{"id":"https://openalex.org/W2085511837","doi":"https://doi.org/10.1137/140971075","title":"Rigorous Validation of Isolating Blocks for Flows and Their Conley Indices","display_name":"Rigorous Validation of Isolating Blocks for Flows and Their Conley Indices","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2085511837","doi":"https://doi.org/10.1137/140971075","mag":"2085511837"},"language":"en","primary_location":{"id":"doi:10.1137/140971075","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140971075","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"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 Dynamical Systems","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/A5036803057","display_name":"Thomas Dean Stephens","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Thomas Stephens","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5065530810","display_name":"Thomas Wanner","orcid":"https://orcid.org/0000-0003-3294-0366"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Thomas Wanner","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5036803057"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.609,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.82716821,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"13","issue":"4","first_page":"1847","last_page":"1878"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12063","display_name":"Heat and Mass Transfer in Porous Media","score":0.9771999716758728,"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/T12063","display_name":"Heat and Mass Transfer in Porous Media","score":0.9771999716758728,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9559999704360962,"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/T12350","display_name":"Particle Dynamics in Fluid Flows","score":0.9448000192642212,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42888548970222473},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.4228178858757019},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41928452253341675},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.32158297300338745}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42888548970222473},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.4228178858757019},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41928452253341675},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32158297300338745}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/140971075","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140971075","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"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 Dynamical Systems","raw_type":"journal-article"},{"id":"pmh:oai:conservancy.umn.edu:11299/181264","is_oa":false,"landing_page_url":"http://hdl.handle.net/11299/181264","pdf_url":null,"source":{"id":"https://openalex.org/S4306402521","display_name":"University of Minnesota Digital Conservancy (University of Minnesota)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130238516","host_organization_name":"University of Minnesota","host_organization_lineage":["https://openalex.org/I130238516"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Preprint"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W162901799","https://openalex.org/W178772886","https://openalex.org/W1507872748","https://openalex.org/W1557324374","https://openalex.org/W1980434682","https://openalex.org/W1995978888","https://openalex.org/W2004192027","https://openalex.org/W2006214482","https://openalex.org/W2036252043","https://openalex.org/W2038991247","https://openalex.org/W2081963949","https://openalex.org/W2085831227","https://openalex.org/W2111474755","https://openalex.org/W2745911235"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2042127053","https://openalex.org/W2142036596"],"abstract_inverted_index":{"Isolated":[0],"invariant":[1,18,27,63],"sets":[2,148],"and":[3,15,35,65,115,127,179],"their":[4,16,21,128],"associated":[5,75],"Conley":[6,76,184],"indices":[7],"are":[8,83,171],"valuable":[9],"tools":[10],"for":[11,60,98,113,141,193],"studying":[12],"dynamical":[13,90,99],"systems":[14,100],"global":[17],"structures.":[19],"Through":[20],"design,":[22],"they":[23],"aim":[24],"to":[25,42,56,67,72,85,173,181],"capture":[26],"behavior":[28],"which":[29,152],"is":[30,188],"robust":[31],"under":[32],"small":[33],"perturbations,":[34],"this":[36,106],"in":[37],"turn":[38],"makes":[39,133],"them":[40],"amenable":[41],"a":[43,49,110,118,136,167,175],"computational":[44],"treatment.":[45],"Over":[46],"the":[47,74,144],"years,":[48],"number":[50],"of":[51,80,121,135,146,149],"algorithms":[52],"have":[53],"been":[54],"proposed":[55],"find":[57],"index":[58,70,122,177],"pairs":[59],"an":[61,69,154,163],"isolated":[62],"set":[64,165],"then":[66],"use":[68,134],"pair":[71,178],"compute":[73,182],"index.":[77,185],"Nevertheless,":[78],"most":[79],"these":[81],"methods":[82,96],"restricted":[84],"discrete,":[86],"albeit":[87],"possibly":[88],"multivalued,":[89],"systems.":[91],"Only":[92],"relatively":[93],"few":[94],"general":[95],"exist":[97],"generated":[101],"by":[102],"differential":[103],"equations.":[104],"In":[105],"paper,":[107],"we":[108,170],"present":[109],"new":[111],"method":[112,132,187],"finding":[114],"rigorously":[116,142],"verifying":[117],"special":[119],"type":[120],"pairs,":[123],"namely":[124],"isolating":[125],"blocks":[126],"exit":[129,164],"sets.":[130],"Our":[131,186],"recently":[137],"developed":[138],"adaptive":[139,155],"algorithm":[140],"determining":[143],"location":[145],"nodal":[147,168],"smooth":[150],"functions,":[151],"combines":[153],"subdivision":[156],"technique":[157],"with":[158],"interval":[159],"arithmetic.":[160],"By":[161],"characterizing":[162],"as":[166],"domain,":[169],"able":[172],"determine":[174],"valid":[176],"proceed":[180],"its":[183],"illustrated":[189],"using":[190],"several":[191],"examples":[192],"three-dimensional":[194],"flows.":[195]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}