{"id":"https://openalex.org/W4380354655","doi":"https://doi.org/10.1137/22m1488582","title":"High Contrasting Diffusion in Heisenberg Group: Homogenization of Optimal Control via Unfolding","display_name":"High Contrasting Diffusion in Heisenberg Group: Homogenization of Optimal Control via Unfolding","publication_year":2023,"publication_date":"2023-06-08","ids":{"openalex":"https://openalex.org/W4380354655","doi":"https://doi.org/10.1137/22m1488582"},"language":"en","primary_location":{"id":"doi:10.1137/22m1488582","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1137/22m1488582","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110132134","display_name":"A. K. Nandakumaran","orcid":null},"institutions":[{"id":"https://openalex.org/I59270414","display_name":"Indian Institute of Science Bangalore","ror":"https://ror.org/04dese585","country_code":"IN","type":"education","lineage":["https://openalex.org/I59270414"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"A. K. Nandakumaran","raw_affiliation_strings":["Indian Institute of Science, Bangalore, India"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Indian Institute of Science, Bangalore, India","institution_ids":["https://openalex.org/I59270414"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091316176","display_name":"Abu Sufian","orcid":"https://orcid.org/0000-0002-6936-000X"},"institutions":[{"id":"https://openalex.org/I94595606","display_name":"TIFR Centre for Applicable Mathematics","ror":"https://ror.org/00dp5a155","country_code":"IN","type":"education","lineage":["https://openalex.org/I11947397","https://openalex.org/I2799351866","https://openalex.org/I3149292468","https://openalex.org/I94595606"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Abu Sufian","raw_affiliation_strings":["TIFR-CAM, Bangalore, Karnataka, 560065, ID"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"TIFR-CAM, Bangalore, Karnataka, 560065, ID","institution_ids":["https://openalex.org/I94595606"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12032905,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"61","issue":"3","first_page":"1350","last_page":"1374"},"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":0.9991999864578247,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9990000128746033,"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/mathematics","display_name":"Mathematics","score":0.816423773765564},{"id":"https://openalex.org/keywords/heisenberg-group","display_name":"Heisenberg group","score":0.747171938419342},{"id":"https://openalex.org/keywords/homogenization","display_name":"Homogenization (climate)","score":0.7459065914154053},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5892379283905029},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5210297107696533},{"id":"https://openalex.org/keywords/euclidean-geometry","display_name":"Euclidean geometry","score":0.437860369682312},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.42446815967559814},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0864744484424591}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.816423773765564},{"id":"https://openalex.org/C127519595","wikidata":"https://www.wikidata.org/wiki/Q1601337","display_name":"Heisenberg group","level":2,"score":0.747171938419342},{"id":"https://openalex.org/C2778722038","wikidata":"https://www.wikidata.org/wiki/Q17030643","display_name":"Homogenization (climate)","level":3,"score":0.7459065914154053},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5892379283905029},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5210297107696533},{"id":"https://openalex.org/C129782007","wikidata":"https://www.wikidata.org/wiki/Q162886","display_name":"Euclidean geometry","level":2,"score":0.437860369682312},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.42446815967559814},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0864744484424591},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C130217890","wikidata":"https://www.wikidata.org/wiki/Q47041","display_name":"Biodiversity","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/22m1488582","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1137/22m1488582","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai::82647","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401429","display_name":"ePrints@IISc (Indian Institute of Science)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I59270414","host_organization_name":"Indian Institute of Science Bangalore","host_organization_lineage":["https://openalex.org/I59270414"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2184541923","display_name":null,"funder_award_id":"CRG/2021/000458","funder_id":"https://openalex.org/F4320320719","funder_display_name":"Department of Science and Technology, Ministry of Science and Technology, India"}],"funders":[{"id":"https://openalex.org/F4320320719","display_name":"Department of Science and Technology, Ministry of Science and Technology, India","ror":"https://ror.org/0101xrq71"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1867671219","https://openalex.org/W1972892940","https://openalex.org/W2011540049","https://openalex.org/W2012489403","https://openalex.org/W2027239222","https://openalex.org/W2029796154","https://openalex.org/W2042185551","https://openalex.org/W2043728054","https://openalex.org/W2049216403","https://openalex.org/W2059460892","https://openalex.org/W2116801612","https://openalex.org/W2177846666","https://openalex.org/W2802298313","https://openalex.org/W2936115196","https://openalex.org/W2957125117","https://openalex.org/W2964067321","https://openalex.org/W2981570475","https://openalex.org/W2995862984","https://openalex.org/W3044696863","https://openalex.org/W3101724720","https://openalex.org/W3157960795","https://openalex.org/W3162270249","https://openalex.org/W3183651512"],"related_works":["https://openalex.org/W2104620528","https://openalex.org/W2757910772","https://openalex.org/W4249473811","https://openalex.org/W2394422079","https://openalex.org/W2025913943","https://openalex.org/W166351930","https://openalex.org/W2312674383","https://openalex.org/W1492688905","https://openalex.org/W140119233","https://openalex.org/W4299444906"],"abstract_inverted_index":{"The":[0,67,160],"periodic":[1,55,86,177],"unfolding":[2,56,92,101,116,131,184],"method":[3],"is":[4],"one":[5],"of":[6,19,30,69,129,182],"the":[7,17,23,35,46,54,58,77,85,90,96,111,115,130,136,152,169,175,183,191],"latest":[8],"tools":[9],"for":[10,57,76,114],"studying":[11],"multiscale":[12,20],"problems":[13],"like":[14],"homogenization":[15],"after":[16],"development":[18],"convergence":[21],"in":[22,34,168,180],"1990s.":[24],"It":[25],"provides":[26],"a":[27,63],"good":[28],"understanding":[29],"various":[31],"microscales":[32],"involved":[33],"problem,":[36],"which":[37,61,118,186],"can":[38,119],"be":[39,120],"conveniently":[40],"and":[41,73,104],"easily":[42],"applied":[43],"to":[44,84,89,189],"get":[45],"asymptotic":[47,192],"limit.":[48],"In":[49],"this":[50],"article,":[51],"we":[52,94,109,133,172],"develop":[53],"Heisenberg":[59,78],"group,":[60],"has":[62,80],"noncommutative":[64],"group":[65,79],"structure.":[66],"concept":[68],"greatest":[70],"integer":[71],"part":[72,75],"fractional":[74],"been":[81],"introduced":[82],"corresponding":[83],"cell.":[87],"Analogous":[88],"Euclidean":[91],"operator,":[93,117,132,185],"prove":[95],"integral":[97],"equality,":[98],"L2-weak":[99],"compactness,":[100],"gradient":[102],"convergence,":[103],"other":[105],"related":[106],"properties.":[107],"Moreover,":[108,171],"have":[110,134,144,173],"adjoint":[112],"operator":[113],"recognized":[121],"as":[122],"an":[123,127,147,165],"average":[124],"operator.":[125],"As":[126],"application":[128],"homogenized":[135],"standard":[137],"elliptic":[138],"PDE":[139],"with":[140,151],"oscillating":[141],"coefficients.":[142,159],"We":[143],"also":[145],"considered":[146],"optimal":[148,178],"control":[149,179],"problem":[150],"state":[153],"equation":[154],"having":[155],"high":[156,161],"contrasting":[157,162],"diffusivity":[158],"coefficients":[163],"are":[164],"added":[166],"difficulty":[167],"analysis.":[170],"characterized":[174],"interior":[176],"terms":[181],"helps":[187],"us":[188],"analyze":[190],"behavior.":[193]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
