{"id":"https://openalex.org/W2026851369","doi":"https://doi.org/10.1137/100806242","title":"Analysis of the Quasi-Nonlocal Approximation of Linear and Circular Chains in the Plane","display_name":"Analysis of the Quasi-Nonlocal Approximation of Linear and Circular Chains in the Plane","publication_year":2011,"publication_date":"2011-10-01","ids":{"openalex":"https://openalex.org/W2026851369","doi":"https://doi.org/10.1137/100806242","mag":"2026851369"},"language":"en","primary_location":{"id":"doi:10.1137/100806242","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100806242","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/A5054206901","display_name":"Pavel B\u011bl\u0131\u0301k","orcid":"https://orcid.org/0000-0001-8455-4913"},"institutions":[{"id":"https://openalex.org/I119916105","display_name":"Augsburg University","ror":"https://ror.org/057ewhh68","country_code":"US","type":"education","lineage":["https://openalex.org/I119916105"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Pavel B\u011bl\u00edk","raw_affiliation_strings":["Augsburg College"],"affiliations":[{"raw_affiliation_string":"Augsburg College","institution_ids":["https://openalex.org/I119916105"]}]},{"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":true,"raw_author_name":"Mitchell Luskin","raw_affiliation_strings":["Pavel B\u011bl\u00edk, Mathematics Department, Augsburg College, 2211 Riverside Avenue, Minneapolis, MN 55454, U.S.A","School of Mathematics, University of Minnesota, 206 Church Street SE, Minneapolis, MN 55455, U.S.A"],"affiliations":[{"raw_affiliation_string":"Pavel B\u011bl\u00edk, Mathematics Department, Augsburg College, 2211 Riverside Avenue, Minneapolis, MN 55454, U.S.A","institution_ids":[]},{"raw_affiliation_string":"School of Mathematics, University of Minnesota, 206 Church Street SE, Minneapolis, MN 55455, U.S.A","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5036018970"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10083262,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"9","issue":"4","first_page":"1495","last_page":"1527"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10204","display_name":"Microstructure and mechanical properties","score":0.9997000098228455,"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":0.9997000098228455,"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/T13531","display_name":"Surface and Thin Film Phenomena","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10923","display_name":"Force Microscopy Techniques and Applications","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cauchy-distribution","display_name":"Cauchy distribution","score":0.722718358039856},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.6623561382293701},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.5116724967956543},{"id":"https://openalex.org/keywords/k-nearest-neighbors-algorithm","display_name":"k-nearest neighbors algorithm","score":0.5076602697372437},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.41390857100486755},{"id":"https://openalex.org/keywords/isotropy","display_name":"Isotropy","score":0.41216713190078735},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.371089905500412},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.36650800704956055},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.2042524516582489}],"concepts":[{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.722718358039856},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.6623561382293701},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5116724967956543},{"id":"https://openalex.org/C113238511","wikidata":"https://www.wikidata.org/wiki/Q1071612","display_name":"k-nearest neighbors algorithm","level":2,"score":0.5076602697372437},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.41390857100486755},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.41216713190078735},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.371089905500412},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36650800704956055},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.2042524516582489},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/100806242","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100806242","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:CiteSeerX.psu:10.1.1.739.8922","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.739.8922","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1008.3716.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","score":0.7200000286102295,"display_name":"Affordable and clean energy"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320309636","display_name":"University of Minnesota","ror":"https://ror.org/03grvy078"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W280536263","https://openalex.org/W1569094508","https://openalex.org/W1581294843","https://openalex.org/W1969593540","https://openalex.org/W1983694495","https://openalex.org/W1983729994","https://openalex.org/W1986409946","https://openalex.org/W1997397055","https://openalex.org/W2002012489","https://openalex.org/W2017430744","https://openalex.org/W2017929480","https://openalex.org/W2025516805","https://openalex.org/W2030430698","https://openalex.org/W2037663519","https://openalex.org/W2042069254","https://openalex.org/W2057604359","https://openalex.org/W2062682443","https://openalex.org/W2063487813","https://openalex.org/W2088805075","https://openalex.org/W2094960154","https://openalex.org/W2104034321","https://openalex.org/W2114291880","https://openalex.org/W2146691861","https://openalex.org/W2147415793","https://openalex.org/W2148059712","https://openalex.org/W2152973912","https://openalex.org/W2164408705","https://openalex.org/W2164629300","https://openalex.org/W2165306490","https://openalex.org/W2618075460","https://openalex.org/W2770485442","https://openalex.org/W2963015481","https://openalex.org/W3098399558","https://openalex.org/W3179033439","https://openalex.org/W4247073029","https://openalex.org/W4296944107"],"related_works":["https://openalex.org/W2794789911","https://openalex.org/W4298134547","https://openalex.org/W2122976425","https://openalex.org/W2088773039","https://openalex.org/W2284229495","https://openalex.org/W2028697747","https://openalex.org/W4382753160","https://openalex.org/W4320084277","https://openalex.org/W166835080","https://openalex.org/W1971695127"],"abstract_inverted_index":{"We":[0,37,119,161],"give":[1,179],"an":[2,180,201],"analysis":[3,190],"of":[4,70,86,103,124,140,157,194],"the":[5,17,20,26,32,60,68,71,74,84,87,93,100,115,122,125,141,155,158,172,184,192,195],"stability":[6,77,102,127,146,165],"and":[7,12,30,46,62,167,175],"displacement":[8],"error":[9,169,189],"for":[10,54,78,99,144,171,191],"linear":[11,55,105],"circular":[13,107],"atomistic":[14,21,39,75,196],"chains":[15,56],"in":[16,114,198],"plane":[18,116],"when":[19,111,130],"energy":[22,29],"is":[23],"approximated":[24],"by":[25,31,135],"Cauchy\u2013Born":[27,61,94,174],"continuum":[28],"quasi-nonlocal":[33,63,176],"atomistic-to-continuum":[34],"coupling":[35],"energy.":[36],"consider":[38],"energies":[40,132,177],"that":[41,59,80,92],"include":[42],"Lennard-Jones-type":[43],"nearest":[44,48],"neighbor":[45,49],"next":[47],"pair-potential":[50,131],"interactions.":[51],"Previous":[52],"analyses":[53],"have":[57],"shown":[58],"approximations":[64],"reproduce":[65],"(up":[66],"to":[67,83,154,178,200],"order":[69,156,182],"lattice":[72,76,101,126,145,159,185],"spacing)":[73],"perturbations":[79,113],"are":[81,117,133,150],"constrained":[82],"line":[85],"chain.":[88],"However,":[89],"we":[90],"show":[91],"gives":[95],"a":[96,104,187],"finite":[97],"increase":[98,123],"or":[106],"chain":[108],"under":[109,128],"compression":[110,129],"general":[112],"allowed.":[118],"also":[120],"analyze":[121],"augmented":[134],"bond-angle":[136],"energies.":[137],"Our":[138],"estimates":[139,166,170],"largest":[142],"strain":[143,197],"(the":[147],"critical":[148],"strain)":[149],"sharp":[151],"(exact":[152],"up":[153],"scale).":[160],"then":[162],"use":[163],"these":[164],"modeling":[168],"linearized":[173],"optimal":[181],"(in":[183],"scale)":[186],"priori":[188],"approximation":[193],"due":[199],"external":[202],"force.":[203]},"counts_by_year":[],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}
