{"id":"https://openalex.org/W2778902546","doi":"https://doi.org/10.1137/140994411","title":"Approximation of Crystalline Defects at Finite Temperature","display_name":"Approximation of Crystalline Defects at Finite Temperature","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2778902546","doi":"https://doi.org/10.1137/140994411","mag":"2778902546"},"language":"en","primary_location":{"id":"doi:10.1137/140994411","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140994411","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/A5007354935","display_name":"Alexander V. Shapeev","orcid":"https://orcid.org/0000-0002-7497-5594"},"institutions":[{"id":"https://openalex.org/I125989756","display_name":"Skolkovo Institute of Science and Technology","ror":"https://ror.org/03f9nc143","country_code":"RU","type":"education","lineage":["https://openalex.org/I125989756"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Alexander V. Shapeev","raw_affiliation_strings":["Skolkovo Institute of Science and Technology#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Skolkovo Institute of Science and Technology#TAB#","institution_ids":["https://openalex.org/I125989756"]}]},{"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":0.6328,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.71509526,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"15","issue":"4","first_page":"1830","last_page":"1864"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.9890000224113464,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.9890000224113464,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9853000044822693,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11471","display_name":"Block Copolymer Self-Assembly","score":0.9775999784469604,"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/computation","display_name":"Computation","score":0.6794423460960388},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5154755711555481},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.48062604665756226},{"id":"https://openalex.org/keywords/asymptotic-expansion","display_name":"Asymptotic expansion","score":0.4761757254600525},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.46558988094329834},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41701897978782654},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3626856803894043},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34069573879241943},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.29427024722099304},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.13346770405769348}],"concepts":[{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6794423460960388},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5154755711555481},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.48062604665756226},{"id":"https://openalex.org/C11683690","wikidata":"https://www.wikidata.org/wiki/Q752726","display_name":"Asymptotic expansion","level":2,"score":0.4761757254600525},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.46558988094329834},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41701897978782654},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3626856803894043},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34069573879241943},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.29427024722099304},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.13346770405769348},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/140994411","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140994411","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":[{"id":"https://openalex.org/G22935939","display_name":null,"funder_award_id":"1310835","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3901740477","display_name":null,"funder_award_id":"339038","funder_id":"https://openalex.org/F4320306164","funder_display_name":"Simons Foundation"},{"id":"https://openalex.org/G7141758789","display_name":null,"funder_award_id":"SC0012733","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G8925050130","display_name":null,"funder_award_id":"SC0002085","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320306164","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1564272409","https://openalex.org/W1755818662","https://openalex.org/W1969593540","https://openalex.org/W1986456294","https://openalex.org/W2003407059","https://openalex.org/W2032634061","https://openalex.org/W2033827320","https://openalex.org/W2042435778","https://openalex.org/W2053087016","https://openalex.org/W2070255068","https://openalex.org/W2088801537","https://openalex.org/W2088805075","https://openalex.org/W2092144432","https://openalex.org/W2092260144","https://openalex.org/W2122074696","https://openalex.org/W2133603336","https://openalex.org/W2137897420","https://openalex.org/W2152156571","https://openalex.org/W2159999066","https://openalex.org/W2398055650","https://openalex.org/W2483288645","https://openalex.org/W2962942108","https://openalex.org/W3102769863"],"related_works":["https://openalex.org/W2046435967","https://openalex.org/W4231775656","https://openalex.org/W2383646825","https://openalex.org/W2371018915","https://openalex.org/W2354191502","https://openalex.org/W1972225038","https://openalex.org/W3134658850","https://openalex.org/W2355938171","https://openalex.org/W2780079842","https://openalex.org/W2115091349"],"abstract_inverted_index":{"The":[0],"present":[1],"paper":[2],"develops":[3],"an":[4,49,68],"approximation":[5],"framework":[6,90],"and":[7,31],"corresponding":[8,27],"results":[9],"for":[10,97],"crystalline":[11],"defects":[12,30,96],"of":[13,51,60,75,88,94],"a":[14,20,82],"lattice":[15],"at":[16],"finite":[17],"temperature.":[18],"In":[19],"one-dimensional":[21],"setting,":[22],"we":[23],"introduce":[24],"Gibbs":[25],"distributions":[26],"to":[28,39,56,81,91],"such":[29,53],"rigorously":[32],"establish":[33],"their":[34],"asymptotic":[35,54],"expansion":[36,55],"with":[37],"respect":[38],"temperature":[40],"uniformly":[41],"in":[42],"the":[43,58,73,77],"system":[44],"size.":[45],"We":[46,85],"then":[47],"give":[48],"example":[50,78],"using":[52,62,67],"compare":[57],"accuracy":[59],"computations":[61],"free":[63],"boundary":[64],"conditions":[65],"versus":[66],"atomistic-to-continuum":[69],"coupling":[70],"method.":[71],"For":[72],"sake":[74],"brevity,":[76],"is":[79],"limited":[80],"defect-free":[83],"crystal.":[84],"leave":[86],"application":[87],"our":[89],"existing":[92],"schemes":[93],"modeling":[95],"future":[98],"publications.":[99]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
