{"id":"https://openalex.org/W2061030918","doi":"https://doi.org/10.1137/s0036139902408163","title":"Strongly Degenerate Parabolic-Hyperbolic Systems Modeling Polydisperse Sedimentation with Compression","display_name":"Strongly Degenerate Parabolic-Hyperbolic Systems Modeling Polydisperse Sedimentation with Compression","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W2061030918","doi":"https://doi.org/10.1137/s0036139902408163","mag":"2061030918"},"language":"en","primary_location":{"id":"doi:10.1137/s0036139902408163","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139902408163","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/A5109179670","display_name":"Elmer M. Tory","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Elmer M. Tory","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034008502","display_name":"Kenneth H. Karlsen","orcid":"https://orcid.org/0000-0003-3375-2084"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kenneth H. Karlsen","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024575553","display_name":"Raimund B\u00fcrger","orcid":"https://orcid.org/0000-0001-9298-8981"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Raimund B\u00fcrger","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5057021984","display_name":"Stefan Berres","orcid":"https://orcid.org/0000-0002-8479-261X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stefan Berres","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5109179670"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":14.1707,"has_fulltext":false,"cited_by_count":174,"citation_normalized_percentile":{"value":0.99641062,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"64","issue":"1","first_page":"41","last_page":"80"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10940","display_name":"Navier-Stokes equation solutions","score":0.9836000204086304,"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":0.9836000204086304,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9818999767303467,"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/T11379","display_name":"Rheology and Fluid Dynamics Studies","score":0.9750999808311462,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6626657843589783},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.5239418148994446},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.511011004447937},{"id":"https://openalex.org/keywords/sedimentation","display_name":"Sedimentation","score":0.43721306324005127},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.43216472864151},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.42880046367645264},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.25069957971572876},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.22838786244392395}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6626657843589783},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.5239418148994446},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.511011004447937},{"id":"https://openalex.org/C29941650","wikidata":"https://www.wikidata.org/wiki/Q635485","display_name":"Sedimentation","level":3,"score":0.43721306324005127},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43216472864151},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.42880046367645264},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.25069957971572876},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.22838786244392395},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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/C2816523","wikidata":"https://www.wikidata.org/wiki/Q180184","display_name":"Sediment","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036139902408163","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139902408163","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":111,"referenced_works":["https://openalex.org/W144446942","https://openalex.org/W328073187","https://openalex.org/W577909876","https://openalex.org/W593307463","https://openalex.org/W657373134","https://openalex.org/W1441154465","https://openalex.org/W1520830016","https://openalex.org/W1523615189","https://openalex.org/W1554134448","https://openalex.org/W1565177988","https://openalex.org/W1602967628","https://openalex.org/W1649909247","https://openalex.org/W1658614176","https://openalex.org/W1964868203","https://openalex.org/W1968735462","https://openalex.org/W1973903805","https://openalex.org/W1977560113","https://openalex.org/W1982517799","https://openalex.org/W1982706969","https://openalex.org/W1983120574","https://openalex.org/W1983760355","https://openalex.org/W1983786793","https://openalex.org/W1985566773","https://openalex.org/W1985982837","https://openalex.org/W1990620734","https://openalex.org/W1991443161","https://openalex.org/W1995959798","https://openalex.org/W1999136531","https://openalex.org/W2000328677","https://openalex.org/W2000867677","https://openalex.org/W2008076987","https://openalex.org/W2008250213","https://openalex.org/W2012938047","https://openalex.org/W2012955628","https://openalex.org/W2017620052","https://openalex.org/W2024357547","https://openalex.org/W2026045861","https://openalex.org/W2027202002","https://openalex.org/W2027980406","https://openalex.org/W2029813107","https://openalex.org/W2032793395","https://openalex.org/W2035930403","https://openalex.org/W2036181736","https://openalex.org/W2036586276","https://openalex.org/W2037453411","https://openalex.org/W2037741679","https://openalex.org/W2038050807","https://openalex.org/W2041914357","https://openalex.org/W2045789072","https://openalex.org/W2048668831","https://openalex.org/W2049313805","https://openalex.org/W2051369747","https://openalex.org/W2051418165","https://openalex.org/W2055555874","https://openalex.org/W2055695184","https://openalex.org/W2056031232","https://openalex.org/W2058964076","https://openalex.org/W2061075376","https://openalex.org/W2062678343","https://openalex.org/W2067034992","https://openalex.org/W2070795183","https://openalex.org/W2073438034","https://openalex.org/W2074249064","https://openalex.org/W2075549787","https://openalex.org/W2078272277","https://openalex.org/W2079470416","https://openalex.org/W2081114767","https://openalex.org/W2081459381","https://openalex.org/W2081651917","https://openalex.org/W2083464092","https://openalex.org/W2083685621","https://openalex.org/W2086443137","https://openalex.org/W2087051197","https://openalex.org/W2094167173","https://openalex.org/W2096548885","https://openalex.org/W2098781861","https://openalex.org/W2101599596","https://openalex.org/W2101641492","https://openalex.org/W2106351439","https://openalex.org/W2107588255","https://openalex.org/W2110395631","https://openalex.org/W2112559245","https://openalex.org/W2114463167","https://openalex.org/W2117955358","https://openalex.org/W2120898720","https://openalex.org/W2125707734","https://openalex.org/W2134164763","https://openalex.org/W2137766562","https://openalex.org/W2150186831","https://openalex.org/W2150347258","https://openalex.org/W2154885094","https://openalex.org/W2155165167","https://openalex.org/W2156669471","https://openalex.org/W2157715842","https://openalex.org/W2169206444","https://openalex.org/W2169720994","https://openalex.org/W2171604049","https://openalex.org/W2265540068","https://openalex.org/W2333318131","https://openalex.org/W2334095483","https://openalex.org/W2369386221","https://openalex.org/W2480404596","https://openalex.org/W2501012850","https://openalex.org/W2507514479","https://openalex.org/W2606888149","https://openalex.org/W3216301249","https://openalex.org/W4240361988","https://openalex.org/W4249708147","https://openalex.org/W4256242560","https://openalex.org/W4292081050","https://openalex.org/W4299406105"],"related_works":["https://openalex.org/W2353039109","https://openalex.org/W2352518699","https://openalex.org/W4315588385","https://openalex.org/W2248119146","https://openalex.org/W3124638673","https://openalex.org/W2066153363","https://openalex.org/W2900100504","https://openalex.org/W2061564118","https://openalex.org/W2479290556","https://openalex.org/W2013381508"],"abstract_inverted_index":{"We":[0],"show":[1,87],"how":[2],"existing":[3],"models":[4],"for":[5,97,105,116,131],"the":[6,31,71,75,78,84,106,126,138,142,146],"sedimentation":[7,32],"of":[8,13,16,30,34,64,70,74,77,83,92,108],"monodisperse":[9],"flocculated":[10],"suspensions":[11,15,36],"and":[12,82,100],"polydisperse":[14,35],"rigid":[17],"spheres":[18],"differing":[19],"in":[20,54],"size":[21,102],"can":[22],"be":[23],"combined":[24],"to":[25,58,144,149],"yield":[26],"a":[27,121,150],"new":[28],"theory":[29,52],"processes":[33],"forming":[37],"compressible":[38],"sediments":[39],"(\"sedimentation":[40],"with":[41],"compression\"'":[42],"or":[43],"\"sedimentation-consolidation":[44],"process\").":[45],"For":[46],"N":[47,99],"solid":[48],"particle":[49,101],"species,":[50],"this":[51,89],"reduces":[53],"one":[55],"space":[56],"dimension":[57],"an":[59],"$N\\times":[60],"N$":[61],"coupled":[62],"system":[63,90],"quasi-linear":[65],"degenerate":[66,94],"convection-diffusion":[67,132],"equations.":[68],"Analyses":[69],"characteristic":[72],"polynomials":[73],"Jacobian":[76],"convective":[79],"flux":[80],"vector":[81],"diffusion":[85,148],"matrix":[86],"that":[88],"is":[91,118],"strongly":[93],"parabolic-hyperbolic":[95],"type":[96],"arbitrary":[98],"distributions.":[103],"Bounds":[104],"eigenvalues":[107,143],"both":[109],"matrices":[110],"are":[111],"derived.":[112],"The":[113,134],"mathematical":[114],"model":[115],"N=3$":[117],"illustrated":[119],"by":[120,125],"numerical":[122,135,147],"simulation":[123],"obtained":[124],"Kurganov-Tadmor":[127],"central":[128],"difference":[129],"scheme":[130,136],"problems.":[133],"exploits":[137],"derived":[139],"bounds":[140],"on":[141],"keep":[145],"minimum.":[151]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":14},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":8}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}