{"id":"https://openalex.org/W2132137181","doi":"https://doi.org/10.1137/03060268x","title":"A Two-Scale Nonperturbative Approach to Uncertainty Analysis of Diffusion in Random Composites","display_name":"A Two-Scale Nonperturbative Approach to Uncertainty Analysis of Diffusion in Random Composites","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2132137181","doi":"https://doi.org/10.1137/03060268x","mag":"2132137181"},"language":"en","primary_location":{"id":"doi:10.1137/03060268x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/03060268x","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 &amp; 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/A5030218917","display_name":"Dongbin Xiu","orcid":null},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Dongbin Xiu","raw_affiliation_strings":["LOS Alamos National Laboratory"],"affiliations":[{"raw_affiliation_string":"LOS Alamos National Laboratory","institution_ids":["https://openalex.org/I1343871089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049066010","display_name":"Daniel M. Tartakovsky","orcid":"https://orcid.org/0000-0001-9019-8935"},"institutions":[{"id":"https://openalex.org/I1343871089","display_name":"Los Alamos National Laboratory","ror":"https://ror.org/01e41cf67","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I1343871089","https://openalex.org/I198811213","https://openalex.org/I4210120050"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daniel M. Tartakovsky","raw_affiliation_strings":["LOS Alamos National Laboratory"],"affiliations":[{"raw_affiliation_string":"LOS Alamos National Laboratory","institution_ids":["https://openalex.org/I1343871089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5030218917"],"corresponding_institution_ids":["https://openalex.org/I1343871089"],"apc_list":null,"apc_paid":null,"fwci":2.1634,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.88861386,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"2","issue":"4","first_page":"662","last_page":"674"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":1.0,"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":1.0,"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":0.9814000129699707,"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/T10716","display_name":"Soil and Unsaturated Flow","score":0.9718999862670898,"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/randomness","display_name":"Randomness","score":0.7432189583778381},{"id":"https://openalex.org/keywords/polynomial-chaos","display_name":"Polynomial chaos","score":0.698571503162384},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.6573169827461243},{"id":"https://openalex.org/keywords/uncertainty-quantification","display_name":"Uncertainty quantification","score":0.607628583908081},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.5195589065551758},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.46622350811958313},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.45522013306617737},{"id":"https://openalex.org/keywords/homogenization","display_name":"Homogenization (climate)","score":0.44848665595054626},{"id":"https://openalex.org/keywords/propagation-of-uncertainty","display_name":"Propagation of uncertainty","score":0.4362521171569824},{"id":"https://openalex.org/keywords/porous-medium","display_name":"Porous medium","score":0.4330020546913147},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42323243618011475},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37495607137680054},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.21636301279067993},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.2106689214706421},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.20445308089256287},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.16121920943260193},{"id":"https://openalex.org/keywords/porosity","display_name":"Porosity","score":0.13544568419456482},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.12934792041778564}],"concepts":[{"id":"https://openalex.org/C125112378","wikidata":"https://www.wikidata.org/wiki/Q176640","display_name":"Randomness","level":2,"score":0.7432189583778381},{"id":"https://openalex.org/C197656079","wikidata":"https://www.wikidata.org/wiki/Q17147719","display_name":"Polynomial chaos","level":3,"score":0.698571503162384},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.6573169827461243},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.607628583908081},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.5195589065551758},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.46622350811958313},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.45522013306617737},{"id":"https://openalex.org/C2778722038","wikidata":"https://www.wikidata.org/wiki/Q17030643","display_name":"Homogenization (climate)","level":3,"score":0.44848665595054626},{"id":"https://openalex.org/C123614077","wikidata":"https://www.wikidata.org/wiki/Q1364905","display_name":"Propagation of uncertainty","level":2,"score":0.4362521171569824},{"id":"https://openalex.org/C105569014","wikidata":"https://www.wikidata.org/wiki/Q3271208","display_name":"Porous medium","level":3,"score":0.4330020546913147},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42323243618011475},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37495607137680054},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.21636301279067993},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.2106689214706421},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.20445308089256287},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.16121920943260193},{"id":"https://openalex.org/C6648577","wikidata":"https://www.wikidata.org/wiki/Q622669","display_name":"Porosity","level":2,"score":0.13544568419456482},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.12934792041778564},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C130217890","wikidata":"https://www.wikidata.org/wiki/Q47041","display_name":"Biodiversity","level":2,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/03060268x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/03060268x","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 &amp; Simulation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.522.2606","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.522.2606","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://math.lanl.gov/~dmt/papers/pc-rdd.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","score":0.4300000071525574,"id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W236234832","https://openalex.org/W587830888","https://openalex.org/W1492622424","https://openalex.org/W1507209783","https://openalex.org/W1538934584","https://openalex.org/W1592093959","https://openalex.org/W1614940587","https://openalex.org/W1654411218","https://openalex.org/W1665602538","https://openalex.org/W1965847964","https://openalex.org/W1971726564","https://openalex.org/W1979367451","https://openalex.org/W1981537261","https://openalex.org/W1987043741","https://openalex.org/W2018159038","https://openalex.org/W2044390636","https://openalex.org/W2078623909","https://openalex.org/W2090693357","https://openalex.org/W2099699547","https://openalex.org/W2101097394","https://openalex.org/W2107773546","https://openalex.org/W2113517083","https://openalex.org/W2119396080","https://openalex.org/W2136602340","https://openalex.org/W2151257620","https://openalex.org/W2159514792","https://openalex.org/W2321957512","https://openalex.org/W2332771484","https://openalex.org/W2610642149","https://openalex.org/W3148924112","https://openalex.org/W4245531751","https://openalex.org/W4256082184"],"related_works":["https://openalex.org/W3215394929","https://openalex.org/W2108001913","https://openalex.org/W2014910883","https://openalex.org/W2517755966","https://openalex.org/W3158222746","https://openalex.org/W2778200063","https://openalex.org/W141012524","https://openalex.org/W2888380064","https://openalex.org/W2998625104","https://openalex.org/W2257115329"],"abstract_inverted_index":{"Many":[0],"physical":[1],"systems,":[2],"such":[3],"as":[4],"natural":[5],"porous":[6],"media,":[7],"are":[8,16],"highly":[9],"heterogeneous":[10],"and":[11,54,72,81,92],"characterized":[12],"by":[13],"parameters":[14,59],"that":[15,67,98],"uncertain":[17],"due":[18],"to":[19,76,96],"the":[20,40,49,58,79,107],"lack":[21],"of":[22,32,44,52,84,109],"sufficient":[23],"data.":[24],"This":[25],"uncertainty":[26,47,56],"(randomness)":[27],"occurs":[28],"on":[29,36],"a":[30,89],"multiplicity":[31],"scales.":[33],"We":[34,63,87],"focus":[35],"random":[37,69],"composites":[38],"with":[39],"two":[41],"dominant":[42],"scales":[43,83],"uncertainty:":[45],"large-scale":[46],"in":[48,57],"spatial":[50],"arrangement":[51],"materials":[53],"small-scale":[55],"within":[60],"each":[61],"material.":[62],"propose":[64],"an":[65],"approach":[66,101],"combines":[68],"domain":[70],"decompositions":[71],"polynomial":[73],"chaos":[74],"expansions":[75],"account":[77],"for":[78,106],"large":[80],"small":[82],"uncertainty,":[85],"respectively.":[86],"present":[88],"general":[90],"framework":[91],"use":[93],"one-dimensional":[94],"diffusion":[95],"demonstrate":[97],"our":[99],"combined":[100],"provides":[102],"robust,":[103],"nonperturbative":[104],"approximations":[105],"statistics":[108],"system":[110],"states.":[111]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
