{"id":"https://openalex.org/W2077557805","doi":"https://doi.org/10.1142/s0218127401003139","title":"ANIMATION OF CHAOTIC MIXING BY A BACKWARD POINCARE CELL-MAP METHOD","display_name":"ANIMATION OF CHAOTIC MIXING BY A BACKWARD POINCARE CELL-MAP METHOD","publication_year":2001,"publication_date":"2001-07-01","ids":{"openalex":"https://openalex.org/W2077557805","doi":"https://doi.org/10.1142/s0218127401003139","mag":"2077557805"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127401003139","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127401003139","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","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/A5074100630","display_name":"Linxiang Wang","orcid":"https://orcid.org/0000-0002-7716-3794"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"LINXIANG WANG","raw_affiliation_strings":["Department of Energy, Shanghai Jiaotong University, Shanghai China, 200030, China"],"affiliations":[{"raw_affiliation_string":"Department of Energy, Shanghai Jiaotong University, Shanghai China, 200030, China","institution_ids":["https://openalex.org/I183067930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100930461","display_name":"Yurun Fan","orcid":null},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"YURUN FAN","raw_affiliation_strings":["State Key Lab for Fluid Power Transmission and Control, Zhejiang University, Hangzhou China, 310027, China"],"affiliations":[{"raw_affiliation_string":"State Key Lab for Fluid Power Transmission and Control, Zhejiang University, Hangzhou China, 310027, China","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100383084","display_name":"Ying Chen","orcid":"https://orcid.org/0000-0002-7769-216X"},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"YING CHEN","raw_affiliation_strings":["State Key Lab for Fluid Power Transmission and Control, Zhejiang University, Hangzhou China, 310027, China"],"affiliations":[{"raw_affiliation_string":"State Key Lab for Fluid Power Transmission and Control, Zhejiang University, Hangzhou China, 310027, China","institution_ids":["https://openalex.org/I76130692"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5074100630"],"corresponding_institution_ids":["https://openalex.org/I183067930"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.15479247,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"11","issue":"07","first_page":"1953","last_page":"1960"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9947999715805054,"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"}},"topics":[{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9947999715805054,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9776999950408936,"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/T11017","display_name":"Chaos-based Image/Signal Encryption","score":0.9605000019073486,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/poincar\u00e9-map","display_name":"Poincar\u00e9 map","score":0.7826577425003052},{"id":"https://openalex.org/keywords/mixing","display_name":"Mixing (physics)","score":0.7566275596618652},{"id":"https://openalex.org/keywords/chaotic-mixing","display_name":"Chaotic mixing","score":0.7552710771560669},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.6875013113021851},{"id":"https://openalex.org/keywords/vector-field","display_name":"Vector field","score":0.5797938108444214},{"id":"https://openalex.org/keywords/poincar\u00e9-conjecture","display_name":"Poincar\u00e9 conjecture","score":0.4779089391231537},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.47784826159477234},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.457507848739624},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4316181242465973},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.43118441104888916},{"id":"https://openalex.org/keywords/animation","display_name":"Animation","score":0.42489221692085266},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.40075141191482544},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.38869622349739075},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.358245849609375},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.32155925035476685},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.31251299381256104},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics (images)","score":0.20628097653388977},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.19803038239479065},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1451701521873474},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.088250070810318}],"concepts":[{"id":"https://openalex.org/C21955772","wikidata":"https://www.wikidata.org/wiki/Q339199","display_name":"Poincar\u00e9 map","level":4,"score":0.7826577425003052},{"id":"https://openalex.org/C138777275","wikidata":"https://www.wikidata.org/wiki/Q6884054","display_name":"Mixing (physics)","level":2,"score":0.7566275596618652},{"id":"https://openalex.org/C131436191","wikidata":"https://www.wikidata.org/wiki/Q5072842","display_name":"Chaotic mixing","level":3,"score":0.7552710771560669},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.6875013113021851},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.5797938108444214},{"id":"https://openalex.org/C88221313","wikidata":"https://www.wikidata.org/wiki/Q203586","display_name":"Poincar\u00e9 conjecture","level":2,"score":0.4779089391231537},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.47784826159477234},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.457507848739624},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4316181242465973},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.43118441104888916},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.42489221692085266},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.40075141191482544},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.38869622349739075},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.358245849609375},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.32155925035476685},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31251299381256104},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.20628097653388977},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.19803038239479065},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1451701521873474},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.088250070810318},{"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:10.1142/s0218127401003139","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218127401003139","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320338464","display_name":"Natural Science Foundation of Zhejiang Province","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1571507625","https://openalex.org/W1665713033","https://openalex.org/W2004218186","https://openalex.org/W2007105181","https://openalex.org/W2017670549","https://openalex.org/W2024103622","https://openalex.org/W2032509958","https://openalex.org/W2042862761","https://openalex.org/W2048878653","https://openalex.org/W2066137852","https://openalex.org/W2074388175","https://openalex.org/W2076327952","https://openalex.org/W2091025069","https://openalex.org/W2101021792","https://openalex.org/W2117633103","https://openalex.org/W2142345941","https://openalex.org/W2147737253","https://openalex.org/W2168945626"],"related_works":["https://openalex.org/W3152996675","https://openalex.org/W2117908751","https://openalex.org/W1527005526","https://openalex.org/W4297199653","https://openalex.org/W2614781401","https://openalex.org/W2125480959","https://openalex.org/W2139638169","https://openalex.org/W2164531605","https://openalex.org/W2002590959","https://openalex.org/W3095527810"],"abstract_inverted_index":{"A":[0],"Backward":[1],"Poincare":[2,86,91],"cell-mapping":[3,87,92],"(BPCM)":[4],"method":[5],"has":[6],"been":[7],"developed":[8],"for":[9,97,104],"animating":[10,105],"chaotic":[11,15,100],"fluid":[12,101],"mixing.":[13],"The":[14,34,63],"mixing":[16,64,102],"field":[17,59],"considered":[18],"is":[19,37,46,66],"induced":[20],"by":[21,55],"periodically":[22],"rotating":[23],"the":[24,57,84,99,106],"secondary":[25],"flow":[26],"of":[27,89,109],"incompressible":[28],"fluids":[29],"in":[30,61],"a":[31,40,50,79,94],"curved":[32],"pipe.":[33],"pipe's":[35],"cross-section":[36],"transformed":[38],"into":[39],"cell":[41,45,72],"space":[42],"where":[43],"each":[44,71],"initially":[47],"assigned":[48],"with":[49,70,75],"color":[51,77],"code":[52],"and":[53,103],"mapped":[54],"integrating":[56],"velocity":[58],"forward":[60],"time.":[62],"process":[65],"thus":[67],"animated":[68],"efficiently":[69],"being":[73],"painted":[74],"its":[76],"on":[78],"computer":[80],"screen.":[81],"We":[82],"propose":[83],"backward":[85],"instead":[88],"direct":[90],"as":[93],"useful":[95],"tool":[96],"probing":[98],"phase":[107],"deformation":[108],"nonlinear":[110],"dynamical":[111],"systems.":[112]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}