{"id":"https://openalex.org/W4214613088","doi":"https://doi.org/10.1137/siread000053000001000127000001","title":"SIGEST","display_name":"SIGEST","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W4214613088","doi":"https://doi.org/10.1137/siread000053000001000127000001"},"language":"en","primary_location":{"id":"doi:10.1137/siread000053000001000127000001","is_oa":false,"landing_page_url":"https://doi.org/10.1137/siread000053000001000127000001","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","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/A5108286254","display_name":"The Editors","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"The Editors","raw_affiliation_strings":[""],"affiliations":[{"raw_affiliation_string":"","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5108286254"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.47264714,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"53","issue":"1","first_page":"127","last_page":"127"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13785","display_name":"Aquatic and Environmental Studies","score":0.800599992275238,"subfield":{"id":"https://openalex.org/subfields/1904","display_name":"Earth-Surface Processes"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13785","display_name":"Aquatic and Environmental Studies","score":0.800599992275238,"subfield":{"id":"https://openalex.org/subfields/1904","display_name":"Earth-Surface Processes"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.7580999732017517,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/burgers-equation","display_name":"Burgers' equation","score":0.7554572820663452},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.6294416785240173},{"id":"https://openalex.org/keywords/metastability","display_name":"Metastability","score":0.6037073135375977},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5338740348815918},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.5249959230422974},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.519013524055481},{"id":"https://openalex.org/keywords/dissipation","display_name":"Dissipation","score":0.49849843978881836},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.4478689432144165},{"id":"https://openalex.org/keywords/fluid-dynamics","display_name":"Fluid dynamics","score":0.44279980659484863},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.4178086519241333},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.41035377979278564},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38999316096305847},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.376687616109848},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3109632134437561},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.30896711349487305},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.2073708176612854},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.12258392572402954}],"concepts":[{"id":"https://openalex.org/C129747778","wikidata":"https://www.wikidata.org/wiki/Q1014918","display_name":"Burgers' equation","level":3,"score":0.7554572820663452},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6294416785240173},{"id":"https://openalex.org/C89464430","wikidata":"https://www.wikidata.org/wiki/Q849516","display_name":"Metastability","level":2,"score":0.6037073135375977},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5338740348815918},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.5249959230422974},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.519013524055481},{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.49849843978881836},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4478689432144165},{"id":"https://openalex.org/C90278072","wikidata":"https://www.wikidata.org/wiki/Q216320","display_name":"Fluid dynamics","level":2,"score":0.44279980659484863},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.4178086519241333},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.41035377979278564},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38999316096305847},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.376687616109848},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3109632134437561},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.30896711349487305},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.2073708176612854},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.12258392572402954},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/siread000053000001000127000001","is_oa":false,"landing_page_url":"https://doi.org/10.1137/siread000053000001000127000001","pdf_url":null,"source":{"id":"https://openalex.org/S160107561","display_name":"SIAM Review","issn_l":"0036-1445","issn":["0036-1445","1095-7200"],"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 Review","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4307107610","https://openalex.org/W3213627526","https://openalex.org/W4226159838","https://openalex.org/W3138976155","https://openalex.org/W1992748572","https://openalex.org/W2082939555","https://openalex.org/W2088012056","https://openalex.org/W2790243943","https://openalex.org/W4323927134","https://openalex.org/W2129026697"],"abstract_inverted_index":{"This":[0],"issue's":[1],"SIGEST":[2,125],"paper":[3,126],"from":[4],"the":[5,20,35,38,59,67,86,92,114,118,132,159,172,193,201,226,232,241],"SIAM":[6],"Journal":[7],"on":[8],"Applied":[9],"Dynamical":[10,56],"Systems,":[11],"\u201cUsing":[12],"Global":[13],"Invariant":[14],"Manifolds":[15],"to":[16,122,131,211,235,240],"Understand":[17],"Metastability":[18],"in":[19,85,145],"Burgers":[21,133,136,173],"Equation":[22],"with":[23,53,175],"Small":[24],"Viscosity,\u201d":[25],"by":[26,95,221],"Margaret":[27],"Beck":[28],"and":[29,152,200,244],"C.":[30],"Eugene":[31],"Wayne,":[32],"is":[33,66,127,138,190],"about":[34,128],"behavior":[36],"of":[37,40,45,69,88,117,147,158,249],"solutions":[39,130],"dynamical":[41],"systems":[42,44,57,74],"(i.e.,":[43],"time-dependent":[46],"differential":[47,141],"equations,":[48],"either":[49],"ordinary":[50],"or":[51,91,99],"partial)":[52],"small":[54,176,227],"dissipation.":[55],"describe":[58],"world":[60],"around":[61],"us;":[62],"a":[63,70,83,96,100,109,139,183,204,212,218,246],"classic":[64],"example":[65],"motion":[68],"fluid.":[71],"When":[72],"these":[73],"are":[75,105],"forced,":[76],"coherent":[77],"structures":[78],"often":[79],"emerge":[80],"such":[81],"as":[82],"tsunami":[84],"aftermath":[87],"an":[89],"earthquake":[90],"vortex":[93],"produced":[94],"plane's":[97],"wingtip":[98],"canoe":[101],"paddle.":[102],"These":[103],"states":[104],"metastable\u2014they":[106],"persist":[107],"for":[108,163,171,225],"long":[110],"time,":[111],"although":[112],"eventually":[113],"viscous":[115],"forces":[116],"fluid":[119,164],"lead":[120],"them":[121],"dissipate.":[123],"The":[124,135,166,215],"metastable":[129,184,242],"equation.":[134],"equation":[137,142,174],"partial":[140],"that":[143,170],"arises":[144],"models":[146],"gas":[148],"dynamics,":[149],"traffic":[150],"flow,":[151],"qualitatively":[153],"captures":[154],"some":[155],"important":[156],"features":[157],"two-dimensional":[160],"Navier\u2013Stokes":[161],"equations":[162],"motion.":[165],"authors":[167,216],"show":[168],"rigorously":[169],"dissipation,":[177],"most":[178],"initial":[179],"conditions":[180],"first":[181],"approach":[182,234],"N-wave":[185],"solution":[186,202],"(which,":[187],"not":[188],"surprisingly,":[189],"shaped":[191],"like":[192],"letter":[194],"N).":[195],"Eventually":[196],"this":[197,251],"state":[198],"dissipates":[199],"approaches":[203],"self-similar":[205],"diffusive":[206],"wave,":[207],"which":[208],"then":[209],"decays":[210],"constant":[213],"solution.":[214],"present":[217],"lucid":[219],"analysis":[220],"developing":[222],"rigorous":[223],"asymptotics":[224],"viscosity":[228],"limit.":[229],"They":[230],"characterize":[231],"solutions'":[233],"global":[236],"invariant":[237],"manifolds,":[238],"corresponding":[239],"states,":[243],"do":[245],"fine":[247],"job":[248],"explaining":[250],"challenging":[252],"mathematics.":[253]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2022-03-02T00:00:00"}
