{"id":"https://openalex.org/W4310418606","doi":"https://doi.org/10.3934/nhm.2023052","title":"Hypertemperature effects in heterogeneous media and thermal flux at small-length scales","display_name":"Hypertemperature effects in heterogeneous media and thermal flux at small-length scales","publication_year":2023,"publication_date":"2023-01-01","ids":{"openalex":"https://openalex.org/W4310418606","doi":"https://doi.org/10.3934/nhm.2023052"},"language":"en","primary_location":{"id":"doi:10.3934/nhm.2023052","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2023052","pdf_url":null,"source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks and Heterogeneous Media","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.3934/nhm.2023052","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063950171","display_name":"Grigor Nika","orcid":"https://orcid.org/0000-0002-4403-6908"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Grigor Nika","raw_affiliation_strings":["Department of Mathematics and Computer Science, Karlstad University (Universitetsgatan 2\r\n651 88 Karlstad - Switzerland)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Karlstad University (Universitetsgatan 2\r\n651 88 Karlstad - Switzerland)","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047645763","display_name":"Adrian Muntean","orcid":"https://orcid.org/0000-0002-1160-0007"},"institutions":[{"id":"https://openalex.org/I43968019","display_name":"Karlstad University","ror":"https://ror.org/05s754026","country_code":"SE","type":"education","lineage":["https://openalex.org/I43968019"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Adrian Muntean","raw_affiliation_strings":["Mathematics & Computer Science, Karlstad University, Universitetsgatan 2, Karlstad, Sweden","Department of Mathematics and Computer Science, Karlstad University (Universitetsgatan 2\r\n651 88 Karlstad - Switzerland)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics & Computer Science, Karlstad University, Universitetsgatan 2, Karlstad, Sweden","institution_ids":["https://openalex.org/I43968019"]},{"raw_affiliation_string":"Department of Mathematics and Computer Science, Karlstad University (Universitetsgatan 2\r\n651 88 Karlstad - Switzerland)","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5063950171"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3857,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.60919272,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"18","issue":"3","first_page":"1207","last_page":"1225"},"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":0.9998000264167786,"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/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"}}],"keywords":[{"id":"https://openalex.org/keywords/homogenization","display_name":"Homogenization (climate)","score":0.8950849175453186},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.6288502216339111},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.6288137435913086},{"id":"https://openalex.org/keywords/thermal-conduction","display_name":"Thermal conduction","score":0.5650824308395386},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.5243954062461853},{"id":"https://openalex.org/keywords/thermal","display_name":"Thermal","score":0.4636007845401764},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.4310283958911896},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3765113949775696},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34471461176872253},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.2137237787246704},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.15885314345359802},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14852234721183777}],"concepts":[{"id":"https://openalex.org/C2778722038","wikidata":"https://www.wikidata.org/wiki/Q17030643","display_name":"Homogenization (climate)","level":3,"score":0.8950849175453186},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.6288502216339111},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.6288137435913086},{"id":"https://openalex.org/C172100665","wikidata":"https://www.wikidata.org/wiki/Q7465774","display_name":"Thermal conduction","level":2,"score":0.5650824308395386},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5243954062461853},{"id":"https://openalex.org/C204530211","wikidata":"https://www.wikidata.org/wiki/Q752823","display_name":"Thermal","level":2,"score":0.4636007845401764},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.4310283958911896},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3765113949775696},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34471461176872253},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.2137237787246704},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.15885314345359802},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14852234721183777},{"id":"https://openalex.org/C130217890","wikidata":"https://www.wikidata.org/wiki/Q47041","display_name":"Biodiversity","level":2,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3934/nhm.2023052","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2023052","pdf_url":null,"source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks and Heterogeneous Media","raw_type":"journal-article"},{"id":"pmh:oai:DiVA.org:kau-93953","is_oa":true,"landing_page_url":"http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-93953","pdf_url":"https://kau.diva-portal.org/smash/get/diva2:1744076/FULLTEXT02","source":{"id":"https://openalex.org/S4306401559","display_name":"KTH Publication Database DiVA (KTH Royal Institute of Technology)","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":"text"},{"id":"pmh:oai:HAL:hal-04067022v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04067022","pdf_url":"https://hal.science/hal-04067022v1/file/HG_Fourier%20%281%29.pdf","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"Networks and Heterogeneous Media, 2023, 18 (3), pp.1207-1225. ⟨10.3934/nhm.2023052⟩","raw_type":"Journal articles"},{"id":"pmh:oai:doaj.org/article:2b06b32245a14390a097201abb054fef","is_oa":true,"landing_page_url":"https://doaj.org/article/2b06b32245a14390a097201abb054fef","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Networks and Heterogeneous Media, Vol 18, Iss 3, Pp 1207-1225 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3934/nhm.2023052","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2023052","pdf_url":null,"source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks and Heterogeneous Media","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W617215881","https://openalex.org/W1496937571","https://openalex.org/W1597941147","https://openalex.org/W1664972889","https://openalex.org/W1965059925","https://openalex.org/W1967203031","https://openalex.org/W1972070585","https://openalex.org/W2004449677","https://openalex.org/W2012683090","https://openalex.org/W2026409993","https://openalex.org/W2027239222","https://openalex.org/W2052082322","https://openalex.org/W2054655049","https://openalex.org/W2059460892","https://openalex.org/W2089312086","https://openalex.org/W2103449449","https://openalex.org/W2111677232","https://openalex.org/W2114393376","https://openalex.org/W2116801612","https://openalex.org/W2137746982","https://openalex.org/W2213800725","https://openalex.org/W2539393292","https://openalex.org/W2899627447","https://openalex.org/W2908536764","https://openalex.org/W3094327246","https://openalex.org/W3103330412","https://openalex.org/W3200743617","https://openalex.org/W3201928451","https://openalex.org/W4205333693","https://openalex.org/W4205736391","https://openalex.org/W4221146902","https://openalex.org/W4241040869","https://openalex.org/W4309405130","https://openalex.org/W6940917004"],"related_works":["https://openalex.org/W2104620528","https://openalex.org/W4402427056","https://openalex.org/W238609530","https://openalex.org/W140119233","https://openalex.org/W2757910772","https://openalex.org/W4249473811","https://openalex.org/W2394422079","https://openalex.org/W1492688905","https://openalex.org/W2524071042","https://openalex.org/W2170856253"],"abstract_inverted_index":{"<abstract><p>We":[0],"propose":[1],"an":[2],"enriched":[3],"microscopic":[4],"heat":[5],"conduction":[6],"model":[7],"that":[8,54],"can":[9],"account":[10],"for":[11],"size":[12],"effects":[13],"in":[14,30,41,57],"heterogeneous":[15,63],"media.":[16],"Benefiting":[17],"from":[18],"physically":[19],"relevant":[20],"scaling":[21],"arguments,":[22],"we":[23,49,95],"improve":[24],"the":[25,28,31,42,51,59,62,67,73,97],"regularity":[26],"of":[27,34,37,76],"corrector":[29,99],"classical":[32,98],"problem":[33],"periodic":[35],"homogenization":[36],"linear":[38],"elliptic":[39],"equations":[40],"three-dimensional":[43],"setting":[44],"and,":[45],"while":[46],"doing":[47],"so,":[48],"clarify":[50],"intimate":[52],"role":[53],"correctors":[55],"play":[56],"measuring":[58],"difference":[60],"between":[61],"solution":[64,69],"(microscopic)":[65],"and":[66],"homogenized":[68],"(macroscopic).":[70],"Moreover,":[71],"if":[72],"data":[74],"are":[75],"form":[77],"$":[78,84,86],"f":[79],"=":[80],"{\\rm":[81,89],"div}\\;":[82],"{\\boldsymbol{F}}":[83,87],"with":[85],"\\in":[88],"L}^{3}(\\Omega,":[90],"{\\mathbb":[91],"R}^3)":[92],"$,":[93],"then":[94],"recover":[96],"convergence":[100],"theorem.</p></abstract>":[101]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-05-07T13:39:58.223016","created_date":"2025-10-10T00:00:00"}