{"id":"https://openalex.org/W3029779899","doi":"https://doi.org/10.1137/20m1341222","title":"Homogenization of Quasi-Crystalline Functionals via Two-Scale-Cut-and-Project Convergence","display_name":"Homogenization of Quasi-Crystalline Functionals via Two-Scale-Cut-and-Project Convergence","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3029779899","doi":"https://doi.org/10.1137/20m1341222","mag":"3029779899"},"language":"en","primary_location":{"id":"doi:10.1137/20m1341222","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1341222","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2005.13356","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062323947","display_name":"Rita Ferreira","orcid":"https://orcid.org/0000-0002-7169-9141"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Rita Ferreira","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-7169-9141","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020315578","display_name":"Irene Fonseca","orcid":"https://orcid.org/0000-0002-7840-8175"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Irene Fonseca","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5077917583","display_name":"Raghavendra Venkatraman","orcid":"https://orcid.org/0009-0002-7667-7598"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Raghavendra Venkatraman","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5062323947"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01897236,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"53","issue":"2","first_page":"1785","last_page":"1817"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"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/T11558","display_name":"Composite Material Mechanics","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/homogenization","display_name":"Homogenization (climate)","score":0.6659663915634155},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.5424980521202087},{"id":"https://openalex.org/keywords/constant-coefficients","display_name":"Constant coefficients","score":0.5390928983688354},{"id":"https://openalex.org/keywords/differential-operator","display_name":"Differential operator","score":0.4800168573856354},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4483706057071686},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4275430738925934},{"id":"https://openalex.org/keywords/lagrangian","display_name":"Lagrangian","score":0.41022640466690063},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.40981072187423706},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.38803064823150635},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3490199148654938},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09518662095069885}],"concepts":[{"id":"https://openalex.org/C2778722038","wikidata":"https://www.wikidata.org/wiki/Q17030643","display_name":"Homogenization (climate)","level":3,"score":0.6659663915634155},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.5424980521202087},{"id":"https://openalex.org/C110342517","wikidata":"https://www.wikidata.org/wiki/Q1129902","display_name":"Constant coefficients","level":2,"score":0.5390928983688354},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.4800168573856354},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4483706057071686},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4275430738925934},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.41022640466690063},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.40981072187423706},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.38803064823150635},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3490199148654938},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09518662095069885},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C130217890","wikidata":"https://www.wikidata.org/wiki/Q47041","display_name":"Biodiversity","level":2,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/20m1341222","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1341222","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2005.13356","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2005.13356","pdf_url":"https://arxiv.org/pdf/2005.13356","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:3029779899","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2005.13356.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:repository.kaust.edu.sa:10754/669008","is_oa":false,"landing_page_url":"http://hdl.handle.net/10754/669008","pdf_url":null,"source":{"id":"https://openalex.org/S4306401596","display_name":"King Abdullah University of Science and Technology Repository (King Abdullah University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I71920554","host_organization_name":"King Abdullah University of Science and Technology","host_organization_lineage":["https://openalex.org/I71920554"],"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"},{"id":"doi:10.48550/arxiv.2005.13356","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2005.13356","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2005.13356","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2005.13356","pdf_url":"https://arxiv.org/pdf/2005.13356","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1464247104","display_name":null,"funder_award_id":"DMS-1906238","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2109335441","display_name":null,"funder_award_id":"DMS-1411646","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7631913608","display_name":"Variational Methods for Materials Science and Mathematical Imaging","funder_award_id":"1906238","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"},{"id":"https://openalex.org/F4320306164","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W135448871","https://openalex.org/W168515221","https://openalex.org/W656727543","https://openalex.org/W1513371278","https://openalex.org/W1531856058","https://openalex.org/W1585859756","https://openalex.org/W1966902592","https://openalex.org/W1967391757","https://openalex.org/W1974775577","https://openalex.org/W1976974439","https://openalex.org/W1986389317","https://openalex.org/W1988619801","https://openalex.org/W1991763132","https://openalex.org/W1993753531","https://openalex.org/W1994144821","https://openalex.org/W1995438173","https://openalex.org/W1997851568","https://openalex.org/W2004765086","https://openalex.org/W2009944793","https://openalex.org/W2014133061","https://openalex.org/W2016653956","https://openalex.org/W2027239222","https://openalex.org/W2049893929","https://openalex.org/W2072113362","https://openalex.org/W2085241746","https://openalex.org/W2091352915","https://openalex.org/W2095072431","https://openalex.org/W2115103988","https://openalex.org/W2116801612","https://openalex.org/W2120615165","https://openalex.org/W2135463780","https://openalex.org/W2158796831","https://openalex.org/W2237632239","https://openalex.org/W2262992936","https://openalex.org/W2280869971","https://openalex.org/W2315326112","https://openalex.org/W2339584446","https://openalex.org/W2557949584","https://openalex.org/W2588355134","https://openalex.org/W2608463343","https://openalex.org/W2781991511","https://openalex.org/W2803104766","https://openalex.org/W2897725581","https://openalex.org/W2903898609","https://openalex.org/W2963561905","https://openalex.org/W2970083578","https://openalex.org/W3005326544","https://openalex.org/W4250881247"],"related_works":["https://openalex.org/W1541437485","https://openalex.org/W1882297283","https://openalex.org/W3137770005","https://openalex.org/W2063385584","https://openalex.org/W2625899435","https://openalex.org/W3122794177","https://openalex.org/W2997099976","https://openalex.org/W3040698651","https://openalex.org/W2225724032","https://openalex.org/W3096020010","https://openalex.org/W2963327704","https://openalex.org/W3118841485","https://openalex.org/W3036268408","https://openalex.org/W3134541634","https://openalex.org/W3143723908","https://openalex.org/W1556958275","https://openalex.org/W1987244432","https://openalex.org/W2996211889","https://openalex.org/W2800739768","https://openalex.org/W2980381655"],"abstract_inverted_index":{"We":[0],"consider":[1],"a":[2,70,100,117],"homogenization":[3],"problem":[4],"associated":[5],"with":[6,137],"quasi-crystalline":[7,31,84],"multiple":[8],"integrals":[9],"of":[10,33,46,69,82,87,89,99,119],"the":[11,34,40,43,47,54,59,80,83,90,97,123,126,145],"form":[12],"$u_\\varepsilon\\in":[13],"L^p(\\Omega;\\mathbbm{R}^d)":[14],"\\mapsto":[15],"\\int_\\Omega":[16],"f_R(x,\\frac{x}{\\varepsilon},":[17],"u_\\varepsilon(x)),":[18],"dx,$":[19],"where":[20],"\\(u_\u01cerepsilon)":[21],"is":[22,37,51,79],"subject":[23],"to":[24,62,131],"constant-coefficient":[25,102],"linear":[26,103],"partial":[27,104],"differential":[28,105,134],"constraints.":[29],"The":[30],"structure":[32],"underlying":[35],"composite":[36],"encoded":[38],"in":[39,76,96,122],"dependence":[41],"on":[42,144],"second":[44],"variable":[45],"Lagrangian,":[48],"(f_R),":[49],"and":[50,140],"modeled":[52],"via":[53],"cut-and-project":[55],"scheme":[56],"that":[57,94,108],"interprets":[58],"heterogeneous":[60],"microstructure":[61],"be":[63],"homogenized":[64],"as":[65],"an":[66],"irrational":[67],"subspace":[68],"higher-dimensional":[71],"space.":[72],"A":[73],"key":[74],"step":[75],"our":[77],"analysis":[78],"characterization":[81],"two-scale":[85],"limits":[86],"sequences":[88],"vector":[91],"fields":[92],"(u_\u01cerepsilon)":[93],"are":[95],"kernel":[98],"given":[101],"operator,":[106],"(\\mathcalA),":[107],"is,":[109],"(\\mathcalA":[110,127],"u":[111],"_\u01cerepsilon":[112],"=0).":[113],"Our":[114],"results":[115],"provide":[116],"generalization":[118],"related":[120],"ones":[121],"literature":[124],"concerning":[125],"=curl":[128],")":[129],"case":[130],"more":[132],"general":[133],"operators":[135],"(\\mathcalA)":[136],"constant":[138],"coefficients":[139],"without":[141],"coercivity":[142],"assumptions":[143],"Lagrangian":[146],"(f_R).":[147]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}