{"id":"https://openalex.org/W2508024210","doi":"https://doi.org/10.1142/s0217984916503048","title":"Scaling behavior of non-equilibrium phase transitions in spontaneously ordered motion of self-propelled particles","display_name":"Scaling behavior of non-equilibrium phase transitions in spontaneously ordered motion of self-propelled particles","publication_year":2016,"publication_date":"2016-09-05","ids":{"openalex":"https://openalex.org/W2508024210","doi":"https://doi.org/10.1142/s0217984916503048","mag":"2508024210"},"language":"en","primary_location":{"id":"doi:10.1142/s0217984916503048","doi":"https://doi.org/10.1142/s0217984916503048","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0217984916503048","pdf_url":null,"source":{"id":"https://openalex.org/S88537382","display_name":"Modern Physics Letters B","issn_l":"0217-9849","issn":["0217-9849","1793-6640"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-1","norway-1","poland-40","russia-white-list-2"],"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":"Modern Physics Letters B","raw_type":"journal-article"},"parent_works":[],"lineage":["https://openalex.org/W2508024210"],"child_works_count":0,"type":"article","is_traditional":true,"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/A5114114430","display_name":"R. Bakir","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210087544","display_name":"\u00c9cole Normale Sup\u00e9rieure Casablanca","ror":"https://ror.org/0052qvr31","country_code":"MA","type":"education","lineage":["https://openalex.org/I4210087544"]},{"id":"https://openalex.org/I99297268","display_name":"University of Hassan II Casablanca","ror":"https://ror.org/001q4kn48","country_code":"MA","type":"education","lineage":["https://openalex.org/I99297268"]}],"countries":["MA"],"is_corresponding":false,"raw_author_name":"R. Bakir","raw_affiliation_strings":["LIMB, Ecole Normale Sup\u00e9rieure, University of Hassan II Casablanca, Casablanca 20000, Morocco","LPMC, Faculty of Sciences Ben M\u2019sik, University of Hasan II Casablanca, Casablanca 20000, Morocco"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LIMB, Ecole Normale Sup\u00e9rieure, University of Hassan II Casablanca, Casablanca 20000, Morocco","institution_ids":["https://openalex.org/I4210087544","https://openalex.org/I99297268"]},{"raw_affiliation_string":"LPMC, Faculty of Sciences Ben M\u2019sik, University of Hasan II Casablanca, Casablanca 20000, Morocco","institution_ids":["https://openalex.org/I99297268"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079292716","display_name":"Iliass Tarras","orcid":"https://orcid.org/0000-0002-0257-1662","observed_orcids":["https://orcid.org/0000-0002-0257-1662"]},"institutions":[{"id":"https://openalex.org/I99297268","display_name":"University of Hassan II Casablanca","ror":"https://ror.org/001q4kn48","country_code":"MA","type":"education","lineage":["https://openalex.org/I99297268"]}],"countries":["MA"],"is_corresponding":true,"raw_author_name":"I. Tarras","raw_affiliation_strings":["LPMC, Faculty of Sciences Ben M\u2019sik, University of Hasan II Casablanca, Casablanca 20000, Morocco"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LPMC, Faculty of Sciences Ben M\u2019sik, University of Hasan II Casablanca, Casablanca 20000, Morocco","institution_ids":["https://openalex.org/I99297268"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027786955","display_name":"Ahmed Hader","orcid":"https://orcid.org/0000-0002-0597-2576","observed_orcids":["https://orcid.org/0000-0002-0597-2576"]},"institutions":[{"id":"https://openalex.org/I4210087544","display_name":"\u00c9cole Normale Sup\u00e9rieure Casablanca","ror":"https://ror.org/0052qvr31","country_code":"MA","type":"education","lineage":["https://openalex.org/I4210087544"]},{"id":"https://openalex.org/I4387155678","display_name":"Centre R\u00e9gional des M\u00e9tiers de l'\u00c9ducation et de la Formation Casablanca-Settat","ror":"https://ror.org/02sct0170","country_code":"MA","type":"education","lineage":["https://openalex.org/I4387155678"]},{"id":"https://openalex.org/I99297268","display_name":"University of Hassan II Casablanca","ror":"https://ror.org/001q4kn48","country_code":"MA","type":"education","lineage":["https://openalex.org/I99297268"]}],"countries":["MA"],"is_corresponding":false,"raw_author_name":"A. Hader","raw_affiliation_strings":["Centre R\u00e9gional des M\u00e9tiers de l\u2019 \u00c9ducation et de la Formation, Settat, Morocco","LIMB, Ecole Normale Sup\u00e9rieure, University of Hassan II Casablanca, Casablanca 20000, Morocco"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre R\u00e9gional des M\u00e9tiers de l\u2019 \u00c9ducation et de la Formation, Settat, Morocco","institution_ids":["https://openalex.org/I4387155678"]},{"raw_affiliation_string":"LIMB, Ecole Normale Sup\u00e9rieure, University of Hassan II Casablanca, Casablanca 20000, Morocco","institution_ids":["https://openalex.org/I4210087544","https://openalex.org/I99297268"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078123598","display_name":"Hicham Sbiaai","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210087544","display_name":"\u00c9cole Normale Sup\u00e9rieure Casablanca","ror":"https://ror.org/0052qvr31","country_code":"MA","type":"education","lineage":["https://openalex.org/I4210087544"]},{"id":"https://openalex.org/I99297268","display_name":"University of Hassan II Casablanca","ror":"https://ror.org/001q4kn48","country_code":"MA","type":"education","lineage":["https://openalex.org/I99297268"]}],"countries":["MA"],"is_corresponding":false,"raw_author_name":"H. Sbiaai","raw_affiliation_strings":["LIMB, Ecole Normale Sup\u00e9rieure, University of Hassan II Casablanca, Casablanca 20000, Morocco"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LIMB, Ecole Normale Sup\u00e9rieure, University of Hassan II Casablanca, Casablanca 20000, Morocco","institution_ids":["https://openalex.org/I4210087544","https://openalex.org/I99297268"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112841802","display_name":"M'hamed Mazroui","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I99297268","display_name":"University of Hassan II Casablanca","ror":"https://ror.org/001q4kn48","country_code":"MA","type":"education","lineage":["https://openalex.org/I99297268"]}],"countries":["MA"],"is_corresponding":false,"raw_author_name":"M. Mazroui","raw_affiliation_strings":["LPMC, Faculty of Sciences Ben M\u2019sik, University of Hasan II Casablanca, Casablanca 20000, Morocco"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LPMC, Faculty of Sciences Ben M\u2019sik, University of Hasan II Casablanca, Casablanca 20000, Morocco","institution_ids":["https://openalex.org/I99297268"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023189932","display_name":"Y. Boughaleb","orcid":"https://orcid.org/0000-0002-1572-0401","observed_orcids":["https://orcid.org/0000-0002-1572-0401"]},"institutions":[{"id":"https://openalex.org/I4210087544","display_name":"\u00c9cole Normale Sup\u00e9rieure Casablanca","ror":"https://ror.org/0052qvr31","country_code":"MA","type":"education","lineage":["https://openalex.org/I4210087544"]},{"id":"https://openalex.org/I4210125507","display_name":"Chouaib Doukkali University","ror":"https://ror.org/036kgyt43","country_code":"MA","type":"education","lineage":["https://openalex.org/I4210125507"]},{"id":"https://openalex.org/I99297268","display_name":"University of Hassan II Casablanca","ror":"https://ror.org/001q4kn48","country_code":"MA","type":"education","lineage":["https://openalex.org/I99297268"]}],"countries":["MA"],"is_corresponding":false,"raw_author_name":"Y. Boughaleb","raw_affiliation_strings":["LIMB, Ecole Normale Sup\u00e9rieure, University of Hassan II Casablanca, Casablanca 20000, Morocco","LPMC, University of Chouaib Doukkali, El Jadida 24000, Morocco"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LIMB, Ecole Normale Sup\u00e9rieure, University of Hassan II Casablanca, Casablanca 20000, Morocco","institution_ids":["https://openalex.org/I4210087544","https://openalex.org/I99297268"]},{"raw_affiliation_string":"LPMC, University of Chouaib Doukkali, El Jadida 24000, Morocco","institution_ids":["https://openalex.org/I4210125507"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5079292716"],"corresponding_institution_ids":["https://openalex.org/I99297268"],"apc_list":null,"apc_paid":null,"fwci":0.3772,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.53674918,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":93,"max":97},"biblio":{"volume":"30","issue":"24","first_page":"1650304","last_page":"1650304"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.7153000235557556,"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/T10591","display_name":"Theoretical and Computational Physics","score":0.7153000235557556,"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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.12030000239610672,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.023399999365210533,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/self-propelled-particles","display_name":"self-propelled particles","score":0.8519999980926514},{"id":"https://openalex.org/keywords/vicsek-model","display_name":"Vicsek model","score":0.9819999933242798},{"id":"https://openalex.org/keywords/nonequilibrium-phase-transitions","display_name":"nonequilibrium phase transitions","score":0.9660000205039978},{"id":"https://openalex.org/keywords/collective-motion","display_name":"collective motion","score":0.7360000014305115},{"id":"https://openalex.org/keywords/flocking","display_name":"flocking","score":0.6579999923706055},{"id":"https://openalex.org/keywords/scaling-exponents","display_name":"scaling exponents","score":0.9539999961853027},{"id":"https://openalex.org/keywords/noise","display_name":"noise","score":0.5139999985694885},{"id":"https://openalex.org/keywords/universality","display_name":"universality","score":0.8320000171661377},{"id":"https://openalex.org/keywords/self-similarity","display_name":"self-similarity","score":0.9520000219345093},{"id":"https://openalex.org/keywords/interface-growth","display_name":"interface growth","score":0.6299999952316284},{"id":"https://openalex.org/keywords/submonolayer-deposition","display_name":"submonolayer deposition","score":0.9860000014305115}],"concepts":[{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.8149299025535583},{"id":"https://openalex.org/C183992945","wikidata":"https://www.wikidata.org/wiki/Q2495574","display_name":"Universality (dynamical systems)","level":2,"score":0.6586551070213318},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.615402340888977},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.48613283038139343},{"id":"https://openalex.org/C2780500908","wikidata":"https://www.wikidata.org/wiki/Q28405357","display_name":"Dynamic scaling","level":3,"score":0.4787237346172333},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.4678790271282196},{"id":"https://openalex.org/C149288129","wikidata":"https://www.wikidata.org/wiki/Q185357","display_name":"Phase transition","level":2,"score":0.46436449885368347},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.43852171301841736},{"id":"https://openalex.org/C135889238","wikidata":"https://www.wikidata.org/wiki/Q46276","display_name":"Kinetic energy","level":2,"score":0.4316064119338989},{"id":"https://openalex.org/C68532491","wikidata":"https://www.wikidata.org/wiki/Q1203669","display_name":"Renormalization group","level":2,"score":0.4162501096725464},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3658906817436218},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.3347020149230957},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.26469773054122925},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14231044054031372},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.13727405667304993},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"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/s0217984916503048","doi":"https://doi.org/10.1142/s0217984916503048","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0217984916503048","pdf_url":null,"source":{"id":"https://openalex.org/S88537382","display_name":"Modern Physics Letters B","issn_l":"0217-9849","issn":["0217-9849","1793-6640"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-d","jufo-1","norway-1","poland-40","russia-white-list-2"],"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":"Modern Physics Letters B","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320323771","display_name":"Centre National pour la Recherche Scientifique et Technique","ror":"https://ror.org/00675rp98"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W591468295","https://openalex.org/W1776498786","https://openalex.org/W1965935485","https://openalex.org/W1966537808","https://openalex.org/W1973596070","https://openalex.org/W1975318518","https://openalex.org/W1982115118","https://openalex.org/W1987365226","https://openalex.org/W2009187744","https://openalex.org/W2015410655","https://openalex.org/W2015490890","https://openalex.org/W2033011321","https://openalex.org/W2062120511","https://openalex.org/W2088046890","https://openalex.org/W2089660038","https://openalex.org/W2143969246","https://openalex.org/W2279927153","https://openalex.org/W2337346296","https://openalex.org/W2372428381","https://openalex.org/W3133413954","https://openalex.org/W4285719527","https://openalex.org/W4388322442"],"related_works":["https://openalex.org/W1776498786","https://openalex.org/W2337346296","https://openalex.org/W1991891170","https://openalex.org/W2171928181","https://openalex.org/W1987593367","https://openalex.org/W2018580609","https://openalex.org/W7096754657","https://openalex.org/W4404402162","https://openalex.org/W7096736809","https://openalex.org/W1593067061"],"abstract_inverted_index":{"Many":[0],"animal":[1],"groups,":[2],"such":[3],"as":[4,15],"bird":[5],"flocks,":[6],"clearly":[7],"present":[8,113],"structural":[9],"order":[10],"and":[11,35,47,88,129,156,164],"appear":[12],"to":[13,22,45,78,153,165],"move":[14],"a":[16,119],"single":[17],"coherent":[18],"entity.":[19],"In":[20],"interest":[21],"understand":[23],"the":[24,50,54,67,80,94,101,106,110,139,148,154,161,166,180,189,193],"complex":[25],"behavior":[26,52,81],"of":[27,41,63,69,82,85,93,109,131,141,173,192,197,203],"these":[28,174,204],"systems,":[29],"many":[30],"models":[31],"have":[32],"been":[33],"proposed":[34],"tested":[36],"so":[37],"far.":[38],"The":[39,91,144,170],"aim":[40],"this":[42],"work":[43],"is":[44,74,97,200],"study":[46,79],"discuss":[48],"numerically":[49],"scaling":[51,95,102],"in":[53,59,66,160],"2D":[55],"non-equilibrium":[56],"phase":[57],"transitions":[58],"spontaneously":[60,194],"ordered":[61,195],"motion":[62,84,196],"self-propelled":[64,198],"particles":[65,111,199],"framework":[68],"Vicsek":[70],"model.":[71],"This":[72],"model":[73],"an":[75],"important":[76],"tool":[77],"collective":[83],"live":[86],"biological":[87],"physical":[89],"organisms.":[90],"calculation":[92],"exponents":[96,150,175],"effected":[98],"by":[99,118],"using":[100],"dynamic":[103],"method.":[104],"However,":[105],"time":[107,121],"evolution":[108,191],"velocity":[112],"two":[114],"different":[115],"regimes":[116],"separated":[117],"cross-over":[120],"which":[122,183],"increases":[123],"linearly":[124],"with":[125,138],"both":[126],"applied":[127],"noise":[128],"radius":[130,140],"repulsive":[132],"zone,":[133],"but":[134],"it":[135],"decreases":[136],"exponentially":[137],"orientation":[142],"zone.":[143],"results":[145],"show":[146],"that":[147],"obtained":[149,171],"are":[151,176,206],"similar":[152],"growth":[155,163],"roughness":[157],"ones":[158],"used":[159],"interfaces":[162],"submonolayer":[167],"deposition":[168],"process.":[169],"values":[172],"not":[177],"dependent":[178],"on":[179],"noises":[181],"value,":[182],"proves":[184],"their":[185],"universality":[186],"characters.":[187],"Hence":[188],"kinetic":[190],"self-similar.":[201],"Implications":[202],"findings":[205],"discussed.":[207]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2017,"cited_by_count":3}],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2016-09-16T00:00:00"}
