{"id":"https://openalex.org/W2465313802","doi":"https://doi.org/10.1137/15m1026535","title":"Stochastic Modeling and Regularity of the Nonlinear Elliptic curl--curl Equation","display_name":"Stochastic Modeling and Regularity of the Nonlinear Elliptic curl--curl Equation","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2465313802","doi":"https://doi.org/10.1137/15m1026535","mag":"2465313802"},"language":"en","primary_location":{"id":"doi:10.1137/15m1026535","is_oa":true,"landing_page_url":"https://doi.org/10.1137/15m1026535","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/15M1026535","source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM/ASA Journal on Uncertainty Quantification","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://epubs.siam.org/doi/pdf/10.1137/15M1026535","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Ulrich R\u00f6mer","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ulrich R\u00f6mer","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Sebastian Sch\u00f6ps","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sebastian Sch\u00f6ps","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Thomas Weiland","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Thomas Weiland","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.0569,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.8932561,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"4","issue":"1","first_page":"952","last_page":"979"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.8938000202178955,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.8938000202178955,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.025800000876188278,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.011300000362098217,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6272000074386597},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.4352000057697296},{"id":"https://openalex.org/keywords/stochastic-modelling","display_name":"Stochastic modelling","score":0.42500001192092896},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.42160001397132874},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.39089998602867126},{"id":"https://openalex.org/keywords/elliptic-curve","display_name":"Elliptic curve","score":0.3693000078201294},{"id":"https://openalex.org/keywords/sensitivity","display_name":"Sensitivity (control systems)","score":0.36629998683929443},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.36629998683929443}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7810999751091003},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6272000074386597},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5594000220298767},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.44609999656677246},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.4352000057697296},{"id":"https://openalex.org/C127491075","wikidata":"https://www.wikidata.org/wiki/Q7617825","display_name":"Stochastic modelling","level":2,"score":0.42500001192092896},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.42160001397132874},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.39089998602867126},{"id":"https://openalex.org/C179603306","wikidata":"https://www.wikidata.org/wiki/Q268493","display_name":"Elliptic curve","level":2,"score":0.3693000078201294},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.36629998683929443},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.36629998683929443},{"id":"https://openalex.org/C158535547","wikidata":"https://www.wikidata.org/wiki/Q5165437","display_name":"Continuous-time stochastic process","level":3,"score":0.3450999855995178},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.33489999175071716},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.32659998536109924},{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.32109999656677246},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.319599986076355},{"id":"https://openalex.org/C25915931","wikidata":"https://www.wikidata.org/wiki/Q4180825","display_name":"Stochastic simulation","level":2,"score":0.30570000410079956},{"id":"https://openalex.org/C55479107","wikidata":"https://www.wikidata.org/wiki/Q97663916","display_name":"Stochastic approximation","level":3,"score":0.2766000032424927},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.25940001010894775},{"id":"https://openalex.org/C84629840","wikidata":"https://www.wikidata.org/wiki/Q16979017","display_name":"Stochastic partial differential equation","level":3,"score":0.25360000133514404},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.2500999867916107}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/15m1026535","is_oa":true,"landing_page_url":"https://doi.org/10.1137/15m1026535","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/15M1026535","source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM/ASA Journal on Uncertainty Quantification","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1606.07643","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1606.07643","pdf_url":"https://arxiv.org/pdf/1606.07643","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"}],"best_oa_location":{"id":"doi:10.1137/15m1026535","is_oa":true,"landing_page_url":"https://doi.org/10.1137/15m1026535","pdf_url":"https://epubs.siam.org/doi/pdf/10.1137/15M1026535","source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM/ASA Journal on Uncertainty Quantification","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2465313802.pdf","grobid_xml":"https://content.openalex.org/works/W2465313802.grobid-xml"},"referenced_works_count":40,"referenced_works":["https://openalex.org/W124257918","https://openalex.org/W1965949455","https://openalex.org/W1967117214","https://openalex.org/W1972684149","https://openalex.org/W1976349149","https://openalex.org/W1982421072","https://openalex.org/W1983156129","https://openalex.org/W1998253133","https://openalex.org/W2002926750","https://openalex.org/W2005606401","https://openalex.org/W2020220876","https://openalex.org/W2028506927","https://openalex.org/W2033721384","https://openalex.org/W2041509689","https://openalex.org/W2049358011","https://openalex.org/W2055460625","https://openalex.org/W2058362163","https://openalex.org/W2060528584","https://openalex.org/W2061174143","https://openalex.org/W2062993069","https://openalex.org/W2066466067","https://openalex.org/W2070021957","https://openalex.org/W2071704402","https://openalex.org/W2073187163","https://openalex.org/W2080928812","https://openalex.org/W2083845086","https://openalex.org/W2091203124","https://openalex.org/W2096045964","https://openalex.org/W2099379835","https://openalex.org/W2112311198","https://openalex.org/W2122538166","https://openalex.org/W2127189786","https://openalex.org/W2135923268","https://openalex.org/W2142863015","https://openalex.org/W2143591652","https://openalex.org/W2143783905","https://openalex.org/W2152181224","https://openalex.org/W2160786691","https://openalex.org/W2172008820","https://openalex.org/W3021293439"],"related_works":[],"abstract_inverted_index":{"This":[0],"paper":[1],"addresses":[2],"the":[3,11,19,26,31,40,71,74,100,108,116,125,129],"nonlinear":[4,55,97],"elliptic":[5,98],"curl--curl":[6,56,131],"equation":[7,132],"with":[8,48,105],"uncertainties":[9],"in":[10,18,70,93],"material":[12],"law.":[13],"It":[14,88],"is":[15,28,44,58,81,89,102,119],"frequently":[16],"employed":[17],"numerical":[20],"evaluation":[21],"of":[22,39,115],"magnetostatic":[23],"fields,":[24],"where":[25],"uncertainty":[27],"ascribed":[29],"to":[30,50,107],"so-called":[32],"$B$--$H$":[33,42],"curve.":[34],"A":[35,53],"truncated":[36],"Karhunen--Lo\u00e8ve":[37,126],"approximation":[38],"stochastic":[41,54,75,79,117,130],"curve":[43],"presented":[45],"and":[46,60,67,73,95,111,128],"analyzed":[47,82],"regard":[49],"monotonicity":[51],"constraints.":[52],"formulation":[57],"introduced":[59],"numerically":[61],"approximated":[62],"by":[63,83],"a":[64,84],"finite":[65],"element":[66],"collocation":[68],"method":[69],"deterministic":[72],"variable,":[76],"respectively.":[77],"The":[78],"regularity":[80],"higher-order":[85],"sensitivity":[86],"analysis.":[87],"shown":[90],"that,":[91],"unlike":[92],"linear":[94],"several":[96],"problems,":[99],"solution":[101],"not":[103],"analytic":[104],"respect":[106],"random":[109],"variables,":[110],"an":[112],"algebraic":[113],"decay":[114],"error":[118],"obtained.":[120],"Numerical":[121],"results":[122],"for":[123,135],"both":[124],"expansion":[127],"are":[133],"given":[134],"illustration.":[136]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2016-07-22T00:00:00"}