{"id":"https://openalex.org/W2074043571","doi":"https://doi.org/10.1090/mcom3033","title":"A blob method for the aggregation equation","display_name":"A blob method for the aggregation equation","publication_year":2015,"publication_date":"2015-02-04","ids":{"openalex":"https://openalex.org/W2074043571","doi":"https://doi.org/10.1090/mcom3033","mag":"2074043571"},"language":"en","primary_location":{"id":"doi:10.1090/mcom3033","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom3033","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://escholarship.org/content/qt8ct3c29b/qt8ct3c29b.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5023507368","display_name":"Katy Craig","orcid":"https://orcid.org/0000-0001-6085-4022"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Katy Craig","raw_affiliation_strings":["Department of Mathematics, University of California, Los Angeles, 520 Portola Plaza, Los Angeles, California 90095-1555","Department of Mathematics, University of California, Los Angeles, 520 Portola Plaza, Los Angeles, California, 90095-1555"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, Los Angeles, 520 Portola Plaza, Los Angeles, California 90095-1555","institution_ids":["https://openalex.org/I161318765"]},{"raw_affiliation_string":"Department of Mathematics, University of California, Los Angeles, 520 Portola Plaza, Los Angeles, California, 90095-1555","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090707978","display_name":"Andrea L. Bertozzi","orcid":"https://orcid.org/0000-0003-0396-7391"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Andrea Bertozzi","raw_affiliation_strings":["Department of Mathematics, University of California, Los Angeles, 520 Portola Plaza, Los Angeles, California 90095-1555","Department of Mathematics, University of California, Los Angeles, 520 Portola Plaza, Los Angeles, California, 90095-1555"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California, Los Angeles, 520 Portola Plaza, Los Angeles, California 90095-1555","institution_ids":["https://openalex.org/I161318765"]},{"raw_affiliation_string":"Department of Mathematics, University of California, Los Angeles, 520 Portola Plaza, Los Angeles, California, 90095-1555","institution_ids":["https://openalex.org/I161318765"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I161318765"],"apc_list":null,"apc_paid":null,"fwci":6.6699,"has_fulltext":true,"cited_by_count":83,"citation_normalized_percentile":{"value":0.97410353,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"85","issue":"300","first_page":"1681","last_page":"1717"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10940","display_name":"Navier-Stokes equation solutions","score":0.995199978351593,"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/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9787999987602234,"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/mathematics","display_name":"Mathematics","score":0.7991008162498474},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5932415723800659},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5674539804458618},{"id":"https://openalex.org/keywords/energy-functional","display_name":"Energy functional","score":0.5664682388305664},{"id":"https://openalex.org/keywords/balanced-flow","display_name":"Balanced flow","score":0.5170691609382629},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48669201135635376},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.47832703590393066},{"id":"https://openalex.org/keywords/particle-system","display_name":"Particle system","score":0.41720956563949585},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4149817228317261},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09814125299453735}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7991008162498474},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5932415723800659},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5674539804458618},{"id":"https://openalex.org/C191640071","wikidata":"https://www.wikidata.org/wiki/Q5377056","display_name":"Energy functional","level":2,"score":0.5664682388305664},{"id":"https://openalex.org/C167879884","wikidata":"https://www.wikidata.org/wiki/Q727568","display_name":"Balanced flow","level":2,"score":0.5170691609382629},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48669201135635376},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.47832703590393066},{"id":"https://openalex.org/C179003449","wikidata":"https://www.wikidata.org/wiki/Q1757458","display_name":"Particle system","level":2,"score":0.41720956563949585},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4149817228317261},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09814125299453735},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/mcom3033","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom3033","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:escholarship.org:ark:/13030/qt8ct3c29b","is_oa":true,"landing_page_url":"https://escholarship.org/uc/item/8ct3c29b","pdf_url":"https://escholarship.org/content/qt8ct3c29b/qt8ct3c29b.pdf","source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics of Computation, vol 85, iss 300","raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:escholarship.org:ark:/13030/qt8ct3c29b","is_oa":true,"landing_page_url":"https://escholarship.org/uc/item/8ct3c29b","pdf_url":"https://escholarship.org/content/qt8ct3c29b/qt8ct3c29b.pdf","source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics of Computation, vol 85, iss 300","raw_type":"article"},"sustainable_development_goals":[{"score":0.8700000047683716,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[{"id":"https://openalex.org/G8291501169","display_name":"PostDoctoral Research Fellowship","funder_award_id":"1401867","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"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2074043571.pdf","grobid_xml":"https://content.openalex.org/works/W2074043571.grobid-xml"},"referenced_works_count":77,"referenced_works":["https://openalex.org/W1509925099","https://openalex.org/W1522579744","https://openalex.org/W1551516234","https://openalex.org/W1591074427","https://openalex.org/W1968334598","https://openalex.org/W1970842146","https://openalex.org/W1974960045","https://openalex.org/W1976981113","https://openalex.org/W1977323060","https://openalex.org/W1978811720","https://openalex.org/W1982147627","https://openalex.org/W1987851352","https://openalex.org/W1992906507","https://openalex.org/W1994204156","https://openalex.org/W2001536020","https://openalex.org/W2008702562","https://openalex.org/W2011301426","https://openalex.org/W2012377735","https://openalex.org/W2017721379","https://openalex.org/W2020995965","https://openalex.org/W2023969066","https://openalex.org/W2025078753","https://openalex.org/W2031055103","https://openalex.org/W2031064936","https://openalex.org/W2031487944","https://openalex.org/W2033141781","https://openalex.org/W2033230365","https://openalex.org/W2034293268","https://openalex.org/W2035731630","https://openalex.org/W2041440299","https://openalex.org/W2042564923","https://openalex.org/W2042764016","https://openalex.org/W2044447043","https://openalex.org/W2045845830","https://openalex.org/W2052946502","https://openalex.org/W2053007385","https://openalex.org/W2054821686","https://openalex.org/W2057721773","https://openalex.org/W2062391453","https://openalex.org/W2066895712","https://openalex.org/W2067711323","https://openalex.org/W2068229646","https://openalex.org/W2070124653","https://openalex.org/W2072076940","https://openalex.org/W2073287439","https://openalex.org/W2077467386","https://openalex.org/W2078689747","https://openalex.org/W2092826938","https://openalex.org/W2093201749","https://openalex.org/W2094402484","https://openalex.org/W2098870063","https://openalex.org/W2102228124","https://openalex.org/W2110208320","https://openalex.org/W2119323323","https://openalex.org/W2119414533","https://openalex.org/W2120051327","https://openalex.org/W2130112233","https://openalex.org/W2132835045","https://openalex.org/W2134370460","https://openalex.org/W2138972560","https://openalex.org/W2144897760","https://openalex.org/W2146292423","https://openalex.org/W2154235382","https://openalex.org/W2155385278","https://openalex.org/W2156934943","https://openalex.org/W2164775983","https://openalex.org/W2168688381","https://openalex.org/W2323854047","https://openalex.org/W2917421472","https://openalex.org/W2963600615","https://openalex.org/W3087595676","https://openalex.org/W3100014801","https://openalex.org/W3104154912","https://openalex.org/W4232565426","https://openalex.org/W4237705937","https://openalex.org/W4245845296","https://openalex.org/W4247469105"],"related_works":["https://openalex.org/W2255557820","https://openalex.org/W2568941439","https://openalex.org/W4287462552","https://openalex.org/W2288320220","https://openalex.org/W3011980909","https://openalex.org/W4291304382","https://openalex.org/W2962839170","https://openalex.org/W2963536277","https://openalex.org/W2507690919","https://openalex.org/W2368565119"],"abstract_inverted_index":{"Motivated":[0],"by":[1],"classical":[2,69],"vortex":[3],"blob":[4,14,42,78],"methods":[5],"for":[6,16,90],"the":[7,17,32,41,73,83,98,119],"Euler":[8],"equations,":[9],"we":[10,60],"develop":[11],"a":[12,22,36,45,52,91],"numerical":[13,105],"method":[15,43,79],"aggregation":[18],"equation.":[19],"This":[20],"provides":[21],"counterpoint":[23],"to":[24,68],"existing":[25],"literature":[26],"on":[27,72],"particle":[28,85],"methods.":[29],"By":[30],"regularizing":[31],"velocity":[33],"field":[34],"with":[35],"mollifier":[37],"or":[38],"\u201cblob":[39],"function\u201d,":[40],"has":[44],"faster":[46],"rate":[47,111],"of":[48,55,66,75,112,118],"convergence":[49,67,113],"and":[50,82,96,114],"allows":[51],"wider":[53],"range":[54],"admissible":[56],"kernels.":[57],"In":[58],"fact,":[59],"prove":[61],"arbitrarily":[62],"high":[63],"polynomial":[64],"rates":[65],"solutions,":[70],"depending":[71],"choice":[74],"mollifier.":[76],"The":[77],"conserves":[80],"mass":[81],"corresponding":[84],"system":[86],"is":[87],"energy":[88,94],"decreasing":[89],"regularized":[92],"free":[93],"functional":[95],"preserves":[97],"Wasserstein":[99],"gradient":[100],"flow":[101],"structure.":[102],"We":[103],"consider":[104],"examples":[106],"that":[107],"validate":[108],"our":[109],"predicted":[110],"illustrate":[115],"qualitative":[116],"properties":[117],"method.":[120]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":13},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":13},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":4}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
