{"id":"https://openalex.org/W2011046719","doi":"https://doi.org/10.1068/a040031","title":"Analytical Properties of Some Multiple-Source Urban Diffusion Models","display_name":"Analytical Properties of Some Multiple-Source Urban Diffusion Models","publication_year":1972,"publication_date":"1972-03-01","ids":{"openalex":"https://openalex.org/W2011046719","doi":"https://doi.org/10.1068/a040031","mag":"2011046719"},"language":"en","primary_location":{"id":"doi:10.1068/a040031","doi":"https://doi.org/10.1068/a040031","is_oa":false,"landing_page_url":"https://doi.org/10.1068/a040031","pdf_url":null,"source":{"id":"https://openalex.org/S87933477","display_name":"Environment and Planning A Economy and Space","issn_l":"0308-518X","issn":["0308-518X","1472-3409"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a-star","anvur-class-a","anvur-scientific","cwts-core","dongbi-b","fnege-2","jufo-3","norway-2","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320017","host_organization_name":"SAGE Publishing","host_organization_lineage":["https://openalex.org/P4310320017"],"host_organization_lineage_names":["SAGE Publishing"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Environment and Planning A: Economy and Space","raw_type":"journal-article"},"volume":null,"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/A5113533905","display_name":"S.\u2010\u00c5. Gustafson","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"S-\u00c5 Gustafson","raw_affiliation_strings":["Department of Numerical Analysis, The Royal Institute of Technology, Stockholm, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Numerical Analysis, The Royal Institute of Technology, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109805555","display_name":"K. O. Kortanek","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"K O Kortanek","raw_affiliation_strings":["School of Urban and Public Affairs, Carnegie-Mellon University, Pittsburgh, Pennsylvania, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Urban and Public Affairs, Carnegie-Mellon University, Pittsburgh, Pennsylvania, USA","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":3900,"currency":"USD","value_usd":3900},"apc_paid":null,"fwci":5.9003,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.94835263,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":null,"biblio":{"volume":"4","issue":"1","first_page":"31","last_page":"41"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11371","display_name":"Wind and Air Flow Studies","score":0.5625,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11371","display_name":"Wind and Air Flow Studies","score":0.5625,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13148","display_name":"Environmental and Air Quality Management","score":0.1046999990940094,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11502","display_name":"Facility Location and Emergency Management","score":0.08799999952316284,"subfield":{"id":"https://openalex.org/subfields/1407","display_name":"Organizational Behavior and Human Resource Management"},"field":{"id":"https://openalex.org/fields/14","display_name":"Business, Management and Accounting"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/urban-air-pollution","display_name":"urban air pollution","score":0.8579999804496765},{"id":"https://openalex.org/keywords/transfer-function","display_name":"transfer function","score":0.9340000152587891},{"id":"https://openalex.org/keywords/emission-rates","display_name":"emission rates","score":0.8259999752044678},{"id":"https://openalex.org/keywords/pollutant-concentration","display_name":"pollutant concentration","score":0.718999981880188},{"id":"https://openalex.org/keywords/analytical-properties","display_name":"analytical properties","score":0.6179999709129333},{"id":"https://openalex.org/keywords/optimization-model","display_name":"optimization model","score":0.7570000290870667}],"concepts":[{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.7193202972412109},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.7125861644744873},{"id":"https://openalex.org/C81299745","wikidata":"https://www.wikidata.org/wiki/Q334269","display_name":"Transfer function","level":2,"score":0.6457309722900391},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5510596632957458},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.51076340675354},{"id":"https://openalex.org/C103783831","wikidata":"https://www.wikidata.org/wiki/Q2552709","display_name":"Point source","level":2,"score":0.5047706365585327},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4748309254646301},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46032726764678955},{"id":"https://openalex.org/C2776175482","wikidata":"https://www.wikidata.org/wiki/Q1195816","display_name":"Transfer (computing)","level":2,"score":0.4359789192676544},{"id":"https://openalex.org/C2780187573","wikidata":"https://www.wikidata.org/wiki/Q3754592","display_name":"Source function","level":2,"score":0.41997480392456055},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41106608510017395},{"id":"https://openalex.org/C186060115","wikidata":"https://www.wikidata.org/wiki/Q30336093","display_name":"Biological system","level":1,"score":0.4079466462135315},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.40245336294174194},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36300933361053467},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3377383351325989},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.3180990219116211},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.24123340845108032},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09465554356575012},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.09183365106582642},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.06536072492599487},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C44870925","wikidata":"https://www.wikidata.org/wiki/Q37547","display_name":"Astrophysics","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"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/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1068/a040031","doi":"https://doi.org/10.1068/a040031","is_oa":false,"landing_page_url":"https://doi.org/10.1068/a040031","pdf_url":null,"source":{"id":"https://openalex.org/S87933477","display_name":"Environment and Planning A Economy and Space","issn_l":"0308-518X","issn":["0308-518X","1472-3409"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a-star","anvur-class-a","anvur-scientific","cwts-core","dongbi-b","fnege-2","jufo-3","norway-2","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320017","host_organization_name":"SAGE Publishing","host_organization_lineage":["https://openalex.org/P4310320017"],"host_organization_lineage_names":["SAGE Publishing"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Environment and Planning A: Economy and Space","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:pio:envira:v:4:y:1972:i:1:p:31-41","doi":null,"is_oa":false,"landing_page_url":"http://www.envplan.com/abstract.cgi?id=a040031","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:RePEc:sae:envira:v:4:y:1972:i:1:p:31-41","doi":null,"is_oa":false,"landing_page_url":"https://journals.sagepub.com/doi/10.1068/a040031","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6618000268936157,"display_name":"Clean water and sanitation","id":"https://metadata.un.org/sdg/6"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W295842966","https://openalex.org/W1011385359","https://openalex.org/W1550518731","https://openalex.org/W1971519494","https://openalex.org/W1979662533","https://openalex.org/W1995769522","https://openalex.org/W2010636146","https://openalex.org/W2025376396","https://openalex.org/W2027358623","https://openalex.org/W2053087211","https://openalex.org/W2062687608","https://openalex.org/W2230245890","https://openalex.org/W4206327777","https://openalex.org/W4230390293","https://openalex.org/W4322575126"],"related_works":["https://openalex.org/W4385467905","https://openalex.org/W2740948327","https://openalex.org/W4255847005","https://openalex.org/W2047881826","https://openalex.org/W1966553321","https://openalex.org/W2497920018","https://openalex.org/W2051682023","https://openalex.org/W6922387082","https://openalex.org/W2185084330","https://openalex.org/W2337477178"],"abstract_inverted_index":{"It":[0],"is":[1],"generally":[2],"required":[3],"that":[4],"the":[5,41,47,61,65],"concentration":[6,49],"of":[7,39,44,55,64,83,86],"a":[8,21,26,80,87],"certain":[9],"pollutant":[10],"at":[11],"any":[12],"given":[13],"point":[14],"(":[15],"x,":[16,30,51],"y)":[17,52],"shall":[18],"be":[19,70],"below":[20],"maximum":[22],"amount":[23],"defined":[24],"by":[25,53,90],"known":[27],"function":[28],"S(":[29],"y).":[31],"In":[32],"this":[33],"paper":[34],"we":[35],"analyze":[36],"different":[37],"ways":[38],"relating":[40],"emission":[42],"rates":[43],"polluters":[45],"with":[46],"resultant":[48],"Q(":[50],"means":[54],"various":[56,73],"transfer":[57,66],"functions.":[58],"We":[59,77],"discuss":[60,79],"analytical":[62],"properties":[63],"functions":[67],"which":[68],"can":[69],"derived":[71],"from":[72],"well-known":[74],"diffusion":[75],"models.":[76],"also":[78],"simple":[81],"instance":[82],"optimization":[84],"models":[85],"type,":[88],"introduced":[89],"Gorr":[91],"and":[92],"Kortanek":[93],"(1970).":[94]},"counts_by_year":[],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2016-06-24T00:00:00"}