{"id":"https://openalex.org/W2234879229","doi":"https://doi.org/10.3390/e18010027","title":"Interacting Brownian Swarms: Some Analytical Results","display_name":"Interacting Brownian Swarms: Some Analytical Results","publication_year":2016,"publication_date":"2016-01-14","ids":{"openalex":"https://openalex.org/W2234879229","doi":"https://doi.org/10.3390/e18010027","mag":"2234879229"},"language":"en","primary_location":{"id":"doi:10.3390/e18010027","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e18010027","pdf_url":"https://www.mdpi.com/1099-4300/18/1/27/pdf?version=1452770459","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/18/1/27/pdf?version=1452770459","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069667034","display_name":"Guillaume Sartoretti","orcid":"https://orcid.org/0000-0002-7579-9916"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Guillaume Sartoretti","raw_affiliation_strings":["STI/IMT/LPM, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne, Station 17 (Batiment BM), CH-1015 Lausanne, Switzerland"],"raw_orcid":"https://orcid.org/0000-0002-7579-9916","affiliations":[{"raw_affiliation_string":"STI/IMT/LPM, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne, Station 17 (Batiment BM), CH-1015 Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112867542","display_name":"Max-Olivier Hongler","orcid":null},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Max-Olivier Hongler","raw_affiliation_strings":["STI/IMT/LPM, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne, Station 17 (Batiment BM), CH-1015 Lausanne, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"STI/IMT/LPM, Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne, Station 17 (Batiment BM), CH-1015 Lausanne, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5069667034","https://openalex.org/A5112867542"],"corresponding_institution_ids":["https://openalex.org/I5124864"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.2833,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.60301314,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"18","issue":"1","first_page":"27","last_page":"27"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9995999932289124,"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":0.9995999932289124,"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/T11252","display_name":"Evolutionary Game Theory and Cooperation","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/3312","display_name":"Sociology and Political Science"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T13187","display_name":"Diffusion and Search Dynamics","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/flocking","display_name":"Flocking (texture)","score":0.71608966588974},{"id":"https://openalex.org/keywords/barycentric-coordinate-system","display_name":"Barycentric coordinate system","score":0.6910324692726135},{"id":"https://openalex.org/keywords/brownian-motion","display_name":"Brownian motion","score":0.6829275488853455},{"id":"https://openalex.org/keywords/swarm-behaviour","display_name":"Swarm behaviour","score":0.6392816305160522},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.6284000277519226},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.46058744192123413},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.45528730750083923},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4487079381942749},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41896432638168335},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3701767027378082},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3255406618118286},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.29958584904670715},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1098611056804657},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09585759043693542}],"concepts":[{"id":"https://openalex.org/C2781220375","wikidata":"https://www.wikidata.org/wiki/Q814208","display_name":"Flocking (texture)","level":2,"score":0.71608966588974},{"id":"https://openalex.org/C128356825","wikidata":"https://www.wikidata.org/wiki/Q738422","display_name":"Barycentric coordinate system","level":2,"score":0.6910324692726135},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.6829275488853455},{"id":"https://openalex.org/C181335050","wikidata":"https://www.wikidata.org/wiki/Q14915018","display_name":"Swarm behaviour","level":2,"score":0.6392816305160522},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.6284000277519226},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.46058744192123413},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.45528730750083923},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4487079381942749},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41896432638168335},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3701767027378082},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3255406618118286},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.29958584904670715},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1098611056804657},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09585759043693542},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e18010027","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e18010027","pdf_url":"https://www.mdpi.com/1099-4300/18/1/27/pdf?version=1452770459","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:f9f177d58b8b40ab946dceac2b97be4d","is_oa":true,"landing_page_url":"https://doaj.org/article/f9f177d58b8b40ab946dceac2b97be4d","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 18, Iss 1, p 27 (2016)","raw_type":"article"},{"id":"pmh:oai:infoscience.epfl.ch:215024","is_oa":false,"landing_page_url":"http://infoscience.epfl.ch/record/215024","pdf_url":null,"source":{"id":"https://openalex.org/S4306400488","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","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":"","raw_type":"Text"},{"id":"pmh:oai:mdpi.com:/1099-4300/18/1/27/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e18010027","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"Entropy; Volume 18; Issue 1; Pages: 27","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e18010027","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e18010027","pdf_url":"https://www.mdpi.com/1099-4300/18/1/27/pdf?version=1452770459","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2234879229.pdf","grobid_xml":"https://content.openalex.org/works/W2234879229.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1565741818","https://openalex.org/W1788502406","https://openalex.org/W1911599023","https://openalex.org/W1975318518","https://openalex.org/W1992209353","https://openalex.org/W2009366157","https://openalex.org/W2010878630","https://openalex.org/W2048118207","https://openalex.org/W2072145663","https://openalex.org/W2130518506","https://openalex.org/W2168448159","https://openalex.org/W2334780960","https://openalex.org/W2476517704","https://openalex.org/W3101862834","https://openalex.org/W3103592675","https://openalex.org/W6640092542"],"related_works":["https://openalex.org/W2097610718","https://openalex.org/W2002188687","https://openalex.org/W2142589698","https://openalex.org/W2794811781","https://openalex.org/W4327740834","https://openalex.org/W4389665619","https://openalex.org/W2138105113","https://openalex.org/W2166744572","https://openalex.org/W1596835606","https://openalex.org/W2182108128"],"abstract_inverted_index":{"We":[0,164],"consider":[1,86],"the":[2,24,28,33,44,58,62,68,79,83,87,131,134,139,153,174],"dynamics":[3],"of":[4,6,23,46,61,82,93,133,138,168,182],"swarms":[5,75,92,101,111,122,147,154],"scalar":[7],"Brownian":[8,94,177],"agents":[9,37,52,95,108,127],"subject":[10],"to":[11],"local":[12],"imitation":[13],"mechanisms":[14],"implemented":[15],"using":[16],"mutual":[17,48],"rank-based":[18,47,176],"interactions.":[19],"For":[20,117],"appropriate":[21,118],"values":[22,132],"underlying":[25],"control":[26,135],"parameters,":[27,136],"swarm":[29],"propagates":[30],"tightly":[31],"and":[32,107,158],"distances":[34],"separating":[35],"successive":[36],"are":[38],"iid":[39],"exponential":[40],"random":[41],"variables.":[42],"Implicitly,":[43],"implementation":[45],"interactions,":[49],"requires":[50],"that":[51,73],"have":[53],"infinite":[54],"interaction":[55,70,98],"ranges.":[56,99],"Using":[57],"probabilistic":[59],"size":[60],"swarm\u2019s":[63],"support,":[64],"we":[65,85],"analytically":[66],"estimate":[67],"critical":[69],"range":[71],"below":[72],"flocked":[74,91],"cannot":[76],"survive.":[77],"In":[78],"second":[80],"part":[81],"paper,":[84],"interactions":[88],"between":[89],"two":[90],"with":[96,103,114],"finite":[97],"Both":[100,146],"travel":[102],"different":[104],"barycentric":[105,162],"velocities,":[106],"from":[109],"both":[110,121],"indifferently":[112],"interact":[113],"each":[115],"other.":[116],"initial":[119],"configurations,":[120],"eventually":[123],"collide":[124],"(i.e.,":[125],"all":[126],"interact).":[128],"Depending":[129],"on":[130,173],"one":[137],"following":[140],"patterns":[141],"emerges":[142],"after":[143],"collision:":[144],"(i)":[145],"remain":[148],"essentially":[149],"flocked,":[150],"or":[151],"(ii)":[152],"become":[155],"ultimately":[156],"quasi-free":[157],"recover":[159],"their":[160],"nominal":[161],"speeds.":[163],"derive":[165],"a":[166],"set":[167,181],"analytical":[169,187],"flocking":[170],"conditions":[171],"based":[172],"generalized":[175],"motion.":[178],"An":[179],"extensive":[180],"numerical":[183],"simulations":[184],"corroborates":[185],"our":[186],"findings.":[188]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2018,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2016-06-24T00:00:00"}
