00205-022-01810-3'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s00205-022-01810-3'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s00205-022-01810-3'

    RDF/XML is a standard XML format for linked data.

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s00205-022-01810-3'


     

    This table displays all metadata directly associated to this object as RDF triples.

    134 TRIPLES      21 PREDICATES      64 URIs      51 LITERALS      6 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s00205-022-01810-3 schema:about anzsrc-for:01
    2 anzsrc-for:0101
    3 schema:author Ne19412459a6247ef8d08cc9d2b42184e
    4 schema:citation sg:pub.10.1007/978-3-540-69952-1
    5 sg:pub.10.1007/s00205-006-0031-7
    6 sg:pub.10.1007/s00205-016-1019-6
    7 sg:pub.10.1007/s00205-020-01568-6
    8 sg:pub.10.1007/s00526-016-1048-x
    9 schema:datePublished 2022-07-22
    10 schema:datePublishedReg 2022-07-22
    11 schema:description Lattice defects in crystalline materials create long-range elastic fields which can be modelled on the atomistic scale using an infinite system of discrete nonlinear force balance equations. Starting with these equations, this work rigorously derives a novel far-field expansion of these fields. The expansion is computable and is expressed as a sum of continuum correctors and discrete multipole terms which decay with increasing algebraic rate as the order of the expansion increases. Truncating the expansion leaves a remainder describing the defect core structure, which is localised in the sense that it decays with an algebraic rate corresponding to the order at which the truncation occurred.
    12 schema:genre article
    13 schema:isAccessibleForFree true
    14 schema:isPartOf N2e148203ac7243688d3edd2344197add
    15 N8af6a6f00ac74382b7e8d451b95d835b
    16 sg:journal.1047617
    17 schema:keywords algebraic rate
    18 asymptotic expansion
    19 atomistic scale
    20 balance equations
    21 core structure
    22 corrector
    23 crystalline defects
    24 crystalline materials
    25 defect core structures
    26 defects
    27 elastic fields
    28 equations
    29 expansion
    30 expansion increases
    31 far field
    32 far-field expansion
    33 field
    34 force balance equation
    35 increase
    36 infinite system
    37 lattice defects
    38 long-range elastic fields
    39 materials
    40 multipole terms
    41 order
    42 rate
    43 remainder
    44 scale
    45 sense
    46 structure
    47 sum
    48 system
    49 terms
    50 truncation
    51 work
    52 schema:name Asymptotic Expansion of the Elastic Far-Field of a Crystalline Defect
    53 schema:pagination 1437-1490
    54 schema:productId N146192b28c2a40d8b08223c4d7ef1353
    55 N723ac6e00fe14d7590e047f269bc27ff
    56 schema:sameAs https://app.dimensions.ai/details/publication/pub.1149653059
    57 https://doi.org/10.1007/s00205-022-01810-3
    58 schema:sdDatePublished 2022-11-24T21:08
    59 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    60 schema:sdPublisher N9091dcd96ea048a4b7f0ee9e7c6552e1
    61 schema:url https://doi.org/10.1007/s00205-022-01810-3
    62 sgo:license sg:explorer/license/
    63 sgo:sdDataset articles
    64 rdf:type schema:ScholarlyArticle
    65 N146192b28c2a40d8b08223c4d7ef1353 schema:name dimensions_id
    66 schema:value pub.1149653059
    67 rdf:type schema:PropertyValue
    68 N2e148203ac7243688d3edd2344197add schema:issueNumber 3
    69 rdf:type schema:PublicationIssue
    70 N723ac6e00fe14d7590e047f269bc27ff schema:name doi
    71 schema:value 10.1007/s00205-022-01810-3
    72 rdf:type schema:PropertyValue
    73 N8af6a6f00ac74382b7e8d451b95d835b schema:volumeNumber 245
    74 rdf:type schema:PublicationVolume
    75 N9091dcd96ea048a4b7f0ee9e7c6552e1 schema:name Springer Nature - SN SciGraph project
    76 rdf:type schema:Organization
    77 Ne19412459a6247ef8d08cc9d2b42184e rdf:first sg:person.013262144421.35
    78 rdf:rest Nff682f7b4f904f3ea437c67fe9730831
    79 Nf616e8e7619e4675ae7bf564836b39c6 rdf:first sg:person.0605542270.52
    80 rdf:rest rdf:nil
    81 Nff682f7b4f904f3ea437c67fe9730831 rdf:first sg:person.011106364171.68
    82 rdf:rest Nf616e8e7619e4675ae7bf564836b39c6
    83 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    84 schema:name Mathematical Sciences
    85 rdf:type schema:DefinedTerm
    86 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
    87 schema:name Pure Mathematics
    88 rdf:type schema:DefinedTerm
    89 sg:grant.7611592 http://pending.schema.org/fundedItem sg:pub.10.1007/s00205-022-01810-3
    90 rdf:type schema:MonetaryGrant
    91 sg:journal.1047617 schema:issn 0003-9527
    92 1432-0673
    93 schema:name Archive for Rational Mechanics and Analysis
    94 schema:publisher Springer Nature
    95 rdf:type schema:Periodical
    96 sg:person.011106364171.68 schema:affiliation grid-institutes:grid.7372.1
    97 schema:familyName Hudson
    98 schema:givenName Thomas
    99 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011106364171.68
    100 rdf:type schema:Person
    101 sg:person.013262144421.35 schema:affiliation grid-institutes:grid.9531.e
    102 schema:familyName Braun
    103 schema:givenName Julian
    104 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013262144421.35
    105 rdf:type schema:Person
    106 sg:person.0605542270.52 schema:affiliation grid-institutes:grid.17091.3e
    107 schema:familyName Ortner
    108 schema:givenName Christoph
    109 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0605542270.52
    110 rdf:type schema:Person
    111 sg:pub.10.1007/978-3-540-69952-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1043166905
    112 https://doi.org/10.1007/978-3-540-69952-1
    113 rdf:type schema:CreativeWork
    114 sg:pub.10.1007/s00205-006-0031-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1046362835
    115 https://doi.org/10.1007/s00205-006-0031-7
    116 rdf:type schema:CreativeWork
    117 sg:pub.10.1007/s00205-016-1019-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1010292279
    118 https://doi.org/10.1007/s00205-016-1019-6
    119 rdf:type schema:CreativeWork
    120 sg:pub.10.1007/s00205-020-01568-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1130863389
    121 https://doi.org/10.1007/s00205-020-01568-6
    122 rdf:type schema:CreativeWork
    123 sg:pub.10.1007/s00526-016-1048-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1026345878
    124 https://doi.org/10.1007/s00526-016-1048-x
    125 rdf:type schema:CreativeWork
    126 grid-institutes:grid.17091.3e schema:alternateName Department of Mathematics, University of British Columbia, 1984 Mathematics Road, V6T 1Z2, Vancouver, BC, Canada
    127 schema:name Department of Mathematics, University of British Columbia, 1984 Mathematics Road, V6T 1Z2, Vancouver, BC, Canada
    128 rdf:type schema:Organization
    129 grid-institutes:grid.7372.1 schema:alternateName Mathematics Institute, University of Warwick, CV4 7AL, Coventry, UK
    130 schema:name Mathematics Institute, University of Warwick, CV4 7AL, Coventry, UK
    131 rdf:type schema:Organization
    132 grid-institutes:grid.9531.e schema:alternateName Department of Mathematics, Heriot-Watt University, EH14 4AS, Edinburgh, UK
    133 schema:name Department of Mathematics, Heriot-Watt University, EH14 4AS, Edinburgh, UK
    134 rdf:type schema:Organization
     




    Preview window. Press ESC to close (or click here)


    ...