{"id":"https://openalex.org/W2077212798","doi":"https://doi.org/10.1137/090780055","title":"The Large Core Limit of Spiral Waves in Excitable Media: A Numerical Approach","display_name":"The Large Core Limit of Spiral Waves in Excitable Media: A Numerical Approach","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2077212798","doi":"https://doi.org/10.1137/090780055","mag":"2077212798"},"language":"en","primary_location":{"id":"doi:10.1137/090780055","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090780055","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"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 Applied Dynamical Systems","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1003.5830","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Sebastian Hermann","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sebastian Hermann","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Georg A. Gottwald","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Georg A. Gottwald","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":1.2156,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.83890845,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"9","issue":"2","first_page":"536","last_page":"567"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9955999851226807,"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":0.9955999851226807,"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/T10244","display_name":"Chaos control and synchronization","score":0.0010999999940395355,"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/T11513","display_name":"stochastic dynamics and bifurcation","score":0.0010999999940395355,"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/spiral","display_name":"Spiral (railway)","score":0.7239999771118164},{"id":"https://openalex.org/keywords/rotation","display_name":"Rotation (mathematics)","score":0.5881999731063843},{"id":"https://openalex.org/keywords/radius","display_name":"RADIUS","score":0.5803999900817871},{"id":"https://openalex.org/keywords/spurious-relationship","display_name":"Spurious relationship","score":0.5321000218391418},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.521399974822998},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.5004000067710876},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.46230000257492065},{"id":"https://openalex.org/keywords/core","display_name":"Core (optical fiber)","score":0.44530001282691956}],"concepts":[{"id":"https://openalex.org/C174128100","wikidata":"https://www.wikidata.org/wiki/Q846907","display_name":"Spiral (railway)","level":2,"score":0.7239999771118164},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6765999794006348},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.5881999731063843},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.5803999900817871},{"id":"https://openalex.org/C97256817","wikidata":"https://www.wikidata.org/wiki/Q1462316","display_name":"Spurious relationship","level":2,"score":0.5321000218391418},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.521399974822998},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.5004000067710876},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.47510001063346863},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.46230000257492065},{"id":"https://openalex.org/C2164484","wikidata":"https://www.wikidata.org/wiki/Q5170150","display_name":"Core (optical fiber)","level":2,"score":0.44530001282691956},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42559999227523804},{"id":"https://openalex.org/C2777485032","wikidata":"https://www.wikidata.org/wiki/Q22908993","display_name":"Spiral wave","level":3,"score":0.4178999960422516},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.4131999909877777},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.3959999978542328},{"id":"https://openalex.org/C203311528","wikidata":"https://www.wikidata.org/wiki/Q34132","display_name":"Cylinder","level":2,"score":0.3921999931335449},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.35499998927116394},{"id":"https://openalex.org/C188721877","wikidata":"https://www.wikidata.org/wiki/Q103510","display_name":"Bar (unit)","level":2,"score":0.34040001034736633},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.33970001339912415},{"id":"https://openalex.org/C2777042112","wikidata":"https://www.wikidata.org/wiki/Q5281658","display_name":"Discontinuity (linguistics)","level":2,"score":0.33009999990463257},{"id":"https://openalex.org/C107706756","wikidata":"https://www.wikidata.org/wiki/Q219637","display_name":"Bessel function","level":2,"score":0.2919999957084656},{"id":"https://openalex.org/C6260449","wikidata":"https://www.wikidata.org/wiki/Q41364","display_name":"Wavelength","level":2,"score":0.2915000021457672},{"id":"https://openalex.org/C112675119","wikidata":"https://www.wikidata.org/wiki/Q2992284","display_name":"Periodic boundary conditions","level":3,"score":0.2793000042438507},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.27570000290870667},{"id":"https://openalex.org/C121130766","wikidata":"https://www.wikidata.org/wiki/Q192510","display_name":"Wavenumber","level":2,"score":0.2732999920845032},{"id":"https://openalex.org/C44886760","wikidata":"https://www.wikidata.org/wiki/Q1758425","display_name":"Wave propagation","level":2,"score":0.26750001311302185},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.262800008058548}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/090780055","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090780055","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"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 Applied Dynamical Systems","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1003.5830","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1003.5830","pdf_url":"https://arxiv.org/pdf/1003.5830","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:1003.5830","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1003.5830","pdf_url":"https://arxiv.org/pdf/1003.5830","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1520610722","https://openalex.org/W1599277155","https://openalex.org/W1963818997","https://openalex.org/W1963994264","https://openalex.org/W1968961435","https://openalex.org/W1972515952","https://openalex.org/W1974602860","https://openalex.org/W1975904858","https://openalex.org/W1978221306","https://openalex.org/W1978566446","https://openalex.org/W1982293853","https://openalex.org/W1995694419","https://openalex.org/W1997277858","https://openalex.org/W2000687618","https://openalex.org/W2005761796","https://openalex.org/W2009969589","https://openalex.org/W2010589199","https://openalex.org/W2012358612","https://openalex.org/W2013837246","https://openalex.org/W2021280511","https://openalex.org/W2021369835","https://openalex.org/W2021921746","https://openalex.org/W2029868048","https://openalex.org/W2040876379","https://openalex.org/W2057743846","https://openalex.org/W2059244117","https://openalex.org/W2060809971","https://openalex.org/W2068665487","https://openalex.org/W2071368801","https://openalex.org/W2092566925","https://openalex.org/W2105696522","https://openalex.org/W2132475559","https://openalex.org/W2134031242","https://openalex.org/W2143747939","https://openalex.org/W2170733390","https://openalex.org/W4313905188"],"related_works":[],"abstract_inverted_index":{"We":[0,75,100,145],"modify":[1],"the":[2,29,33,42,85,88,108,119,147,156,160],"freezing":[3],"method":[4,23,104,114],"introduced":[5],"by":[6,67,71],"Beyn":[7],"and":[8,32,70,132,159],"Th\u00fcmmler":[9],"in":[10,18,48],"2004":[11],"for":[12,84,155],"analyzing":[13],"rigidly":[14],"rotating":[15,37],"spiral":[16,46,55,64,125,164],"waves":[17,47,126],"excitable":[19],"media.":[20],"The":[21,112],"proposed":[22,113],"is":[24,90,172],"designed":[25],"to":[26,105,117,122,140,168],"stably":[27],"determine":[28],"rotation":[30,134,157],"frequency":[31,135,158],"core":[34,110,129,161],"radius":[35,130,162],"of":[36,45,63,73,81,151,163],"spirals,":[38],"as":[39,41],"well":[40],"approximate":[43],"shape":[44],"unbounded":[49],"domains.":[50],"In":[51],"particular,":[52],"we":[53],"introduce":[54],"wave":[56,65,165],"boundary":[57,82],"conditions":[58,83],"based":[59],"on":[60],"geometric":[61],"approximations":[62],"solutions":[66,166],"Archimedean":[68],"spirals":[69],"involutes":[72],"circles.":[74],"further":[76],"propose":[77],"a":[78,92,152],"simple":[79],"implementation":[80],"case":[86,93,120],"when":[87],"inhibitor":[89],"nondiffusive,":[91],"which":[94],"had":[95],"previously":[96],"caused":[97],"spurious":[98],"oscillations.":[99],"then":[101],"utilize":[102],"our":[103],"numerically":[106],"analyze":[107],"large":[109],"limit.":[111],"allows":[115],"us":[116],"investigate":[118],"close":[121,167],"criticality":[123],"where":[124],"acquire":[127],"infinite":[128],"$r_c$":[131],"zero":[133],"$\\omega$,":[136],"before":[137],"they":[138],"begin":[139],"develop":[141],"into":[142],"retracting":[143],"fingers.":[144],"confirm":[146],"linear":[148],"scaling":[149],"regime":[150,171],"drift":[153],"bifurcation":[154],"criticality.":[169],"This":[170],"unattainable":[173],"with":[174],"conventional":[175],"numerical":[176],"methods.":[177]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2016-06-24T00:00:00"}