{"id":"https://openalex.org/W3081689550","doi":"https://doi.org/10.1137/20m1365429","title":"How Reaction-Diffusion PDEs Approximate the Large-Population Limit of Stochastic Particle Models","display_name":"How Reaction-Diffusion PDEs Approximate the Large-Population Limit of Stochastic Particle Models","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3081689550","doi":"https://doi.org/10.1137/20m1365429","mag":"3081689550"},"language":"en","primary_location":{"id":"doi:10.1137/20m1365429","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1365429","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"],"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/A5044930696","display_name":"Samuel A. Isaacson","orcid":"https://orcid.org/0000-0002-7543-8619"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Samuel A. Isaacson","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037938468","display_name":"Jingwei Ma","orcid":"https://orcid.org/0000-0002-6232-4938"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jingwei Ma","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5103169334","display_name":"Konstantinos Spiliopoulos","orcid":"https://orcid.org/0000-0003-2021-6426"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Konstantinos Spiliopoulos","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5044930696"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8044,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.69726064,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"81","issue":"6","first_page":"2622","last_page":"2657"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9977999925613403,"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"}},"topics":[{"id":"https://openalex.org/T10621","display_name":"Gene Regulatory Network Analysis","score":0.9977999925613403,"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"}},{"id":"https://openalex.org/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9959999918937683,"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":0.9957000017166138,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/reaction\u2013diffusion-system","display_name":"Reaction\u2013diffusion system","score":0.6307066679000854},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.6189142465591431},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.5905513763427734},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.5074226260185242},{"id":"https://openalex.org/keywords/particle","display_name":"Particle (ecology)","score":0.47544193267822266},{"id":"https://openalex.org/keywords/stochastic-modelling","display_name":"Stochastic modelling","score":0.468227356672287},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4447418749332428},{"id":"https://openalex.org/keywords/subject","display_name":"Subject (documents)","score":0.43329474329948425},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3733861446380615},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3664201498031616},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.34955596923828125},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.21380040049552917},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.17021161317825317},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.16053292155265808},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1588083803653717},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.07523095607757568},{"id":"https://openalex.org/keywords/sociology","display_name":"Sociology","score":0.07213875651359558},{"id":"https://openalex.org/keywords/demography","display_name":"Demography","score":0.06250837445259094}],"concepts":[{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.6307066679000854},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6189142465591431},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5905513763427734},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.5074226260185242},{"id":"https://openalex.org/C2778517922","wikidata":"https://www.wikidata.org/wiki/Q7140482","display_name":"Particle (ecology)","level":2,"score":0.47544193267822266},{"id":"https://openalex.org/C127491075","wikidata":"https://www.wikidata.org/wiki/Q7617825","display_name":"Stochastic modelling","level":2,"score":0.468227356672287},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4447418749332428},{"id":"https://openalex.org/C2777855551","wikidata":"https://www.wikidata.org/wiki/Q12310021","display_name":"Subject (documents)","level":2,"score":0.43329474329948425},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3733861446380615},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3664201498031616},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34955596923828125},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.21380040049552917},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17021161317825317},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.16053292155265808},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1588083803653717},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.07523095607757568},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.07213875651359558},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.06250837445259094},{"id":"https://openalex.org/C161191863","wikidata":"https://www.wikidata.org/wiki/Q199655","display_name":"Library science","level":1,"score":0.0},{"id":"https://openalex.org/C111368507","wikidata":"https://www.wikidata.org/wiki/Q43518","display_name":"Oceanography","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/20m1365429","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1365429","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:null:2144/46559","is_oa":false,"landing_page_url":"https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000735860100015&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=6e74115fe3da270499c3d65c9b17d654","pdf_url":null,"source":{"id":"https://openalex.org/S4306402384","display_name":"OpenBU (Boston University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I111088046","host_organization_name":"Boston University","host_organization_lineage":["https://openalex.org/I111088046"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1225483166","display_name":null,"funder_award_id":"W911NF-20-1-0244","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G6833510753","display_name":null,"funder_award_id":"672441","funder_id":"https://openalex.org/F4320306164","funder_display_name":"Simons Foundation"},{"id":"https://openalex.org/G8710554737","display_name":null,"funder_award_id":"DMS-1550918","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306164","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W1506032630","https://openalex.org/W1635622277","https://openalex.org/W1928640800","https://openalex.org/W1971972446","https://openalex.org/W1975543975","https://openalex.org/W2002251982","https://openalex.org/W2015899817","https://openalex.org/W2016503463","https://openalex.org/W2025219222","https://openalex.org/W2046451925","https://openalex.org/W2072467858","https://openalex.org/W2072685235","https://openalex.org/W2078734278","https://openalex.org/W2078759209","https://openalex.org/W2093617915","https://openalex.org/W2133812685","https://openalex.org/W2138620270","https://openalex.org/W2161112329","https://openalex.org/W2594491463","https://openalex.org/W2600262831","https://openalex.org/W2760905750","https://openalex.org/W2769021112","https://openalex.org/W2912415252","https://openalex.org/W2963996531","https://openalex.org/W2964118932","https://openalex.org/W2966670425","https://openalex.org/W2970922709","https://openalex.org/W2995931831","https://openalex.org/W3013862997","https://openalex.org/W3023933354","https://openalex.org/W3159189180"],"related_works":["https://openalex.org/W2353396818","https://openalex.org/W2370473919","https://openalex.org/W2390496461","https://openalex.org/W2389654532","https://openalex.org/W2369545560","https://openalex.org/W2355429547","https://openalex.org/W2373218684","https://openalex.org/W2389219417","https://openalex.org/W2762984199","https://openalex.org/W2393881125"],"abstract_inverted_index":{"Reaction-diffusion":[0],"PDEs":[1],"and":[2,19,33,35,91,119,160,167,174,180],"particle-based":[3],"stochastic":[4],"reaction-diffusion":[5,23,88,139],"(PBSRD)":[6],"models":[7,25,68,90],"are":[8,36,45,117],"commonly":[9],"used":[10],"approaches":[11,127],"for":[12,157,163,184],"modeling":[13],"the":[14,27,57,65,83,92,98,108,111,122,131,152,172,177],"spatial":[15,31],"dynamics":[16],"of":[17,30,48,61,74,151],"chemical":[18],"biological":[20],"systems.":[21],"Standard":[22],"PDE":[24,89,140],"ignore":[26],"underlying":[28,181],"stochasticity":[29],"transport":[32],"reactions":[34],"often":[37],"described":[38],"as":[39,103],"appropriate":[40],"in":[41,50,110,155],"regimes":[42],"where":[43],"there":[44],"large":[46],"numbers":[47],"particles":[49],"a":[51],"system.":[52],"Recent":[53],"studies":[54],"have":[55],"proven":[56],"rigorous":[58,84],"large-population":[59],"limit":[60,112],"PBSRD":[62],"models,":[63],"showing":[64],"resulting":[66],"mean-field":[67],"(MFMs)":[69],"correspond":[70],"to":[71,107,137],"nonlocal":[72],"systems":[73,159,166],"partial-integro":[75],"differential":[76],"equations.":[77],"In":[78,142],"this":[79,144],"work":[80],"we":[81,129,146,170],"explore":[82],"relationship":[85],"between":[86,176],"standard":[87,138],"derived":[93],"MFM.":[94],"We":[95],"prove":[96,130],"that":[97,113],"former":[99],"can":[100],"be":[101],"interpreted":[102],"an":[104],"asymptotic":[105],"approximation":[106],"later":[109],"bimolecular":[114],"reaction":[115,165],"kernels":[116],"short-range":[118],"averaging.":[120],"As":[121],"reactive":[123],"interaction":[124],"length":[125],"scale":[126],"zero,":[128],"MFMs":[132],"converge":[133],"at":[134],"second":[135],"order":[136],"models.":[141],"proving":[143],"result":[145],"also":[147],"establish":[148],"local":[149],"well-posedness":[150,162],"MFM":[153],"model":[154,183],"time":[156],"general":[158],"global":[161],"specific":[164],"kernels.":[168],"Finally,":[169],"illustrate":[171],"agreement":[173],"disagreement":[175],"MFM,":[178],"SM,":[179],"particle":[182],"several":[185],"numerical":[186],"examples.":[187]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}