{"id":"https://openalex.org/W2963890864","doi":"https://doi.org/10.1137/090776895","title":"Exit Times of Diffusions with Incompressible Drift","display_name":"Exit Times of Diffusions with Incompressible Drift","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2963890864","doi":"https://doi.org/10.1137/090776895","mag":"2963890864"},"language":"en","primary_location":{"id":"doi:10.1137/090776895","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090776895","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","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://figshare.com/articles/journal_contribution/Exit_Times_of_Diffusions_with_Incompressible_Drift/6477383","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040944169","display_name":"Gautam Iyer","orcid":"https://orcid.org/0000-0001-9638-0455"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gautam Iyer","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018654479","display_name":"Alexei Novikov","orcid":"https://orcid.org/0000-0002-3649-5864"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alexei Novikov","raw_affiliation_strings":["Mathematics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079159174","display_name":"Lenya Ryzhik","orcid":"https://orcid.org/0000-0003-1892-4861"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lenya Ryzhik","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5059199669","display_name":"Andrej Zlato\u0161","orcid":"https://orcid.org/0000-0003-0660-7404"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Andrej Zlato\u0161","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1612,"has_fulltext":true,"cited_by_count":17,"citation_normalized_percentile":{"value":0.77945552,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"42","issue":"6","first_page":"2484","last_page":"2498"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.987500011920929,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9818000197410583,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.905739426612854},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7498289346694946},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6808871030807495},{"id":"https://openalex.org/keywords/ball","display_name":"Ball (mathematics)","score":0.6683984994888306},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.6386708617210388},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.5789783000946045},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5117794871330261},{"id":"https://openalex.org/keywords/incompressible-flow","display_name":"Incompressible flow","score":0.49505510926246643},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.4809255301952362},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.47263237833976746},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.44199711084365845},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.40635186433792114},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3632144629955292},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2749629616737366},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.24985668063163757},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.08209535479545593},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.0693926215171814}],"concepts":[{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.905739426612854},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7498289346694946},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6808871030807495},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.6683984994888306},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.6386708617210388},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.5789783000946045},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5117794871330261},{"id":"https://openalex.org/C50415386","wikidata":"https://www.wikidata.org/wiki/Q1663717","display_name":"Incompressible flow","level":3,"score":0.49505510926246643},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.4809255301952362},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.47263237833976746},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.44199711084365845},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.40635186433792114},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3632144629955292},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2749629616737366},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.24985668063163757},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.08209535479545593},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0693926215171814},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/090776895","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090776895","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"},{"id":"pmh:oai:figshare.com:article/6477383","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Exit_Times_of_Diffusions_with_Incompressible_Drift/6477383","pdf_url":"https://figshare.com/articles/journal_contribution/Exit_Times_of_Diffusions_with_Incompressible_Drift/6477383","source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"doi:10.1184/r1/6477383.v1","is_oa":true,"landing_page_url":"https://doi.org/10.1184/r1/6477383.v1","pdf_url":null,"source":{"id":"https://openalex.org/S7407050927","display_name":"KiltHub Repository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"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":null,"raw_source_name":null,"raw_type":"JournalArticle"}],"best_oa_location":{"id":"pmh:oai:figshare.com:article/6477383","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Exit_Times_of_Diffusions_with_Incompressible_Drift/6477383","pdf_url":"https://figshare.com/articles/journal_contribution/Exit_Times_of_Diffusions_with_Incompressible_Drift/6477383","source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G425378776","display_name":"FRG: Collaborative Research: Stochastics and Dynamics: Asymptotic problems","funder_award_id":"0854952","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7675856711","display_name":"Reaction, Diffusion, and Fluid Flow","funder_award_id":"0901363","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8471992961","display_name":"Collaborative Research: Waves and Fronts in Heterogeneous Media","funder_award_id":"0908011","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8512507000","display_name":"Collaborative Research: Waves and Fronts in Heterogeneous Media","funder_award_id":"0908507","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":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2963890864.pdf","grobid_xml":"https://content.openalex.org/works/W2963890864.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W1671098680","https://openalex.org/W1967237247","https://openalex.org/W1978029761","https://openalex.org/W1980078733","https://openalex.org/W1995358755","https://openalex.org/W2014158631","https://openalex.org/W2062697573","https://openalex.org/W2076940118","https://openalex.org/W2106967316","https://openalex.org/W2112250505","https://openalex.org/W2125721920","https://openalex.org/W2153003691","https://openalex.org/W2161233505"],"related_works":["https://openalex.org/W238609530","https://openalex.org/W2734192830","https://openalex.org/W4205377127","https://openalex.org/W86477321","https://openalex.org/W1669816071","https://openalex.org/W2131115966","https://openalex.org/W2039262714","https://openalex.org/W1133295873","https://openalex.org/W2093607043","https://openalex.org/W2743552406"],"abstract_inverted_index":{"Let":[0],"$\\Omega\\subset\\mathbb{R}^n$":[1],"be":[2,11],"a":[3,19,89],"bounded":[4],"domain,":[5],"and":[6,25,92],"for":[7,70],"$x\\in\\Omega$":[8],"let":[9],"$\\tau(x)$":[10],"the":[12,36,49,64,67,72,102,106],"expected":[13],"exit":[14],"time":[15],"from":[16],"$\\Omega$":[17],"of":[18,51],"diffusing":[20],"particle":[21],"starting":[22],"at":[23],"x":[24],"advected":[26],"by":[27,101],"an":[28],"incompressible":[29,94],"flow":[30,74,104],"u.":[31],"We":[32,78],"are":[33,45,66],"interested":[34],"in":[35,48,61,82],"question":[37],"which":[38,71],"flows":[39,95],"maximize":[40],"$\\|\\tau\\|_{L^\\infty(\\Omega)}$,":[41],"that":[42,81],"is,":[43],"they":[44],"most":[46],"efficient":[47],"creation":[50],"hotspots":[52],"inside":[53],"$\\Omega$.":[54],"Surprisingly,":[55],"among":[56,85],"all":[57,86,93],"simply":[58],"connected":[59],"domains":[60,87],"two":[62],"dimensions,":[63],"discs":[65],"only":[68],"ones":[69],"zero":[73,103],"$u\\equiv0$":[75],"maximizes":[76],"$\\|\\tau\\|_{L^\\infty(\\Omega)}$.":[77],"also":[79],"show":[80],"any":[83],"dimension,":[84],"with":[88],"fixed":[90],"volume":[91],"on":[96,105],"them,":[97],"$\\|\\tau\\|_{L^\\infty(\\Omega)}$":[98],"is":[99],"maximized":[100],"ball.":[107]},"counts_by_year":[{"year":2022,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-08-06T08:24:18.245995","created_date":"2025-10-10T00:00:00"}