{"id":"https://openalex.org/W2069956218","doi":"https://doi.org/10.1137/s0036139903426976","title":"Homogenization Theory and the Assessment of Extreme Field Values in Composites with Random Microstructure","display_name":"Homogenization Theory and the Assessment of Extreme Field Values in Composites with Random Microstructure","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2069956218","doi":"https://doi.org/10.1137/s0036139903426976","mag":"2069956218"},"language":"en","primary_location":{"id":"doi:10.1137/s0036139903426976","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139903426976","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/A5040697039","display_name":"Robert Lipton","orcid":"https://orcid.org/0000-0002-1382-3204"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Robert Lipton","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5040697039"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.4199,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.8862069,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"65","issue":"2","first_page":"475","last_page":"493"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"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/T11558","display_name":"Composite Material Mechanics","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9990000128746033,"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/pointwise","display_name":"Pointwise","score":0.8344465494155884},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.6826396584510803},{"id":"https://openalex.org/keywords/electric-field","display_name":"Electric field","score":0.6092914938926697},{"id":"https://openalex.org/keywords/microstructure","display_name":"Microstructure","score":0.5468130707740784},{"id":"https://openalex.org/keywords/homogenization","display_name":"Homogenization (climate)","score":0.5131621956825256},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.48918917775154114},{"id":"https://openalex.org/keywords/anisotropy","display_name":"Anisotropy","score":0.4497067332267761},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4319643974304199},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3553922772407532},{"id":"https://openalex.org/keywords/condensed-matter-physics","display_name":"Condensed matter physics","score":0.35006439685821533},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3336641490459442},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3218466341495514},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.2962864637374878},{"id":"https://openalex.org/keywords/composite-material","display_name":"Composite material","score":0.24605149030685425},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.22942307591438293}],"concepts":[{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.8344465494155884},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.6826396584510803},{"id":"https://openalex.org/C60799052","wikidata":"https://www.wikidata.org/wiki/Q46221","display_name":"Electric field","level":2,"score":0.6092914938926697},{"id":"https://openalex.org/C87976508","wikidata":"https://www.wikidata.org/wiki/Q1498213","display_name":"Microstructure","level":2,"score":0.5468130707740784},{"id":"https://openalex.org/C2778722038","wikidata":"https://www.wikidata.org/wiki/Q17030643","display_name":"Homogenization (climate)","level":3,"score":0.5131621956825256},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.48918917775154114},{"id":"https://openalex.org/C85725439","wikidata":"https://www.wikidata.org/wiki/Q466686","display_name":"Anisotropy","level":2,"score":0.4497067332267761},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4319643974304199},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3553922772407532},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.35006439685821533},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3336641490459442},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3218466341495514},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.2962864637374878},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.24605149030685425},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.22942307591438293},{"id":"https://openalex.org/C130217890","wikidata":"https://www.wikidata.org/wiki/Q47041","display_name":"Biodiversity","level":2,"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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s0036139903426976","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139903426976","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:digitalcommons.lsu.edu:mathematics_pubs-1746","is_oa":false,"landing_page_url":"https://digitalcommons.lsu.edu/mathematics_pubs/747","pdf_url":null,"source":{"id":"https://openalex.org/S4210169993","display_name":"Civil War Book Review","issn_l":"1528-6592","issn":["1528-6592"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310315936","host_organization_name":"Louisiana State University","host_organization_lineage":["https://openalex.org/P4310315936"],"host_organization_lineage_names":["Louisiana State University"],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty Publications","raw_type":"text"},{"id":"pmh:oai:repository.lsu.edu:mathematics_pubs-1746","is_oa":false,"landing_page_url":"https://repository.lsu.edu/mathematics_pubs/747","pdf_url":null,"source":{"id":"https://openalex.org/S4210169993","display_name":"Civil War Book Review","issn_l":"1528-6592","issn":["1528-6592"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310315936","host_organization_name":"Louisiana State University","host_organization_lineage":["https://openalex.org/P4310315936"],"host_organization_lineage_names":["Louisiana State University"],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty Publications","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W39412911","https://openalex.org/W58981949","https://openalex.org/W149855415","https://openalex.org/W1512543386","https://openalex.org/W1547249381","https://openalex.org/W1641896143","https://openalex.org/W1676467742","https://openalex.org/W1995374819","https://openalex.org/W2001657683","https://openalex.org/W2099103066","https://openalex.org/W2131307019","https://openalex.org/W2154905879","https://openalex.org/W2491075445","https://openalex.org/W4300943935"],"related_works":["https://openalex.org/W2140020064","https://openalex.org/W143502885","https://openalex.org/W2103468410","https://openalex.org/W1856228368","https://openalex.org/W1968809652","https://openalex.org/W3197542402","https://openalex.org/W2971527398","https://openalex.org/W2104620528","https://openalex.org/W2086538707","https://openalex.org/W1025150868"],"abstract_inverted_index":{"Suitable":[0],"macroscopic":[1,134],"quantities":[2],"are":[3,29,57,105,108,153,208],"identified":[4],"and":[5,50,165],"used":[6],"to":[7,39,173,210],"assess":[8,211],"the":[9,36,40,44,53,67,73,78,81,91,113,122,125,131,139,142,158,192,201,212],"field":[10,83,128,204,217],"distribution":[11,213],"within":[12],"a":[13,181,188,197,225],"composite":[14,55],"specimen":[15,45],"of":[16,24,35,43,52,75,80,112,124,141,157,168,214],"finite":[17],"size":[18],"with":[19,171,178,224],"random":[20,54,176,226],"microstructure.":[21,228],"Composites":[22],"made":[23],"N":[25],"anisotropic":[26],"dielectric":[27],"materials":[28],"considered.":[30],"The":[31,69,87,117],"characteristic":[32],"length":[33,41],"scale":[34,42,184],"microstructure":[37,56,177],"relative":[38],"is":[46],"denoted":[47],"by":[48,59],"$\\varepsilon$,":[49],"realizations":[51],"labeled":[58],"$\\omega$.":[60],"Consider":[61],"any":[62],"cube":[63],"$C_0$":[64,76],"located":[65],"inside":[66],"composite.":[68],"function":[70,195],"$P^\\varepsilon(t,C_0,\\omega)$":[71],"gives":[72],"proportion":[74],"where":[77],"square":[79],"electric":[82,127,135,203,216],"intensity":[84,218],"exceeds":[85],"t.":[86],"analysis":[88],"focuses":[89],"on":[90,102,138,148,180,191,200],"case":[92],"when":[93],"$0":[94],"<":[95],"\\varepsilon":[96],"\\ll":[97],"1$.":[98],"Rigorous":[99],"upper":[100],"bounds":[101,147],"${\\lim}_{\\varepsilon\\rightarrow":[103,149,169],"0}P^\\varepsilon(t,C_0,\\omega)$":[104,170],"found.":[106],"They":[107],"given":[109,154],"in":[110,155],"terms":[111,156],"macrofield":[114,118,143,159,193],"modulation":[115,119,160,194],"functions.":[116],"functions":[120,161],"capture":[121],"excursions":[123],"local":[126],"fluctuations":[129],"about":[130],"homogenized":[132],"or":[133],"field.":[136],"Information":[137],"regularity":[140],"modulations":[144],"translates":[145],"into":[146],"0}P^\\varepsilon(t,C_0,\\omega)$.":[150],"Sufficient":[151],"conditions":[152],"that":[162,187],"guarantee":[163],"polynomial":[164],"exponential":[166],"decay":[167],"respect":[172],"``t.'":[174],"For":[175],"oscillation":[179],"sufficiently":[182],"small":[183],"we":[185],"demonstrate":[186],"pointwise":[189,198],"bound":[190,199],"provides":[196],"actual":[202],"intensity.":[205],"These":[206],"results":[207],"applied":[209],"extreme":[215],"for":[219],"an":[220],"L-shaped":[221],"domain":[222],"filled":[223],"laminar":[227]},"counts_by_year":[],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
