{"id":"https://openalex.org/W2051530082","doi":"https://doi.org/10.1137/110844696","title":"A Simple Linear Response Closure Approximation for Slow Dynamics of a Multiscale System with Linear Coupling","display_name":"A Simple Linear Response Closure Approximation for Slow Dynamics of a Multiscale System with Linear Coupling","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2051530082","doi":"https://doi.org/10.1137/110844696","mag":"2051530082"},"language":"en","primary_location":{"id":"doi:10.1137/110844696","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110844696","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling & Simulation","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1107.3548","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Rafail V. Abramov","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Rafail V. Abramov","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":1.197,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.82814812,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"10","issue":"1","first_page":"28","last_page":"47"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.5400000214576721,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.5400000214576721,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.1858000010251999,"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/T11513","display_name":"stochastic dynamics and bifurcation","score":0.0917000025510788,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6377000212669373},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6074000000953674},{"id":"https://openalex.org/keywords/coupling","display_name":"Coupling (piping)","score":0.6015999913215637},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5663999915122986},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.504800021648407},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.43970000743865967},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4156999886035919},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.41339999437332153},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.38449999690055847}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6377000212669373},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6074000000953674},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.6015999913215637},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5663999915122986},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.504800021648407},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5015000104904175},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4593999981880188},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44269999861717224},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.43970000743865967},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4156999886035919},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.41339999437332153},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.38449999690055847},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.35420000553131104},{"id":"https://openalex.org/C77405623","wikidata":"https://www.wikidata.org/wiki/Q598451","display_name":"System dynamics","level":2,"score":0.34689998626708984},{"id":"https://openalex.org/C129537906","wikidata":"https://www.wikidata.org/wiki/Q7603913","display_name":"State variable","level":2,"score":0.3422999978065491},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.335099995136261},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32409998774528503},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3237999975681305},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3100999891757965},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.2992999851703644},{"id":"https://openalex.org/C170122806","wikidata":"https://www.wikidata.org/wiki/Q1914828","display_name":"Linear scale","level":2,"score":0.28850001096725464},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.2847999930381775},{"id":"https://openalex.org/C73586568","wikidata":"https://www.wikidata.org/wiki/Q2600211","display_name":"Parameter space","level":2,"score":0.2791999876499176},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2768999934196472},{"id":"https://openalex.org/C138777275","wikidata":"https://www.wikidata.org/wiki/Q6884054","display_name":"Mixing (physics)","level":2,"score":0.2743000090122223},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.2711000144481659},{"id":"https://openalex.org/C163175372","wikidata":"https://www.wikidata.org/wiki/Q3339222","display_name":"Linear model","level":2,"score":0.26930001378059387},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.26829999685287476},{"id":"https://openalex.org/C160824197","wikidata":"https://www.wikidata.org/wiki/Q2071054","display_name":"Linear approximation","level":3,"score":0.26739999651908875},{"id":"https://openalex.org/C126701199","wikidata":"https://www.wikidata.org/wiki/Q264224","display_name":"Complex dynamics","level":2,"score":0.25870001316070557},{"id":"https://openalex.org/C47822265","wikidata":"https://www.wikidata.org/wiki/Q854457","display_name":"Complex system","level":2,"score":0.25119999051094055}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/110844696","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110844696","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling & Simulation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1107.3548","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1107.3548","pdf_url":"https://arxiv.org/pdf/1107.3548","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1107.3548","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1107.3548","pdf_url":"https://arxiv.org/pdf/1107.3548","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W196973002","https://openalex.org/W1572902284","https://openalex.org/W1985664661","https://openalex.org/W1990845344","https://openalex.org/W1998727969","https://openalex.org/W2003156978","https://openalex.org/W2017957151","https://openalex.org/W2024907874","https://openalex.org/W2024913569","https://openalex.org/W2028990747","https://openalex.org/W2034956278","https://openalex.org/W2041360742","https://openalex.org/W2041965365","https://openalex.org/W2049013344","https://openalex.org/W2064000876","https://openalex.org/W2074126690","https://openalex.org/W2078156396","https://openalex.org/W2103757834","https://openalex.org/W2136887674","https://openalex.org/W2139139723","https://openalex.org/W2154358707","https://openalex.org/W2167197920","https://openalex.org/W2171441956","https://openalex.org/W4239456296","https://openalex.org/W4247068909","https://openalex.org/W4255454912"],"related_works":[],"abstract_inverted_index":{"Many":[0],"applications":[1],"of":[2,19,21,33,45,48,61,80,90,105,117,130,181,192],"contemporary":[3],"science":[4],"involve":[5],"multiscale":[6,195],"dynamics,":[7],"which":[8,99,141,204],"are":[9],"typically":[10],"characterized":[11],"by":[12,173],"the":[13,46,49,58,64,77,92,109,118,126,131,138,146,182,190,193],"time":[14,71],"and":[15,28,63,160],"space":[16],"scale":[17,39,211],"separation":[18,40],"patterns":[20],"motion,":[22],"with":[23,112,135,153],"fewer":[24],"slowly":[25],"evolving":[26,35],"variables":[27,62,97],"a":[29,68,87,102,113,174],"much":[30],"larger":[31],"set":[32],"faster":[34],"variables.":[36,120],"This":[37],"time-space":[38],"causes":[41],"direct":[42],"numerical":[43],"simulation":[44],"evolution":[47],"dynamics":[50,111],"to":[51,56,66,75,137,169,201],"be":[52,143,198],"computationally":[53],"expensive":[54],"due":[55,200],"both":[57,158],"large":[59,210],"number":[60],"necessity":[65],"choose":[67],"small":[69],"discretization":[70],"step":[72],"in":[73,157],"order":[74],"resolve":[76],"fast":[78,110,161],"components":[79],"dynamics.":[81],"In":[82],"this":[83,163],"work":[84],"we":[85],"propose":[86],"simple":[88,154],"method":[89,122,164,183],"determining":[91],"closed":[93],"model":[94,196],"for":[95,108,208],"slow":[96,119,139,159],"alone,":[98],"requires":[100],"only":[101],"single":[103],"computation":[104],"appropriate":[106],"statistics":[107,168,191],"certain":[114],"fixed":[115],"state":[116],"The":[121,178],"is":[123,171,184],"based":[124],"on":[125],"first-order":[127],"Taylor":[128],"expansion":[129],"averaged":[132],"coupling":[133,156],"term":[134],"respect":[136],"variables,":[140,162],"can":[142],"computed":[144],"using":[145],"linear":[147,155],"fluctuation-dissipation":[148],"theorem.":[149],"We":[150],"show":[151],"that,":[152],"produces":[165],"quite":[166],"comparable":[167],"what":[170],"exhibited":[172],"complete":[175],"two-scale":[176],"model.":[177],"main":[179],"advantage":[180],"that":[185],"it":[186,206],"applies":[187],"even":[188],"when":[189],"full":[194],"cannot":[197],"simulated":[199],"computational":[202],"complexity,":[203],"makes":[205],"practical":[207],"real-world":[209],"applications.":[212]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2016-06-24T00:00:00"}