{"id":"https://openalex.org/W2030209658","doi":"https://doi.org/10.1137/s0036139994265846","title":"Integral Method Solution of Time-Dependent Strained Diffusion-Reaction Layers with Multistep Kinetics","display_name":"Integral Method Solution of Time-Dependent Strained Diffusion-Reaction Layers with Multistep Kinetics","publication_year":1996,"publication_date":"1996-08-01","ids":{"openalex":"https://openalex.org/W2030209658","doi":"https://doi.org/10.1137/s0036139994265846","mag":"2030209658"},"language":"en","primary_location":{"id":"doi:10.1137/s0036139994265846","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139994265846","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/A5080558897","display_name":"Werner J. A. Dahm","orcid":null},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Werner J. A. Dahm","raw_affiliation_strings":["University of Michigan , Ann Arbor"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Michigan , Ann Arbor","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075006459","display_name":"Gr\u00e9tar Tryggvason","orcid":"https://orcid.org/0000-0002-9884-8901"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Gr\u00e9tar Tryggvason","raw_affiliation_strings":["University of Michigan , Ann Arbor"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Michigan , Ann Arbor","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111613853","display_name":"Mei Zhuang","orcid":null},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]},{"id":"https://openalex.org/I87216513","display_name":"Michigan State University","ror":"https://ror.org/05hs6h993","country_code":"US","type":"education","lineage":["https://openalex.org/I87216513"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mei Zhuang","raw_affiliation_strings":["University of Michigan, Ann Arbor","Michigan State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Michigan, Ann Arbor","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"Michigan State University","institution_ids":["https://openalex.org/I87216513"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.3294,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.8691568,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"56","issue":"4","first_page":"1039","last_page":"1059"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10553","display_name":"Combustion and flame dynamics","score":0.9998999834060669,"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/T10553","display_name":"Combustion and flame dynamics","score":0.9998999834060669,"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/T11619","display_name":"Combustion and Detonation Processes","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9973999857902527,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/kinetics","display_name":"Kinetics","score":0.6074721813201904},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.6048423051834106},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5987389087677002},{"id":"https://openalex.org/keywords/chemical-kinetics","display_name":"Chemical kinetics","score":0.5644628405570984},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.5031086802482605},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.4687122702598572},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.42206281423568726},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.42203304171562195},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.3401021957397461},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3312976360321045},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.2814655900001526},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.21479177474975586},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.21114492416381836},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19787538051605225}],"concepts":[{"id":"https://openalex.org/C148898269","wikidata":"https://www.wikidata.org/wiki/Q1108792","display_name":"Kinetics","level":2,"score":0.6074721813201904},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6048423051834106},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5987389087677002},{"id":"https://openalex.org/C36663273","wikidata":"https://www.wikidata.org/wiki/Q209082","display_name":"Chemical kinetics","level":3,"score":0.5644628405570984},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5031086802482605},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.4687122702598572},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.42206281423568726},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.42203304171562195},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.3401021957397461},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3312976360321045},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.2814655900001526},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.21479177474975586},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.21114492416381836},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19787538051605225},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036139994265846","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139994265846","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W1648423107","https://openalex.org/W1964445719","https://openalex.org/W2050345909","https://openalex.org/W2087909119","https://openalex.org/W2105835698","https://openalex.org/W2154857023","https://openalex.org/W4229919325"],"related_works":["https://openalex.org/W2369058408","https://openalex.org/W2999616507","https://openalex.org/W4250341545","https://openalex.org/W2364614865","https://openalex.org/W3158316286","https://openalex.org/W2057849849","https://openalex.org/W2349812023","https://openalex.org/W2019594594","https://openalex.org/W2372045828","https://openalex.org/W2092321213"],"abstract_inverted_index":{"Multiple":[0],"coupled":[1,105,117],"chemical":[2,38],"reactions":[3],"occurring":[4],"within":[5,174],"strained":[6],"diffusion":[7],"layers":[8,34],"are":[9,68,111,124,161],"key":[10,139],"to":[11,25,100],"a":[12,71,79,101],"wide":[13],"range":[14],"of":[15,28,31,53,73,82,87,90,95,103,129,138,141,155,171,176],"reactive":[16,33],"flow":[17],"problems.":[18],"An":[19],"integral":[20,88],"approach":[21],"is":[22],"presented":[23,112,165],"here":[24],"allow":[26],"calculations":[27],"global":[29,147],"properties":[30,134],"such":[32,172],"for":[35,58,84,113],"complex":[36],"multistep":[37,96],"kinetics":[39,98,116,122],"and":[40,61,123,135,146],"time-varying":[41],"strain":[42],"rates.":[43],"The":[44,93,163],"infinite-degree-of-freedom":[45],"partial":[46],"differential":[47,75],"equations":[48,76],"(PDEs)":[49],"governing":[50],"the":[51,54,66,85,130,142,151],"dynamics":[52],"species":[55],"concentration":[56],"profiles":[57],"reactants,":[59],"intermediates,":[60],"products":[62],"as":[63,65],"well":[64],"temperature":[67],"projected":[69],"onto":[70],"set":[72,102],"ordinary":[74],"having":[77],"just":[78],"few":[80],"degrees":[81],"freedom":[83],"evolution":[86],"moments":[89],"these":[91],"profiles.":[92],"presence":[94],"reaction":[97,159],"leads":[99],"highly":[104],"nonlinear":[106],"moment":[107],"equations.":[108],"Numerical":[109],"solutions":[110,128],"four-step":[114],"methane-air":[115],"with":[118,126],"thermal":[119],"nitric":[120],"oxide":[121],"compared":[125],"direct":[127],"original":[131],"PDEs.":[132],"Some":[133],"numerical":[136],"illustrations":[137],"features":[140],"internal":[143],"layer":[144],"structure":[145],"flame":[148],"properties,":[149],"including":[150],"extinction":[152],"phenomenon":[153],"characteristic":[154],"large":[156],"Zel\u2019dovich":[157],"number":[158],"kinetics,":[160],"discussed.":[162],"method":[164],"brings":[166],"comparatively":[167],"detailed":[168],"parametric":[169],"studies":[170],"problems":[173],"reach":[175],"rather":[177],"modest":[178],"computational":[179],"requirements.":[180]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
