{"id":"https://openalex.org/W7164913697","doi":"https://doi.org/10.48550/arxiv.2606.16251","title":"Topological spectral gap, multiscale Weyl's law, and homogenization in high-contrast PDEs","display_name":"Topological spectral gap, multiscale Weyl's law, and homogenization in high-contrast PDEs","publication_year":2026,"publication_date":"2026-06-15","ids":{"openalex":"https://openalex.org/W7164913697","doi":"https://doi.org/10.48550/arxiv.2606.16251"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.16251","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.16251","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":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.16251","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5138737179","display_name":"Eric T. Chung","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chung, Eric T.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027608261","display_name":"Lijian Jiang","orcid":"https://orcid.org/0000-0002-3410-1219"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jiang, Lijian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5138754069","display_name":"Yajun Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Yajun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9775000214576721,"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":0.9775000214576721,"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":0.004800000227987766,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.0015999999595806003,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/homogenization","display_name":"Homogenization (climate)","score":0.7013000249862671},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5742999911308289},{"id":"https://openalex.org/keywords/spectral-gap","display_name":"Spectral gap","score":0.4767000079154968},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.414900004863739},{"id":"https://openalex.org/keywords/dirichlet-distribution","display_name":"Dirichlet distribution","score":0.40869998931884766},{"id":"https://openalex.org/keywords/decoupling","display_name":"Decoupling (probability)","score":0.38499999046325684},{"id":"https://openalex.org/keywords/dirichlet-boundary-condition","display_name":"Dirichlet boundary condition","score":0.3650999963283539},{"id":"https://openalex.org/keywords/spectrum","display_name":"Spectrum (functional analysis)","score":0.35910001397132874},{"id":"https://openalex.org/keywords/spectral-method","display_name":"Spectral method","score":0.35600000619888306}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7200000286102295},{"id":"https://openalex.org/C2778722038","wikidata":"https://www.wikidata.org/wiki/Q17030643","display_name":"Homogenization (climate)","level":3,"score":0.7013000249862671},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5742999911308289},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4959000051021576},{"id":"https://openalex.org/C2778114796","wikidata":"https://www.wikidata.org/wiki/Q7575194","display_name":"Spectral gap","level":2,"score":0.4767000079154968},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.414900004863739},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.40869998931884766},{"id":"https://openalex.org/C205606062","wikidata":"https://www.wikidata.org/wiki/Q5249645","display_name":"Decoupling (probability)","level":2,"score":0.38499999046325684},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.3650999963283539},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.35910001397132874},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.35600000619888306},{"id":"https://openalex.org/C81332173","wikidata":"https://www.wikidata.org/wiki/Q179899","display_name":"Topological space","level":2,"score":0.3400000035762787},{"id":"https://openalex.org/C98306654","wikidata":"https://www.wikidata.org/wiki/Q2409122","display_name":"Spectral theory","level":3,"score":0.3375000059604645},{"id":"https://openalex.org/C51364350","wikidata":"https://www.wikidata.org/wiki/Q3123529","display_name":"Spectral geometry","level":2,"score":0.328900009393692},{"id":"https://openalex.org/C9259290","wikidata":"https://www.wikidata.org/wiki/Q745215","display_name":"Variational principle","level":2,"score":0.3264999985694885},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.32580000162124634},{"id":"https://openalex.org/C2780297109","wikidata":"https://www.wikidata.org/wiki/Q917390","display_name":"Essential spectrum","level":3,"score":0.3073999881744385},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.29490000009536743},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.2939000129699707},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.2831000089645386},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.2809000015258789},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.2736000120639801},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.27230000495910645},{"id":"https://openalex.org/C80845027","wikidata":"https://www.wikidata.org/wiki/Q15144062","display_name":"Continuous spectrum","level":2,"score":0.2694999873638153},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.26350000500679016}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.16251","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.16251","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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.16251","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.16251","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":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.6407252550125122}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0],"paper":[1],"introduces":[2],"a":[3,70,75],"unified":[4],"abstract":[5],"variational":[6],"and":[7,15,101,153],"topological":[8,64,125],"framework":[9],"to":[10],"characterize":[11],"the":[12,29,33,40,43,49,63,82,86,94,98,102,107,118,129,134],"spectral":[13,34,76,110,131],"gap":[14,35],"eigenvalue":[16],"distribution":[17],"in":[18,117],"high-contrast":[19,50],"multiscale":[20,71,87],"partial":[21],"differential":[22],"equations":[23],"(PDEs).":[24],"We":[25],"rigorously":[26],"prove":[27],"that":[28,80,116],"exact":[30],"location":[31,58],"of":[32,42,97,106,120,133],"is":[36,59],"universally":[37],"determined":[38,61],"by":[39,62],"dimension":[41],"local":[44],"null":[45],"space":[46,132],"associated":[47],"with":[48,54],"inclusions.":[51,108],"For":[52],"systems":[53],"infinite-dimensional":[55],"kernels,":[56],"this":[57,123],"strictly":[60],"Betti":[65],"numbers.":[66],"Furthermore,":[67],"we":[68,113],"establish":[69],"Weyl's":[72],"law":[73],"via":[74],"decoupling":[77],"theorem,":[78],"demonstrating":[79],"as":[81],"contrast":[83],"approaches":[84],"infinity,":[85],"spectrum":[88,96,105],"bifurcates":[89],"into":[90],"two":[91],"independent":[92],"components:":[93],"Dirichlet":[95],"background":[99],"matrix":[100],"internal":[103],"Neumann":[104],"Using":[109],"homogenization":[111],"theory,":[112],"also":[114],"show":[115],"limit":[119],"vanishing":[121],"periodicity,":[122],"expanding":[124],"eigenspace":[126],"asymptotically":[127],"spans":[128],"entire":[130],"macroscopic":[135],"homogenized":[136],"operator.":[137],"These":[138],"theoretical":[139],"results":[140],"are":[141],"comprehensively":[142],"verified":[143],"through":[144],"numerical":[145],"experiments":[146],"on":[147],"diffusion,":[148],"elasticity,":[149],"fourth-order":[150],"plate,":[151],"Maxwell,":[152],"grad-div":[154],"operators.":[155]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-06-17T00:00:00"}