{"id":"https://openalex.org/W2953358258","doi":"https://doi.org/10.1017/s0021900200009414","title":"Coagulation Processes with Gibbsian Time Evolution","display_name":"Coagulation Processes with Gibbsian Time Evolution","publication_year":2012,"publication_date":"2012-09-01","ids":{"openalex":"https://openalex.org/W2953358258","doi":"https://doi.org/10.1017/s0021900200009414","mag":"2953358258"},"language":"en","primary_location":{"id":"doi:10.1017/s0021900200009414","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0021900200009414","pdf_url":null,"source":{"id":"https://openalex.org/S160779208","display_name":"Journal of Applied Probability","issn_l":"0021-9002","issn":["0021-9002","1475-6072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Probability","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/A5061818263","display_name":"Boris L. Granovsky","orcid":null},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Boris L. Granovsky","raw_affiliation_strings":["Technion - Israel Institute of Technology"],"affiliations":[{"raw_affiliation_string":"Technion - Israel Institute of Technology","institution_ids":["https://openalex.org/I174306211"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088926633","display_name":"Alexander V. Kryvoshaev","orcid":null},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Alexander V. Kryvoshaev","raw_affiliation_strings":["Technion - Israel Institute of Technology"],"affiliations":[{"raw_affiliation_string":"Technion - Israel Institute of Technology","institution_ids":["https://openalex.org/I174306211"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5061818263","https://openalex.org/A5088926633"],"corresponding_institution_ids":["https://openalex.org/I174306211"],"apc_list":null,"apc_paid":null,"fwci":0.368,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.76548852,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"49","issue":"03","first_page":"612","last_page":"626"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11188","display_name":"Coagulation and Flocculation Studies","score":0.9919999837875366,"subfield":{"id":"https://openalex.org/subfields/2312","display_name":"Water Science and Technology"},"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/T11188","display_name":"Coagulation and Flocculation Studies","score":0.9919999837875366,"subfield":{"id":"https://openalex.org/subfields/2312","display_name":"Water Science and Technology"},"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.984000027179718,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10591","display_name":"Theoretical and Computational Physics","score":0.9609000086784363,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter 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/mathematics","display_name":"Mathematics","score":0.8872416615486145},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.49275854229927063},{"id":"https://openalex.org/keywords/coagulation","display_name":"Coagulation","score":0.49261122941970825},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.472078800201416},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.44604647159576416},{"id":"https://openalex.org/keywords/generating-function","display_name":"Generating function","score":0.44001123309135437},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38767948746681213},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06479084491729736}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8872416615486145},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.49275854229927063},{"id":"https://openalex.org/C2778382381","wikidata":"https://www.wikidata.org/wiki/Q179217","display_name":"Coagulation","level":2,"score":0.49261122941970825},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.472078800201416},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.44604647159576416},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.44001123309135437},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38767948746681213},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06479084491729736},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C118552586","wikidata":"https://www.wikidata.org/wiki/Q7867","display_name":"Psychiatry","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0021900200009414","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0021900200009414","pdf_url":null,"source":{"id":"https://openalex.org/S160779208","display_name":"Journal of Applied Probability","issn_l":"0021-9002","issn":["0021-9002","1475-6072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Probability","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1489554514","https://openalex.org/W1523957791","https://openalex.org/W1566264342","https://openalex.org/W1627845523","https://openalex.org/W1976525723","https://openalex.org/W1994341001","https://openalex.org/W1997158470","https://openalex.org/W2001763758","https://openalex.org/W2002260608","https://openalex.org/W2009393079","https://openalex.org/W2036813689","https://openalex.org/W2042500308","https://openalex.org/W2053491613","https://openalex.org/W2057073325","https://openalex.org/W2076127587","https://openalex.org/W2095625561","https://openalex.org/W2102495095","https://openalex.org/W2799137445","https://openalex.org/W3140826630","https://openalex.org/W4242893957","https://openalex.org/W4297935012"],"related_works":["https://openalex.org/W2367636083","https://openalex.org/W2016370395","https://openalex.org/W2980963558","https://openalex.org/W2353786952","https://openalex.org/W2095464070","https://openalex.org/W2029396767","https://openalex.org/W1563884130","https://openalex.org/W1882246857","https://openalex.org/W3103304230","https://openalex.org/W2185360082"],"abstract_inverted_index":{"We":[0,66],"prove":[1],"that":[2,78],"a":[3,16,69],"stochastic":[4],"process":[5],"of":[6,31,35,63,74,86,97,111],"pure":[7],"coagulation":[8,112],"has":[9],"at":[10],"any":[11],"time":[12,118],"t":[13,119],"\u2265":[14],"0":[15],"time-dependent":[17],"Gibbs":[18,76],"distribution":[19],"if":[20,23,44],"and":[21,89],"only":[22],"the":[24,36,61,83,87,90,98,103,109],"rates":[25],"\u03c8(":[26,38],"i":[27,39,51],",":[28],"j":[29,41,46],")":[30,42,47],"single":[32],"coagulations":[33],"are":[34],"form":[37,85],";":[40],"=":[43],"(":[45,50],"+":[48],"jf":[49],"),":[52],"where":[53],"f":[54,100],"is":[55],"an":[56],"arbitrary":[57],"nonnegative":[58],"function":[59,99],"on":[60],"set":[62],"positive":[64],"integers.":[65],"also":[67],"obtain":[68],"recurrence":[70],"relation":[71],"for":[72],"weights":[73],"these":[75],"distributions":[77],"allow":[79],"us":[80],"to":[81],"derive":[82],"general":[84],"solution":[88],"explicit":[91],"solutions":[92],"in":[93],"three":[94,104],"particular":[95],"cases":[96],".":[101],"For":[102],"corresponding":[105],"models,":[106],"we":[107],"study":[108],"probability":[110],"into":[113],"one":[114],"giant":[115],"cluster":[116],"by":[117],"&amp;gt;":[120],"0.":[121]},"counts_by_year":[{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
