{"id":"https://openalex.org/W2019030399","doi":"https://doi.org/10.1098/rspa.2012.0550","title":"Attractor local dimensionality, nonlinear energy transfers and finite-time instabilities in unstable dynamical systems with applications to two-dimensional fluid flows","display_name":"Attractor local dimensionality, nonlinear energy transfers and finite-time instabilities in unstable dynamical systems with applications to two-dimensional fluid flows","publication_year":2013,"publication_date":"2013-03-13","ids":{"openalex":"https://openalex.org/W2019030399","doi":"https://doi.org/10.1098/rspa.2012.0550","mag":"2019030399"},"language":"en","primary_location":{"id":"doi:10.1098/rspa.2012.0550","doi":"https://doi.org/10.1098/rspa.2012.0550","is_oa":false,"landing_page_url":"https://doi.org/10.1098/rspa.2012.0550","pdf_url":null,"source":{"id":"https://openalex.org/S3006183880","display_name":"Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences","issn_l":"1364-5021","issn":["1364-5021","1471-2946"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319787","host_organization_name":"Royal Society","host_organization_lineage":["https://openalex.org/P4310319787"],"host_organization_lineage_names":["Royal Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"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/A5037328807","display_name":"Themistoklis P. Sapsis","orcid":"https://orcid.org/0000-0003-0302-0691","observed_orcids":["https://orcid.org/0000-0003-0302-0691"]},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Themistoklis P. Sapsis","raw_affiliation_strings":["Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA","Find this author on PubMed","Google Scholar","Themistoklis P. Sapsis"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Find this author on PubMed","institution_ids":[]},{"raw_affiliation_string":"Google Scholar","institution_ids":[]},{"raw_affiliation_string":"Themistoklis P. Sapsis","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5037328807"],"corresponding_institution_ids":["https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":3.5078,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.91375316,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":87,"max":99},"biblio":{"volume":"469","issue":"2153","first_page":"20120550","last_page":"20120550"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.4812000095844269,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.4812000095844269,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.28220000863075256,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear 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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.08030000329017639,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/nonlinear-energy-transfer","display_name":"nonlinear energy transfer","score":0.7720000147819519},{"id":"https://openalex.org/keywords/finite-time-lyapunov-exponents","display_name":"finite-time Lyapunov exponents","score":0.9049999713897705},{"id":"https://openalex.org/keywords/navier-stokes-equations","display_name":"Navier-Stokes equations","score":0.7739999890327454},{"id":"https://openalex.org/keywords/two-dimensional-flow","display_name":"two-dimensional flow","score":0.9269999861717224},{"id":"https://openalex.org/keywords/stochastic-attractors","display_name":"stochastic attractors","score":0.8650000095367432},{"id":"https://openalex.org/keywords/model-reduction","display_name":"model reduction","score":0.7480000257492065},{"id":"https://openalex.org/keywords/local-fractal-dimension","display_name":"local fractal dimension","score":0.734000027179718},{"id":"https://openalex.org/keywords/unstable-modes","display_name":"unstable modes","score":0.6499999761581421},{"id":"https://openalex.org/keywords/stable-modes","display_name":"stable modes","score":0.6489999890327454},{"id":"https://openalex.org/keywords/quadratic-terms","display_name":"quadratic terms","score":0.5759999752044678},{"id":"https://openalex.org/keywords/energy-circulation","display_name":"energy circulation","score":0.8050000071525574}],"concepts":[{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.8501375913619995},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.7240754961967468},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5698407292366028},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.5545210838317871},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5357173681259155},{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.48312994837760925},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.47265565395355225},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.46961623430252075},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.45440784096717834},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4331144392490387},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3748284876346588},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1750713586807251},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08977049589157104},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1098/rspa.2012.0550","doi":"https://doi.org/10.1098/rspa.2012.0550","is_oa":false,"landing_page_url":"https://doi.org/10.1098/rspa.2012.0550","pdf_url":null,"source":{"id":"https://openalex.org/S3006183880","display_name":"Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences","issn_l":"1364-5021","issn":["1364-5021","1471-2946"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319787","host_organization_name":"Royal Society","host_organization_lineage":["https://openalex.org/P4310319787"],"host_organization_lineage_names":["Royal Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.660.6434","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.660.6434","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://rspa.royalsocietypublishing.org/content/royprsa/469/2153/20120550.full.pdf?origin%3Dpublication_detail","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.661.294","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.661.294","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://rspa.royalsocietypublishing.org/content/royprsa/469/2153/20120550.full.pdf","raw_type":"text"},{"id":"mag:2403285571","doi":null,"is_oa":false,"landing_page_url":"https://sand-lab.com/Papers/13_PRS.pdf","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W20854365","https://openalex.org/W76814795","https://openalex.org/W196973002","https://openalex.org/W240029891","https://openalex.org/W312648962","https://openalex.org/W605594215","https://openalex.org/W626778183","https://openalex.org/W1578950605","https://openalex.org/W1579236455","https://openalex.org/W1594759473","https://openalex.org/W1632346486","https://openalex.org/W1907737910","https://openalex.org/W1966901194","https://openalex.org/W1972098742","https://openalex.org/W1974365244","https://openalex.org/W1978254533","https://openalex.org/W1988376519","https://openalex.org/W2021054665","https://openalex.org/W2021311852","https://openalex.org/W2022264564","https://openalex.org/W2023480419","https://openalex.org/W2029401646","https://openalex.org/W2045906052","https://openalex.org/W2054115876","https://openalex.org/W2056883816","https://openalex.org/W2065297008","https://openalex.org/W2067265108","https://openalex.org/W2070643904","https://openalex.org/W2077180405","https://openalex.org/W2087312526","https://openalex.org/W2095377493","https://openalex.org/W2097179328","https://openalex.org/W2126506946","https://openalex.org/W2139168617","https://openalex.org/W2141394518","https://openalex.org/W2152481940","https://openalex.org/W2159271996","https://openalex.org/W2162752666","https://openalex.org/W2164954534","https://openalex.org/W2168760661","https://openalex.org/W2170995987","https://openalex.org/W3118711955","https://openalex.org/W4244538750","https://openalex.org/W4292366025"],"related_works":["https://openalex.org/W7095957900","https://openalex.org/W2403285571","https://openalex.org/W1974365244","https://openalex.org/W2146696177","https://openalex.org/W7097560165","https://openalex.org/W2007194763","https://openalex.org/W1985279130","https://openalex.org/W2163568640","https://openalex.org/W2127501773","https://openalex.org/W2034530802"],"abstract_inverted_index":{"We":[0,64],"examine":[1],"the":[2,5,29,39,49,53,60,66,74,77,85,100,104,110,122,125,132,135,138,141,147,151,162,166,179,184,188],"geometry":[3,75],"of":[4,28,59,68,76,87,103,113,124,134,137,143,192],"finite-dimensional":[6],"attractor":[7,51,78,106,139],"associated":[8,61],"with":[9,84,140],"fluid":[10,97],"flows":[11,98],"described":[12],"by":[13,109],"Navier\u2013Stokes":[14],"equations":[15,42],"and":[16,47,79,116,176],"relate":[17],"its":[18],"nonlinear":[19,172],"dimensionality":[20,71,102],"to":[21,43,72,150,155,165,170,183,187],"energy":[22,173],"exchanges":[23],"between":[24],"dynamical":[25],"components":[26],"(modes)":[27],"flow.":[30],"Specifically,":[31],"we":[32,80,93,130],"use":[33],"a":[34,82,171],"stochastic":[35,50,105],"framework":[36],"based":[37],"on":[38],"dynamically":[40],"orthogonal":[41],"perform":[44],"efficient":[45],"order-reduction":[46],"describe":[48,73],"in":[52,57,95],"reduced-order":[54],"phase":[55],"space":[56],"terms":[58],"probability":[62],"measure.":[63],"introduce":[65],"notion":[67],"local":[69],"fractal":[70],"establish":[81],"connection":[83,133],"number":[86],"positive":[88],"finite-time":[89],"Lyapunov":[90],"exponents.":[91],"Subsequently,":[92],"illustrate":[94,131],"specific":[96],"that":[99],"low":[101],"is":[107],"caused":[108],"synergistic":[111],"activity":[112],"linearly":[114,157,189],"unstable":[115,152,158,163],"stable":[117,167,180,190],"modes":[118,153,164,181],"as":[119,121],"well":[120],"action":[123],"quadratic":[126],"terms.":[127],"In":[128],"particular,":[129],"low-dimensionality":[136],"circulation":[142],"energy:":[144],"(i)":[145],"from":[146,161,178],"mean":[148,185],"flow":[149],"(due":[154,169,186],"their":[156],"character),":[159],"(ii)":[160],"ones":[168],"transfer":[174],"mechanism)":[175],"(iii)":[177],"back":[182],"character":[191],"these":[193],"modes).":[194]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":5}],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2016-06-24T00:00:00"}
