{"id":"https://openalex.org/W3184554923","doi":"https://doi.org/10.1137/21m145241x","title":"Gradient Estimates for Electric Fields with MultiScale Inclusions in the Quasi-Static Regime","display_name":"Gradient Estimates for Electric Fields with MultiScale Inclusions in the Quasi-Static Regime","publication_year":2022,"publication_date":"2022-06-24","ids":{"openalex":"https://openalex.org/W3184554923","doi":"https://doi.org/10.1137/21m145241x","mag":"3184554923"},"language":"en","primary_location":{"id":"doi:10.1137/21m145241x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m145241x","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":true,"oa_status":"bronze","oa_url":"https://scholars.cityu.edu.hk/en/publications/gradient-estimates-for-electric-fields-with-multiscale-inclusions","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5062312270","display_name":"Youjun Deng","orcid":"https://orcid.org/0000-0001-8508-4773"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Youjun Deng","raw_affiliation_strings":["School of Mathematics and Statistics, Central South University, Changsha, Hunan, China ()"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Central South University, Changsha, Hunan, China ()","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5107902926","display_name":"Xiaoping Fang","orcid":null},"institutions":[{"id":"https://openalex.org/I16609230","display_name":"Hunan University","ror":"https://ror.org/05htk5m33","country_code":"CN","type":"education","lineage":["https://openalex.org/I16609230"]},{"id":"https://openalex.org/I49934816","display_name":"Hunan University of Technology","ror":"https://ror.org/04j3vr751","country_code":"CN","type":"education","lineage":["https://openalex.org/I49934816"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoping Fang","raw_affiliation_strings":["College of Science, Hunan University of Technology and Business, Changsha 410205, China; Key Laboratory of Hunan Province for Statistical Learning and Intelligent Computation, Changsha 410205, China; and National Key Laboratory of Data Intelligence and Smart Society, Changsha 410205, China ()","College of Science, Hunan University of Technology and Business, Changsha 410205, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, Hunan University of Technology and Business, Changsha 410205, China; Key Laboratory of Hunan Province for Statistical Learning and Intelligent Computation, Changsha 410205, China; and National Key Laboratory of Data Intelligence and Smart Society, Changsha 410205, China ()","institution_ids":["https://openalex.org/I16609230"]},{"raw_affiliation_string":"College of Science, Hunan University of Technology and Business, Changsha 410205, China","institution_ids":["https://openalex.org/I49934816"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025082141","display_name":"Hongyu Liu","orcid":"https://orcid.org/0000-0002-2930-3510"},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Hongyu Liu","raw_affiliation_strings":["Department of Mathematics, City University of Hong Kong, Hong Kong SAR, China (, )"],"raw_orcid":"https://orcid.org/0000-0002-2930-3510","affiliations":[{"raw_affiliation_string":"Department of Mathematics, City University of Hong Kong, Hong Kong SAR, China (, )","institution_ids":["https://openalex.org/I168719708"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5062312270"],"corresponding_institution_ids":["https://openalex.org/I139660479"],"apc_list":null,"apc_paid":null,"fwci":4.2981,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.95403084,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"20","issue":"2","first_page":"641","last_page":"656"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9991999864578247,"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":0.9991999864578247,"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/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11558","display_name":"Composite Material Mechanics","score":0.9980999827384949,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/electric-field","display_name":"Electric field","score":0.5916029810905457},{"id":"https://openalex.org/keywords/temperature-gradient","display_name":"Temperature gradient","score":0.5541222095489502},{"id":"https://openalex.org/keywords/dielectric","display_name":"Dielectric","score":0.5443082451820374},{"id":"https://openalex.org/keywords/transverse-plane","display_name":"Transverse plane","score":0.5105346441268921},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.45655789971351624},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.43623876571655273},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4234566390514374},{"id":"https://openalex.org/keywords/electric-field-gradient","display_name":"Electric field gradient","score":0.41648024320602417},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.35551899671554565},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.34971553087234497},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.28033018112182617},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06414702534675598},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.05763992667198181}],"concepts":[{"id":"https://openalex.org/C60799052","wikidata":"https://www.wikidata.org/wiki/Q46221","display_name":"Electric field","level":2,"score":0.5916029810905457},{"id":"https://openalex.org/C137109543","wikidata":"https://www.wikidata.org/wiki/Q554388","display_name":"Temperature gradient","level":2,"score":0.5541222095489502},{"id":"https://openalex.org/C133386390","wikidata":"https://www.wikidata.org/wiki/Q184996","display_name":"Dielectric","level":2,"score":0.5443082451820374},{"id":"https://openalex.org/C154954056","wikidata":"https://www.wikidata.org/wiki/Q1604164","display_name":"Transverse plane","level":2,"score":0.5105346441268921},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.45655789971351624},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.43623876571655273},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4234566390514374},{"id":"https://openalex.org/C168384580","wikidata":"https://www.wikidata.org/wiki/Q5357592","display_name":"Electric field gradient","level":3,"score":0.41648024320602417},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.35551899671554565},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.34971553087234497},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.28033018112182617},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06414702534675598},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.05763992667198181},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/21m145241x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m145241x","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"},{"is_oa":true,"landing_page_url":"https://scholars.cityu.edu.hk/en/publications/gradient-estimates-for-electric-fields-with-multiscale-inclusions","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:pure.atira.dk:publications/9ce502de-6495-4673-81cd-1880ca7ee668","is_oa":true,"landing_page_url":"https://scholars.cityu.edu.hk/en/publications/9ce502de-6495-4673-81cd-1880ca7ee668","pdf_url":null,"source":{"id":"https://openalex.org/S7407055387","display_name":"CityU Scholars","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"DENG, Y, FANG, X & LIU, H 2022, 'GRADIENT ESTIMATES FOR ELECTRIC FIELDS WITH MULTISCALE INCLUSIONS IN THE QUASI-STATIC REGIME', Multiscale Modeling and Simulation, vol. 20, no. 2, pp. 641-656. https://doi.org/10.1137/21M145241X","raw_type":"article"}],"best_oa_location":{"is_oa":true,"landing_page_url":"https://scholars.cityu.edu.hk/en/publications/gradient-estimates-for-electric-fields-with-multiscale-inclusions","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"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1313804163","display_name":null,"funder_award_id":"China 72001077","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3212072810","display_name":null,"funder_award_id":"China 11971487","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3809083144","display_name":null,"funder_award_id":"Hunan 2021JJ30192","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4977696590","display_name":null,"funder_award_id":"Hunan 2020JJ2038","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":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1529860930","https://openalex.org/W1991720518","https://openalex.org/W2016819005","https://openalex.org/W2027321277","https://openalex.org/W2042177828","https://openalex.org/W2052034949","https://openalex.org/W2052923851","https://openalex.org/W2056584884","https://openalex.org/W2070316157","https://openalex.org/W2076112678","https://openalex.org/W2077024482","https://openalex.org/W2111145614","https://openalex.org/W2124611398","https://openalex.org/W2130119488","https://openalex.org/W2143743737","https://openalex.org/W2157437628","https://openalex.org/W2158166759","https://openalex.org/W2159797289","https://openalex.org/W2731351117","https://openalex.org/W2877502722","https://openalex.org/W2963102779","https://openalex.org/W2963785070","https://openalex.org/W2964317187","https://openalex.org/W3002243537","https://openalex.org/W3011527404","https://openalex.org/W3016865950","https://openalex.org/W3095699539","https://openalex.org/W3103377900","https://openalex.org/W3105203753","https://openalex.org/W3114459875","https://openalex.org/W3179305408","https://openalex.org/W3184179291","https://openalex.org/W4214703147","https://openalex.org/W4300223101"],"related_works":["https://openalex.org/W2043673973","https://openalex.org/W3092585306","https://openalex.org/W2804544673","https://openalex.org/W4253731651","https://openalex.org/W1994753809","https://openalex.org/W2053508813","https://openalex.org/W2998536557","https://openalex.org/W2382792452","https://openalex.org/W2039490414","https://openalex.org/W2350923774"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,88],"are":[4,67,102],"concerned":[5,103],"with":[6,104],"the":[7,11,27,38,42,47,53,60,75,78,93,99,105],"gradient":[8,39,61],"estimate":[9],"of":[10,29,37,59,71,77,84,98],"electric":[12],"field":[13],"due":[14],"to":[15],"two":[16,69,79],"nearly":[17],"touching":[18],"dielectric":[19],"inclusions,":[20],"which":[21,50],"is":[22],"a":[23],"central":[24],"topic":[25],"in":[26,41,63,92],"theory":[28],"composite":[30],"materials.":[31],"We":[32],"derive":[33],"accurate":[34],"quantitative":[35],"characterizations":[36],"fields":[40,62],"transverse":[43],"electromagnetic":[44],"case":[45],"within":[46],"quasi-static":[48,94],"regime,":[49,95],"clearly":[51],"indicate":[52],"optimal":[54],"blowup":[55],"rate":[56],"or":[57],"nonblowup":[58],"different":[64,85],"scenarios.":[65],"There":[66],"mainly":[68],"novelties":[70],"our":[72,90],"study.":[73],"First,":[74],"sizes":[76],"material":[80],"inclusions":[81],"may":[82],"be":[83],"scales.":[86],"Second,":[87],"consider":[89],"study":[91],"whereas":[96],"most":[97],"existing":[100],"studies":[101],"static":[106],"case.":[107]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3}],"updated_date":"2026-05-05T08:41:31.759640","created_date":"2025-10-10T00:00:00"}
