{"id":"https://openalex.org/W3205371765","doi":"https://doi.org/10.1137/21m1452524","title":"Phase Separation in Systems of Interacting Active Brownian Particles","display_name":"Phase Separation in Systems of Interacting Active Brownian Particles","publication_year":2022,"publication_date":"2022-08-01","ids":{"openalex":"https://openalex.org/W3205371765","doi":"https://doi.org/10.1137/21m1452524","mag":"3205371765"},"language":"en","primary_location":{"id":"doi:10.1137/21m1452524","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1452524","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.repository.cam.ac.uk/handle/1810/343109","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066357021","display_name":"Maria Bruna","orcid":"https://orcid.org/0000-0001-7829-5652"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Maria Bruna","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-7829-5652","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069220813","display_name":"Martin Burger","orcid":"https://orcid.org/0000-0003-2619-2912"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Martin Burger","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0003-2619-2912","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045052930","display_name":"Antonio Esposito","orcid":"https://orcid.org/0000-0002-4230-4729"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Antonio Esposito","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-4230-4729","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5100898757","display_name":"Simon Schulz","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Simon M. Schulz","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":1.7383,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.83799728,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"82","issue":"4","first_page":"1635","last_page":"1660"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11486","display_name":"Micro and Nano Robotics","score":1.0,"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":1.0,"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/T11915","display_name":"Pickering emulsions and particle stabilization","score":0.9922999739646912,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13187","display_name":"Diffusion and Search Dynamics","score":0.9889000058174133,"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/brownian-motion","display_name":"Brownian motion","score":0.6906968355178833},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.639618456363678},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.5494694709777832},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4606284201145172},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.4561048150062561},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.45290833711624146},{"id":"https://openalex.org/keywords/phase-space","display_name":"Phase space","score":0.44855839014053345},{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.43755781650543213},{"id":"https://openalex.org/keywords/particle","display_name":"Particle (ecology)","score":0.43325984477996826},{"id":"https://openalex.org/keywords/particle-system","display_name":"Particle system","score":0.4120640754699707},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.17842096090316772},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.12022912502288818},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10490846633911133}],"concepts":[{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.6906968355178833},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.639618456363678},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5494694709777832},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4606284201145172},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.4561048150062561},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.45290833711624146},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.44855839014053345},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.43755781650543213},{"id":"https://openalex.org/C2778517922","wikidata":"https://www.wikidata.org/wiki/Q7140482","display_name":"Particle (ecology)","level":2,"score":0.43325984477996826},{"id":"https://openalex.org/C179003449","wikidata":"https://www.wikidata.org/wiki/Q1757458","display_name":"Particle system","level":2,"score":0.4120640754699707},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.17842096090316772},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.12022912502288818},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10490846633911133},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.0},{"id":"https://openalex.org/C111368507","wikidata":"https://www.wikidata.org/wiki/Q43518","display_name":"Oceanography","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/21m1452524","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1452524","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:1d468f5d-3b87-4be8-97f3-1a53f840d218","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:1d468f5d-3b87-4be8-97f3-1a53f840d218","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symplectic Elements","raw_type":"Journal article"},{"id":"pmh:oai:www.repository.cam.ac.uk:1810/343109","is_oa":true,"landing_page_url":"https://www.repository.cam.ac.uk/handle/1810/343109","pdf_url":null,"source":{"id":"https://openalex.org/S4306401777","display_name":"Apollo (University of Cambridge)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I241749","host_organization_name":"University of Cambridge","host_organization_lineage":["https://openalex.org/I241749"],"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":null,"raw_type":"Article"},{"id":"doi:10.17863/cam.90520","is_oa":true,"landing_page_url":"https://doi.org/10.17863/cam.90520","pdf_url":null,"source":{"id":"https://openalex.org/S7407050737","display_name":"Apollo","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","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"JournalArticle"}],"best_oa_location":{"id":"pmh:oai:www.repository.cam.ac.uk:1810/343109","is_oa":true,"landing_page_url":"https://www.repository.cam.ac.uk/handle/1810/343109","pdf_url":null,"source":{"id":"https://openalex.org/S4306401777","display_name":"Apollo (University of Cambridge)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I241749","host_organization_name":"University of Cambridge","host_organization_lineage":["https://openalex.org/I241749"],"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":null,"raw_type":"Article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2560186855","display_name":null,"funder_award_id":"RGF/EA/181043","funder_id":"https://openalex.org/F4320320006","funder_display_name":"Royal Society"},{"id":"https://openalex.org/G2691952350","display_name":null,"funder_award_id":"883363","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5282983359","display_name":"Nonlocal PDEs for Complex Particle Dynamics: Phase Transitions, Patterns and Synchronization","funder_award_id":"883363","funder_id":"https://openalex.org/F4320338335","funder_display_name":"H2020 European Research Council"},{"id":"https://openalex.org/G541621470","display_name":null,"funder_award_id":"URF/R1/180040","funder_id":"https://openalex.org/F4320320006","funder_display_name":"Royal Society"},{"id":"https://openalex.org/G98328834","display_name":null,"funder_award_id":"CRC TR 154","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320308269","display_name":"Alexander von Humboldt-Stiftung","ror":"https://ror.org/012kf4317"},{"id":"https://openalex.org/F4320320006","display_name":"Royal Society","ror":"https://ror.org/03wnrjx87"},{"id":"https://openalex.org/F4320320290","display_name":"University of Oxford","ror":"https://ror.org/052gg0110"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320328447","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31"},{"id":"https://openalex.org/F4320338335","display_name":"H2020 European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W1836107020","https://openalex.org/W1954810786","https://openalex.org/W1969754919","https://openalex.org/W1979380796","https://openalex.org/W1989543568","https://openalex.org/W1999377530","https://openalex.org/W2005751229","https://openalex.org/W2006628332","https://openalex.org/W2012240485","https://openalex.org/W2012405657","https://openalex.org/W2020158707","https://openalex.org/W2023952789","https://openalex.org/W2055674605","https://openalex.org/W2071252926","https://openalex.org/W2074203477","https://openalex.org/W2076797206","https://openalex.org/W2084559690","https://openalex.org/W2093840813","https://openalex.org/W2094495898","https://openalex.org/W2108939302","https://openalex.org/W2119636813","https://openalex.org/W2128254052","https://openalex.org/W2153920886","https://openalex.org/W2254944678","https://openalex.org/W2519998528","https://openalex.org/W2605723436","https://openalex.org/W2612414054","https://openalex.org/W2762719199","https://openalex.org/W2785325634","https://openalex.org/W2985499145","https://openalex.org/W3037683188","https://openalex.org/W3071158295","https://openalex.org/W3099141040","https://openalex.org/W3106339744","https://openalex.org/W3125727070"],"related_works":["https://openalex.org/W126238052","https://openalex.org/W3034342236","https://openalex.org/W2027826475","https://openalex.org/W625004508","https://openalex.org/W4379924685","https://openalex.org/W4287758773","https://openalex.org/W3011586872","https://openalex.org/W2065917584","https://openalex.org/W2312544580","https://openalex.org/W2043277408"],"abstract_inverted_index":{"The":[0,50],"aim":[1],"of":[2,11,32,65,85,108,119,145,161],"this":[3],"paper":[4],"is":[5,166],"to":[6,81],"discuss":[7],"the":[8,57,66,74,106,116,136,146,149,159,169,179],"mathematical":[9],"modeling":[10],"Brownian":[12],"active":[13,86],"particle":[14],"systems,":[15],"a":[16,96,110,127],"recently":[17],"popular":[18],"paradigmatic":[19],"system":[20],"for":[21,56,112,168],"self-propelled":[22],"particles.":[23],"We":[24,104,141],"present":[25],"four":[26],"microscopic":[27,137],"models":[28,172],"with":[29],"different":[30,47],"types":[31],"repulsive":[33,155],"interactions":[34,176],"between":[35],"particles":[36,67,87],"and":[37,63,68,76,123,131,138],"their":[38],"associated":[39],"macroscopic":[40,51,139],"models,":[41,147],"which":[42,152],"are":[43,53],"formally":[44],"obtained":[45],"using":[46],"coarse-graining":[48],"methods.":[49],"limits":[52],"integro-differential":[54],"equations":[55],"density":[58],"in":[59,72,115,182],"phase":[60,90,101],"space":[61,118],"(positions":[62],"orientations)":[64],"may":[69],"include":[70],"nonlinearities":[71],"both":[73,135],"diffusive":[75],"advective":[77],"components.":[78],"In":[79,163],"contrast":[80],"passive":[82],"particles,":[83],"systems":[84],"can":[88],"undergo":[89],"separation":[91,102],"without":[92],"any":[93],"attractive":[94],"interactions,":[95,156],"mechanism":[97],"known":[98],"as":[99],"motility-induced":[100],"(MIPS).":[103],"explore":[105],"onset":[107],"such":[109],"transition":[111],"each":[113],"model":[114,151],"parameter":[117],"occupied":[120],"volume":[121],"fraction":[122],"P\u00e9clet":[124],"number":[125],"via":[126],"linear":[128],"stability":[129],"analysis":[130],"numerical":[132],"simulations":[133],"at":[134],"levels.":[140],"establish":[142],"that":[143,173,177],"one":[144],"namely,":[148],"mean-field":[150],"assumes":[153],"long-range":[154],"cannot":[157],"explain":[158],"emergence":[160],"MIPS.":[162],"contrast,":[164],"MIPS":[165],"observed":[167],"remaining":[170],"three":[171],"assume":[174],"short-range":[175],"localize":[178],"interaction":[180],"terms":[181],"space.":[183]},"counts_by_year":[{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1}],"updated_date":"2026-07-20T07:56:41.581041","created_date":"2025-10-10T00:00:00"}
