{"id":"https://openalex.org/W2011180991","doi":"https://doi.org/10.1137/s0036139995291180","title":"Reciprocal Relations, Bounds, and Size Effects for Composites with Highly Conducting Interface","display_name":"Reciprocal Relations, Bounds, and Size Effects for Composites with Highly Conducting Interface","publication_year":1997,"publication_date":"1997-04-01","ids":{"openalex":"https://openalex.org/W2011180991","doi":"https://doi.org/10.1137/s0036139995291180","mag":"2011180991"},"language":"en","primary_location":{"id":"doi:10.1137/s0036139995291180","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139995291180","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":[{"id":"https://openalex.org/I107077323","display_name":"Worcester Polytechnic Institute","ror":"https://ror.org/05ejpqr48","country_code":"US","type":"education","lineage":["https://openalex.org/I107077323"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Robert Lipton","raw_affiliation_strings":["Worcester Polytechnic Institute, Worcester, MA 01609"],"affiliations":[{"raw_affiliation_string":"Worcester Polytechnic Institute, Worcester, MA 01609","institution_ids":["https://openalex.org/I107077323"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5040697039"],"corresponding_institution_ids":["https://openalex.org/I107077323"],"apc_list":null,"apc_paid":null,"fwci":2.2679,"has_fulltext":false,"cited_by_count":41,"citation_normalized_percentile":{"value":0.87271634,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"57","issue":"2","first_page":"347","last_page":"363"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10474","display_name":"Material Dynamics and Properties","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10474","display_name":"Material Dynamics and Properties","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10822","display_name":"Acoustic Wave Phenomena Research","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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":0.995199978351593,"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/materials-science","display_name":"Materials science","score":0.8259196281433105},{"id":"https://openalex.org/keywords/composite-number","display_name":"Composite number","score":0.7670034170150757},{"id":"https://openalex.org/keywords/isotropy","display_name":"Isotropy","score":0.6552172899246216},{"id":"https://openalex.org/keywords/composite-material","display_name":"Composite material","score":0.6493582129478455},{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.5988204479217529},{"id":"https://openalex.org/keywords/radius","display_name":"RADIUS","score":0.527873694896698},{"id":"https://openalex.org/keywords/electric-field","display_name":"Electric field","score":0.5151423215866089},{"id":"https://openalex.org/keywords/conductivity","display_name":"Conductivity","score":0.4936257600784302},{"id":"https://openalex.org/keywords/dispersity","display_name":"Dispersity","score":0.4896250367164612},{"id":"https://openalex.org/keywords/spheres","display_name":"SPHERES","score":0.44905993342399597},{"id":"https://openalex.org/keywords/surface-energy","display_name":"Surface energy","score":0.4465746283531189},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.1492074429988861},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11024439334869385}],"concepts":[{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.8259196281433105},{"id":"https://openalex.org/C104779481","wikidata":"https://www.wikidata.org/wiki/Q50707","display_name":"Composite number","level":2,"score":0.7670034170150757},{"id":"https://openalex.org/C184050105","wikidata":"https://www.wikidata.org/wiki/Q273163","display_name":"Isotropy","level":2,"score":0.6552172899246216},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.6493582129478455},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.5988204479217529},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.527873694896698},{"id":"https://openalex.org/C60799052","wikidata":"https://www.wikidata.org/wiki/Q46221","display_name":"Electric field","level":2,"score":0.5151423215866089},{"id":"https://openalex.org/C131540310","wikidata":"https://www.wikidata.org/wiki/Q907564","display_name":"Conductivity","level":2,"score":0.4936257600784302},{"id":"https://openalex.org/C11432220","wikidata":"https://www.wikidata.org/wiki/Q1975334","display_name":"Dispersity","level":2,"score":0.4896250367164612},{"id":"https://openalex.org/C72422203","wikidata":"https://www.wikidata.org/wiki/Q7392545","display_name":"SPHERES","level":2,"score":0.44905993342399597},{"id":"https://openalex.org/C195839","wikidata":"https://www.wikidata.org/wiki/Q901959","display_name":"Surface energy","level":2,"score":0.4465746283531189},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.1492074429988861},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11024439334869385},{"id":"https://openalex.org/C188027245","wikidata":"https://www.wikidata.org/wiki/Q750446","display_name":"Polymer chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","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/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1137/s0036139995291180","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036139995291180","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:conservancy.umn.edu:11299/2799","is_oa":false,"landing_page_url":"http://purl.umn.edu/2799","pdf_url":null,"source":{"id":"https://openalex.org/S4306402521","display_name":"University of Minnesota Digital Conservancy (University of Minnesota)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130238516","host_organization_name":"University of Minnesota","host_organization_lineage":["https://openalex.org/I130238516"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},{"id":"pmh:oai:digitalcommons.lsu.edu:mathematics_pubs-1780","is_oa":false,"landing_page_url":"https://digitalcommons.lsu.edu/mathematics_pubs/781","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:CiteSeerX.psu:10.1.1.55.9253","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.55.9253","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ima.umn.edu/preprints/October1995/1339.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.581.3513","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.581.3513","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://www.math.lsu.edu/~lipton/reciprocalsiap.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.64.5697","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.64.5697","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ima.umn.edu/preprints/October1995/1339.pdf","raw_type":"text"},{"id":"pmh:oai:repository.lsu.edu:mathematics_pubs-1780","is_oa":false,"landing_page_url":"https://repository.lsu.edu/mathematics_pubs/781","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":[{"display_name":"Affordable and clean energy","score":0.8999999761581421,"id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G6006794474","display_name":"Mathematical Sciences: Analysis of Transport Properties     for Composites and Multi-Phase Flows with Application to    Optimal Design","funder_award_id":"9403866","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1498734336","https://openalex.org/W1513878287","https://openalex.org/W1517403807","https://openalex.org/W1676467742","https://openalex.org/W1971973036","https://openalex.org/W1984720921","https://openalex.org/W2000757613","https://openalex.org/W2015925618","https://openalex.org/W2038777987","https://openalex.org/W2041610501","https://openalex.org/W2058394211","https://openalex.org/W2109843552","https://openalex.org/W2113841508"],"related_works":["https://openalex.org/W2054682972","https://openalex.org/W4232936117","https://openalex.org/W2004192282","https://openalex.org/W2122226500","https://openalex.org/W2360085188","https://openalex.org/W1998788310","https://openalex.org/W2005766378","https://openalex.org/W2040752023","https://openalex.org/W1971745998","https://openalex.org/W2035779693"],"abstract_inverted_index":{"We":[0],"provide":[1],"a":[2,10,20,43,54,113,131],"reciprocal":[3],"relation":[4],"linking":[5,38],"the":[6,23,39,51,90,93,138,144],"effective":[7,78,122],"conductivity":[8,123],"of":[9,19,80,92,101,109,129],"composite":[11,21,44,55],"with":[12,22,28,45,56,71,120],"highly":[13,46,72],"conducting":[14,47,73],"phase":[15,25,33,48],"interfaces":[16,49],"to":[17,50,85,97],"that":[18],"same":[24],"geometry":[26],"but":[27],"an":[29],"electrical":[30],"contactresistance":[31],"at":[32],"interfaces.":[34],"A":[35],"field":[36,41,140],"relationship":[37],"electric":[40,139],"inside":[42],"current":[52],"in":[53],"contact":[57],"resistance":[58],"between":[59],"phases":[60],"is":[61,111,124,134,141],"found.":[62,125],"New":[63],"size":[64,91],"effects":[65],"exhibited":[66],"by":[67],"isotropic":[68,117],"particulate":[69],"suspensions":[70,108,119,128],"interface":[74],"are":[75,83],"obtained.":[76],"The":[77,99],"properties":[79],"periodic":[81],"composites":[82],"shown":[84],"be":[86],"monotonically":[87],"increasing":[88],"as":[89],"period":[94],"cell":[95],"tends":[96],"zero.":[98],"role":[100],"surface":[102],"energy":[103,105],"for":[104,116,136],"minimizing":[106],"polydisperse":[107,118],"disks":[110],"examined;":[112],"necessary":[114],"condition":[115],"minimal":[121],"For":[126],"monodisperse":[127],"spheres,":[130],"critical":[132],"radius":[133],"found":[135],"which":[137],"uniform":[142],"throughout":[143],"composite.":[145]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}
