{"id":"https://openalex.org/W7211892903","doi":"https://doi.org/10.48550/arxiv.2609.04936","title":"Homogenization of anisotropic diffusion on pre-Sierpi\u0144ski carpets","display_name":"Homogenization of anisotropic diffusion on pre-Sierpi\u0144ski carpets","publication_year":2026,"publication_date":"2026-09-04","ids":{"openalex":"https://openalex.org/W7211892903","doi":"https://doi.org/10.48550/arxiv.2609.04936"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.04936","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.04936","pdf_url":"https://arxiv.org/pdf/2609.04936","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.04936","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083867120","display_name":"Shiping Cao","orcid":"https://orcid.org/0000-0002-5711-6632","observed_orcids":["https://orcid.org/0000-0002-5711-6632"]},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"HK","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Cao, Shiping","raw_affiliation_strings":["Department of Mathematics , The Chinese University of Hong Kong , Shatin , Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , The Chinese University of Hong Kong , Shatin , Hong Kong","institution_ids":["https://openalex.org/I177725633"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5125757204","display_name":"Zhen-Qing Chen","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, Zhen-Qing","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5103021071","display_name":"Hua Qiu","orcid":"https://orcid.org/0000-0001-5837-0643","observed_orcids":["https://orcid.org/0000-0001-5837-0643"]},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"HK","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Qiu, Hua","raw_affiliation_strings":["Department of Mathematics , The Chinese University of Hong Kong , Shatin , Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , The Chinese University of Hong Kong , Shatin , Hong Kong","institution_ids":["https://openalex.org/I177725633"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.6455000042915344,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.6455000042915344,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.1151999980211258,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.0851999968290329,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/homogenization","display_name":"homogenization","score":0.921999990940094},{"id":"https://openalex.org/keywords/anisotropic-diffusion","display_name":"anisotropic diffusion","score":0.9990000128746033},{"id":"https://openalex.org/keywords/sierpinski-carpet","display_name":"Sierpinski carpet","score":0.9819999933242798},{"id":"https://openalex.org/keywords/effective-resistance","display_name":"effective resistance","score":0.6629999876022339},{"id":"https://openalex.org/keywords/weak-convergence","display_name":"weak convergence","score":0.6570000052452087},{"id":"https://openalex.org/keywords/brownian-motion","display_name":"Brownian motion","score":0.9179999828338623},{"id":"https://openalex.org/keywords/random-walks-on-fractals","display_name":"random walks on fractals","score":0.6729999780654907}],"concepts":[{"id":"https://openalex.org/C2778722038","wikidata":"https://www.wikidata.org/wiki/Q17030643","display_name":"Homogenization (climate)","level":3,"score":0.9283000230789185},{"id":"https://openalex.org/C85725439","wikidata":"https://www.wikidata.org/wiki/Q466686","display_name":"Anisotropy","level":2,"score":0.8054999709129333},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.739799976348877},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5938000082969666},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5392000079154968},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.5145999789237976},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.4862000048160553},{"id":"https://openalex.org/C203504353","wikidata":"https://www.wikidata.org/wiki/Q4765461","display_name":"Anisotropic diffusion","level":3,"score":0.4131999909877777},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.304500013589859},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.267300009727478},{"id":"https://openalex.org/C68710425","wikidata":"https://www.wikidata.org/wiki/Q5275442","display_name":"Diffusion process","level":3,"score":0.2563000023365021},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.25200000405311584},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2513999938964844}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.04936","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.04936","pdf_url":"https://arxiv.org/pdf/2609.04936","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2609.04936","doi":"https://doi.org/10.48550/arxiv.2609.04936","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.04936","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.04936","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.04936","pdf_url":"https://arxiv.org/pdf/2609.04936","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G2163107562","display_name":null,"funder_award_id":"12471087","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5755477424","display_name":null,"funder_award_id":"12531004","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7211892903.pdf","grobid_xml":"https://content.openalex.org/works/W7211892903.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W3048540563","https://openalex.org/W7133334112","https://openalex.org/W7133925832"],"related_works":["https://openalex.org/W7097221111","https://openalex.org/W2073112478","https://openalex.org/W2594606821","https://openalex.org/W7133334112","https://openalex.org/W4416943789","https://openalex.org/W1982306005","https://openalex.org/W7133925832","https://openalex.org/W1849524934","https://openalex.org/W2050860085","https://openalex.org/W2076124993"],"abstract_inverted_index":{"We":[0,44],"investigate":[1],"the":[2,13,35,41,46,57,69],"restoration":[3],"of":[4,37,40,49],"isotropy":[5],"for":[6,34],"anisotropic":[7,42,51],"diffusions":[8,52],"on":[9,56],"pre-Sierpi\u0144ski":[10],"carpets":[11],"in":[12,26,74],"plane,":[14],"a":[15,30,61],"problem":[16],"previously":[17],"studied":[18],"by":[19],"Barlow,":[20],"Hattori,":[21],"Hattori":[22],"and":[23],"Watanabe":[24],"\\cite{BHHW}":[25],"which":[27],"they":[28],"obtained":[29],"weak":[31,47],"homogenization":[32,71],"property":[33],"ratio":[36],"effective":[38],"resistances":[39],"diffusions.":[43],"establish":[45],"convergence":[48],"these":[50],"to":[53,68],"Brownian":[54],"motion":[55],"Sierpi\u0144ski":[58],"carpet.":[59],"As":[60],"consequence,":[62],"we":[63],"give":[64],"an":[65],"affirmative":[66],"answer":[67],"strong":[70],"conjecture":[72],"raised":[73],"\\cite[p.3]{BHHW}.":[75]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-08T00:00:00"}
