{"id":"https://openalex.org/W2108299407","doi":"https://doi.org/10.1137/050647785","title":"A Solidification Phenomenon in Random Packings","display_name":"A Solidification Phenomenon in Random Packings","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2108299407","doi":"https://doi.org/10.1137/050647785","mag":"2108299407"},"language":"en","primary_location":{"id":"doi:10.1137/050647785","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050647785","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","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/A5052265146","display_name":"Lewis Bowen","orcid":"https://orcid.org/0000-0002-5161-9618"},"institutions":[{"id":"https://openalex.org/I592451","display_name":"Indiana University","ror":"https://ror.org/01kg8sb98","country_code":"US","type":"education","lineage":["https://openalex.org/I592451"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"L. Bowen","raw_affiliation_strings":["\u2021Indiana University"],"affiliations":[{"raw_affiliation_string":"\u2021Indiana University","institution_ids":["https://openalex.org/I592451"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091396290","display_name":"Russell Lyons","orcid":"https://orcid.org/0000-0001-8618-6173"},"institutions":[{"id":"https://openalex.org/I4210119109","display_name":"Indiana University Bloomington","ror":"https://ror.org/02k40bc56","country_code":"US","type":"education","lineage":["https://openalex.org/I4210119109","https://openalex.org/I592451"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"R. Lyons","raw_affiliation_strings":["Indiana University. Bloomington"],"affiliations":[{"raw_affiliation_string":"Indiana University. Bloomington","institution_ids":["https://openalex.org/I4210119109"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066144062","display_name":"Charles Radin","orcid":"https://orcid.org/0000-0002-4776-7335"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"C. Radin","raw_affiliation_strings":["Department of Mathematics, University of Texas, Austin, TX 78712"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Texas, Austin, TX 78712","institution_ids":["https://openalex.org/I86519309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056680757","display_name":"Peter Winkler","orcid":"https://orcid.org/0000-0002-1259-3574"},"institutions":[{"id":"https://openalex.org/I4210166639","display_name":"Dartmouth Hospital","ror":"https://ror.org/02j3qj605","country_code":"GB","type":"healthcare","lineage":["https://openalex.org/I4210166639"]},{"id":"https://openalex.org/I107672454","display_name":"Dartmouth College","ror":"https://ror.org/049s0rh22","country_code":"US","type":"education","lineage":["https://openalex.org/I107672454"]}],"countries":["GB","US"],"is_corresponding":false,"raw_author_name":"P. Winkler","raw_affiliation_strings":["Dartmouth College"],"affiliations":[{"raw_affiliation_string":"Dartmouth College","institution_ids":["https://openalex.org/I4210166639","https://openalex.org/I107672454"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5052265146"],"corresponding_institution_ids":["https://openalex.org/I592451"],"apc_list":null,"apc_paid":null,"fwci":1.2371,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.77265221,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"38","issue":"4","first_page":"1075","last_page":"1089"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9843999743461609,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9843999743461609,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.9825000166893005,"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/T11887","display_name":"Quasicrystal Structures and Properties","score":0.9803000092506409,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5270564556121826},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.502068281173706},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3833022117614746},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.35373902320861816},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17058438062667847}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5270564556121826},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.502068281173706},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3833022117614746},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.35373902320861816},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17058438062667847}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/050647785","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050647785","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3379960307","display_name":"The Symmetry of Densest Packings of Space","funder_award_id":"0352999","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8855510892","display_name":"Probability on Combinatorial Structures","funder_award_id":"0406017","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/F4320329205","display_name":"Banff International Research Station for Mathematical Innovation and Discovery","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1589055062","https://openalex.org/W1964089819","https://openalex.org/W2111882381","https://openalex.org/W2116072499","https://openalex.org/W2139745213","https://openalex.org/W2156065028","https://openalex.org/W2170591015","https://openalex.org/W2962915957","https://openalex.org/W4250758406"],"related_works":["https://openalex.org/W2935759653","https://openalex.org/W3105167352","https://openalex.org/W54078636","https://openalex.org/W2954470139","https://openalex.org/W1501425562","https://openalex.org/W2902782467","https://openalex.org/W3084825885","https://openalex.org/W2298861036","https://openalex.org/W3148032049","https://openalex.org/W2271181815"],"abstract_inverted_index":{"Previous":[0,238],"article":[1,3,239,241],"Next":[2,240],"A":[4],"Solidification":[5],"Phenomenon":[6],"in":[7,45,78,113,151,250,303],"Random":[8,319],"PackingsL.":[9],"Bowen,":[10,18,64,98],"R.":[11,19,66,148],"Lyons,":[12,20,67],"C.":[13,21,69,100,103,188,211],"Radin,":[14,22,189,212],"and":[15,23,71,73,105,107,111,145,147,154,185,187,362,380],"P.":[16,24,74],"WinklerL.":[17],"Winklerhttps://doi.org/10.1137/050647785PDFBibTexSections":[25],"ToolsAdd":[26],"to":[27],"favoritesExport":[28],"CitationTrack":[29],"CitationsEmail":[30],"SectionsAboutAbstractWe":[31],"prove":[32],"that":[33],"uniformly":[34],"random":[35],"packings":[36],"of":[37,39,115,214,246,264,267,281,284,299,307,322,325],"copies":[38],"a":[40,79],"certain":[41],"simply":[42],"connected":[43],"figure":[44],"the":[46],"plane":[47],"exhibit":[48],"global":[49],"connectedness":[50],"at":[51,58],"all":[52],"sufficiently":[53],"high":[54],"densities,":[55],"but":[56],"not":[57],"low":[59],"densities.[1]":[60],"Google":[61,134,172,174,176,178,235],"Scholar[2]":[62],"L.":[63,97,108,183],",":[65,68,72,99,102,106,138,141,146,182,186],"Radin":[70,104],"Winkler,":[75],"Fluid/solid":[76],"transition":[77],"hard\u2010core":[80],"system,":[81],"Phys.":[82,92,120,131,169,196,206],"Rev.":[83,93,197,207],"Lett.,":[84],"96":[85],"(2006),":[86],"paper":[87,125,201],"025701.":[88],"prl":[89],"PRLTAO":[90],"0031-9007":[91],"Lett.":[94],"CrossrefISIGoogle":[95,170,209,233],"Scholar[3]":[96],"Holton,":[101],"Sadun,":[109],"Uniqueness":[110],"symmetry":[112,302],"problems":[114],"optimally":[116],"dense":[117],"packings,":[118,156],"Math.":[119,130,222,231],"Electron.":[121,132],"J.,":[122],"11":[123],"(2005),":[124,200],"1.":[126],"9cb":[127],"MPEJFJ":[128],"1086-6655":[129],"J.":[133,157,167],"Scholar[4]":[135],"A.":[136],"Donev,":[137],"S.":[139],"Torquato,":[140],"F.":[142],"H.":[143,180],"Stillinger":[144],"Connelly,":[149],"Jamming":[150],"hard":[152,194],"sphere":[153],"disk":[155],"Appl.":[158,168],"Phys.,":[159],"95":[160],"(2004),":[161,225],"pp.":[162,226],"989\u2013999.":[163],"jap":[164],"JAPIAU":[165],"0021-8979":[166],"Scholar[5]":[171],"Scholar[6]":[173],"Scholar[7]":[175],"Scholar[8]":[177],"Scholar[9]":[179],"Koch,":[181],"Sadun":[184],"Most":[190],"stable":[191],"structure":[192],"for":[193,360,378],"spheres,":[195],"E,":[198],"72":[199],"016708.":[202],"pre":[203],"PLEEE8":[204],"1063-651X":[205],"E":[208],"Scholar[10]":[210],"Orbits":[213],"orbs:":[215],"Sphere":[216],"packing":[217],"meets":[218],"Penrose":[219],"tilings,":[220],"Amer.":[221],"Monthly,":[223],"111":[224],"137\u2013149.":[227],"aml":[228],"AMMYAE":[229],"Am.":[230],"Monthly":[232],"Scholar[11]":[234],"ScholarKeywordssphere":[236],"packingsolidification":[237],"FiguresRelatedReferencesCited":[242],"ByDetails":[243],"On":[244],"Percolation":[245,263,280],"Two-Dimensional":[247],"Hard":[248,265,282],"DisksCommunications":[249],"Mathematical":[251,345],"Physics,":[252,327],"Vol.":[253,270,287,309,328],"364,":[254],"No.":[255,272,289,311,330],"1":[256,290,314],"|":[257,274,291,313,332],"6":[258],"July":[259,351],"2018":[260,294],"Cross":[261,278,295,317,336],"Ref":[262,279,296,318,337],"DisksJournal":[266,283],"Applied":[268,285,363,381],"Probability,":[269,286,308],"51,":[271,288],"01":[273],"19":[275],"February":[276],"2016":[277],"30":[292],"January":[293],"Spontaneous":[297],"breaking":[298],"continuous":[300],"rotational":[301],"two":[304],"dimensionsElectronic":[305],"Journal":[306,343],"14,":[310],"none":[312],"Jan":[315],"2009":[316],"Close":[320],"Packing":[321],"Granular":[323],"MatterJournal":[324],"Statistical":[326],"131,":[329],"4":[331],"22":[333],"March":[334],"2008":[335],"Volume":[338],"38,":[339],"Issue":[340],"4|":[341],"2006SIAM":[342],"on":[344],"Analysis1035-1370":[346],"History":[347],"Submitted:16":[348],"December":[349],"2005Accepted:19":[350],"2006Published":[352],"online:20":[353],"November":[354],"2006":[355,358],"InformationCopyright":[356],"\u00a9":[357],"Society":[359],"Industrial":[361,379],"MathematicsKeywordssphere":[364],"packingsolidificationMSC":[365],"codes52C2552C17PDF":[366],"Download":[367],"Article":[368],"&":[369],"Publication":[370],"DataArticle":[371],"DOI:10.1137/050647785Article":[372],"page":[373],"range:pp.":[374],"1075-1089ISSN":[375],"(print):0036-1410ISSN":[376],"(online):1095-7154Publisher:Society":[377],"Mathematics":[382]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}
