{"id":"https://openalex.org/W3047740297","doi":"https://doi.org/10.1109/tac.2020.3014457","title":"On Exponential Bistability of Equilibrium Profiles of Nonisothermal Axial Dispersion Tubular Reactors","display_name":"On Exponential Bistability of Equilibrium Profiles of Nonisothermal Axial Dispersion Tubular Reactors","publication_year":2020,"publication_date":"2020-08-05","ids":{"openalex":"https://openalex.org/W3047740297","doi":"https://doi.org/10.1109/tac.2020.3014457","mag":"3047740297"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2020.3014457","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2020.3014457","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/2078.1/240681","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058150041","display_name":"Anthony Hastir","orcid":"https://orcid.org/0000-0002-3776-6339"},"institutions":[{"id":"https://openalex.org/I149768937","display_name":"University of Namur","ror":"https://ror.org/03d1maw17","country_code":"BE","type":"education","lineage":["https://openalex.org/I149768937"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"Anthony Hastir","raw_affiliation_strings":["Department of Mathematics and Namur Institute for Complex Systems (naXys), University of Namur, Namur, Belgium"],"raw_orcid":"https://orcid.org/0000-0002-3776-6339","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Namur Institute for Complex Systems (naXys), University of Namur, Namur, Belgium","institution_ids":["https://openalex.org/I149768937"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022463640","display_name":"Joseph J. Winkin","orcid":"https://orcid.org/0000-0002-1283-2889"},"institutions":[{"id":"https://openalex.org/I149768937","display_name":"University of Namur","ror":"https://ror.org/03d1maw17","country_code":"BE","type":"education","lineage":["https://openalex.org/I149768937"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Joseph J. Winkin","raw_affiliation_strings":["Department of Mathematics and Namur Institute for Complex Systems (naXys), University of Namur, Namur, Belgium"],"raw_orcid":"https://orcid.org/0000-0002-1283-2889","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Namur Institute for Complex Systems (naXys), University of Namur, Namur, Belgium","institution_ids":["https://openalex.org/I149768937"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024190334","display_name":"Denis Dochain","orcid":"https://orcid.org/0000-0001-5206-7352"},"institutions":[{"id":"https://openalex.org/I95674353","display_name":"UCLouvain","ror":"https://ror.org/02495e989","country_code":"BE","type":"education","lineage":["https://openalex.org/I95674353"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Denis Dochain","raw_affiliation_strings":["Institute of Information and Communication Technologies, Electronics and Applied Mathematics, Université Catholique de Louvain, Louvain-La-Neuve, Belgium"],"raw_orcid":"https://orcid.org/0000-0001-5206-7352","affiliations":[{"raw_affiliation_string":"Institute of Information and Communication Technologies, Electronics and Applied Mathematics, Université Catholique de Louvain, Louvain-La-Neuve, Belgium","institution_ids":["https://openalex.org/I95674353"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5058150041"],"corresponding_institution_ids":["https://openalex.org/I149768937"],"apc_list":null,"apc_paid":null,"fwci":0.5952,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.67233803,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"66","issue":"7","first_page":"3235","last_page":"3242"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9977999925613403,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.996399998664856,"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/exponential-stability","display_name":"Exponential stability","score":0.6697403788566589},{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.6538622379302979},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5767508149147034},{"id":"https://openalex.org/keywords/dispersion","display_name":"Dispersion (optics)","score":0.4977898597717285},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.49601301550865173},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4919452369213104},{"id":"https://openalex.org/keywords/instability","display_name":"Instability","score":0.4447583556175232},{"id":"https://openalex.org/keywords/p\u00e9clet-number","display_name":"P\u00e9clet number","score":0.4322344660758972},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.3834688067436218},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33743417263031006},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.3358531594276428},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3350314497947693},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.24170517921447754}],"concepts":[{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.6697403788566589},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.6538622379302979},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5767508149147034},{"id":"https://openalex.org/C177562468","wikidata":"https://www.wikidata.org/wiki/Q182893","display_name":"Dispersion (optics)","level":2,"score":0.4977898597717285},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.49601301550865173},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4919452369213104},{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.4447583556175232},{"id":"https://openalex.org/C205684552","wikidata":"https://www.wikidata.org/wiki/Q899769","display_name":"P\u00e9clet number","level":2,"score":0.4322344660758972},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.3834688067436218},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33743417263031006},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3358531594276428},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3350314497947693},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.24170517921447754},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tac.2020.3014457","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2020.3014457","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"},{"id":"pmh:oai:pure.unamur.be:openaire_cris_publications/399fa647-68f4-4191-a13d-047882de8e84","is_oa":false,"landing_page_url":"https://researchportal.unamur.be/en/publications/399fa647-68f4-4191-a13d-047882de8e84","pdf_url":null,"source":{"id":"https://openalex.org/S4406922457","display_name":"Repository of the University of Namur","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Hastir, A, Winkin, J J & Dochain, D 2021, 'On exponential bistability of equilibrium profiles of nonisothermal axial dispersion tubular reactors', IEEE Transactions on Automatic Control, vol. 66, no. 7, 9159873, pp. 3235-3242. https://doi.org/10.1109/tac.2020.3014457","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:HAL:hal-04035705v1","is_oa":false,"landing_page_url":"https://hal.science/hal-04035705","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Automatic Control, 2021, 66 (7), pp.3235-3242. ⟨10.1109/TAC.2020.3014457⟩","raw_type":"Journal articles"},{"id":"pmh:oai:dial.uclouvain.be:boreal:240681","is_oa":true,"landing_page_url":"http://hdl.handle.net/2078.1/240681","pdf_url":null,"source":{"id":"https://openalex.org/S4306401902","display_name":"Digital Access to Libraries (Universit\u00e9 catholique de Louvain (UCL), l'Universit\u00e9 de Namur (UNamur) and the Universit\u00e9 Saint-Louis (USL-B))","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I95674353","host_organization_name":"UCLouvain","host_organization_lineage":["https://openalex.org/I95674353"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Automatic Control, , p. 1-1 (2020)","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:dial.uclouvain.be:boreal:240681","is_oa":true,"landing_page_url":"http://hdl.handle.net/2078.1/240681","pdf_url":null,"source":{"id":"https://openalex.org/S4306401902","display_name":"Digital Access to Libraries (Universit\u00e9 catholique de Louvain (UCL), l'Universit\u00e9 de Namur (UNamur) and the Universit\u00e9 Saint-Louis (USL-B))","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I95674353","host_organization_name":"UCLouvain","host_organization_lineage":["https://openalex.org/I95674353"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Automatic Control, , p. 1-1 (2020)","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"display_name":"Clean water and sanitation","id":"https://metadata.un.org/sdg/6","score":0.4099999964237213}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321390","display_name":"Fonds De La Recherche Scientifique - FNRS","ror":"https://ror.org/03q83t159"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1538686203","https://openalex.org/W1560060148","https://openalex.org/W1606157354","https://openalex.org/W1607530402","https://openalex.org/W1987627551","https://openalex.org/W2004794228","https://openalex.org/W2008850282","https://openalex.org/W2013513283","https://openalex.org/W2024451229","https://openalex.org/W2029382655","https://openalex.org/W2042708338","https://openalex.org/W2054649564","https://openalex.org/W2057771841","https://openalex.org/W2140134500","https://openalex.org/W2499641798","https://openalex.org/W2535652564","https://openalex.org/W2562001747","https://openalex.org/W2770034186","https://openalex.org/W2781946908","https://openalex.org/W3013685261","https://openalex.org/W4210923002","https://openalex.org/W6681202733","https://openalex.org/W6746330663"],"related_works":["https://openalex.org/W2034199904","https://openalex.org/W2978248670","https://openalex.org/W2288026075","https://openalex.org/W1999383129","https://openalex.org/W2101340403","https://openalex.org/W2160092417","https://openalex.org/W2164703465","https://openalex.org/W2168383058","https://openalex.org/W2143247663","https://openalex.org/W2050693590"],"abstract_inverted_index":{"Sufficient":[0],"conditions":[1],"are":[2,25,64,78,128,147],"established":[3],"for":[4,12,141],"the":[5,9,33,43,46,51,56,81,104,107,118,134,142],"exponential":[6,99],"stability/instability":[7],"of":[8,16,32,72,74],"equilibrium":[10,87,126],"profiles":[11,127],"a":[13,29,96],"linearized":[14,83,143],"model":[15,84],"nonisothermal":[17],"axial":[18],"dispersion":[19],"tubular":[20],"reactors.":[21],"The":[22,145],"considered":[23,82],"reactors":[24],"assumed":[26,65],"to":[27,66,90],"involve":[28],"chemical":[30],"reaction":[31],"form":[34],"A":[35,39],"\u2192":[36],"B,":[37],"where":[38,50],"and":[40,45,49,58],"B":[41],"denote":[42],"reactant":[44],"product,":[47],"respectively,":[48],"Peclet":[52],"numbers":[53],"appearing":[54],"in":[55],"energy":[57],"mass":[59],"balance":[60],"partial":[61],"differential":[62],"equations":[63],"be":[67,91],"equal.":[68],"First,":[69],"different":[70],"kinds":[71],"linearization":[73],"infinite-dimensional":[75],"dynamical":[76],"systems":[77],"presented.":[79],"Then,":[80],"around":[85],"any":[86],"is":[88,101,115,120,131,139],"shown":[89,116],"well-posed.":[92],"Moreover,":[93],"by":[94,149],"using":[95],"Lyapunov-based":[97],"approach,":[98],"stability":[100,135],"addressed.":[102],"In":[103],"case":[105],"when":[106],"reactor":[108],"can":[109],"exhibit":[110],"only":[111],"one":[112],"equilibrium,":[113],"it":[114],"that":[117],"latter":[119],"always":[121],"exponentially":[122],"stable.":[123],"When":[124],"three":[125],"exhibited,":[129],"bistability":[130],"established,":[132],"i.e.":[133],"pattern":[136],"\u201c(exponentially)":[137],"stable-unstable-stable\u201d":[138],"proven":[140],"model.":[144],"results":[146],"illustrated":[148],"some":[150],"numerical":[151],"simulations.":[152]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2}],"updated_date":"2026-05-07T13:39:58.223016","created_date":"2025-10-10T00:00:00"}