{"id":"https://openalex.org/W7212045199","doi":"https://doi.org/10.48550/arxiv.2609.09043","title":"Speed and stability of segregated waves in a pressure-based model of heterogeneous cell populations","display_name":"Speed and stability of segregated waves in a pressure-based model of heterogeneous cell populations","publication_year":2026,"publication_date":"2026-09-08","ids":{"openalex":"https://openalex.org/W7212045199","doi":"https://doi.org/10.48550/arxiv.2609.09043"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.09043","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.09043","pdf_url":"https://arxiv.org/pdf/2609.09043","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.09043","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027440870","display_name":"Carles Falc\u00f3","orcid":"https://orcid.org/0000-0001-9832-2697","observed_orcids":["https://orcid.org/0000-0001-9832-2697"]},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Falc\u00f3, Carles","raw_affiliation_strings":["Mathematical Institute , University of Oxford , Oxford , United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute , University of Oxford , Oxford , United Kingdom","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033912322","display_name":"Rebecca  Marie Crossley","orcid":"https://orcid.org/0000-0001-7342-0207","observed_orcids":["https://orcid.org/0000-0001-7342-0207"]},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Crossley, Rebecca M.","raw_affiliation_strings":["Mathematical Institute , University of Oxford , Oxford , United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematical Institute , University of Oxford , Oxford , United Kingdom","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5125585546","display_name":"Martina Conte","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I177477856","display_name":"Politecnico di Torino","ror":"https://ror.org/00bgk9508","country_code":"IT","type":"education","lineage":["https://openalex.org/I177477856"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Conte, Martina","raw_affiliation_strings":["Department of Mathematical Sciences \"G.L. Lagrange\" , Politecnico di Torino , Turin , Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences \"G.L. Lagrange\" , Politecnico di Torino , Turin , Italy","institution_ids":["https://openalex.org/I177477856"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020270129","display_name":"Tommaso Lorenzi","orcid":"https://orcid.org/0000-0001-9165-1666","observed_orcids":["https://orcid.org/0000-0001-9165-1666"]},"institutions":[{"id":"https://openalex.org/I177477856","display_name":"Politecnico di Torino","ror":"https://ror.org/00bgk9508","country_code":"IT","type":"education","lineage":["https://openalex.org/I177477856"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Lorenzi, Tommaso","raw_affiliation_strings":["Department of Mathematical Sciences \"G.L. Lagrange\" , Politecnico di Torino , Turin , Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences \"G.L. Lagrange\" , Politecnico di Torino , Turin , Italy","institution_ids":["https://openalex.org/I177477856"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9955999851226807,"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"}},"topics":[{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9955999851226807,"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"}},{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.0015999999595806003,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.0013000000035390258,"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/variational-bounds","display_name":"variational bounds","score":0.6880000233650208},{"id":"https://openalex.org/keywords/free-boundary-problem","display_name":"free boundary problem","score":0.9679999947547913},{"id":"https://openalex.org/keywords/wave-stability","display_name":"wave stability","score":0.7720000147819519},{"id":"https://openalex.org/keywords/cell-mobility","display_name":"cell mobility","score":0.5580000281333923},{"id":"https://openalex.org/keywords/fingering-instability","display_name":"fingering instability","score":0.902999997138977},{"id":"https://openalex.org/keywords/circular-waves","display_name":"circular waves","score":0.718999981880188},{"id":"https://openalex.org/keywords/incompressible-limit","display_name":"incompressible limit","score":0.7400000095367432}],"concepts":[{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.7110999822616577},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.5537999868392944},{"id":"https://openalex.org/C2775884256","wikidata":"https://www.wikidata.org/wiki/Q5265080","display_name":"Destabilisation","level":2,"score":0.5493999719619751},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4814000129699707},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4697999954223633},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.46380001306533813},{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.45249998569488525},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.43709999322891235},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.41110000014305115},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.4066999852657318},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3930000066757202},{"id":"https://openalex.org/C143170015","wikidata":"https://www.wikidata.org/wiki/Q17007850","display_name":"Stability conditions","level":3,"score":0.3723999857902527},{"id":"https://openalex.org/C2988173416","wikidata":"https://www.wikidata.org/wiki/Q37172","display_name":"Traveling wave","level":2,"score":0.35920000076293945},{"id":"https://openalex.org/C41949839","wikidata":"https://www.wikidata.org/wiki/Q1756677","display_name":"Stability theory","level":3,"score":0.3499999940395355},{"id":"https://openalex.org/C44886760","wikidata":"https://www.wikidata.org/wiki/Q1758425","display_name":"Wave propagation","level":2,"score":0.3474999964237213},{"id":"https://openalex.org/C207016750","wikidata":"https://www.wikidata.org/wiki/Q1955627","display_name":"Pattern formation","level":2,"score":0.3239000141620636},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.31380000710487366},{"id":"https://openalex.org/C113843644","wikidata":"https://www.wikidata.org/wiki/Q901882","display_name":"Interface (matter)","level":4,"score":0.31369999051094055},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2802000045776367},{"id":"https://openalex.org/C50488108","wikidata":"https://www.wikidata.org/wiki/Q618684","display_name":"Marginal stability","level":3,"score":0.27970001101493835},{"id":"https://openalex.org/C146864707","wikidata":"https://www.wikidata.org/wiki/Q382774","display_name":"Internal wave","level":2,"score":0.2775999903678894},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2551000118255615}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.09043","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.09043","pdf_url":"https://arxiv.org/pdf/2609.09043","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.09043","doi":"https://doi.org/10.48550/arxiv.2609.09043","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.09043","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.09043","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.09043","pdf_url":"https://arxiv.org/pdf/2609.09043","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G4345866938","display_name":null,"funder_award_id":"E5324001950001","funder_id":"https://openalex.org/F4320334080","funder_display_name":"Gruppo Nazionale per la Fisica Matematica"},{"id":"https://openalex.org/G4845925241","display_name":null,"funder_award_id":"E5324001950001","funder_id":"https://openalex.org/F4320311030","funder_display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\""},{"id":"https://openalex.org/G8213836532","display_name":"UDLA 2527 University of Oxford","funder_award_id":"EP/Z534870/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320334080","display_name":"Gruppo Nazionale per la Fisica Matematica","ror":"https://ror.org/01d6bq278"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212045199.pdf","grobid_xml":"https://content.openalex.org/works/W7212045199.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4410496502","https://openalex.org/W2014674469","https://openalex.org/W7223146872","https://openalex.org/W2158317652","https://openalex.org/W2551793381","https://openalex.org/W2315503359","https://openalex.org/W2944805673","https://openalex.org/W2797001598","https://openalex.org/W1538857097","https://openalex.org/W4402579109"],"abstract_inverted_index":{"We":[0,147],"consider":[1],"a":[2,24,54,100,104,139],"minimal":[3],"pressure-based":[4],"model":[5,20,38],"of":[6,11,26,33,75,125,143,152,177,184,205,220,235,247,257],"heterogeneous":[7],"cell":[8,35,259],"populations":[9],"consisting":[10],"proliferative":[12,62,170],"and":[13,73,117,128,202,251],"non-proliferative":[14,51,164],"cells":[15,52,63,165],"with":[16,47,122,229],"different":[17],"mobilities.":[18],"The":[19,37,108],"is":[21,39,239],"formulated":[22],"as":[23,99],"system":[25],"reaction--cross--diffusion":[27],"equations":[28],"describing":[29],"the":[30,34,58,66,69,92,97,123,132,144,150,153,182,198,211,218,230,233,244,248,262],"spatio-temporal":[31],"dynamics":[32],"densities.":[36],"known":[40],"to":[41,113,155,217],"admit":[42],"one-dimensional":[43,231],"travelling":[44],"wave":[45,93,145],"solutions":[46],"strictly":[48],"segregated":[49,158,186],"components:":[50],"occupy":[53],"finite":[55],"region":[56],"at":[57,65],"leading":[59],"edge,":[60],"while":[61],"remain":[64,78],"rear.":[67],"However,":[68],"speed,":[70],"parameter":[71],"dependence,":[72],"stability":[74,151,183,234],"these":[76],"waves":[77,154,159,188,238],"poorly":[79],"understood.":[80],"In":[81],"this":[82],"work,":[83],"we":[84,110,136,180,224],"derive":[85],"an":[86],"almost":[87],"explicit":[88,141,195],"variational":[89],"bound":[90],"on":[91],"speed":[94],"by":[95,174,243],"reformulating":[96],"problem":[98,102],"free-boundary":[101],"for":[103,197],"generalised":[105],"porous--Fisher":[106],"equation.":[107],"estimates":[109],"obtain":[111],"apply":[112],"general":[114],"pressure":[115],"laws":[116],"growth":[118,203],"kinetics,":[119],"agree":[120],"closely":[121],"results":[124],"numerical":[126,175],"simulations,":[127],"become":[129],"sharp":[130],"in":[131,227],"incompressible":[133,185],"limit,":[134],"where":[135],"formally":[137],"recover":[138],"fully":[140],"characterisation":[142],"speed.":[146],"then":[148],"analyse":[149],"show":[156],"that":[157,214],"are":[160,166],"stable":[161],"only":[162],"when":[163],"more":[167],"mobile":[168],"than":[169],"cells.":[171],"Finally,":[172],"motivated":[173],"observations":[176],"finger-like":[178],"protrusions,":[179],"investigate":[181],"circular":[187,237],"through":[189],"asymptotic":[190],"shape-perturbation":[191],"analysis.":[192],"This":[193],"yields":[194],"expressions":[196],"pressure,":[199],"interface":[200],"velocity,":[201],"rates":[204],"angular":[206],"modes,":[207],"thereby":[208],"making":[209],"evident":[210],"destabilisation":[212],"mechanisms":[213],"may":[215,254],"lead":[216],"emergence":[219],"fingering":[221],"instability.":[222],"Interestingly,":[223],"find":[225],"that,":[226],"contrast":[228],"case,":[232],"such":[236],"not":[240],"determined":[241],"solely":[242],"relative":[245],"value":[246],"mobility":[249],"coefficients,":[250],"thus":[252],"instabilities":[253],"arise":[255],"irrespective":[256],"which":[258],"type":[260],"has":[261],"larger":[263],"mobility.":[264]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-10T00:00:00"}
