{"id":"https://openalex.org/W2071265840","doi":"https://doi.org/10.1137/120870220","title":"Symmetries of 2-Lattices and Second Order Accuracy of the Cauchy--Born Model","display_name":"Symmetries of 2-Lattices and Second Order Accuracy of the Cauchy--Born Model","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2071265840","doi":"https://doi.org/10.1137/120870220","mag":"2071265840"},"language":"en","primary_location":{"id":"doi:10.1137/120870220","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120870220","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Multiscale Modeling &amp; Simulation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057688610","display_name":"Brian Van Koten","orcid":"https://orcid.org/0000-0002-0225-7550"},"institutions":[{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]},{"id":"https://openalex.org/I4210102534","display_name":"St. Vincent Hospital","ror":"https://ror.org/00rjw0467","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I4210102534"]}],"countries":["GB","US"],"is_corresponding":true,"raw_author_name":"Brian Van Koten","raw_affiliation_strings":["127 Vincent Hall, 206 Church St. SE, Minneapolis, MN 55455, USA","Mathematics Institute, Zeeman Building, University of Warwick, Coventry CV4 7AL, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"127 Vincent Hall, 206 Church St. SE, Minneapolis, MN 55455, USA","institution_ids":["https://openalex.org/I4210102534"]},{"raw_affiliation_string":"Mathematics Institute, Zeeman Building, University of Warwick, Coventry CV4 7AL, UK","institution_ids":["https://openalex.org/I39555362"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061841111","display_name":"Christoph Ortner","orcid":"https://orcid.org/0000-0003-1498-8120"},"institutions":[{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]},{"id":"https://openalex.org/I4210102534","display_name":"St. Vincent Hospital","ror":"https://ror.org/00rjw0467","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I4210102534"]}],"countries":["GB","US"],"is_corresponding":false,"raw_author_name":"Christoph Ortner","raw_affiliation_strings":["127 Vincent Hall, 206 Church St. SE, Minneapolis, MN 55455, USA","Mathematics Institute, Zeeman Building, University of Warwick, Coventry CV4 7AL, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"127 Vincent Hall, 206 Church St. SE, Minneapolis, MN 55455, USA","institution_ids":["https://openalex.org/I4210102534"]},{"raw_affiliation_string":"Mathematics Institute, Zeeman Building, University of Warwick, Coventry CV4 7AL, UK","institution_ids":["https://openalex.org/I39555362"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5057688610"],"corresponding_institution_ids":["https://openalex.org/I39555362","https://openalex.org/I4210102534"],"apc_list":null,"apc_paid":null,"fwci":0.1386,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.46600402,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"11","issue":"2","first_page":"615","last_page":"634"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11646","display_name":"Nonlocal and gradient elasticity in micro/nano structures","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11646","display_name":"Nonlocal and gradient elasticity in micro/nano structures","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11366","display_name":"Elasticity and Material Modeling","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11565","display_name":"Thermoelastic and Magnetoelastic Phenomena","score":0.9932000041007996,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bravais-lattice","display_name":"Bravais lattice","score":0.8779560327529907},{"id":"https://openalex.org/keywords/cauchy-distribution","display_name":"Cauchy distribution","score":0.7583411335945129},{"id":"https://openalex.org/keywords/homogeneous-space","display_name":"Homogeneous space","score":0.6623751521110535},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5052371621131897},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.49704793095588684},{"id":"https://openalex.org/keywords/theoretical-physics","display_name":"Theoretical physics","score":0.49601373076438904},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4257379174232483},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4182058572769165},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35906583070755005},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29462945461273193},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.22497498989105225},{"id":"https://openalex.org/keywords/crystal-structure","display_name":"Crystal structure","score":0.17525488138198853},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.10780638456344604},{"id":"https://openalex.org/keywords/crystallography","display_name":"Crystallography","score":0.10257688164710999}],"concepts":[{"id":"https://openalex.org/C203833618","wikidata":"https://www.wikidata.org/wiki/Q865788","display_name":"Bravais lattice","level":3,"score":0.8779560327529907},{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.7583411335945129},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.6623751521110535},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5052371621131897},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.49704793095588684},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.49601373076438904},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4257379174232483},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4182058572769165},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35906583070755005},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29462945461273193},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.22497498989105225},{"id":"https://openalex.org/C115624301","wikidata":"https://www.wikidata.org/wiki/Q895901","display_name":"Crystal structure","level":2,"score":0.17525488138198853},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.10780638456344604},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.10257688164710999},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/120870220","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120870220","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Multiscale Modeling &amp; Simulation","raw_type":"journal-article"},{"id":"pmh:oai:wrap.warwick.ac.uk:59236","is_oa":false,"landing_page_url":"http://wrap.warwick.ac.uk/59236/1/WRAP_2012-MMS-multi1.pdf","pdf_url":"http://wrap.warwick.ac.uk/59236/1/WRAP_2012-MMS-multi1.pdf","source":{"id":"https://openalex.org/S4306400665","display_name":"Warwick Research Archive Portal (University of Warwick)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39555362","host_organization_name":"University of Warwick","host_organization_lineage":["https://openalex.org/I39555362"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.8700000047683716}],"awards":[{"id":"https://openalex.org/G7165973225","display_name":null,"funder_award_id":"EP/H003096/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1965730134","https://openalex.org/W1971576921","https://openalex.org/W1979119351","https://openalex.org/W1984921537","https://openalex.org/W1986456294","https://openalex.org/W1990668712","https://openalex.org/W1997397055","https://openalex.org/W2002012489","https://openalex.org/W2017430744","https://openalex.org/W2023616054","https://openalex.org/W2032969394","https://openalex.org/W2040028577","https://openalex.org/W2079404534","https://openalex.org/W2088805075","https://openalex.org/W2092260144","https://openalex.org/W2122074696","https://openalex.org/W2144344472","https://openalex.org/W2147415793","https://openalex.org/W2152156571","https://openalex.org/W2398055650","https://openalex.org/W2770485442","https://openalex.org/W2962942108"],"related_works":["https://openalex.org/W2580115906","https://openalex.org/W2520410766","https://openalex.org/W2002419800","https://openalex.org/W2106720105","https://openalex.org/W2990020684","https://openalex.org/W2625112437","https://openalex.org/W2122074696","https://openalex.org/W2071265840","https://openalex.org/W2950937195","https://openalex.org/W4297908771"],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2,63],"the":[3,14,33],"Cauchy--Born":[4],"model":[5],"of":[6,32,36],"a":[7,22,28,51],"single-species":[8],"2-lattice":[9],"is":[10,64],"second":[11,66],"order":[12,67],"if":[13],"atomistic":[15],"and":[16,80,91],"continuum":[17,78],"kinematics":[18],"are":[19],"connected":[20],"in":[21,44],"novel":[23],"way.":[24],"Our":[25],"proof":[26],"uses":[27],"generalization":[29],"to":[30,74],"2-lattices":[31],"point":[34],"symmetry":[35],"Bravais":[37],"lattices.":[38],"Moreover,":[39],"by":[40],"identifying":[41],"similar":[42],"symmetries":[43],"multispecies":[45],"pair":[46],"interaction":[47],"models,":[48],"we":[49],"construct":[50],"new":[52],"stored":[53],"energy":[54],"density,":[55],"using":[56],"shift":[57],"gradients":[58],"but":[59],"not":[60],"strain":[61],"gradients,":[62],"also":[65],"accurate.":[68],"These":[69],"results":[70],"can":[71],"be":[72],"used":[73],"develop":[75],"highly":[76],"accurate":[77],"models":[79],"atomistic/continuum":[81],"coupling":[82],"methods":[83],"for":[84],"materials":[85],"such":[86],"as":[87],"graphene,":[88],"hcp":[89],"metals,":[90],"shape":[92],"memory":[93],"alloys.":[94]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-11T07:18:39.950985","created_date":"2025-10-10T00:00:00"}
