{"id":"https://openalex.org/W4214494656","doi":"https://doi.org/10.1137/21m1401206","title":"Rigidity Percolation in Disordered 3D Rod Systems","display_name":"Rigidity Percolation in Disordered 3D Rod Systems","publication_year":2022,"publication_date":"2022-02-24","ids":{"openalex":"https://openalex.org/W4214494656","doi":"https://doi.org/10.1137/21m1401206","mag":"3139343024"},"language":"en","primary_location":{"id":"doi:10.1137/21m1401206","doi":"https://doi.org/10.1137/21m1401206","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1401206","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,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","norway-1","poland-100","russia-white-list-2"],"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"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2103.12612","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049009656","display_name":"Samuel Heroy","orcid":"https://orcid.org/0000-0003-2936-9437","observed_orcids":["https://orcid.org/0000-0003-2936-9437"]},"institutions":[{"id":"https://openalex.org/I114027177","display_name":"University of North Carolina at Chapel Hill","ror":"https://ror.org/0130frc33","country_code":"US","type":"education","lineage":["https://openalex.org/I114027177"]},{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]},{"id":"https://openalex.org/I45129253","display_name":"University College London","ror":"https://ror.org/02jx3x895","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I45129253"]}],"countries":["GB","US"],"is_corresponding":false,"raw_author_name":"Samuel Heroy","raw_affiliation_strings":["Carolina Center for Interdisciplinary Applied Mathematics, Department of Mathematics, Uni-versity of North Carolina, Chapel Hill, NC 27599 USA","Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK","The Bartlett Centre for Advanced Spatial Analysis, University College London, London W1 4TJ, UK"],"raw_orcid":"https://orcid.org/0000-0003-2936-9437","affiliations":[{"raw_affiliation_string":"Carolina Center for Interdisciplinary Applied Mathematics, Department of Mathematics, Uni-versity of North Carolina, Chapel Hill, NC 27599 USA","institution_ids":["https://openalex.org/I114027177"]},{"raw_affiliation_string":"Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK","institution_ids":["https://openalex.org/I40120149"]},{"raw_affiliation_string":"The Bartlett Centre for Advanced Spatial Analysis, University College London, London W1 4TJ, UK","institution_ids":["https://openalex.org/I45129253"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037020807","display_name":"Dane Taylor","orcid":"https://orcid.org/0000-0003-1851-3309","observed_orcids":["https://orcid.org/0000-0003-1851-3309"]},"institutions":[{"id":"https://openalex.org/I114027177","display_name":"University of North Carolina at Chapel Hill","ror":"https://ror.org/0130frc33","country_code":"US","type":"education","lineage":["https://openalex.org/I114027177"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Dane Taylor","raw_affiliation_strings":["Carolina Center for Interdisciplinary Applied Mathematics, Department of Mathematics, Uni-versity of North Carolina, Chapel Hill, NC 27599 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Carolina Center for Interdisciplinary Applied Mathematics, Department of Mathematics, Uni-versity of North Carolina, Chapel Hill, NC 27599 USA","institution_ids":["https://openalex.org/I114027177"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044868467","display_name":"Feng Shi","orcid":"https://orcid.org/0000-0003-1522-9943","observed_orcids":["https://orcid.org/0000-0003-1522-9943"]},"institutions":[{"id":"https://openalex.org/I114027177","display_name":"University of North Carolina at Chapel Hill","ror":"https://ror.org/0130frc33","country_code":"US","type":"education","lineage":["https://openalex.org/I114027177"]},{"id":"https://openalex.org/I63190737","display_name":"University at Buffalo, State University of New York","ror":"https://ror.org/01y64my43","country_code":"US","type":"education","lineage":["https://openalex.org/I63190737"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Feng Shi","raw_affiliation_strings":["Carolina Center for Interdisciplinary Applied Mathematics, Department of Mathematics, Uni-versity of North Carolina, Chapel Hill, NC 27599 USA","Department of Mathematics, University at Buffalo, State University of New York, Buffalo, NY 14260 USA","The Odum Institute for Research in Social Science, University of North Carolina, Chapel Hill, NC 27599 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Carolina Center for Interdisciplinary Applied Mathematics, Department of Mathematics, Uni-versity of North Carolina, Chapel Hill, NC 27599 USA","institution_ids":["https://openalex.org/I114027177"]},{"raw_affiliation_string":"Department of Mathematics, University at Buffalo, State University of New York, Buffalo, NY 14260 USA","institution_ids":["https://openalex.org/I63190737"]},{"raw_affiliation_string":"The Odum Institute for Research in Social Science, University of North Carolina, Chapel Hill, NC 27599 USA","institution_ids":["https://openalex.org/I114027177"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030886600","display_name":"M. Gregory Forest","orcid":"https://orcid.org/0000-0002-7718-4456","observed_orcids":["https://orcid.org/0000-0002-7718-4456"]},"institutions":[{"id":"https://openalex.org/I114027177","display_name":"University of North Carolina at Chapel Hill","ror":"https://ror.org/0130frc33","country_code":"US","type":"education","lineage":["https://openalex.org/I114027177"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"M. Gregory Forest","raw_affiliation_strings":["Carolina Center for Interdisciplinary Applied Mathematics, Department of Mathematics, Uni-versity of North Carolina, Chapel Hill, NC 27599 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Carolina Center for Interdisciplinary Applied Mathematics, Department of Mathematics, Uni-versity of North Carolina, Chapel Hill, NC 27599 USA","institution_ids":["https://openalex.org/I114027177"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054890347","display_name":"Peter J. Mucha","orcid":"https://orcid.org/0000-0002-0648-7230","observed_orcids":["https://orcid.org/0000-0002-0648-7230"]},"institutions":[{"id":"https://openalex.org/I107672454","display_name":"Dartmouth College","ror":"https://ror.org/049s0rh22","country_code":"US","type":"education","lineage":["https://openalex.org/I107672454"]},{"id":"https://openalex.org/I114027177","display_name":"University of North Carolina at Chapel Hill","ror":"https://ror.org/0130frc33","country_code":"US","type":"education","lineage":["https://openalex.org/I114027177"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Peter J. Mucha","raw_affiliation_strings":["Carolina Center for Interdisciplinary Applied Mathematics, Department of Mathematics, Uni-versity of North Carolina, Chapel Hill, NC 27599 USA","Department of Mathematics, Dartmouth College, Hanover, NH 03755 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Carolina Center for Interdisciplinary Applied Mathematics, Department of Mathematics, Uni-versity of North Carolina, Chapel Hill, NC 27599 USA","institution_ids":["https://openalex.org/I114027177"]},{"raw_affiliation_string":"Department of Mathematics, Dartmouth College, Hanover, NH 03755 USA","institution_ids":["https://openalex.org/I107672454"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2706,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.33573368,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"20","issue":"1","first_page":"250","last_page":"281"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.7598000168800354,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.7598000168800354,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10474","display_name":"Material Dynamics and Properties","score":0.0786999985575676,"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/T11379","display_name":"Rheology and Fluid Dynamics Studies","score":0.03880000114440918,"subfield":{"id":"https://openalex.org/subfields/1507","display_name":"Fluid Flow and Transfer Processes"},"field":{"id":"https://openalex.org/fields/15","display_name":"Chemical Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/rigidity-percolation","display_name":"rigidity percolation","score":0.9850000143051147},{"id":"https://openalex.org/keywords/rheological-percolation","display_name":"rheological percolation","score":0.9509999752044678},{"id":"https://openalex.org/keywords/high-aspect-ratio-particles","display_name":"high aspect ratio particles","score":0.6769999861717224},{"id":"https://openalex.org/keywords/critical-density","display_name":"critical density","score":0.8930000066757202},{"id":"https://openalex.org/keywords/rod-aspect-ratio","display_name":"rod aspect ratio","score":0.734000027179718},{"id":"https://openalex.org/keywords/excluded-volume","display_name":"excluded volume","score":0.906000018119812}],"concepts":[{"id":"https://openalex.org/C2729557","wikidata":"https://www.wikidata.org/wiki/Q7167170","display_name":"Percolation threshold","level":3,"score":0.7460920214653015},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.6634349822998047},{"id":"https://openalex.org/C160343418","wikidata":"https://www.wikidata.org/wiki/Q185256","display_name":"Rigidity (electromagnetism)","level":2,"score":0.6524298191070557},{"id":"https://openalex.org/C2780457167","wikidata":"https://www.wikidata.org/wiki/Q17156484","display_name":"Percolation (cognitive psychology)","level":2,"score":0.5231710076332092},{"id":"https://openalex.org/C104779481","wikidata":"https://www.wikidata.org/wiki/Q50707","display_name":"Composite number","level":2,"score":0.4721256196498871},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.45954981446266174},{"id":"https://openalex.org/C15867958","wikidata":"https://www.wikidata.org/wiki/Q5280413","display_name":"Directed percolation","level":4,"score":0.4466467499732971},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.44627058506011963},{"id":"https://openalex.org/C200990466","wikidata":"https://www.wikidata.org/wiki/Q271707","display_name":"Rheology","level":2,"score":0.43672996759414673},{"id":"https://openalex.org/C11557063","wikidata":"https://www.wikidata.org/wiki/Q900918","display_name":"Percolation theory","level":3,"score":0.41157758235931396},{"id":"https://openalex.org/C131540310","wikidata":"https://www.wikidata.org/wiki/Q907564","display_name":"Conductivity","level":2,"score":0.27887147665023804},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.16228613257408142},{"id":"https://openalex.org/C69990965","wikidata":"https://www.wikidata.org/wiki/Q65402698","display_name":"Electrical resistivity and conductivity","level":2,"score":0.1528095304965973},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13390055298805237},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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/C169760540","wikidata":"https://www.wikidata.org/wiki/Q207011","display_name":"Neuroscience","level":1,"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":6,"locations":[{"id":"doi:10.1137/21m1401206","doi":"https://doi.org/10.1137/21m1401206","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1401206","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,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","norway-1","poland-100","russia-white-list-2"],"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:arXiv.org:2103.12612","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2103.12612","pdf_url":"https://arxiv.org/pdf/2103.12612","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:3139343024","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2103.12612","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:cdr.lib.unc.edu:sn00b829f","doi":null,"is_oa":false,"landing_page_url":"https://cdr.lib.unc.edu/downloads/vd66wb38m","pdf_url":null,"source":{"id":"https://openalex.org/S4306401075","display_name":"Carolina Digital Repository (University of North Carolina at Chapel Hill)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I114027177","host_organization_name":"University of North Carolina at Chapel Hill","host_organization_lineage":["https://openalex.org/I114027177"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Multiscale Modeling and Simulation, 20(1)","raw_type":"Article"},{"id":"doi:10.48550/arxiv.2103.12612","doi":"https://doi.org/10.48550/arxiv.2103.12612","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2103.12612","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.17615/kqj0-y121","doi":"https://doi.org/10.17615/kqj0-y121","is_oa":true,"landing_page_url":"https://doi.org/10.17615/kqj0-y121","pdf_url":null,"source":{"id":"https://openalex.org/S7407051488","display_name":"UNC Libraries","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2103.12612","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2103.12612","pdf_url":"https://arxiv.org/pdf/2103.12612","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1750867041","display_name":"Collaborative Research: Frameworks: Multiphase Fluid-Structure Interaction Software Infrastructure to Enable Applications in Medicine, Biology, and Engineering","funder_award_id":"1931516","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2471274064","display_name":"Community Detection in Networks Across Time","funder_award_id":"220020315","funder_id":"https://openalex.org/F4320306183","funder_display_name":"James S. McDonnell Foundation"},{"id":"https://openalex.org/G2747436919","display_name":null,"funder_award_id":"W911NF-13-1-","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G5715569224","display_name":"Models and Tools for Dynamic Health-Relevant Diffusion over Complex Networks","funder_award_id":"R01HD075712","funder_id":"https://openalex.org/F4320337611","funder_display_name":"Eunice Kennedy Shriver National Institute of Child Health and Human Development"},{"id":"https://openalex.org/G6274897657","display_name":null,"funder_award_id":"W911NF-13","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G6294465038","display_name":null,"funder_award_id":"CISE-1931516","funder_id":"https://openalex.org/F4320332161","funder_display_name":"National Institutes of Health"},{"id":"https://openalex.org/G657448715","display_name":null,"funder_award_id":"W911NF-16-1-","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G6671601314","display_name":"FRG: Collaborative Research: Computational Methods for Complex Fluids: Adaptivity, Fluid-Structure Interaction, and Applications in Biology","funder_award_id":"1664645","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7452299184","display_name":null,"funder_award_id":"W911NF","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G7991482914","display_name":null,"funder_award_id":"W911NF-13-1-0013","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G8201722305","display_name":null,"funder_award_id":"W911NF-16-1-0356","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G8727049869","display_name":null,"funder_award_id":"W911NF-13","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"},{"id":"https://openalex.org/F4320306183","display_name":"James S. McDonnell Foundation","ror":"https://ror.org/03dy4aq19"},{"id":"https://openalex.org/F4320332161","display_name":"National Institutes of Health","ror":"https://ror.org/01cwqze88"},{"id":"https://openalex.org/F4320332169","display_name":"Directorate for Computer and Information Science and Engineering","ror":"https://ror.org/025kzpk63"},{"id":"https://openalex.org/F4320332172","display_name":"Directorate for Mathematical and Physical Sciences","ror":"https://ror.org/029b7h395"},{"id":"https://openalex.org/F4320337611","display_name":"Eunice Kennedy Shriver National Institute of Child Health and Human Development","ror":"https://ror.org/04byxyr05"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4214494656.pdf","grobid_xml":"https://content.openalex.org/works/W4214494656.grobid-xml"},"referenced_works_count":63,"referenced_works":["https://openalex.org/W90692444","https://openalex.org/W133608936","https://openalex.org/W409604127","https://openalex.org/W1691290619","https://openalex.org/W1964537414","https://openalex.org/W1964537835","https://openalex.org/W1971076774","https://openalex.org/W1977438424","https://openalex.org/W1990857375","https://openalex.org/W1993298413","https://openalex.org/W1999823897","https://openalex.org/W2000687288","https://openalex.org/W2003885039","https://openalex.org/W2005691120","https://openalex.org/W2005809817","https://openalex.org/W2013872595","https://openalex.org/W2013986732","https://openalex.org/W2016462427","https://openalex.org/W2018170932","https://openalex.org/W2018478039","https://openalex.org/W2019512046","https://openalex.org/W2021404574","https://openalex.org/W2025983591","https://openalex.org/W2026706088","https://openalex.org/W2028085499","https://openalex.org/W2031656496","https://openalex.org/W2042103753","https://openalex.org/W2043485501","https://openalex.org/W2049951355","https://openalex.org/W2050577338","https://openalex.org/W2051024480","https://openalex.org/W2052323431","https://openalex.org/W2052629304","https://openalex.org/W2057400263","https://openalex.org/W2058015664","https://openalex.org/W2061308709","https://openalex.org/W2066003352","https://openalex.org/W2067556026","https://openalex.org/W2071592134","https://openalex.org/W2076661618","https://openalex.org/W2080169039","https://openalex.org/W2084749141","https://openalex.org/W2085379240","https://openalex.org/W2089575834","https://openalex.org/W2090340473","https://openalex.org/W2093547815","https://openalex.org/W2097002452","https://openalex.org/W2102713398","https://openalex.org/W2106499390","https://openalex.org/W2109072330","https://openalex.org/W2116349871","https://openalex.org/W2132087474","https://openalex.org/W2139834426","https://openalex.org/W2145760403","https://openalex.org/W2164928285","https://openalex.org/W2770751439","https://openalex.org/W2937808157","https://openalex.org/W2963979144","https://openalex.org/W3105129604","https://openalex.org/W3143219376","https://openalex.org/W4232388734","https://openalex.org/W4250817735","https://openalex.org/W4251519580"],"related_works":["https://openalex.org/W3139343024","https://openalex.org/W3010429308","https://openalex.org/W2104331847","https://openalex.org/W6903634357","https://openalex.org/W2012015130","https://openalex.org/W335599297","https://openalex.org/W2000448423","https://openalex.org/W2121127543","https://openalex.org/W2770751439","https://openalex.org/W2299208954"],"abstract_inverted_index":{"In":[0],"composite":[1,15],"materials":[2],"composed":[3],"of":[4,94,132,157,169,210,213,264,278],"a":[5,17,28,48,64,107,124,128,170,203,211,235,265],"soft":[6],"polymer":[7],"matrix":[8],"and":[9,44,91,111,165,197,241,297],"rigid,":[10],"high":[11],"aspect-ratio":[12],"particles,":[13],"the":[14,23,53,60,70,92,135,144,153,167,261,271,276,283,301],"undergoes":[16],"transition":[18,253],"in":[19,41,74,87,148,229],"mechanical":[20],"strength":[21],"when":[22,59],"incorporated":[24],"particle":[25],"phase":[26],"surpasses":[27],"critical":[29,49,272],"density.":[30],"This":[31],"phenomenon,":[32,126],"termed":[33],"rheological":[34,102,119],"percolation,":[35,103],"is":[36,97,117,121,287,298],"well":[37,98],"known":[38],"to":[39,81,123,142,222,233],"occur":[40],"many":[42],"polymer-rod":[43],"polymer-platelet":[45],"composites":[46,76,154],"at":[47,162,282],"density":[50],"that":[51,68,118,189,226,251,270],"exceeds":[52],"conductivity":[54,86],"percolation":[55,73,96,120,146,237,257,285],"threshold":[56,147,238],"(which":[57],"occurs":[58],"conducting":[61],"particles":[62],"form":[63],"large":[65,129],"connected":[66],"component":[67,131,206],"spans":[69,134],"composite).":[71],"Contact":[72],"rod-like":[75],"has":[77,105],"been":[78],"routinely":[79],"exploited":[80],"engineer":[82],"thermal":[83],"or":[84,101],"electrical":[85],"otherwise":[88],"nonconducting":[89],"polymers,":[90],"characterization":[93],"contact":[95,256,273],"established.":[99],"Mechanical":[100],"however,":[104],"evaded":[106],"complete":[108],"theoretical":[109],"explanation":[110],"predictive":[112],"description.":[113],"A":[114],"natural":[115],"hypothesis":[116],"due":[122],"rigidity":[125,145,236,284],"whereby":[127],"rigid":[130,174,192,200,205,208,216],"inclusions":[133],"composite.":[136],"Here":[137],"we":[138,184],"build":[139],"an":[140,186],"algorithm":[141,188,221],"detect":[143],"rod-polymer":[149],"composites.":[150],"We":[151,218,249],"model":[152],"as":[155],"systems":[156,225],"randomly":[158],"distributed,":[159],"soft-core":[160],"(intersecting":[161],"contact)":[163],"rods":[164],"study":[166],"emergence":[168],"giant":[171,204],"(i.e.,":[172,275],"spanning)":[173],"component.":[175],"Building":[176],"on":[177,245],"our":[178],"previous":[179],"results":[180],"for":[181,289],"two-dimensional":[182],"composites,":[183],"develop":[185],"approximate":[187],"identifies":[190],"spanning":[191],"components":[193],"through":[194],"hierarchically":[195],"identifying":[196],"compressing":[198],"provably":[199],"motifs---equivalently,":[201],"decomposing":[202],"into":[207],"assemblies":[209],"hierarchy":[212],"successively":[214],"smaller":[215],"components.":[217],"apply":[219],"this":[220,252,268],"random":[223],"monodisperse":[224],"are":[227],"generated":[228],"Monte":[230],"Carlo":[231],"simulations":[232],"estimate":[234],"(critical":[239],"density)":[240],"explore":[242],"its":[243,255],"dependence":[244],"rod":[246,281],"aspect":[247,290],"ratio.":[248],"show":[250],"point---like":[254],"analogue---scales":[258],"inversely":[259],"with":[260],"excluded":[262],"volume":[263],"rod.":[266],"Moreover,":[267],"implies":[269],"number":[274,277],"contacts":[279],"per":[280],"threshold)":[286],"constant":[288],"ratios":[291],"above":[292],"some":[293],"relatively":[294],"low":[295],"value":[296],"lower":[299],"than":[300],"prediction":[302],"from":[303],"Maxwell's":[304],"isostatic":[305],"condition.":[306]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2}],"updated_date":"2026-11-05T12:25:35.769452","created_date":"2022-03-02T00:00:00"}