{"id":"https://openalex.org/W2012886351","doi":"https://doi.org/10.1137/s0036139900370388","title":"On the Principle of Exchange of Stabilities in Rayleigh--B\u00e9nard Convection","display_name":"On the Principle of Exchange of Stabilities in Rayleigh--B\u00e9nard Convection","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W2012886351","doi":"https://doi.org/10.1137/s0036139900370388","mag":"2012886351"},"language":"en","primary_location":{"id":"doi:10.1137/s0036139900370388","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139900370388","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Applied Mathematics","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/A5020028598","display_name":"Isom H. Herron","orcid":"https://orcid.org/0000-0003-0157-3241"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Isom H. Herron","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5020028598"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2061,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.75892121,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"61","issue":"4","first_page":"1362","last_page":"1368"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","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"}},"topics":[{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","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"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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":0.9976000189781189,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/convection","display_name":"Convection","score":0.6244469285011292},{"id":"https://openalex.org/keywords/rayleigh\u2013b\u00e9nard-convection","display_name":"Rayleigh\u2013B\u00e9nard convection","score":0.5644492506980896},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5132498741149902},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5118952989578247},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47090625762939453},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4354260265827179},{"id":"https://openalex.org/keywords/heat-exchanger","display_name":"Heat exchanger","score":0.4341464042663574},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4308403730392456},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.39947187900543213},{"id":"https://openalex.org/keywords/rayleigh-number","display_name":"Rayleigh number","score":0.3888920247554779},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.3351149559020996},{"id":"https://openalex.org/keywords/natural-convection","display_name":"Natural convection","score":0.3331298232078552},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.21993431448936462},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.13374167680740356}],"concepts":[{"id":"https://openalex.org/C10899652","wikidata":"https://www.wikidata.org/wiki/Q160329","display_name":"Convection","level":2,"score":0.6244469285011292},{"id":"https://openalex.org/C132812236","wikidata":"https://www.wikidata.org/wiki/Q1019460","display_name":"Rayleigh\u2013B\u00e9nard convection","level":5,"score":0.5644492506980896},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5132498741149902},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5118952989578247},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47090625762939453},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4354260265827179},{"id":"https://openalex.org/C107706546","wikidata":"https://www.wikidata.org/wiki/Q189124","display_name":"Heat exchanger","level":2,"score":0.4341464042663574},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4308403730392456},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.39947187900543213},{"id":"https://openalex.org/C106836276","wikidata":"https://www.wikidata.org/wiki/Q898249","display_name":"Rayleigh number","level":4,"score":0.3888920247554779},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.3351149559020996},{"id":"https://openalex.org/C54791560","wikidata":"https://www.wikidata.org/wiki/Q3285020","display_name":"Natural convection","level":3,"score":0.3331298232078552},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.21993431448936462},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.13374167680740356},{"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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0036139900370388","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139900370388","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.487.7589","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.487.7589","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://eaton.math.rpi.edu/Faculty/Herron/SIAP(2000).pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W210876736","https://openalex.org/W1575147392","https://openalex.org/W1591499074","https://openalex.org/W1624465419","https://openalex.org/W1970707528","https://openalex.org/W2001014149","https://openalex.org/W2005722356","https://openalex.org/W2005960859","https://openalex.org/W2008226211","https://openalex.org/W2022700318","https://openalex.org/W2028820496","https://openalex.org/W2055931342","https://openalex.org/W2112396914","https://openalex.org/W2131705730","https://openalex.org/W2155679236","https://openalex.org/W2318370559","https://openalex.org/W4285719527","https://openalex.org/W4300771172"],"related_works":["https://openalex.org/W131415422","https://openalex.org/W2731857948","https://openalex.org/W4310379157","https://openalex.org/W2531228161","https://openalex.org/W2111130705","https://openalex.org/W4283721563","https://openalex.org/W4386810572","https://openalex.org/W2606608893","https://openalex.org/W2744764441","https://openalex.org/W2046854329"],"abstract_inverted_index":{"The":[0,53],"problem":[1],"of":[2,19,29,31,39,45,60,69],"Rayleigh--B\u00e9nard":[3],"convection":[4],"with":[5],"internal":[6],"heat":[7,47],"sources":[8],"and":[9,42,64],"a":[10,61],"variable":[11],"gravity":[12,40],"field":[13,41],"is":[14,24,55],"treated.":[15],"For":[16],"the":[17,27,37,43,46,51,58,66],"case":[18],"stress-free":[20],"boundary":[21],"conditions,":[22],"it":[23],"proved":[25],"that":[26],"principle":[28],"exchange":[30],"stabilities":[32],"holds":[33],"as":[34,36],"long":[35],"product":[38],"integral":[44],"sourcesis":[48],"nonnegative":[49],"throughout":[50],"layer.":[52],"proof":[54],"based":[56],"on":[57],"idea":[59],"positive":[62],"operator,":[63],"uses":[65],"positivity":[67],"properties":[68],"Green's":[70],"function.":[71]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}