{"id":"https://openalex.org/W1965229672","doi":"https://doi.org/10.1137/130934210","title":"Higher Order Mixed-Moment Approximations for the Fokker--Planck Equation in One Space Dimension","display_name":"Higher Order Mixed-Moment Approximations for the Fokker--Planck Equation in One Space Dimension","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W1965229672","doi":"https://doi.org/10.1137/130934210","mag":"1965229672"},"language":"en","primary_location":{"id":"doi:10.1137/130934210","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130934210","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/A5070253689","display_name":"Florian Schneider","orcid":"https://orcid.org/0000-0002-7052-8404"},"institutions":[{"id":"https://openalex.org/I153267046","display_name":"University of Kaiserslautern","ror":"https://ror.org/04zrf7b53","country_code":"DE","type":"education","lineage":["https://openalex.org/I153267046"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Florian Schneider","raw_affiliation_strings":["University of Kaiserslautern;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Kaiserslautern;","institution_ids":["https://openalex.org/I153267046"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051248269","display_name":"Graham W. Alldredge","orcid":null},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Graham Alldredge","raw_affiliation_strings":["Department of Mathematics, RWTH Aachen University, Schinkelstr. 2,52062 Aachen, Germany,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, RWTH Aachen University, Schinkelstr. 2,52062 Aachen, Germany,","institution_ids":["https://openalex.org/I887968799"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101567482","display_name":"Martin Frank","orcid":"https://orcid.org/0000-0001-8562-6982"},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Martin Frank","raw_affiliation_strings":["Department of Mathematics, RWTH Aachen University, Schinkelstr. 2,52062 Aachen, Germany,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, RWTH Aachen University, Schinkelstr. 2,52062 Aachen, Germany,","institution_ids":["https://openalex.org/I887968799"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058610061","display_name":"Axel Klar","orcid":"https://orcid.org/0000-0003-1679-9438"},"institutions":[{"id":"https://openalex.org/I3019415892","display_name":"Fraunhofer Institute for Industrial Mathematics","ror":"https://ror.org/019hjw009","country_code":"DE","type":"facility","lineage":["https://openalex.org/I3019415892","https://openalex.org/I4923324"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Axel Klar","raw_affiliation_strings":["Fachbereich Mathematik, TU Kaiserslautern and Fraunhofer Institut f\u00fcr Techno-und Wirtschaftsmathematik, 67663 Kaiserslautern, Germany,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fachbereich Mathematik, TU Kaiserslautern and Fraunhofer Institut f\u00fcr Techno-und Wirtschaftsmathematik, 67663 Kaiserslautern, Germany,","institution_ids":["https://openalex.org/I3019415892"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":6.4825,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.96818514,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"74","issue":"4","first_page":"1087","last_page":"1114"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9987000226974487,"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/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9987000226974487,"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":0.9983000159263611,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","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/mathematics","display_name":"Mathematics","score":0.7427711486816406},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.6768991947174072},{"id":"https://openalex.org/keywords/fokker\u2013planck-equation","display_name":"Fokker\u2013Planck equation","score":0.6314780116081238},{"id":"https://openalex.org/keywords/realizability","display_name":"Realizability","score":0.580112099647522},{"id":"https://openalex.org/keywords/moment-closure","display_name":"Moment closure","score":0.5469505786895752},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.5069966316223145},{"id":"https://openalex.org/keywords/central-moment","display_name":"Central moment","score":0.503311812877655},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.491780549287796},{"id":"https://openalex.org/keywords/closure-problem","display_name":"Closure problem","score":0.4763883948326111},{"id":"https://openalex.org/keywords/finite-volume-method","display_name":"Finite volume method","score":0.4732014834880829},{"id":"https://openalex.org/keywords/second-moment-of-area","display_name":"Second moment of area","score":0.4577575623989105},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.41957294940948486},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36354780197143555},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3434765636920929},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.22339078783988953},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.1834658682346344},{"id":"https://openalex.org/keywords/moment-generating-function","display_name":"Moment-generating function","score":0.18121010065078735},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.14397624135017395},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.11933475732803345},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10919302701950073},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09686514735221863},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.06353175640106201}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7427711486816406},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.6768991947174072},{"id":"https://openalex.org/C69123182","wikidata":"https://www.wikidata.org/wiki/Q891766","display_name":"Fokker\u2013Planck equation","level":3,"score":0.6314780116081238},{"id":"https://openalex.org/C2776378722","wikidata":"https://www.wikidata.org/wiki/Q3454417","display_name":"Realizability","level":2,"score":0.580112099647522},{"id":"https://openalex.org/C2778513689","wikidata":"https://www.wikidata.org/wiki/Q6897109","display_name":"Moment closure","level":3,"score":0.5469505786895752},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.5069966316223145},{"id":"https://openalex.org/C120229918","wikidata":"https://www.wikidata.org/wiki/Q1088747","display_name":"Central moment","level":4,"score":0.503311812877655},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.491780549287796},{"id":"https://openalex.org/C58626813","wikidata":"https://www.wikidata.org/wiki/Q5135529","display_name":"Closure problem","level":3,"score":0.4763883948326111},{"id":"https://openalex.org/C50478463","wikidata":"https://www.wikidata.org/wiki/Q1401936","display_name":"Finite volume method","level":2,"score":0.4732014834880829},{"id":"https://openalex.org/C61062188","wikidata":"https://www.wikidata.org/wiki/Q835065","display_name":"Second moment of area","level":2,"score":0.4577575623989105},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.41957294940948486},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36354780197143555},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3434765636920929},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.22339078783988953},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.1834658682346344},{"id":"https://openalex.org/C101796028","wikidata":"https://www.wikidata.org/wiki/Q535587","display_name":"Moment-generating function","level":3,"score":0.18121010065078735},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.14397624135017395},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.11933475732803345},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10919302701950073},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09686514735221863},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.06353175640106201},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C196558001","wikidata":"https://www.wikidata.org/wiki/Q190132","display_name":"Turbulence","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/130934210","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130934210","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.748.3411","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.748.3411","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1405.5305.pdf","raw_type":"text"},{"id":"pmh:oai:publica.fraunhofer.de:publica/247978","is_oa":false,"landing_page_url":"https://publica.fraunhofer.de/handle/publica/247978","pdf_url":null,"source":{"id":"https://openalex.org/S4306400318","display_name":"Fraunhofer-Publica (Fraunhofer-Gesellschaft)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4923324","host_organization_name":"Fraunhofer-Gesellschaft","host_organization_lineage":["https://openalex.org/I4923324"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"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":41,"referenced_works":["https://openalex.org/W579082404","https://openalex.org/W968933197","https://openalex.org/W1180203196","https://openalex.org/W1517934135","https://openalex.org/W1543064558","https://openalex.org/W1583892864","https://openalex.org/W1986769465","https://openalex.org/W1988844796","https://openalex.org/W1991332489","https://openalex.org/W2003210164","https://openalex.org/W2012831195","https://openalex.org/W2012938047","https://openalex.org/W2015474278","https://openalex.org/W2015847667","https://openalex.org/W2020298878","https://openalex.org/W2021311647","https://openalex.org/W2025376439","https://openalex.org/W2028961914","https://openalex.org/W2034976587","https://openalex.org/W2037978467","https://openalex.org/W2044048010","https://openalex.org/W2045455639","https://openalex.org/W2048368445","https://openalex.org/W2051247278","https://openalex.org/W2060059568","https://openalex.org/W2061186416","https://openalex.org/W2063430114","https://openalex.org/W2067134228","https://openalex.org/W2067172078","https://openalex.org/W2067828523","https://openalex.org/W2068264811","https://openalex.org/W2079263908","https://openalex.org/W2116729868","https://openalex.org/W2137192387","https://openalex.org/W2152550639","https://openalex.org/W2329315946","https://openalex.org/W2512259174","https://openalex.org/W3025765350","https://openalex.org/W3129186208","https://openalex.org/W4244681853","https://openalex.org/W4252361735"],"related_works":["https://openalex.org/W2135856271","https://openalex.org/W1673739928","https://openalex.org/W2360922486","https://openalex.org/W1980797978","https://openalex.org/W4299832939","https://openalex.org/W2527779051","https://openalex.org/W172313056","https://openalex.org/W2150055571","https://openalex.org/W1629457063","https://openalex.org/W1965229672"],"abstract_inverted_index":{"We":[0],"study":[1],"mixed-moment":[2],"models":[3,20],"(full":[4],"zeroth":[5],"moment,":[6],"half":[7],"higher":[8],"moments)":[9],"for":[10,37],"a":[11,49,82],"Fokker--Planck":[12,85],"equation":[13],"in":[14],"one":[15],"space":[16],"dimension.":[17],"Mixed-moment":[18],"minimum-entropy":[19,31],"are":[21,71],"known":[22],"to":[23,55],"overcome":[24],"the":[25],"zero":[26],"net-flux":[27],"problem":[28],"of":[29,41],"full-moment":[30],"M${}_n$":[32],"models.":[33],"A":[34],"realizability":[35],"theory":[36],"these":[38],"mixed":[39],"moments":[40],"arbitrary":[42],"order":[43],"is":[44],"derived,":[45],"as":[46,48,56],"well":[47],"new":[50],"closure,":[51],"which":[52],"we":[53],"refer":[54],"Kershaw":[57],"closure.":[58,68],"They":[59],"provide":[60],"nonnegative":[61],"distribution":[62],"functions":[63],"combined":[64],"with":[65,73,81],"an":[66],"analytical":[67],"Numerical":[69],"tests":[70],"performed":[72],"standard":[74],"first-order":[75],"finite":[76,83],"volume":[77],"schemes":[78],"and":[79],"compared":[80],"difference":[84],"scheme.":[86]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":4}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
