{"id":"https://openalex.org/W7138833329","doi":"https://doi.org/10.48550/arxiv.2603.17572","title":"Optimal Control for Steady Circulation of a Diffusion Process via Spectral Decomposition of Fokker-Planck Equation","display_name":"Optimal Control for Steady Circulation of a Diffusion Process via Spectral Decomposition of Fokker-Planck Equation","publication_year":2026,"publication_date":"2026-03-18","ids":{"openalex":"https://openalex.org/W7138833329","doi":"https://doi.org/10.48550/arxiv.2603.17572"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.17572","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.17572","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.17572","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080291372","display_name":"Norihisa Namura","orcid":"https://orcid.org/0000-0002-3115-2950"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Namura, Norihisa","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5059087659","display_name":"Hiroya Nakao","orcid":"https://orcid.org/0000-0003-3394-0392"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nakao, Hiroya","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"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/T11513","display_name":"stochastic dynamics and bifurcation","score":0.19539999961853027,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11513","display_name":"stochastic dynamics and bifurcation","score":0.19539999961853027,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.19269999861717224,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.09489999711513519,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.792900025844574},{"id":"https://openalex.org/keywords/eigenfunction","display_name":"Eigenfunction","score":0.7286999821662903},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5680000185966492},{"id":"https://openalex.org/keywords/steady-state","display_name":"Steady state (chemistry)","score":0.557699978351593},{"id":"https://openalex.org/keywords/diffusion-equation","display_name":"Diffusion equation","score":0.5350000262260437},{"id":"https://openalex.org/keywords/diffusion-process","display_name":"Diffusion process","score":0.4812000095844269},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.47850000858306885},{"id":"https://openalex.org/keywords/circulation","display_name":"Circulation (fluid dynamics)","score":0.4381999969482422},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.4052000045776367},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.40130001306533813}],"concepts":[{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.792900025844574},{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.7286999821662903},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5680000185966492},{"id":"https://openalex.org/C8171440","wikidata":"https://www.wikidata.org/wiki/Q903414","display_name":"Steady state (chemistry)","level":2,"score":0.557699978351593},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5468000173568726},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.5350000262260437},{"id":"https://openalex.org/C68710425","wikidata":"https://www.wikidata.org/wiki/Q5275442","display_name":"Diffusion process","level":3,"score":0.4812000095844269},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.47850000858306885},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47269999980926514},{"id":"https://openalex.org/C11111821","wikidata":"https://www.wikidata.org/wiki/Q205880","display_name":"Circulation (fluid dynamics)","level":2,"score":0.4381999969482422},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4056999981403351},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.4052000045776367},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.40130001306533813},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.3905999958515167},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3831999897956848},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.3763999938964844},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3474999964237213},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.3449000120162964},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.337799996137619},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.3337000012397766},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.33219999074935913},{"id":"https://openalex.org/C69123182","wikidata":"https://www.wikidata.org/wiki/Q891766","display_name":"Fokker\u2013Planck equation","level":3,"score":0.32659998536109924},{"id":"https://openalex.org/C68709404","wikidata":"https://www.wikidata.org/wiki/Q1134475","display_name":"Flux (metallurgy)","level":2,"score":0.30889999866485596},{"id":"https://openalex.org/C17456955","wikidata":"https://www.wikidata.org/wiki/Q343279","display_name":"Convection\u2013diffusion equation","level":2,"score":0.3075000047683716},{"id":"https://openalex.org/C98458673","wikidata":"https://www.wikidata.org/wiki/Q917657","display_name":"Step function","level":2,"score":0.29820001125335693},{"id":"https://openalex.org/C186603090","wikidata":"https://www.wikidata.org/wiki/Q55505926","display_name":"Distribution function","level":2,"score":0.28450000286102295},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.28209999203681946},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2768000066280365},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.2718000113964081},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.2694999873638153},{"id":"https://openalex.org/C74859849","wikidata":"https://www.wikidata.org/wiki/Q2466686","display_name":"Non-equilibrium thermodynamics","level":2,"score":0.2669000029563904},{"id":"https://openalex.org/C153240184","wikidata":"https://www.wikidata.org/wiki/Q3243772","display_name":"Control variable","level":2,"score":0.2606000006198883}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.17572","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.17572","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.17572","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.17572","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,57,78],"present":[1],"a":[2,10,16,21,26,75],"formulation":[3],"of":[4,66],"an":[5],"optimal":[6,60,83],"control":[7,39,61,84],"problem":[8,62],"for":[9,44],"two-dimensional":[11],"diffusion":[12],"process":[13],"governed":[14],"by":[15],"Fokker-Planck":[17,68],"equation":[18,69],"to":[19,53,92],"achieve":[20,37],"nonequilibrium":[22],"steady":[23],"state":[24],"with":[25],"desired":[27,87],"circulation":[28,88],"while":[29,89],"accelerating":[30,90],"convergence":[31,91],"toward":[32],"the":[33,38,46,54,59,67,81,86,93],"stationary":[34,94],"distribution.":[35],"To":[36],"objective,":[40],"we":[41],"introduce":[42],"costs":[43],"both":[45],"probability":[47],"density":[48],"function":[49],"and":[50],"flux":[51],"rotation":[52],"objective":[55],"functional.":[56],"formulate":[58],"through":[63,96],"dimensionality":[64],"reduction":[65],"via":[70],"eigenfunction":[71],"expansion,":[72],"which":[73],"requires":[74],"low-computational":[76],"cost.":[77],"demonstrate":[79],"that":[80],"proposed":[82],"achieves":[85],"distribution":[95],"numerical":[97],"simulations.":[98]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-03-20T00:00:00"}