{"id":"https://openalex.org/W7214237014","doi":"https://doi.org/10.48550/arxiv.2609.27062","title":"A catalog of exact steady states in Kolmogorov flow","display_name":"A catalog of exact steady states in Kolmogorov flow","publication_year":2026,"publication_date":"2026-09-22","ids":{"openalex":"https://openalex.org/W7214237014","doi":"https://doi.org/10.48550/arxiv.2609.27062"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.27062","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.27062","pdf_url":"https://arxiv.org/pdf/2609.27062","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/2609.27062","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110853668","display_name":"Matthew Golden","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]},{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Golden, Matthew","raw_affiliation_strings":["School of Physics , Georgia Institute of Technology , Atlanta , GA 30318 , USA","Theoretical Division , Los Alamos National Laboratory , Los Alamos , NM 87544 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Physics , Georgia Institute of Technology , Atlanta , GA 30318 , USA","institution_ids":["https://openalex.org/I130701444"]},{"raw_affiliation_string":"Theoretical Division , Los Alamos National Laboratory , Los Alamos , NM 87544 , USA","institution_ids":["https://openalex.org/I1343871089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5110853668"],"corresponding_institution_ids":["https://openalex.org/I130701444","https://openalex.org/I1343871089"],"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.0006000000284984708,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.00039999998989515007,"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/kolmogorov-flow","display_name":"Kolmogorov flow","score":0.9919999837875366},{"id":"https://openalex.org/keywords/two-dimensional-turbulence","display_name":"two-dimensional turbulence","score":0.5950000286102295},{"id":"https://openalex.org/keywords/unstable-periodic-orbits","display_name":"unstable periodic orbits","score":0.8109999895095825},{"id":"https://openalex.org/keywords/transient-dynamics","display_name":"transient dynamics","score":0.3919999897480011}],"concepts":[{"id":"https://openalex.org/C197115733","wikidata":"https://www.wikidata.org/wiki/Q1003136","display_name":"Forcing (mathematics)","level":2,"score":0.6342999935150146},{"id":"https://openalex.org/C196558001","wikidata":"https://www.wikidata.org/wiki/Q190132","display_name":"Turbulence","level":2,"score":0.6233999729156494},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.6155999898910522},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6121000051498413},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.590499997138977},{"id":"https://openalex.org/C121130766","wikidata":"https://www.wikidata.org/wiki/Q192510","display_name":"Wavenumber","level":2,"score":0.5561000108718872},{"id":"https://openalex.org/C182748727","wikidata":"https://www.wikidata.org/wiki/Q178932","display_name":"Reynolds number","level":3,"score":0.5522000193595886},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4627000093460083},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4309999942779541},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4307999908924103},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.4058000147342682},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.4016000032424927},{"id":"https://openalex.org/C87801597","wikidata":"https://www.wikidata.org/wiki/Q1527018","display_name":"Kolmogorov microscales","level":5,"score":0.39070001244544983},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3400000035762787},{"id":"https://openalex.org/C2777447984","wikidata":"https://www.wikidata.org/wiki/Q23304018","display_name":"Two-dimensional flow","level":3,"score":0.32429999113082886},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.30630001425743103},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.2985999882221222},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.2928999960422516},{"id":"https://openalex.org/C204573209","wikidata":"https://www.wikidata.org/wiki/Q1417609","display_name":"Turbulence modeling","level":3,"score":0.29269999265670776},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.29120001196861267},{"id":"https://openalex.org/C189223162","wikidata":"https://www.wikidata.org/wiki/Q18386383","display_name":"K-omega turbulence model","level":4,"score":0.2906000018119812},{"id":"https://openalex.org/C2988173416","wikidata":"https://www.wikidata.org/wiki/Q37172","display_name":"Traveling wave","level":2,"score":0.28700000047683716},{"id":"https://openalex.org/C2779374083","wikidata":"https://www.wikidata.org/wiki/Q5011038","display_name":"CHAOS (operating system)","level":2,"score":0.28299999237060547},{"id":"https://openalex.org/C150711758","wikidata":"https://www.wikidata.org/wiki/Q17148242","display_name":"K-epsilon turbulence model","level":3,"score":0.27379998564720154},{"id":"https://openalex.org/C8171440","wikidata":"https://www.wikidata.org/wiki/Q903414","display_name":"Steady state (chemistry)","level":2,"score":0.26899999380111694},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.25130000710487366}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.27062","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.27062","pdf_url":"https://arxiv.org/pdf/2609.27062","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.2609.27062","doi":"https://doi.org/10.48550/arxiv.2609.27062","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.27062","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.27062","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.27062","pdf_url":"https://arxiv.org/pdf/2609.27062","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/G2434068577","display_name":"Institute for Pure and Applied Mathematics","funder_award_id":"1925919","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3053897049","display_name":"Institute for Pure and Applied Mathematics","funder_award_id":"2422832","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214237014.pdf","grobid_xml":"https://content.openalex.org/works/W7214237014.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W7118800581","https://openalex.org/W7126212571","https://openalex.org/W7131821059"],"related_works":["https://openalex.org/W1538174909","https://openalex.org/W2264468601","https://openalex.org/W2168861422","https://openalex.org/W2044658345","https://openalex.org/W2146934025","https://openalex.org/W2016143948","https://openalex.org/W7008108518","https://openalex.org/W4415274628","https://openalex.org/W4285999487","https://openalex.org/W7126212571"],"abstract_inverted_index":{"Two-dimensional":[0],"Kolmogorov":[1],"flow":[2,64],"is":[3,38],"a":[4,41,47,55,73],"common":[5],"proving":[6],"ground":[7],"for":[8,23],"the":[9,34,63,77],"dynamical":[10],"systems":[11],"picture":[12],"of":[13,16,50,57,62,79],"turbulence.":[14],"Hundreds":[15],"unstable":[17],"periodic":[18],"orbits":[19],"have":[20],"been":[21],"found":[22],"this":[24,66],"system":[25],"across":[26],"many":[27],"Reynolds":[28],"numbers":[29],"and":[30,82],"domain":[31,45],"sizes,":[32],"although":[33],"most":[35],"well":[36],"explored":[37],"Re$=40$":[39],"on":[40],"square":[42],"$2\u03c0\\times":[43],"2\u03c0$":[44],"with":[46],"forcing":[48],"wavenumber":[49],"$k=4.$":[51],"Here":[52],"I":[53],"present":[54],"catalog":[56],"8952":[58],"exact":[59],"steady":[60],"states":[61],"in":[65],"canonical":[67],"parameter":[68],"regime.":[69],"These":[70],"solutions":[71],"provide":[72],"fixed":[74],"constellation":[75],"informing":[76],"dynamics":[78],"both":[80],"turbulence":[81],"transients.":[83]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-25T00:00:00"}