{"id":"https://openalex.org/W2914958979","doi":"https://doi.org/10.3233/asy-181495","title":"Series expansion for the effective conductivity of a periodic dilute composite with thermal resistance at the two-phase interface","display_name":"Series expansion for the effective conductivity of a periodic dilute composite with thermal resistance at the two-phase interface","publication_year":2019,"publication_date":"2019-02-13","ids":{"openalex":"https://openalex.org/W2914958979","doi":"https://doi.org/10.3233/asy-181495","mag":"2914958979"},"language":"en","primary_location":{"id":"doi:10.3233/asy-181495","is_oa":true,"landing_page_url":"https://doi.org/10.3233/asy-181495","pdf_url":"https://content.iospress.com:443/download/asymptotic-analysis/asy1495?id=asymptotic-analysis%2Fasy1495","source":{"id":"https://openalex.org/S141283892","display_name":"Asymptotic Analysis","issn_l":"0921-7134","issn":["0921-7134","1875-8576"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asymptotic Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://content.iospress.com:443/download/asymptotic-analysis/asy1495?id=asymptotic-analysis%2Fasy1495","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081976249","display_name":"\u041c\u0430\u0442\u0442\u0435\u043e \u0414\u0430\u043b\u043b\u0430 \u0420\u0456\u0432\u0430","orcid":"https://orcid.org/0000-0002-5519-3327"},"institutions":[{"id":"https://openalex.org/I16038530","display_name":"Aberystwyth University","ror":"https://ror.org/015m2p889","country_code":"GB","type":"education","lineage":["https://openalex.org/I16038530"]},{"id":"https://openalex.org/I87208437","display_name":"University of Tulsa","ror":"https://ror.org/04wn28048","country_code":"US","type":"education","lineage":["https://openalex.org/I87208437"]}],"countries":["GB","US"],"is_corresponding":false,"raw_author_name":"Matteo Dalla Riva","raw_affiliation_strings":["Department of Mathematics, Aberystwyth University, Ceredigion SY23 3BZ, Wales, UK","Department of Mathematics, The University of Tulsa, 800 South Tucker Drive, Tulsa, Oklahoma 74104, USA. E-mail:\u00a0","Department of Mathematics, The University of Tulsa, 800 South Tucker Drive, Tulsa, Oklahoma 74104, USA. E-mail:\u00a0matteo-dallariva@utulsa.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Aberystwyth University, Ceredigion SY23 3BZ, Wales, UK","institution_ids":["https://openalex.org/I16038530"]},{"raw_affiliation_string":"Department of Mathematics, The University of Tulsa, 800 South Tucker Drive, Tulsa, Oklahoma 74104, USA. E-mail:\u00a0","institution_ids":["https://openalex.org/I87208437"]},{"raw_affiliation_string":"Department of Mathematics, The University of Tulsa, 800 South Tucker Drive, Tulsa, Oklahoma 74104, USA. E-mail:\u00a0matteo-dallariva@utulsa.edu","institution_ids":["https://openalex.org/I87208437"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045759139","display_name":"\u041f\u0430\u043e\u043b\u043e \u041c\u0443\u0441\u043e\u043b\u0456\u043d\u043e","orcid":"https://orcid.org/0000-0001-7366-5124"},"institutions":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]},{"id":"https://openalex.org/I4210150992","display_name":"Civita","ror":"https://ror.org/04hn89439","country_code":"IT","type":"other","lineage":["https://openalex.org/I4210150992"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Paolo Musolino","raw_affiliation_strings":["Dipartimento di Matematica \u2018Tullio Levi-Civita\u2019, Universit\u00e0 degli Studi di Padova, Via Trieste 63, Padova 35121, Italy. E-mails:\u00a0,\u00a0","Dipartimento di Matematica \u2018Tullio Levi-Civita\u2019, Universit\u00e0 degli Studi di Padova, Via Trieste 63, Padova 35121, Italy. E-mails:\u00a0musolino@math.unipd.it,\u00a0rpukhtaievych@gmail.com"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica \u2018Tullio Levi-Civita\u2019, Universit\u00e0 degli Studi di Padova, Via Trieste 63, Padova 35121, Italy. E-mails:\u00a0,\u00a0","institution_ids":["https://openalex.org/I138689650"]},{"raw_affiliation_string":"Dipartimento di Matematica \u2018Tullio Levi-Civita\u2019, Universit\u00e0 degli Studi di Padova, Via Trieste 63, Padova 35121, Italy. E-mails:\u00a0musolino@math.unipd.it,\u00a0rpukhtaievych@gmail.com","institution_ids":["https://openalex.org/I138689650","https://openalex.org/I4210150992"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061201638","display_name":"Roman Pukhtaievych","orcid":"https://orcid.org/0000-0002-7279-8213"},"institutions":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]},{"id":"https://openalex.org/I4210150992","display_name":"Civita","ror":"https://ror.org/04hn89439","country_code":"IT","type":"other","lineage":["https://openalex.org/I4210150992"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Roman Pukhtaievych","raw_affiliation_strings":["Dipartimento di Matematica \u2018Tullio Levi-Civita\u2019, Universit\u00e0 degli Studi di Padova, Via Trieste 63, Padova 35121, Italy. E-mails:\u00a0,\u00a0","Dipartimento di Matematica \u2018Tullio Levi-Civita\u2019, Universit\u00e0 degli Studi di Padova, Via Trieste 63, Padova 35121, Italy. E-mails:\u00a0musolino@math.unipd.it,\u00a0rpukhtaievych@gmail.com"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica \u2018Tullio Levi-Civita\u2019, Universit\u00e0 degli Studi di Padova, Via Trieste 63, Padova 35121, Italy. E-mails:\u00a0,\u00a0","institution_ids":["https://openalex.org/I138689650"]},{"raw_affiliation_string":"Dipartimento di Matematica \u2018Tullio Levi-Civita\u2019, Universit\u00e0 degli Studi di Padova, Via Trieste 63, Padova 35121, Italy. E-mails:\u00a0musolino@math.unipd.it,\u00a0rpukhtaievych@gmail.com","institution_ids":["https://openalex.org/I138689650","https://openalex.org/I4210150992"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5045759139"],"corresponding_institution_ids":["https://openalex.org/I138689650","https://openalex.org/I4210150992"],"apc_list":null,"apc_paid":null,"fwci":1.6477,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.80193392,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"111","issue":"3-4","first_page":"217","last_page":"250"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"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"}},"topics":[{"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9998999834060669,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9987000226974487,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/thermal-conductivity","display_name":"Thermal conductivity","score":0.6953637003898621},{"id":"https://openalex.org/keywords/heat-flux","display_name":"Heat flux","score":0.5677510499954224},{"id":"https://openalex.org/keywords/jump","display_name":"Jump","score":0.5674605369567871},{"id":"https://openalex.org/keywords/composite-number","display_name":"Composite number","score":0.5623337626457214},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.5497862696647644},{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.517308235168457},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5154877305030823},{"id":"https://openalex.org/keywords/power-series","display_name":"Power series","score":0.5154279470443726},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.4589245617389679},{"id":"https://openalex.org/keywords/conductivity","display_name":"Conductivity","score":0.43426424264907837},{"id":"https://openalex.org/keywords/asymptotic-expansion","display_name":"Asymptotic expansion","score":0.42995917797088623},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.4211260974407196},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4197150766849518},{"id":"https://openalex.org/keywords/thermal-resistance","display_name":"Thermal resistance","score":0.416353702545166},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3906973898410797},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.3423662781715393},{"id":"https://openalex.org/keywords/thermal","display_name":"Thermal","score":0.3285536468029022},{"id":"https://openalex.org/keywords/heat-transfer","display_name":"Heat transfer","score":0.3168661594390869},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2908421754837036},{"id":"https://openalex.org/keywords/composite-material","display_name":"Composite material","score":0.12969836592674255}],"concepts":[{"id":"https://openalex.org/C97346530","wikidata":"https://www.wikidata.org/wiki/Q487005","display_name":"Thermal conductivity","level":2,"score":0.6953637003898621},{"id":"https://openalex.org/C159188206","wikidata":"https://www.wikidata.org/wiki/Q1478382","display_name":"Heat flux","level":3,"score":0.5677510499954224},{"id":"https://openalex.org/C2780695682","wikidata":"https://www.wikidata.org/wiki/Q4005959","display_name":"Jump","level":2,"score":0.5674605369567871},{"id":"https://openalex.org/C104779481","wikidata":"https://www.wikidata.org/wiki/Q50707","display_name":"Composite number","level":2,"score":0.5623337626457214},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5497862696647644},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.517308235168457},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5154877305030823},{"id":"https://openalex.org/C73905626","wikidata":"https://www.wikidata.org/wiki/Q206925","display_name":"Power series","level":2,"score":0.5154279470443726},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.4589245617389679},{"id":"https://openalex.org/C131540310","wikidata":"https://www.wikidata.org/wiki/Q907564","display_name":"Conductivity","level":2,"score":0.43426424264907837},{"id":"https://openalex.org/C11683690","wikidata":"https://www.wikidata.org/wiki/Q752726","display_name":"Asymptotic expansion","level":2,"score":0.42995917797088623},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.4211260974407196},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4197150766849518},{"id":"https://openalex.org/C137693562","wikidata":"https://www.wikidata.org/wiki/Q899628","display_name":"Thermal resistance","level":3,"score":0.416353702545166},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3906973898410797},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.3423662781715393},{"id":"https://openalex.org/C204530211","wikidata":"https://www.wikidata.org/wiki/Q752823","display_name":"Thermal","level":2,"score":0.3285536468029022},{"id":"https://openalex.org/C50517652","wikidata":"https://www.wikidata.org/wiki/Q179635","display_name":"Heat transfer","level":2,"score":0.3168661594390869},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2908421754837036},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.12969836592674255},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3233/asy-181495","is_oa":true,"landing_page_url":"https://doi.org/10.3233/asy-181495","pdf_url":"https://content.iospress.com:443/download/asymptotic-analysis/asy1495?id=asymptotic-analysis%2Fasy1495","source":{"id":"https://openalex.org/S141283892","display_name":"Asymptotic Analysis","issn_l":"0921-7134","issn":["0921-7134","1875-8576"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asymptotic Analysis","raw_type":"journal-article"},{"id":"pmh:oai:www.research.unipd.it:11577/3292609","is_oa":true,"landing_page_url":"http://hdl.handle.net/11577/3292609","pdf_url":"http://hdl.handle.net/11577/3292609","source":{"id":"https://openalex.org/S4377196283","display_name":"Research Padua  Archive (University of Padua)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I138689650","host_organization_name":"University of Padua","host_organization_lineage":["https://openalex.org/I138689650"],"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":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:iris.unipa.it:10447/546256","is_oa":true,"landing_page_url":"http://hdl.handle.net/10447/546256","pdf_url":null,"source":{"id":"https://openalex.org/S4306401065","display_name":"Nova Science Publishers (Nova Science Publishers, Inc.)","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":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:iris.unive.it:10278/3723496","is_oa":false,"landing_page_url":"http://hdl.handle.net/10278/3723496","pdf_url":null,"source":{"id":"https://openalex.org/S4306402336","display_name":"ARCA (Universit\u00e0 Ca' Foscari Venezia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149461666","host_organization_name":"Ca' Foscari University of Venice","host_organization_lineage":["https://openalex.org/I149461666"],"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":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.3233/asy-181495","is_oa":true,"landing_page_url":"https://doi.org/10.3233/asy-181495","pdf_url":"https://content.iospress.com:443/download/asymptotic-analysis/asy1495?id=asymptotic-analysis%2Fasy1495","source":{"id":"https://openalex.org/S141283892","display_name":"Asymptotic Analysis","issn_l":"0921-7134","issn":["0921-7134","1875-8576"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asymptotic Analysis","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.49000000953674316,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G3330850500","display_name":null,"funder_award_id":"663830","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G665006981","display_name":null,"funder_award_id":"BIRD168373/16","funder_id":"https://openalex.org/F4320309832","funder_display_name":"Fondazione Cassa di Risparmio di Padova e Rovigo"},{"id":"https://openalex.org/G7278778494","display_name":null,"funder_award_id":"BIRD168373/16","funder_id":"https://openalex.org/F4320321966","funder_display_name":"Universit\u00e0 degli Studi di Padova"},{"id":"https://openalex.org/G8591062235","display_name":"A functional analytic approach for the analysis of nonlinear transmission problems","funder_award_id":"654795","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320309832","display_name":"Fondazione Cassa di Risparmio di Padova e Rovigo","ror":"https://ror.org/02jecj653"},{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320320032","display_name":"Aberystwyth University","ror":"https://ror.org/015m2p889"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320321966","display_name":"Universit\u00e0 degli Studi di Padova","ror":"https://ror.org/00240q980"},{"id":"https://openalex.org/F4320333369","display_name":"Gruppo Nazionale per l'Analisi Matematica, la Probabilit\u00e0 e le loro Applicazioni","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2914958979.pdf","grobid_xml":"https://content.openalex.org/works/W2914958979.grobid-xml"},"referenced_works_count":48,"referenced_works":["https://openalex.org/W21326251","https://openalex.org/W55883389","https://openalex.org/W1253195520","https://openalex.org/W1555674425","https://openalex.org/W1571246270","https://openalex.org/W1581883261","https://openalex.org/W1595817412","https://openalex.org/W1644802453","https://openalex.org/W1866311589","https://openalex.org/W1963648105","https://openalex.org/W1964136357","https://openalex.org/W1966275668","https://openalex.org/W1976431068","https://openalex.org/W1980472311","https://openalex.org/W1982552629","https://openalex.org/W1984720921","https://openalex.org/W1987047965","https://openalex.org/W1988347501","https://openalex.org/W2002918068","https://openalex.org/W2002929626","https://openalex.org/W2008886880","https://openalex.org/W2022072806","https://openalex.org/W2036382303","https://openalex.org/W2053768949","https://openalex.org/W2062386992","https://openalex.org/W2064488669","https://openalex.org/W2075085615","https://openalex.org/W2077472331","https://openalex.org/W2084912163","https://openalex.org/W2087404487","https://openalex.org/W2091242967","https://openalex.org/W2132495781","https://openalex.org/W2162094457","https://openalex.org/W2171238083","https://openalex.org/W2268951382","https://openalex.org/W2330494323","https://openalex.org/W2478917285","https://openalex.org/W2613050483","https://openalex.org/W2616191639","https://openalex.org/W2771226454","https://openalex.org/W2773648237","https://openalex.org/W2778581860","https://openalex.org/W2788278501","https://openalex.org/W2963502043","https://openalex.org/W3104632379","https://openalex.org/W4210451606","https://openalex.org/W4244750309","https://openalex.org/W4302606882"],"related_works":["https://openalex.org/W2807893864","https://openalex.org/W3104725479","https://openalex.org/W3122054165","https://openalex.org/W1931485777","https://openalex.org/W2092397289","https://openalex.org/W2334597029","https://openalex.org/W2356689904","https://openalex.org/W1995104609","https://openalex.org/W2505792258","https://openalex.org/W4240485258"],"abstract_inverted_index":{"We":[0,44],"study":[1],"the":[2,6,47,51,57,64,72,82,98,103],"asymptotic":[3],"behavior":[4],"of":[5,10,27,29,34,36,50,102,105,108],"effective":[7,83],"thermal":[8],"conductivity":[9,84],"a":[11,24,30,40,68,89],"periodic":[12,25],"two-phase":[13,58],"dilute":[14],"composite":[15],"obtained":[16],"by":[17],"introducing":[18],"into":[19],"an":[20],"infinite":[21],"homogeneous":[22],"matrix":[23],"set":[26],"inclusions":[28],"different":[31],"material,":[32],"each":[33],"them":[35],"size":[37],"proportional":[38,70],"to":[39,71],"positive":[41],"parameter":[42],"\u03f5.":[43],"assume":[45],"that":[46,63,81],"normal":[48,73],"component":[49],"heat":[52,74],"flux":[53],"is":[54],"continuous":[55],"at":[56],"interface,":[59],"while":[60],"we":[61,79,96],"impose":[62],"temperature":[65],"field":[66],"displays":[67],"jump":[69],"flux.":[75],"For":[76],"\u03f5":[77,94],"small,":[78],"prove":[80],"can":[85],"be":[86],"represented":[87],"as":[88],"convergent":[90],"power":[91],"series":[92],"in":[93,100],"and":[95],"determine":[97],"coefficients":[99],"terms":[101],"solutions":[104],"explicit":[106],"systems":[107],"integral":[109],"equations.":[110]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1}],"updated_date":"2026-05-17T08:19:37.847499","created_date":"2019-02-21T00:00:00"}