{"id":"https://openalex.org/W1995172315","doi":"https://doi.org/10.1137/050630192","title":"Coarsening Rates for a Droplet Model: Rigorous Upper Bounds","display_name":"Coarsening Rates for a Droplet Model: Rigorous Upper Bounds","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W1995172315","doi":"https://doi.org/10.1137/050630192","mag":"1995172315"},"language":"en","primary_location":{"id":"doi:10.1137/050630192","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050630192","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/A5073872018","display_name":"F\u00e9lix Otto","orcid":"https://orcid.org/0000-0002-2327-5950"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Felix Otto","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062573165","display_name":"Tobias Rump","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tobias Rump","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5004682327","display_name":"Dejan Slep\u010dev","orcid":"https://orcid.org/0000-0002-7600-1144"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dejan Slepcev","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5073872018"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.9441,"has_fulltext":false,"cited_by_count":62,"citation_normalized_percentile":{"value":0.96399708,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"38","issue":"2","first_page":"503","last_page":"529"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12141","display_name":"Fluid Dynamics and Thin Films","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12141","display_name":"Fluid Dynamics and Thin Films","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10591","display_name":"Theoretical and Computational Physics","score":0.9984999895095825,"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/T11471","display_name":"Block Copolymer Self-Assembly","score":0.9980999827384949,"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":0.7728270292282104},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.6925199627876282},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.621834933757782},{"id":"https://openalex.org/keywords/balanced-flow","display_name":"Balanced flow","score":0.5564308762550354},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5506613850593567},{"id":"https://openalex.org/keywords/energy-landscape","display_name":"Energy landscape","score":0.500861406326294},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.46955233812332153},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4611876606941223},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4375028908252716},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.43691059947013855},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.4338739514350891},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.42907822132110596},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.18240362405776978},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.16808459162712097},{"id":"https://openalex.org/keywords/motion","display_name":"Motion (physics)","score":0.16651055216789246},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.1420353353023529},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.13566628098487854},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.12485817074775696}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7728270292282104},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.6925199627876282},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.621834933757782},{"id":"https://openalex.org/C167879884","wikidata":"https://www.wikidata.org/wiki/Q727568","display_name":"Balanced flow","level":2,"score":0.5564308762550354},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5506613850593567},{"id":"https://openalex.org/C119621388","wikidata":"https://www.wikidata.org/wiki/Q5377166","display_name":"Energy landscape","level":2,"score":0.500861406326294},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.46955233812332153},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4611876606941223},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4375028908252716},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.43691059947013855},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.4338739514350891},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.42907822132110596},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.18240362405776978},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.16808459162712097},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.16651055216789246},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.1420353353023529},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.13566628098487854},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.12485817074775696},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/050630192","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050630192","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":[{"id":"https://metadata.un.org/sdg/7","score":0.8500000238418579,"display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W88488163","https://openalex.org/W1585160083","https://openalex.org/W1964493760","https://openalex.org/W1964900692","https://openalex.org/W1968356938","https://openalex.org/W1971723555","https://openalex.org/W1982602909","https://openalex.org/W1987093292","https://openalex.org/W1998191230","https://openalex.org/W2002404461","https://openalex.org/W2004603974","https://openalex.org/W2018833892","https://openalex.org/W2038096604","https://openalex.org/W2065122370","https://openalex.org/W2067999970","https://openalex.org/W2068716887","https://openalex.org/W2072679197","https://openalex.org/W2075426913","https://openalex.org/W2086824004","https://openalex.org/W2110062911","https://openalex.org/W2112348611","https://openalex.org/W2112938067","https://openalex.org/W2116257437","https://openalex.org/W2124614417","https://openalex.org/W2126831171","https://openalex.org/W2130401121","https://openalex.org/W2143037651","https://openalex.org/W2159316557","https://openalex.org/W2168065659"],"related_works":["https://openalex.org/W2467119940","https://openalex.org/W3194077685","https://openalex.org/W2044897135","https://openalex.org/W2152758797","https://openalex.org/W2382762871","https://openalex.org/W2950599922","https://openalex.org/W2062219402","https://openalex.org/W3049435653","https://openalex.org/W2391509332","https://openalex.org/W4287865632"],"abstract_inverted_index":{"Certain":[0],"liquids":[1],"on":[2,55,62,110,139,151],"solid":[3],"substrates":[4],"form":[5],"a":[6,12,44,87,93,115,126,130],"configuration":[7,16],"of":[8,26,40,66,142,190],"droplets":[9,27],"connected":[10],"by":[11,47,92],"precursor":[13],"layer.":[14],"This":[15,154],"coarsens:":[17],"The":[18,194],"average":[19],"droplet":[20],"size":[21],"grows":[22],"while":[23],"the":[24,30,52,63,98,111,120,123,140,143,152,182,187,191],"number":[25],"decreases":[28],"and":[29,68,83,163,205],"characteristic":[31],"distance":[32],"between":[33],"them":[34],"increases.":[35],"We":[36,118],"study":[37],"this":[38,102],"type":[39],"coarsening":[41,99,112],"behavior":[42,90],"in":[43,114,133,159,200],"model":[45],"given":[46],"an":[48,56,107,134,178],"evolution":[49,124],"equation":[50],"for":[51],"film":[53],"height":[54],"n-dimensional":[57],"substrate.":[58],"Heuristic":[59],"arguments":[60,204],"based":[61],"asymptotic":[64],"analysis":[65],"Glasner":[67],"Witelski":[69],"[Phys.":[70],"Rev.":[71],"E,":[72],"67":[73],"(2003),":[74],"p.":[75],"016302,":[76],"Phys.":[77],"D.,":[78],"209":[79],"(2005),":[80],"pp.":[81,171],"80-104]":[82],"numerical":[84,206],"simulations":[85],"suggest":[86],"statistically":[88],"self-similar":[89],"characterized":[91],"single":[94],"exponent":[95],"which":[96,185],"determines":[97],"rate.":[100],"In":[101],"paper,":[103],"we":[104,197],"establish":[105],"rigorously":[106],"upper":[108,195],"bound":[109,196],"rate":[113],"time-averaged":[116],"sense.":[117],"use":[119],"fact":[121],"that":[122],"is":[125,177,199],"gradient":[127],"flow,":[128],"i.e.,":[129],"steepest":[131],"descent":[132],"energy":[135,144,192],"landscape.":[136,193],"Coarse":[137],"information":[138,150],"geometry":[141],"landscape":[145],"serves":[146],"to":[147],"obtain":[148,198],"coarse":[149,188],"dynamics.":[153],"robust":[155],"method":[156],"was":[157],"proposed":[158],"[R.":[160],"V.":[161],"Kohn":[162],"F.":[164],"Otto,":[165],"Comm.":[166],"Math.":[167],"Phys.,":[168],"229":[169],"(2002),":[170],"375-395].":[172],"Our":[173],"main":[174],"analytical":[175],"contribution":[176],"interpolation":[179],"inequality":[180],"involving":[181],"Wasserstein":[183],"distance,":[184],"characterizes":[186],"shape":[189],"agreement":[201],"with":[202],"heuristic":[203],"simulations.":[207]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":5}],"updated_date":"2026-04-25T08:17:42.794288","created_date":"2025-10-10T00:00:00"}
