{"id":"https://openalex.org/W3107553151","doi":"https://doi.org/10.48550/arxiv.2011.13129","title":"Pattern formation in a cell migration model with aggregation and diffusion","display_name":"Pattern formation in a cell migration model with aggregation and diffusion","publication_year":2020,"publication_date":"2020-11-26","ids":{"openalex":"https://openalex.org/W3107553151","doi":"https://doi.org/10.48550/arxiv.2011.13129","mag":"3107553151"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2011.13129","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2011.13129","pdf_url":"https://arxiv.org/pdf/2011.13129","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2011.13129","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057064374","display_name":"Lianzhang Bao","orcid":"https://orcid.org/0000-0003-4772-7621","observed_orcids":["https://orcid.org/0000-0003-4772-7621"]},"institutions":[{"id":"https://openalex.org/I82497590","display_name":"Auburn University","ror":"https://ror.org/02v80fc35","country_code":"US","type":"education","lineage":["https://openalex.org/I82497590"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Bao, Lianzhang","raw_affiliation_strings":["Department of Mathematics and Statistics , Auburn University , AL 36849 , U. S. A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics , Auburn University , AL 36849 , U. S. A","institution_ids":["https://openalex.org/I82497590"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5057064374"],"corresponding_institution_ids":["https://openalex.org/I82497590"],"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.47360000014305115,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},"topics":[{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.47360000014305115,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.448199987411499,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.06679999828338623,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/pattern-formation","display_name":"pattern formation","score":0.9850000143051147},{"id":"https://openalex.org/keywords/cell-migration","display_name":"cell migration","score":0.8479999899864197},{"id":"https://openalex.org/keywords/aggregation","display_name":"aggregation","score":0.6399999856948853},{"id":"https://openalex.org/keywords/diffusion","display_name":"diffusion","score":0.8679999709129333},{"id":"https://openalex.org/keywords/dirichlet-boundary-conditions","display_name":"Dirichlet boundary conditions","score":0.8510000109672546},{"id":"https://openalex.org/keywords/nonlinear-parabolic-equations","display_name":"nonlinear parabolic equations","score":0.7820000052452087},{"id":"https://openalex.org/keywords/steady-state-solutions","display_name":"stationary solutions","score":0.4869999885559082},{"id":"https://openalex.org/keywords/maximum-principle","display_name":"maximum principle","score":0.7009999752044678},{"id":"https://openalex.org/keywords/asymptotic-behavior","display_name":"asymptotic behavior","score":0.7860000133514404}],"concepts":[{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.6008723974227905},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5478560328483582},{"id":"https://openalex.org/C37668627","wikidata":"https://www.wikidata.org/wiki/Q3381809","display_name":"Thermal diffusivity","level":2,"score":0.5393493175506592},{"id":"https://openalex.org/C110729304","wikidata":"https://www.wikidata.org/wiki/Q1224521","display_name":"Diffusion-limited aggregation","level":4,"score":0.5272678136825562},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.472535640001297},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.4685935080051422},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.46745333075523376},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.4635187089443207},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45524710416793823},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.45047080516815186},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44715237617492676},{"id":"https://openalex.org/C207016750","wikidata":"https://www.wikidata.org/wiki/Q1955627","display_name":"Pattern formation","level":2,"score":0.442862868309021},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.43641045689582825},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.41839081048965454},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4101671278476715},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.1280539333820343},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07525020837783813},{"id":"https://openalex.org/C2780378061","wikidata":"https://www.wikidata.org/wiki/Q25351891","display_name":"Service (business)","level":2,"score":0.0},{"id":"https://openalex.org/C40636538","wikidata":"https://www.wikidata.org/wiki/Q81392","display_name":"Fractal","level":2,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C26546657","wikidata":"https://www.wikidata.org/wiki/Q1412452","display_name":"Fractal dimension","level":3,"score":0.0},{"id":"https://openalex.org/C136264566","wikidata":"https://www.wikidata.org/wiki/Q159810","display_name":"Economy","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2011.13129","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2011.13129","pdf_url":"https://arxiv.org/pdf/2011.13129","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2011.13129","doi":"https://doi.org/10.48550/arxiv.2011.13129","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2011.13129","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2011.13129","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2011.13129","pdf_url":"https://arxiv.org/pdf/2011.13129","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1532261161","https://openalex.org/W1538754544","https://openalex.org/W1965052842","https://openalex.org/W1972800766","https://openalex.org/W1979472121","https://openalex.org/W1984878971","https://openalex.org/W1986584872","https://openalex.org/W2021117151","https://openalex.org/W2021603944","https://openalex.org/W2040953186","https://openalex.org/W2041714615","https://openalex.org/W2042892258","https://openalex.org/W2066347815","https://openalex.org/W2075304340","https://openalex.org/W2079949023","https://openalex.org/W2083071301","https://openalex.org/W2105662343","https://openalex.org/W2120095336","https://openalex.org/W2135778954","https://openalex.org/W2166733021","https://openalex.org/W2314060633","https://openalex.org/W2314714958","https://openalex.org/W2369386221","https://openalex.org/W2952732267","https://openalex.org/W2963009650","https://openalex.org/W2963896811","https://openalex.org/W2997333843","https://openalex.org/W3025246673"],"related_works":["https://openalex.org/W2132847744","https://openalex.org/W2736613791","https://openalex.org/W2016061347","https://openalex.org/W2004552211","https://openalex.org/W2062325324","https://openalex.org/W2008073915","https://openalex.org/W2043092042","https://openalex.org/W2361780829","https://openalex.org/W2097086987","https://openalex.org/W174233448"],"abstract_inverted_index":{"In":[0,54,150],"this":[1],"paper,":[2],"we":[3],"study":[4],"pattern":[5],"formations":[6],"in":[7,50,89,110,118,148],"an":[8],"aggregation":[9,48,77,92,116,143],"and":[10,44,47,63,144],"diffusion":[11,57,93,112,145],"cell":[12,40,81],"migration":[13,58],"model":[14,25,59,120],"with":[15,31,60,70,105,129],"Dirichlet":[16,71],"boundary":[17],"condition.":[18],"The":[19],"formal":[20],"continuum":[21],"limit":[22],"of":[23,75,160,168],"the":[24,39,51,55,76,83,90,96,106,111,115,119,140,151,158,161,165,169],"is":[26,42,87,171],"a":[27,32,101,136],"nonlinear":[28],"parabolic":[29,156],"equation":[30],"diffusivity":[33,62],"which":[34,134],"can":[35],"become":[36],"negative":[37],"if":[38],"density":[41,86,108],"small":[43,80],"spatial":[45],"oscillations":[46],"occur":[49],"numerical":[52],"simulations.":[53],"classical":[56],"positive":[61,103],"non-birth":[64],"term,":[65],"species":[66,85],"will":[67],"vanish":[68],"eventually":[69],"boundary.":[72],"However,":[73],"because":[74],"mechanism":[78,117],"under":[79],"density,":[82],"total":[84],"conservative":[88],"discrete":[91,97,131],"model.":[94],"Also,":[95],"system":[98],"converges":[99],"to":[100],"unique":[102],"steady-state":[104],"initial":[107],"lying":[109],"domain.":[113],"Furthermore,":[114],"induces":[121,146],"rich":[122],"asymptotic":[123,166],"dynamical":[124],"behaviors":[125],"or":[126],"patterns":[127,147],"even":[128],"5":[130],"space":[132],"points":[133],"gives":[135],"theoretical":[137],"explanation":[138],"that":[139],"interaction":[141],"between":[142],"biology.":[149],"corresponding":[152],"continuous":[153],"backward":[154],"forward":[155],"equation,":[157],"existence":[159],"solution,":[162],"maximum":[163],"principle,":[164],"behavior":[167],"solution":[170],"also":[172],"investigated.":[173]},"counts_by_year":[],"updated_date":"2026-09-30T09:27:27.532063","created_date":"2025-10-10T00:00:00"}
