{"id":"https://openalex.org/W2583771427","doi":"https://doi.org/10.1137/16m1106778","title":"Optimal Strokes at Low Reynolds Number: A Geometric and Numerical Study of Copepod and Purcell Swimmers","display_name":"Optimal Strokes at Low Reynolds Number: A Geometric and Numerical Study of Copepod and Purcell Swimmers","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2583771427","doi":"https://doi.org/10.1137/16m1106778","mag":"2583771427"},"language":"en","primary_location":{"id":"doi:10.1137/16m1106778","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1106778","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","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/A5109351634","display_name":"Piernicola Bettiol","orcid":"https://orcid.org/0000-0003-4969-6144"},"institutions":[{"id":"https://openalex.org/I2802204017","display_name":"Universit\u00e9 de Bretagne Sud","ror":"https://ror.org/04ed7fw48","country_code":"FR","type":"education","lineage":["https://openalex.org/I2802204017"]},{"id":"https://openalex.org/I161929037","display_name":"Universit\u00e9 de Bretagne Occidentale","ror":"https://ror.org/01b8h3982","country_code":"FR","type":"education","lineage":["https://openalex.org/I161929037"]},{"id":"https://openalex.org/I4210119023","display_name":"Laboratoire de Math\u00e9matiques de Bretagne Atlantique","ror":"https://ror.org/02ght4n58","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I2802204017","https://openalex.org/I4210119023","https://openalex.org/I4210141950","https://openalex.org/I4412460332"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"P. Bettiol","raw_affiliation_strings":["LMBA - Laboratoire de Math\u00e9matiques de Bretagne Atlantique (Universit\u00e9 de Brest, 6 avenue Le Gorgeu, CS 93837, 29238 Brest cedex 3 / Universit\u00e9 de Bretagne-Sud, Centre Yves Coppens, B\u00e2t. B, Campus de Tohannic, BP 573, 56017 Vannes - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LMBA - Laboratoire de Math\u00e9matiques de Bretagne Atlantique (Universit\u00e9 de Brest, 6 avenue Le Gorgeu, CS 93837, 29238 Brest cedex 3 / Universit\u00e9 de Bretagne-Sud, Centre Yves Coppens, B\u00e2t. B, Campus de Tohannic, BP 573, 56017 Vannes - France)","institution_ids":["https://openalex.org/I2802204017","https://openalex.org/I161929037","https://openalex.org/I4210119023"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5107838661","display_name":"Bernard Bonnard","orcid":null},"institutions":[{"id":"https://openalex.org/I4210166017","display_name":"Institut de Math\u00e9matiques de Bordeaux","ror":"https://ror.org/05m3r1b84","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I15057530","https://openalex.org/I4210141950","https://openalex.org/I4210160189","https://openalex.org/I4210166017"]},{"id":"https://openalex.org/I177064439","display_name":"Universit\u00e9 de Bourgogne","ror":"https://ror.org/03k1bsr36","country_code":"FR","type":"education","lineage":["https://openalex.org/I177064439"]},{"id":"https://openalex.org/I4210112333","display_name":"Institut de Math\u00e9matiques de Bourgogne","ror":"https://ror.org/021f0sa24","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I4210112333","https://openalex.org/I4407990431"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"B. Bonnard","raw_affiliation_strings":["IMB - Institut de Math\u00e9matiques de Bourgogne [Dijon] (Universit\u00e9 de Bourgogne - 9, avenue Alain Savary - B.P. 47 870 - 21078 Dijon Cedex - France)","McTAO - Mathematics for Control, Transport and Applications (2004 route des Lucioles BP 93 F-06902 Sophia Antipolis (France) - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IMB - Institut de Math\u00e9matiques de Bourgogne [Dijon] (Universit\u00e9 de Bourgogne - 9, avenue Alain Savary - B.P. 47 870 - 21078 Dijon Cedex - France)","institution_ids":["https://openalex.org/I4210166017","https://openalex.org/I4210112333","https://openalex.org/I177064439"]},{"raw_affiliation_string":"McTAO - Mathematics for Control, Transport and Applications (2004 route des Lucioles BP 93 F-06902 Sophia Antipolis (France) - France)","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062564633","display_name":"J\u00e9r\u00e9my Rouot","orcid":"https://orcid.org/0000-0001-6832-2856"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. Rouot","raw_affiliation_strings":["McTAO - Mathematics for Control, Transport and Applications (2004 route des Lucioles BP 93 F-06902 Sophia Antipolis (France) - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"McTAO - Mathematics for Control, Transport and Applications (2004 route des Lucioles BP 93 F-06902 Sophia Antipolis (France) - France)","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5109351634"],"corresponding_institution_ids":["https://openalex.org/I161929037","https://openalex.org/I2802204017","https://openalex.org/I4210119023"],"apc_list":null,"apc_paid":null,"fwci":0.7417,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.70517183,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"56","issue":"3","first_page":"1794","last_page":"1822"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11486","display_name":"Micro and Nano Robotics","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter 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/T11486","display_name":"Micro and Nano Robotics","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter 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/T11170","display_name":"Biomimetic flight and propulsion mechanisms","score":0.9905999898910522,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"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/T12350","display_name":"Particle Dynamics in Fluid Flows","score":0.955299973487854,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/reynolds-number","display_name":"Reynolds number","score":0.7044721245765686},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.646752655506134},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5507336258888245},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4371330440044403},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4200516939163208},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3703615069389343},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2538028359413147},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.18407684564590454},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.14236539602279663},{"id":"https://openalex.org/keywords/turbulence","display_name":"Turbulence","score":0.07096892595291138}],"concepts":[{"id":"https://openalex.org/C182748727","wikidata":"https://www.wikidata.org/wiki/Q178932","display_name":"Reynolds number","level":3,"score":0.7044721245765686},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.646752655506134},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5507336258888245},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4371330440044403},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4200516939163208},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3703615069389343},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2538028359413147},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.18407684564590454},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.14236539602279663},{"id":"https://openalex.org/C196558001","wikidata":"https://www.wikidata.org/wiki/Q190132","display_name":"Turbulence","level":2,"score":0.07096892595291138},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/16m1106778","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1106778","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-01326790v4","is_oa":false,"landing_page_url":"https://inria.hal.science/hal-01326790","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://epubs.siam.org/doi/10.1137/16M1106778","raw_type":"Journal articles"},{"id":"pmh:oai:HAL:hal-04404194v1","is_oa":false,"landing_page_url":"https://hal.univ-brest.fr/hal-04404194","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://epubs.siam.org/doi/10.1137/16M1106778","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Life below water","id":"https://metadata.un.org/sdg/14","score":0.5099999904632568}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1598905606","https://openalex.org/W1927459862","https://openalex.org/W1964211981","https://openalex.org/W1974957251","https://openalex.org/W2007612798","https://openalex.org/W2014546372","https://openalex.org/W2016147656","https://openalex.org/W2025597993","https://openalex.org/W2056370235","https://openalex.org/W2063551455","https://openalex.org/W2121948997","https://openalex.org/W2215175913","https://openalex.org/W2229744558","https://openalex.org/W2949182269","https://openalex.org/W3105292323"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W4285308861"],"abstract_inverted_index":{"In":[0,68],"this":[1,69],"article":[2],"we":[3],"provide":[4],"a":[5,97],"comparative":[6],"geometric":[7],"and":[8,35,103,110,129,143,151,166],"numerical":[9,117,145,156],"analysis":[10,99],"of":[11,45,65,100,139],"optimal":[12,55,123,169],"strokes":[13,46,77,105,124],"for":[14,125],"two":[15],"different":[16],"rigid":[17],"links":[18],"swimmer":[19,27,30,40],"models":[20],"at":[21],"low":[22],"Reynolds":[23],"number:":[24],"the":[25,36,63,94,127,130,137,163,168],"copepod":[26,95,128],"(a":[28],"symmetric":[29],"recently":[31],"introduced":[32],"by":[33,41],"Takagi)":[34],"long-standing":[37],"three-link":[38],"Purcell":[39,131],"Purcell.":[42],"The":[43],"design":[44],"satisfying":[47],"standard":[48],"performance":[49],"criteria":[50],"leads":[51],"one":[52,74],"to":[53,75,88,121,154,161],"investigate":[54],"control":[56],"problems":[57],"which":[58,81,158],"can":[59,84],"be":[60,85],"analyzed":[61],"in":[62,82,149],"framework":[64],"subRiemannian":[66],"geometry.":[67],"context":[70],"nilpotent":[71],"approximations":[72],"allow":[73,119],"compute":[76],"with":[78,116],"small":[79],"amplitudes,":[80],"turn":[83],"used":[86],"numerically":[87],"obtain":[89],"more":[90],"general":[91],"strokes.":[92],"For":[93],"model":[96],"detailed":[98],"both":[101,126],"abnormal":[102],"normal":[104],"is":[106,134],"also":[107],"described.":[108],"First":[109],"second":[111],"order":[112],"optimality":[113],"conditions,":[114],"combined":[115],"analysis,":[118],"us":[120],"detect":[122],"swimmers.":[132],"$C^1$-optimality":[133],"investigated":[135],"using":[136],"concept":[138],"conjugate":[140],"point.":[141],"Direct":[142],"indirect":[144],"schemes":[146],"are":[147,159],"implemented":[148],"Bocop":[150],"HamPath":[152],"software":[153],"perform":[155],"simulations,":[157],"crucial":[160],"complete":[162],"theoretical":[164],"study":[165],"evaluate":[167],"solutions.":[170]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-05-07T13:39:58.223016","created_date":"2025-10-10T00:00:00"}
