{"id":"https://openalex.org/W2132304446","doi":"https://doi.org/10.1137/090747713","title":"A Bounded Random Matrix Approach for Stochastic Upscaling","display_name":"A Bounded Random Matrix Approach for Stochastic Upscaling","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2132304446","doi":"https://doi.org/10.1137/090747713","mag":"2132304446"},"language":"en","primary_location":{"id":"doi:10.1137/090747713","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090747713","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102829313","display_name":"Sonjoy Das","orcid":"https://orcid.org/0000-0001-9711-8272"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sonjoy Das","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5006138292","display_name":"Roger Ghanem","orcid":"https://orcid.org/0000-0002-1890-920X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Roger Ghanem","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.2763,"has_fulltext":false,"cited_by_count":63,"citation_normalized_percentile":{"value":0.96979002,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"8","issue":"1","first_page":"296","last_page":"325"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9994999766349792,"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":0.9994999766349792,"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/T11115","display_name":"Topology Optimization in Engineering","score":0.9991999864578247,"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"}},{"id":"https://openalex.org/T11558","display_name":"Composite Material Mechanics","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/wishart-distribution","display_name":"Wishart distribution","score":0.6407339572906494},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6166666746139526},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5331510901451111},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5244629383087158},{"id":"https://openalex.org/keywords/random-variate","display_name":"Random variate","score":0.47166240215301514},{"id":"https://openalex.org/keywords/random-matrix","display_name":"Random matrix","score":0.4703531265258789},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43273818492889404},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.3642467260360718},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.35839080810546875},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.18891581892967224},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1518489122390747},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11009076237678528}],"concepts":[{"id":"https://openalex.org/C33962027","wikidata":"https://www.wikidata.org/wiki/Q1930697","display_name":"Wishart distribution","level":3,"score":0.6407339572906494},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6166666746139526},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5331510901451111},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5244629383087158},{"id":"https://openalex.org/C141547133","wikidata":"https://www.wikidata.org/wiki/Q7291996","display_name":"Random variate","level":3,"score":0.47166240215301514},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.4703531265258789},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43273818492889404},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.3642467260360718},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35839080810546875},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.18891581892967224},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1518489122390747},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11009076237678528},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"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:10.1137/090747713","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090747713","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"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.8199999928474426,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W32980360","https://openalex.org/W177018731","https://openalex.org/W1964745033","https://openalex.org/W1972455988","https://openalex.org/W1975238866","https://openalex.org/W1980171944","https://openalex.org/W1986058039","https://openalex.org/W1986286822","https://openalex.org/W1988859494","https://openalex.org/W1989993440","https://openalex.org/W1990515790","https://openalex.org/W1993130704","https://openalex.org/W1995875735","https://openalex.org/W1996044187","https://openalex.org/W1997969642","https://openalex.org/W2003191951","https://openalex.org/W2007028052","https://openalex.org/W2008584207","https://openalex.org/W2008826560","https://openalex.org/W2027616605","https://openalex.org/W2028718402","https://openalex.org/W2032558547","https://openalex.org/W2037770685","https://openalex.org/W2049034740","https://openalex.org/W2058469366","https://openalex.org/W2061443745","https://openalex.org/W2062369863","https://openalex.org/W2074176021","https://openalex.org/W2082368918","https://openalex.org/W2084113519","https://openalex.org/W2093083737","https://openalex.org/W2101241849","https://openalex.org/W2108888387","https://openalex.org/W2117385840","https://openalex.org/W2132400089","https://openalex.org/W2136545651","https://openalex.org/W2141622991","https://openalex.org/W2461765758","https://openalex.org/W2912522929","https://openalex.org/W3037265734","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W3143198474","https://openalex.org/W3184522547","https://openalex.org/W2964186098","https://openalex.org/W2097123157","https://openalex.org/W2510945920","https://openalex.org/W2949578938","https://openalex.org/W2908095763","https://openalex.org/W2008697571","https://openalex.org/W1543460404","https://openalex.org/W3179903767"],"abstract_inverted_index":{"A":[0,113],"maximum":[1],"entropy":[2],"(MaxEnt)":[3],"based":[4],"probabilistic":[5],"approach":[6],"is":[7,107,125,132,148,191],"developed":[8,160],"to":[9,66,86,134,175],"model":[10,73,155],"mechanical":[11],"systems":[12],"characterized":[13],"by":[14,40],"symmetric":[15,80],"positive-definite":[16,81],"matrices":[17,24,82],"bounded":[18],"from":[19],"below":[20],"and":[21,48,83,94,127,151,156,161],"above.":[22],"These":[23],"are":[25,38,63,159],"typically":[26],"encountered":[27],"in":[28,56],"the":[29,36,42,57,67,76,92,104,118,122,145,177,180,195],"constitutive":[30,105],"modeling":[31],"of":[32,44,59,79,137,144,179],"heterogeneous":[33],"materials,":[34],"where":[35],"bounds":[37,96,124],"deduced":[39],"employing":[41],"principles":[43],"minimum":[45,49],"complementary":[46],"energy":[47],"potential":[50],"energy.":[51],"Current":[52],"random":[53,111,139],"matrix":[54,106,147],"approaches":[55],"context":[58],"computational":[60],"stochastic":[61],"mechanics":[62],"adapted":[64],"only":[65],"Wishart":[68,181],"or":[69,182],"matrix-variate":[70,183],"Gamma":[71,184],"probability":[72,114,154,185],"supported":[74],"over":[75],"entire":[77],"space":[78],"therefore":[84],"unable":[85],"exploit":[87],"additional":[88,142],"information":[89],"available":[90],"through":[91],"lower":[93],"upper":[95],"when":[97],"appropriate.":[98],"Specifically,":[99],"for":[100,164],"a":[101,110,172],"given":[102],"material,":[103],"construed":[108],"as":[109],"matrix.":[112,140],"measure":[115],"that":[116],"reflects":[117],"constraints":[119],"consistent":[120,193],"with":[121,194],"energy-based":[123],"constructed,":[126],"an":[128,152],"associated":[129],"sampling":[130,157],"scheme":[131,158,190],"described":[133],"synthesize":[135],"realizations":[136],"this":[138,165],"An":[141],"constraint":[143],"mean":[146],"also":[149,170],"considered,":[150],"appropriate":[153],"illustrated":[162],"numerically":[163],"case.":[166],"The":[167],"present":[168],"work":[169],"develops":[171],"new":[173,188],"algorithm":[174],"compute":[176],"parameters":[178],"model.":[186],"This":[187],"algorithmic":[189],"more":[192],"MaxEnt":[196],"proposition.":[197]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":10}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}