{"id":"https://openalex.org/W2085781934","doi":"https://doi.org/10.1137/120898346","title":"Stochastic Model and Generator for Random Fields with Symmetry Properties: Application to the Mesoscopic Modeling of Elastic Random Media","display_name":"Stochastic Model and Generator for Random Fields with Symmetry Properties: Application to the Mesoscopic Modeling of Elastic Random Media","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2085781934","doi":"https://doi.org/10.1137/120898346","mag":"2085781934"},"language":"en","primary_location":{"id":"doi:10.1137/120898346","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120898346","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling & Simulation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-00854121","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025395694","display_name":"Johann Guilleminot","orcid":"https://orcid.org/0000-0003-3738-4370"},"institutions":[{"id":"https://openalex.org/I197681013","display_name":"Universit\u00e9 Paris-Est Cr\u00e9teil","ror":"https://ror.org/05ggc9x40","country_code":"FR","type":"education","lineage":["https://openalex.org/I197681013"]},{"id":"https://openalex.org/I4210160945","display_name":"Laboratoire Mod\u00e9lisation et Simulation Multi-Echelle","ror":"https://ror.org/04rrzfd14","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I197681013","https://openalex.org/I4210095849","https://openalex.org/I4210154111","https://openalex.org/I4210160945"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"J. Guilleminot","raw_affiliation_strings":["MSME - Laboratoire de Mod\u00e9lisation et Simulation Multi Echelle (Universit\u00e9 Paris-Est, 5 Bd Descartes, 77454 Marne-la-Vall\u00e9e, Cedex 2\r\nUniversit\u00e9 Paris-Est Cr\u00e9teil Val de Marne (UPEC) Facult\u00e9 des Sciences et Technologie - Equipe de Biom\u00e9canique\r\n61 avenue du g\u00e9n\u00e9ral de Gaulle 94010 Cr\u00e9teil Cedex - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MSME - Laboratoire de Mod\u00e9lisation et Simulation Multi Echelle (Universit\u00e9 Paris-Est, 5 Bd Descartes, 77454 Marne-la-Vall\u00e9e, Cedex 2\r\nUniversit\u00e9 Paris-Est Cr\u00e9teil Val de Marne (UPEC) Facult\u00e9 des Sciences et Technologie - Equipe de Biom\u00e9canique\r\n61 avenue du g\u00e9n\u00e9ral de Gaulle 94010 Cr\u00e9teil Cedex - France)","institution_ids":["https://openalex.org/I4210160945","https://openalex.org/I197681013"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003805312","display_name":"Christian Soize","orcid":"https://orcid.org/0000-0002-1083-6771"},"institutions":[{"id":"https://openalex.org/I197681013","display_name":"Universit\u00e9 Paris-Est Cr\u00e9teil","ror":"https://ror.org/05ggc9x40","country_code":"FR","type":"education","lineage":["https://openalex.org/I197681013"]},{"id":"https://openalex.org/I4210160945","display_name":"Laboratoire Mod\u00e9lisation et Simulation Multi-Echelle","ror":"https://ror.org/04rrzfd14","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I197681013","https://openalex.org/I4210095849","https://openalex.org/I4210154111","https://openalex.org/I4210160945"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"C. Soize","raw_affiliation_strings":["MSME - Laboratoire de Mod\u00e9lisation et Simulation Multi Echelle (Universit\u00e9 Paris-Est, 5 Bd Descartes, 77454 Marne-la-Vall\u00e9e, Cedex 2\r\nUniversit\u00e9 Paris-Est Cr\u00e9teil Val de Marne (UPEC) Facult\u00e9 des Sciences et Technologie - Equipe de Biom\u00e9canique\r\n61 avenue du g\u00e9n\u00e9ral de Gaulle 94010 Cr\u00e9teil Cedex - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MSME - Laboratoire de Mod\u00e9lisation et Simulation Multi Echelle (Universit\u00e9 Paris-Est, 5 Bd Descartes, 77454 Marne-la-Vall\u00e9e, Cedex 2\r\nUniversit\u00e9 Paris-Est Cr\u00e9teil Val de Marne (UPEC) Facult\u00e9 des Sciences et Technologie - Equipe de Biom\u00e9canique\r\n61 avenue du g\u00e9n\u00e9ral de Gaulle 94010 Cr\u00e9teil Cedex - France)","institution_ids":["https://openalex.org/I4210160945","https://openalex.org/I197681013"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.7156,"has_fulltext":false,"cited_by_count":69,"citation_normalized_percentile":{"value":0.97639532,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"11","issue":"3","first_page":"840","last_page":"870"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9948999881744385,"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":0.9948999881744385,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9932000041007996,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12293","display_name":"Dam Engineering and Safety","score":0.9851999878883362,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"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/random-field","display_name":"Random field","score":0.7277244329452515},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6384642124176025},{"id":"https://openalex.org/keywords/random-matrix","display_name":"Random matrix","score":0.45086508989334106},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43263402581214905},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3847552537918091},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.2997417449951172},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1618461012840271},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.11342021822929382}],"concepts":[{"id":"https://openalex.org/C130402806","wikidata":"https://www.wikidata.org/wiki/Q5361768","display_name":"Random field","level":2,"score":0.7277244329452515},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6384642124176025},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.45086508989334106},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43263402581214905},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3847552537918091},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.2997417449951172},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1618461012840271},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.11342021822929382},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/120898346","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120898346","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling & Simulation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.402.8828","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.402.8828","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hal-upec-upem.archives-ouvertes.fr/docs/00/85/41/21/PDF/publi-2013-SIAM-MMS-guilleminot-soize-preprint.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00854121v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00854121","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2013, 11 (3), pp.840-870. ⟨10.1137/120898346⟩","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-00854121v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00854121","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2013, 11 (3), pp.840-870. ⟨10.1137/120898346⟩","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8928873552","display_name":"Stochastic modeling in nonlinear micromechanics","funder_award_id":"ANR-12-JS09-0001","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":60,"referenced_works":["https://openalex.org/W38700864","https://openalex.org/W643550028","https://openalex.org/W656368203","https://openalex.org/W1538934584","https://openalex.org/W1544770838","https://openalex.org/W1580736543","https://openalex.org/W1590002219","https://openalex.org/W1644159847","https://openalex.org/W1966109017","https://openalex.org/W1971216560","https://openalex.org/W1976942431","https://openalex.org/W1980661057","https://openalex.org/W1981159745","https://openalex.org/W1983874447","https://openalex.org/W1987170756","https://openalex.org/W1988859494","https://openalex.org/W1993130704","https://openalex.org/W1994400618","https://openalex.org/W1994497938","https://openalex.org/W1995293185","https://openalex.org/W1995717170","https://openalex.org/W1995875735","https://openalex.org/W1997084530","https://openalex.org/W1997808578","https://openalex.org/W1998914834","https://openalex.org/W1999290501","https://openalex.org/W2003191951","https://openalex.org/W2010737928","https://openalex.org/W2013525813","https://openalex.org/W2017724688","https://openalex.org/W2019555730","https://openalex.org/W2027757474","https://openalex.org/W2028195074","https://openalex.org/W2032558547","https://openalex.org/W2038883910","https://openalex.org/W2047591160","https://openalex.org/W2053133911","https://openalex.org/W2058035660","https://openalex.org/W2058362163","https://openalex.org/W2064862875","https://openalex.org/W2065620939","https://openalex.org/W2081531828","https://openalex.org/W2081670785","https://openalex.org/W2082368918","https://openalex.org/W2084575597","https://openalex.org/W2090858114","https://openalex.org/W2091268519","https://openalex.org/W2100928696","https://openalex.org/W2102037464","https://openalex.org/W2132304446","https://openalex.org/W2143638480","https://openalex.org/W2151566907","https://openalex.org/W2164741953","https://openalex.org/W2321957512","https://openalex.org/W2484588736","https://openalex.org/W2884826872","https://openalex.org/W2904611875","https://openalex.org/W3098094852","https://openalex.org/W4248305267","https://openalex.org/W4252028749"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"Abstract.":[0],"This":[1],"paper":[2],"is":[3,65],"concerned":[4],"with":[5,51],"the":[6,26,29,40,58,69,76,99,116,128,144,153,178,184,188],"construction":[7],"of":[8,12,39,42,60,72,98,101,107,118,137,180,183],"a":[9,91,123,158,164],"new":[10],"class":[11],"generalized":[13],"nonparametric":[14],"probabilistic":[15],"models":[16],"for":[17,127,170],"matrix-valued":[18],"non-Gaussian":[19],"random":[20,30,129,185],"fields.":[21],"More":[22],"specifically,":[23],"we":[24,109],"consider":[25],"case":[27],"where":[28,75],"field":[31,186],"may":[32,80,87],"take":[33],"its":[34],"values":[35],"in":[36,68,147],"some":[37,82,168],"subset":[38,93],"set":[41,100],"real":[43,104],"symmetric":[44,102],"positive-definite":[45,103],"matrices":[46,79],"presenting":[47],"sparsity":[48],"and":[49,86,121,152,173,187],"invariance":[50],"respect":[52],"to":[53,90],"given":[54,92],"orthogonal":[55],"transformations.":[56],"Within":[57],"context":[59],"linear":[61],"elasticity,":[62],"this":[63],"situation":[64],"typically":[66],"faced":[67],"multiscale":[70],"analysis":[71],"heterogeneous":[73],"microstructures,":[74],"constitutive":[77],"elasticity":[78],"exhibit":[81],"material":[83],"symmetry":[84],"properties":[85],"then":[88],"belong":[89],"M":[94,148],"sym":[95,149],"n":[96,150],"(R)":[97,151],"matrices.":[105],"First":[106],"all,":[108],"present":[110],"an":[111],"overall":[112],"methodology":[113],"relying":[114],"on":[115],"framework":[117],"information":[119],"theory":[120],"define":[122],"particular":[124],"algebraic":[125],"form":[126],"field.":[130],"The":[131],"representation":[132],"involves":[133],"two":[134],"independent":[135],"sources":[136],"uncertainties,":[138],"namely":[139],"one":[140,155],"preserving":[141],"almost":[142],"surely":[143],"topological":[145],"structure":[146],"other":[154],"acting":[156],"as":[157],"fully":[159],"anisotropic":[160],"stochastic":[161],"germ.":[162],"Such":[163],"parametrization":[165],"does":[166],"offer":[167],"flexibility":[169],"forward":[171],"simulations":[172],"inverse":[174],"identification":[175],"by":[176],"uncoupling":[177],"level":[179,189],"statistical":[181],"fluctuations":[182]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":13},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":2}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}