{"id":"https://openalex.org/W1987603782","doi":"https://doi.org/10.1137/070688559","title":"Error Estimation and Atomistic-Continuum Adaptivity for the Quasicontinuum Approximation of a Frenkel\u2013Kontorova Model","display_name":"Error Estimation and Atomistic-Continuum Adaptivity for the Quasicontinuum Approximation of a Frenkel\u2013Kontorova Model","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W1987603782","doi":"https://doi.org/10.1137/070688559","mag":"1987603782"},"language":"en","primary_location":{"id":"doi:10.1137/070688559","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070688559","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/A5010342270","display_name":"Marcel Arndt","orcid":null},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]},{"id":"https://openalex.org/I4210101327","display_name":"Twin Cities Orthopedics","ror":"https://ror.org/01en4s460","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I4210101327"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Marcel Arndt","raw_affiliation_strings":["University of Minnesota Twin Cities"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Minnesota Twin Cities","institution_ids":["https://openalex.org/I4210101327","https://openalex.org/I130238516"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036018970","display_name":"Mitchell Luskin","orcid":"https://orcid.org/0000-0003-1981-199X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mitchell Luskin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.3776,"has_fulltext":false,"cited_by_count":46,"citation_normalized_percentile":{"value":0.95246479,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"7","issue":"1","first_page":"147","last_page":"170"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10204","display_name":"Microstructure and mechanical properties","score":0.9998000264167786,"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/T10204","display_name":"Microstructure and mechanical properties","score":0.9998000264167786,"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/T11646","display_name":"Nonlocal and gradient elasticity in micro/nano structures","score":0.9930999875068665,"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/T12613","display_name":"X-ray Diffraction in Crystallography","score":0.9926999807357788,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.8227211236953735},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.7439495921134949},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.6319335103034973},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5468147397041321},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47589099407196045},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.454444020986557},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4348889887332916},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3263787627220154},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2702399790287018},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.06265279650688171}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.8227211236953735},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.7439495921134949},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.6319335103034973},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5468147397041321},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47589099407196045},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.454444020986557},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4348889887332916},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3263787627220154},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2702399790287018},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.06265279650688171},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/070688559","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070688559","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1579665999","https://openalex.org/W1971576921","https://openalex.org/W1975613240","https://openalex.org/W1980235468","https://openalex.org/W1986409946","https://openalex.org/W1995404822","https://openalex.org/W1997397055","https://openalex.org/W2017430744","https://openalex.org/W2033086537","https://openalex.org/W2042069254","https://openalex.org/W2046231727","https://openalex.org/W2063487813","https://openalex.org/W2067511555","https://openalex.org/W2094562890","https://openalex.org/W2094960154","https://openalex.org/W2095270108","https://openalex.org/W2104034321","https://openalex.org/W2114291880","https://openalex.org/W2136043508","https://openalex.org/W2164408705","https://openalex.org/W2182308808","https://openalex.org/W2206315619","https://openalex.org/W2487440882","https://openalex.org/W2952848444","https://openalex.org/W2992726982","https://openalex.org/W3100526783","https://openalex.org/W4296944107"],"related_works":["https://openalex.org/W2808231882","https://openalex.org/W4318824563","https://openalex.org/W2311985367","https://openalex.org/W2953763369","https://openalex.org/W2097626286","https://openalex.org/W2079924178","https://openalex.org/W1495993365","https://openalex.org/W2742518869","https://openalex.org/W1984379032","https://openalex.org/W41161438"],"abstract_inverted_index":{"We":[0,47],"propose":[1],"and":[2,33,66,87],"analyze":[3],"a":[4,6,38,44,58,63,100,104],"goal-oriented":[5],"posteriori":[7],"error":[8,14,22,86],"estimator":[9],"for":[10],"the":[11,16,31,49,52,55,68,85,94],"atomistic-continuum":[12,90],"modeling":[13],"in":[15],"quasicontinuum":[17],"method.":[18],"Based":[19],"on":[20],"this":[21],"estimator,":[23],"we":[24],"develop":[25],"an":[26,81],"algorithm":[27,50,92],"which":[28],"adaptively":[29],"determines":[30],"atomistic":[32,107],"continuum":[34],"regions":[35],"to":[36,42,51,98],"compute":[37],"quantity":[39,95],"of":[40,54,57,70,84,96],"interest":[41,97],"within":[43,99],"given":[45,101],"tolerance.":[46],"apply":[48],"computation":[53],"structure":[56],"crystallographic":[59],"defect":[60],"described":[61],"by":[62],"Frenkel\u2013Kontorova":[64],"model":[65],"present":[67],"results":[69,75],"numerical":[71,74],"experiments.":[72],"The":[73],"show":[76],"that":[77,88],"our":[78,89],"method":[79],"gives":[80],"efficient":[82],"estimate":[83],"adaptivity":[91],"computes":[93],"tolerance":[102],"with":[103],"nearly":[105],"minimal":[106],"region.":[108]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
