{"id":"https://openalex.org/W3112962829","doi":"https://doi.org/10.1137/19m1301266","title":"On the Approximate Solution and Modeling of the Kernel of Nonlinear Breakage Population Balance Equation","display_name":"On the Approximate Solution and Modeling of the Kernel of Nonlinear Breakage Population Balance Equation","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3112962829","doi":"https://doi.org/10.1137/19m1301266","mag":"3112962829"},"language":"en","primary_location":{"id":"doi:10.1137/19m1301266","doi":"https://doi.org/10.1137/19m1301266","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1301266","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-3","norway-2","poland-140","russia-white-list-1"],"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 Scientific Computing","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/A5059661645","display_name":"Ashok Das","orcid":"https://orcid.org/0000-0001-7510-0194","observed_orcids":["https://orcid.org/0000-0001-7510-0194"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ashok Das","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-7510-0194","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003203645","display_name":"Jitendra Kumar","orcid":"https://orcid.org/0000-0002-2472-579X","observed_orcids":["https://orcid.org/0000-0002-2472-579X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jitendra Kumar","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088729329","display_name":"Maksym Dosta","orcid":"https://orcid.org/0000-0002-7578-8408","observed_orcids":["https://orcid.org/0000-0002-7578-8408"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Maksym Dosta","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5005863866","display_name":"Stefan Heinrich","orcid":"https://orcid.org/0000-0002-7901-1698","observed_orcids":["https://orcid.org/0000-0002-7901-1698"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stefan Heinrich","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.5439,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.80053249,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"42","issue":"6","first_page":"B1570","last_page":"B1598"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10615","display_name":"Granular flow and fluidized beds","score":0.5473999977111816,"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/T10615","display_name":"Granular flow and fluidized beds","score":0.5473999977111816,"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/T12282","display_name":"Mineral Processing and Grinding","score":0.32839998602867126,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"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/T12350","display_name":"Particle Dynamics in Fluid Flows","score":0.040699999779462814,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/population-balance-equation","display_name":"population balance equation","score":0.847000002861023},{"id":"https://openalex.org/keywords/breakage-kernel","display_name":"breakage kernel","score":0.9470000267028809},{"id":"https://openalex.org/keywords/monte-carlo-simulation","display_name":"Monte Carlo simulation","score":0.7129999995231628},{"id":"https://openalex.org/keywords/event-driven-simulation","display_name":"event-driven simulation","score":0.6420000195503235},{"id":"https://openalex.org/keywords/mass-conservation","display_name":"mass conservation","score":0.6579999923706055},{"id":"https://openalex.org/keywords/particle-size-distribution","display_name":"particle size distribution","score":0.8579999804496765},{"id":"https://openalex.org/keywords/particulate-processes","display_name":"particulate processes","score":0.800000011920929},{"id":"https://openalex.org/keywords/breakage-distribution-function","display_name":"breakage distribution function","score":0.6919999718666077}],"concepts":[{"id":"https://openalex.org/C2779015675","wikidata":"https://www.wikidata.org/wiki/Q92796261","display_name":"Breakage","level":2,"score":0.873706579208374},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.7143000364303589},{"id":"https://openalex.org/C2780041671","wikidata":"https://www.wikidata.org/wiki/Q7229796","display_name":"Population balance equation","level":3,"score":0.6240845918655396},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5879641175270081},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.5782583951950073},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5726609230041504},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4994215965270996},{"id":"https://openalex.org/C121704057","wikidata":"https://www.wikidata.org/wiki/Q352070","display_name":"Collision","level":2,"score":0.48785853385925293},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4373505711555481},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.41535478830337524},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2521897554397583},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.24445372819900513},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23393085598945618},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/19m1301266","doi":"https://doi.org/10.1137/19m1301266","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1301266","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-a","jufo-3","norway-2","poland-140","russia-white-list-1"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:tore.tuhh.de:11420/8574","doi":null,"is_oa":false,"landing_page_url":"http://hdl.handle.net/11420/8574","pdf_url":null,"source":{"id":"https://openalex.org/S4306401751","display_name":"tub.dok (Hamburg University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I884043246","host_organization_name":"Hamburg University of Technology","host_organization_lineage":["https://openalex.org/I884043246"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320308269","display_name":"Alexander von Humboldt-Stiftung","ror":"https://ror.org/012kf4317"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W180995184","https://openalex.org/W927674661","https://openalex.org/W1963781580","https://openalex.org/W1966941542","https://openalex.org/W1974030702","https://openalex.org/W1974186958","https://openalex.org/W1979505266","https://openalex.org/W1980990910","https://openalex.org/W1989523418","https://openalex.org/W1990269797","https://openalex.org/W1993574927","https://openalex.org/W1995470169","https://openalex.org/W1998569210","https://openalex.org/W2000829066","https://openalex.org/W2004296053","https://openalex.org/W2004439028","https://openalex.org/W2014947973","https://openalex.org/W2019052540","https://openalex.org/W2023191572","https://openalex.org/W2023760604","https://openalex.org/W2025939869","https://openalex.org/W2030598268","https://openalex.org/W2032070954","https://openalex.org/W2033816084","https://openalex.org/W2035955549","https://openalex.org/W2045462035","https://openalex.org/W2051203581","https://openalex.org/W2056568875","https://openalex.org/W2059229412","https://openalex.org/W2075416456","https://openalex.org/W2078475531","https://openalex.org/W2081587196","https://openalex.org/W2082899224","https://openalex.org/W2091257030","https://openalex.org/W2105236049","https://openalex.org/W2109769479","https://openalex.org/W2146486351","https://openalex.org/W2157190652","https://openalex.org/W2174467764","https://openalex.org/W2174746638","https://openalex.org/W2283136666","https://openalex.org/W2791657560","https://openalex.org/W2888609828","https://openalex.org/W2932218057","https://openalex.org/W3003650774"],"related_works":["https://openalex.org/W4327921917","https://openalex.org/W7126088707","https://openalex.org/W3003650774","https://openalex.org/W7119482846","https://openalex.org/W4410195989","https://openalex.org/W4385830645","https://openalex.org/W4285340767","https://openalex.org/W4319922959","https://openalex.org/W1974030702","https://openalex.org/W4220947836"],"abstract_inverted_index":{"The":[0,80,133],"study":[1],"of":[2,16,76,97,105,136,162,171,177,201],"collision-induced":[3,77,202],"nonlinear":[4,43,203],"breakage":[5,28,44,55,78,139,184,204],"phenomenon":[6],"is":[7,11,31,71,85,119,141],"mostly":[8],"unexplored":[9],"but":[10],"important":[12],"in":[13,87,107,144],"the":[14,22,35,42,48,74,94,98,102,108,122,137,145,150,168,174,188,197],"area":[15],"particulate":[17,164],"processes.":[18],"In":[19],"this":[20],"work,":[21],"volume":[23,51,83,134],"and":[24,60,121,173,199],"time":[25,152],"dependent":[26],"collisional":[27,138],"kernel":[29,140],"function":[30],"modeled":[32],"based":[33],"on":[34],"population":[36,45],"balance":[37,46],"modeling":[38],"approach.":[39],"To":[40],"solve":[41],"equation,":[47],"weighted":[49,81],"finite":[50,82],"scheme":[52,84],"for":[53,73,149,156,182],"linear":[54],"process":[56],"from":[57],"Kumar,":[58],"Saha,":[59],"Tsotsas":[61],"[":[62],"SIAM":[63],"J.":[64],"Numer.":[65],"Anal.,":[66],"53":[67],"(2015),":[68],"pp.":[69],"1672--1689]":[70],"extended":[72],"case":[75],"process.":[79],"developed":[86],"such":[88,166],"a":[89],"way":[90],"that":[91],"it":[92],"conserves":[93],"total":[95,103,169],"mass":[96],"system":[99],"while":[100,153],"preserving":[101],"number":[104,114,170],"particles":[106,155,172],"system.":[109],"Moreover,":[110],"an":[111,128],"event-driven":[112],"constant":[113],"Monte":[115,146,189],"Carlo":[116,147,190],"simulation":[117,123,148],"algorithm":[118],"presented,":[120],"results":[124],"are":[125,179],"used":[126],"as":[127,167],"alternative":[129],"to":[130],"experimental":[131],"results.":[132,191],"dependency":[135],"incorporated":[142],"successfully":[143,181],"first":[151],"selecting":[154],"collision":[157],"events.":[158],"Some":[159],"essential":[160],"properties":[161],"any":[163],"process,":[165],"size":[175],"distribution":[176,185],"particles,":[178],"validated":[180],"several":[183],"functions":[186],"using":[187],"This":[192],"offers":[193],"new":[194],"insights":[195],"into":[196],"estimation":[198],"interpretation":[200],"kinetics.":[205]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2020-12-21T00:00:00"}
