{"id":"https://openalex.org/W2031120510","doi":"https://doi.org/10.1137/120895354","title":"A $\\Gamma$-Convergence Analysis of the Quasicontinuum Method","display_name":"A $\\Gamma$-Convergence Analysis of the Quasicontinuum Method","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2031120510","doi":"https://doi.org/10.1137/120895354","mag":"2031120510"},"language":"en","primary_location":{"id":"doi:10.1137/120895354","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120895354","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 & Simulation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://authors.library.caltech.edu/42235/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006843608","display_name":"Malena I. Espa\u00f1ol","orcid":"https://orcid.org/0000-0002-9290-3228"},"institutions":[{"id":"https://openalex.org/I110152177","display_name":"University of Akron","ror":"https://ror.org/02kyckx55","country_code":"US","type":"education","lineage":["https://openalex.org/I110152177"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Malena I. Espan\u0342ol","raw_affiliation_strings":["#N#University of Akron#N#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"#N#University of Akron#N#","institution_ids":["https://openalex.org/I110152177"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083881460","display_name":"Dennis M. Kochmann","orcid":"https://orcid.org/0000-0002-9112-6615"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Dennis M. Kochmann","raw_affiliation_strings":["California  Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"California  Institute of Technology","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086193278","display_name":"Sergio Conti","orcid":"https://orcid.org/0000-0001-7987-9174"},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Sergio Conti","raw_affiliation_strings":["University of Bonn"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Bonn","institution_ids":["https://openalex.org/I135140700"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054661641","display_name":"M. Ort\u00edz","orcid":"https://orcid.org/0000-0001-5877-4824"},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Michael Ortiz","raw_affiliation_strings":["California  Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"California  Institute of Technology","institution_ids":["https://openalex.org/I122411786"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.5817,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.92403043,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"11","issue":"3","first_page":"766","last_page":"794"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6101883053779602},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.582775354385376},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5596010088920593},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5410794615745544},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.48073554039001465},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4359777569770813},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4088807702064514},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3979998826980591},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.30296435952186584}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6101883053779602},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.582775354385376},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5596010088920593},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5410794615745544},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.48073554039001465},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4359777569770813},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4088807702064514},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3979998826980591},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.30296435952186584},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/120895354","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120895354","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 & Simulation","raw_type":"journal-article"},{"id":"pmh:oai:authors.library.caltech.edu:42235","is_oa":true,"landing_page_url":"https://authors.library.caltech.edu/42235/","pdf_url":"https://authors.library.caltech.edu/42235/","source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:authors.library.caltech.edu:42235","is_oa":true,"landing_page_url":"https://authors.library.caltech.edu/42235/","pdf_url":"https://authors.library.caltech.edu/42235/","source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.800000011920929}],"awards":[{"id":"https://openalex.org/G7041476167","display_name":"PIRE: Science at the Triple Point Between Mathematics, Mechanics and Materials Science","funder_award_id":"0967140","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2031120510.pdf","grobid_xml":"https://content.openalex.org/works/W2031120510.grobid-xml"},"referenced_works_count":46,"referenced_works":["https://openalex.org/W1965730134","https://openalex.org/W1965849453","https://openalex.org/W1969593540","https://openalex.org/W1972531430","https://openalex.org/W1975613240","https://openalex.org/W1986409946","https://openalex.org/W1986456294","https://openalex.org/W1996930158","https://openalex.org/W1997397055","https://openalex.org/W2000407532","https://openalex.org/W2015939454","https://openalex.org/W2017915195","https://openalex.org/W2017929480","https://openalex.org/W2021602369","https://openalex.org/W2022364772","https://openalex.org/W2030430698","https://openalex.org/W2032457401","https://openalex.org/W2033086537","https://openalex.org/W2037782625","https://openalex.org/W2038896522","https://openalex.org/W2042069254","https://openalex.org/W2042435778","https://openalex.org/W2075811679","https://openalex.org/W2076762517","https://openalex.org/W2077070913","https://openalex.org/W2089501471","https://openalex.org/W2094562890","https://openalex.org/W2107321638","https://openalex.org/W2110088713","https://openalex.org/W2110385014","https://openalex.org/W2118485994","https://openalex.org/W2120209442","https://openalex.org/W2122074696","https://openalex.org/W2125473452","https://openalex.org/W2127777830","https://openalex.org/W2131651508","https://openalex.org/W2136043508","https://openalex.org/W2137238625","https://openalex.org/W2146691861","https://openalex.org/W2161329428","https://openalex.org/W2161980787","https://openalex.org/W2165306490","https://openalex.org/W2167899745","https://openalex.org/W2167953790","https://openalex.org/W2985218554","https://openalex.org/W3102769863"],"related_works":["https://openalex.org/W2127887854","https://openalex.org/W15730607","https://openalex.org/W2072997652","https://openalex.org/W2153822684","https://openalex.org/W4237154648","https://openalex.org/W2008259798","https://openalex.org/W2331934617","https://openalex.org/W3041459233","https://openalex.org/W1987597427","https://openalex.org/W2620661725"],"abstract_inverted_index":{"We":[0,99,151],"present":[1],"a":[2,23,111,135,141],"$\\Gamma$-convergence":[3],"analysis":[4,29],"of":[5,13,22,35,39,77,96,144,148,155,162,165],"the":[6,11,14,19,40,42,49,63,72,78,94,97,122,129,146,153,156],"quasicontinuum":[7,79,149],"method":[8],"focused":[9],"on":[10],"behavior":[12],"approximate":[15,121],"energy":[16,80],"functionals":[17,81],"in":[18,56,89],"continuum":[20,43,130],"limit":[21,44],"harmonic":[24],"and":[25,37,60],"defect-free":[26],"crystal.":[27],"The":[28,75],"shows":[30],"that,":[31,106],"under":[32,102],"general":[33,104],"conditions":[34,105],"stability":[36],"boundedness":[38],"energy,":[41],"is":[45,82],"attained":[46],"provided":[47,61],"that":[48,62,119,139],"continuum---e.g.,":[50],"finite-element---approximation":[51],"spaces":[52],"are":[53],"strongly":[54],"dense":[55],"an":[57],"appropriate":[58],"topology":[59],"lattice":[64],"size":[65],"converges":[66],"to":[67],"zero":[68],"more":[69],"rapidly":[70],"than":[71],"mesh":[73],"size.":[74],"equicoercivity":[76],"likewise":[83],"established":[84],"with":[85,91],"broad":[86],"generality,":[87],"which,":[88],"conjunction":[90],"$\\Gamma$-convergence,":[92],"ensures":[93],"convergence":[95,147],"minimizers.":[98],"also":[100],"show":[101],"rather":[103],"for":[107],"interatomic":[108],"energies":[109,125],"having":[110],"clusterwise":[112],"additive":[113],"structure,":[114],"summation":[115],"or":[116],"quadrature":[117],"rules":[118],"suitably":[120],"local":[123],"element":[124],"do":[126],"not":[127],"affect":[128],"limit.":[131],"Finally,":[132],"we":[133],"propose":[134],"discrete":[136,157],"patch":[137,158],"test":[138,159],"provides":[140],"practical":[142],"means":[143,161],"assessing":[145],"approximations.":[150],"demonstrate":[152],"utility":[154],"by":[160],"selected":[163],"examples":[164],"application.":[166]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-08-18T07:49:30.821534","created_date":"2016-06-24T00:00:00"}