{"id":"https://openalex.org/W2943855279","doi":"https://doi.org/10.1007/s00332-020-09632-x","title":"Phase Transitions and Macroscopic Limits in a BGK Model of Body-Attitude Coordination","display_name":"Phase Transitions and Macroscopic Limits in a BGK Model of Body-Attitude Coordination","publication_year":2020,"publication_date":"2020-05-30","ids":{"openalex":"https://openalex.org/W2943855279","doi":"https://doi.org/10.1007/s00332-020-09632-x","mag":"2943855279"},"language":"en","primary_location":{"id":"doi:10.1007/s00332-020-09632-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00332-020-09632-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00332-020-09632-x.pdf","source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00332-020-09632-x.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"P. Degond","orcid":"https://orcid.org/0000-0002-4886-6968"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"P. Degond","raw_affiliation_strings":["Department of Mathematics, Imperial College London, South Kensington Campus, London, SW7 2AZ, UK"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Imperial College London, South Kensington Campus, London, SW7 2AZ, UK","institution_ids":["https://openalex.org/I47508984"]}]},{"author_position":"middle","author":{"id":null,"display_name":"A. Diez","orcid":null},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"A. Diez","raw_affiliation_strings":["Department of Mathematics, Imperial College London, South Kensington Campus, London, SW7 2AZ, UK"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Imperial College London, South Kensington Campus, London, SW7 2AZ, UK","institution_ids":["https://openalex.org/I47508984"]}]},{"author_position":"middle","author":{"id":null,"display_name":"A. Frouvelle","orcid":null},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I171048554","display_name":"Centre de Recherche en Math\u00e9matiques de la D\u00e9cision","ror":"https://ror.org/03s0gj002","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I171048554","https://openalex.org/I2746051580","https://openalex.org/I4210141950","https://openalex.org/I56435720"]},{"id":"https://openalex.org/I2746051580","display_name":"Universit\u00e9 Paris Sciences et Lettres","ror":"https://ror.org/013cjyk83","country_code":"FR","type":"education","lineage":["https://openalex.org/I2746051580"]},{"id":"https://openalex.org/I56435720","display_name":"Universit\u00e9 Paris Dauphine-PSL","ror":"https://ror.org/052bz7812","country_code":"FR","type":"education","lineage":["https://openalex.org/I2746051580","https://openalex.org/I56435720"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"A. Frouvelle","raw_affiliation_strings":["CEREMADE, CNRS, Universit\u00e9 Paris-Dauphine, Universit\u00e9 PSL, 75016, Paris, France"],"affiliations":[{"raw_affiliation_string":"CEREMADE, CNRS, Universit\u00e9 Paris-Dauphine, Universit\u00e9 PSL, 75016, Paris, France","institution_ids":["https://openalex.org/I56435720","https://openalex.org/I171048554","https://openalex.org/I2746051580","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":null,"display_name":"S. Merino-Aceituno","orcid":null},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]},{"id":"https://openalex.org/I162608824","display_name":"University of Sussex","ror":"https://ror.org/00ayhx656","country_code":"GB","type":"education","lineage":["https://openalex.org/I162608824"]}],"countries":["AT","GB"],"is_corresponding":false,"raw_author_name":"S. Merino-Aceituno","raw_affiliation_strings":["Department of Mathematics, University of Sussex, Falmer, BN1 9RH, UK","Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Wien, Austria"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Sussex, Falmer, BN1 9RH, UK","institution_ids":["https://openalex.org/I162608824"]},{"raw_affiliation_string":"Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Wien, Austria","institution_ids":["https://openalex.org/I129774422"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I47508984"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":1.5726,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.81885463,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"30","issue":"6","first_page":"2671","last_page":"2736"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11486","display_name":"Micro and Nano Robotics","score":0.7357000112533569,"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":0.7357000112533569,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.02459999918937683,"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/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.01899999938905239,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/phase-transition","display_name":"Phase transition","score":0.5820000171661377},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.5806999802589417},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5633999705314636},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.5551000237464905},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.45260000228881836},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.4510999917984009},{"id":"https://openalex.org/keywords/distribution-function","display_name":"Distribution function","score":0.44999998807907104},{"id":"https://openalex.org/keywords/rotation","display_name":"Rotation (mathematics)","score":0.41339999437332153},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4131999909877777}],"concepts":[{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.6492999792098999},{"id":"https://openalex.org/C149288129","wikidata":"https://www.wikidata.org/wiki/Q185357","display_name":"Phase transition","level":2,"score":0.5820000171661377},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.5806999802589417},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.571399986743927},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5633999705314636},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.5551000237464905},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.45260000228881836},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4510999917984009},{"id":"https://openalex.org/C186603090","wikidata":"https://www.wikidata.org/wiki/Q55505926","display_name":"Distribution function","level":2,"score":0.44999998807907104},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.41339999437332153},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4131999909877777},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.4099999964237213},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.39570000767707825},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.3723999857902527},{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.3723999857902527},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.37229999899864197},{"id":"https://openalex.org/C73586568","wikidata":"https://www.wikidata.org/wiki/Q2600211","display_name":"Parameter space","level":2,"score":0.36419999599456787},{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.3614000082015991},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3578999936580658},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.35589998960494995},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.3508000075817108},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3434000015258789},{"id":"https://openalex.org/C135889238","wikidata":"https://www.wikidata.org/wiki/Q46276","display_name":"Kinetic energy","level":2,"score":0.3172000050544739},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.30799999833106995},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.3012000024318695},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.28870001435279846},{"id":"https://openalex.org/C2780791683","wikidata":"https://www.wikidata.org/wiki/Q846785","display_name":"Action (physics)","level":2,"score":0.28209999203681946},{"id":"https://openalex.org/C10184394","wikidata":"https://www.wikidata.org/wiki/Q5165491","display_name":"Continuous modelling","level":2,"score":0.26649999618530273},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.26600000262260437},{"id":"https://openalex.org/C13274807","wikidata":"https://www.wikidata.org/wiki/Q203989","display_name":"Liquid crystal","level":2,"score":0.2624000012874603},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.25540000200271606}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s00332-020-09632-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00332-020-09632-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00332-020-09632-x.pdf","source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1905.04885","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1905.04885","pdf_url":"https://arxiv.org/pdf/1905.04885","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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"},{"id":"pmh:oai:HAL:hal-02126060v1","is_oa":false,"landing_page_url":"https://hal.science/hal-02126060","pdf_url":null,"source":{"id":"https://openalex.org/S4406922466","display_name":"SPIRE - Sciences Po Institutional REpository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://link.springer.com/article/10.1007/s00332-020-09632-x","raw_type":"Journal articles"},{"id":"pmh:oai:spiral.imperial.ac.uk:10044/1/79919","is_oa":true,"landing_page_url":"http://hdl.handle.net/10044/1/79919","pdf_url":null,"source":{"id":"https://openalex.org/S4306401396","display_name":"Spiral (Imperial College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I47508984","host_organization_name":"Imperial College London","host_organization_lineage":["https://openalex.org/I47508984"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"}],"best_oa_location":{"id":"doi:10.1007/s00332-020-09632-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00332-020-09632-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00332-020-09632-x.pdf","source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1661186933","display_name":null,"funder_award_id":"17-CE40-0030","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G1661566268","display_name":"Modelling sperm-mucus interactions across scales","funder_award_id":"EP/P013651/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G1934935867","display_name":null,"funder_award_id":"Engineering and Physical Sciences R","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G2210890369","display_name":null,"funder_award_id":"RNMS11-07444 (KI-Net)","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2465084072","display_name":null,"funder_award_id":"ANR-17-CE40-0030","funder_id":"https://openalex.org/F4320321003","funder_display_name":"Vienna Science and Technology Fund"},{"id":"https://openalex.org/G3100797910","display_name":null,"funder_award_id":"ANR-17-CE40-0030","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G317715447","display_name":null,"funder_award_id":"Wolfson","funder_id":"https://openalex.org/F4320320006","funder_display_name":"Royal Society"},{"id":"https://openalex.org/G3330119427","display_name":null,"funder_award_id":"EPSRC","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3909495268","display_name":null,"funder_award_id":"WM130048","funder_id":"https://openalex.org/F4320320006","funder_display_name":"Royal Society"},{"id":"https://openalex.org/G4304059183","display_name":"Macroscopic dynamics and bifurcations of active particle systems","funder_award_id":"EP/M006883/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G4357590839","display_name":null,"funder_award_id":"ANR-13-BS01-0004","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G4528557337","display_name":null,"funder_award_id":"RNMS11-07444","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5733226094","display_name":null,"funder_award_id":"EP/P013651/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6022573062","display_name":null,"funder_award_id":"VRG17-014","funder_id":"https://openalex.org/F4320321003","funder_display_name":"Vienna Science and Technology Fund"},{"id":"https://openalex.org/G6043388943","display_name":null,"funder_award_id":"11-07444","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6080763000","display_name":null,"funder_award_id":"D\u00e9fi S2C3","funder_id":"https://openalex.org/F4320322892","funder_display_name":"Centre National de la Recherche Scientifique"},{"id":"https://openalex.org/G6803667113","display_name":null,"funder_award_id":"ANR-17","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G6851345361","display_name":null,"funder_award_id":"Grant","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G6972643991","display_name":null,"funder_award_id":"2129658","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7681843745","display_name":null,"funder_award_id":"WM130048","funder_id":"https://openalex.org/F4320320670","funder_display_name":"Wolfson Foundation"},{"id":"https://openalex.org/G7758152977","display_name":null,"funder_award_id":"support","funder_id":"https://openalex.org/F4320322892","funder_display_name":"Centre National de la Recherche Scientifique"},{"id":"https://openalex.org/G8298899259","display_name":null,"funder_award_id":"EP/M006883/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8719353587","display_name":null,"funder_award_id":"EP/P0","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309966","display_name":"\u00c9cole Normale Sup\u00e9rieure","ror":"https://ror.org/05a0dhs15"},{"id":"https://openalex.org/F4320316917","display_name":"Institut de Math\u00e9matiques de Toulouse","ror":"https://ror.org/014vp6c30"},{"id":"https://openalex.org/F4320320006","display_name":"Royal Society","ror":"https://ror.org/03wnrjx87"},{"id":"https://openalex.org/F4320320325","display_name":"University of Sussex","ror":"https://ror.org/00ayhx656"},{"id":"https://openalex.org/F4320320670","display_name":"Wolfson Foundation","ror":"https://ror.org/0333xzh65"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320321003","display_name":"Vienna Science and Technology Fund","ror":"https://ror.org/01f9mc681"},{"id":"https://openalex.org/F4320322892","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73"},{"id":"https://openalex.org/F4320329934","display_name":"\u00c9cole Normale Sup\u00e9rieure de Lyon","ror":"https://ror.org/04zmssz18"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320335551","display_name":"Erasmus+","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2943855279.pdf","grobid_xml":"https://content.openalex.org/works/W2943855279.grobid-xml"},"referenced_works_count":55,"referenced_works":["https://openalex.org/W182704713","https://openalex.org/W1501394657","https://openalex.org/W1925947257","https://openalex.org/W2007601369","https://openalex.org/W2015410655","https://openalex.org/W2016768925","https://openalex.org/W2017992740","https://openalex.org/W2018577880","https://openalex.org/W2025035458","https://openalex.org/W2026275744","https://openalex.org/W2029211607","https://openalex.org/W2035610779","https://openalex.org/W2066060292","https://openalex.org/W2066875242","https://openalex.org/W2070015342","https://openalex.org/W2074574519","https://openalex.org/W2077881080","https://openalex.org/W2084992778","https://openalex.org/W2085146763","https://openalex.org/W2094642272","https://openalex.org/W2103714988","https://openalex.org/W2113453261","https://openalex.org/W2113829847","https://openalex.org/W2114446871","https://openalex.org/W2129823023","https://openalex.org/W2140774441","https://openalex.org/W2144570667","https://openalex.org/W2146673305","https://openalex.org/W2149600326","https://openalex.org/W2155084532","https://openalex.org/W2156450311","https://openalex.org/W2157344226","https://openalex.org/W2165098579","https://openalex.org/W2168335667","https://openalex.org/W2253784914","https://openalex.org/W2256347232","https://openalex.org/W2312951351","https://openalex.org/W2313456324","https://openalex.org/W2320126040","https://openalex.org/W2334964350","https://openalex.org/W2345531252","https://openalex.org/W2537953840","https://openalex.org/W2566344954","https://openalex.org/W2594637640","https://openalex.org/W2896310263","https://openalex.org/W2948110959","https://openalex.org/W2962917543","https://openalex.org/W2963338890","https://openalex.org/W2963938287","https://openalex.org/W2964052864","https://openalex.org/W2966697418","https://openalex.org/W6601103585","https://openalex.org/W6601561694","https://openalex.org/W6602667358","https://openalex.org/W6738317309"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2,61,85,146],"article":[3],"we":[4,129,149],"investigate":[5],"the":[6,21,68,71,75,92,103,131,135,154,157,160,163,169,174,178],"phase":[7],"transition":[8],"phenomena":[9],"that":[10,90],"occur":[11],"in":[12,33,46,91,124,162,177],"a":[13,30,64,78,112,141],"model":[14],"of":[15,24,60,70,74,84,106,119,122,134,180],"self-organisation":[16,96],"through":[17],"body-attitude":[18],"coordination.":[19],"Here,":[20],"body":[22],"attitude":[23],"an":[25],"agent":[26],"is":[27,63,87],"modelled":[28],"by":[29],"rotation":[31],"matrix":[32],"$${\\mathbb":[34],"{R}}^3$$":[35],"<mml:math":[36],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[37],"<mml:msup>":[38],"<mml:mrow>":[39],"<mml:mi>R</mml:mi>":[40],"</mml:mrow>":[41],"<mml:mn>3</mml:mn>":[42],"</mml:msup>":[43],"</mml:math>":[44],"as":[45],"Degond":[47,181],"et":[48,182],"al.":[49,183],"(Math":[50],"Models":[51,191],"Methods":[52,192],"Appl":[53,193],"Sci":[54,194],"27(6):1005\u20131049,":[55,195],"2017).":[56,196],"The":[57,81],"starting":[58],"point":[59],"study":[62],"BGK":[65,147],"equation":[66],"modelling":[67],"evolution":[69],"distribution":[72],"function":[73],"system":[76],"at":[77],"kinetic":[79],"level.":[80],"main":[82],"novelty":[83],"work":[86],"to":[88,140,145,152],"show":[89],"spatially":[93],"homogeneous":[94],"case,":[95],"may":[97],"appear":[98],"or":[99],"not":[100],"depending":[101],"on":[102],"local":[104],"density":[105],"agents":[107],"involved.":[108],"We":[109,166],"first":[110],"exhibit":[111],"connection":[113],"between":[114],"body-orientation":[115],"models":[116,118,171],"and":[117,156],"nematic":[120],"alignment":[121],"polymers":[123],"higher-dimensional":[125],"space":[126],"from":[127],"which":[128],"deduce":[130],"complete":[132],"description":[133],"possible":[136],"equilibria.":[137],"Then,":[138],"thanks":[139],"gradient-flow":[142],"structure":[143],"specific":[144],"model,":[148],"are":[150],"able":[151],"prove":[153],"stability":[155],"convergence":[158],"towards":[159],"equilibria":[161,176],"different":[164],"regimes.":[165],"then":[167],"derive":[168],"macroscopic":[170],"associated":[172],"with":[173],"stable":[175],"spirit":[179],"(Arch":[184],"Ration":[185],"Mech":[186],"Anal":[187],"216(1):63\u2013115,":[188],"2015,":[189],"Math":[190]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":3}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2019-05-16T00:00:00"}
