{"id":"https://openalex.org/W1994527935","doi":"https://doi.org/10.1137/0156002","title":"Biorthogonal Series Solution of Stokes Flow Problems in Sectorial Regions","display_name":"Biorthogonal Series Solution of Stokes Flow Problems in Sectorial Regions","publication_year":1996,"publication_date":"1996-02-01","ids":{"openalex":"https://openalex.org/W1994527935","doi":"https://doi.org/10.1137/0156002","mag":"1994527935"},"language":"en","primary_location":{"id":"doi:10.1137/0156002","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0156002","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/A5109849624","display_name":"Sami Khuri","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"S. A. Khuri","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5109849624"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.715,"has_fulltext":false,"cited_by_count":59,"citation_normalized_percentile":{"value":0.79735997,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"56","issue":"1","first_page":"19","last_page":"39"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11379","display_name":"Rheology and Fluid Dynamics Studies","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/1507","display_name":"Fluid Flow and Transfer Processes"},"field":{"id":"https://openalex.org/fields/15","display_name":"Chemical Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11379","display_name":"Rheology and Fluid Dynamics Studies","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/1507","display_name":"Fluid Flow and Transfer Processes"},"field":{"id":"https://openalex.org/fields/15","display_name":"Chemical Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9983000159263611,"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/T11254","display_name":"Fluid Dynamics and Vibration Analysis","score":0.998199999332428,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/eigenfunction","display_name":"Eigenfunction","score":0.9535149931907654},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7054319977760315},{"id":"https://openalex.org/keywords/biorthogonal-system","display_name":"Biorthogonal system","score":0.6687552332878113},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6364327669143677},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.56858891248703},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.5467218160629272},{"id":"https://openalex.org/keywords/truncation","display_name":"Truncation (statistics)","score":0.46375730633735657},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4299250543117523},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.41866233944892883},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3467402458190918},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.3172428011894226},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2505648136138916},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14784342050552368},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07866984605789185}],"concepts":[{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.9535149931907654},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7054319977760315},{"id":"https://openalex.org/C158453530","wikidata":"https://www.wikidata.org/wiki/Q864692","display_name":"Biorthogonal system","level":4,"score":0.6687552332878113},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6364327669143677},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.56858891248703},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.5467218160629272},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.46375730633735657},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4299250543117523},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.41866233944892883},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3467402458190918},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.3172428011894226},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2505648136138916},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14784342050552368},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07866984605789185},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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":1,"locations":[{"id":"doi:10.1137/0156002","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0156002","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W638400770","https://openalex.org/W1502611531","https://openalex.org/W1583796029","https://openalex.org/W1963817243","https://openalex.org/W1969287097","https://openalex.org/W1975302377","https://openalex.org/W1977327560","https://openalex.org/W1977982082","https://openalex.org/W1981898438","https://openalex.org/W1983289959","https://openalex.org/W1983819408","https://openalex.org/W1983979591","https://openalex.org/W1997067479","https://openalex.org/W2003311335","https://openalex.org/W2005780385","https://openalex.org/W2028473550","https://openalex.org/W2040567707","https://openalex.org/W2040611245","https://openalex.org/W2043668128","https://openalex.org/W2045302876","https://openalex.org/W2052931275","https://openalex.org/W2065865908","https://openalex.org/W2075117237","https://openalex.org/W2085778865","https://openalex.org/W2087238197","https://openalex.org/W2097427900","https://openalex.org/W2102398521","https://openalex.org/W2108969467","https://openalex.org/W2119562470","https://openalex.org/W2139795117","https://openalex.org/W2151890455","https://openalex.org/W2315065769","https://openalex.org/W2970586971","https://openalex.org/W4242505406","https://openalex.org/W4250842328","https://openalex.org/W4285719527","https://openalex.org/W4292079233"],"related_works":["https://openalex.org/W2014800978","https://openalex.org/W2061421451","https://openalex.org/W1969730698","https://openalex.org/W1552276833","https://openalex.org/W2132583619","https://openalex.org/W1995228206","https://openalex.org/W4243371733","https://openalex.org/W2093822129","https://openalex.org/W2013379693","https://openalex.org/W3160358654"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"develop":[4],"an":[5,38],"eigenfunction":[6,48,83],"expansion":[7,84],"method":[8,23,113],"for":[9,40,91],"solving":[10],"Stokes":[11,110],"flow":[12,120],"problems":[13,98],"in":[14,19,121],"sectorial":[15,124],"cavities":[16],"that":[17,102],"arise":[18,103],"fluid":[20,127],"dynamics.":[21],"The":[22,50,86,112],"leads":[24],"to":[25,77,116],"the":[26,41,44,47,69,79,82,108,117,126,133],"development":[27],"of":[28,31,43,46,54,81,94,107,136],"a":[29,92,122,137],"set":[30,129],"eigenfunctions,":[32,34,73],"adjoint":[33,72],"biorthogonality":[35,63,87],"conditions,":[36],"and":[37,71],"algorithm":[39],"computation":[42],"coefficients":[45,80,101],"expansion.":[49],"resulting":[51],"infinite":[52],"system":[53],"linear":[55],"equations":[56],"is":[57,114,128],"then":[58],"solved":[59],"by":[60,68,132],"truncation.":[61],"These":[62],"conditions":[64,88],"are":[65,75,89],"properties":[66],"satisfied":[67],"eigenfunctions":[70],"which":[74],"used":[76],"compute":[78],"solution.":[85],"derived":[90],"class":[93],"fourth-order":[95],"boundary":[96],"value":[97],"with":[99],"variable":[100],"from":[104],"separating":[105],"variables":[106],"governing":[109],"equation.":[111],"applied":[115],"slow,":[118],"steady":[119],"two-dimensional":[123],"cavity;":[125],"into":[130],"motion":[131],"uniform":[134],"translation":[135],"covering":[138],"plate":[139],"or":[140],"belt.":[141]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":5}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}