{"id":"https://openalex.org/W1933192240","doi":"https://doi.org/10.1137/140999451","title":"The Nonclassical Boltzmann Equation and DIffusion-Based Approximations to the Boltzmann Equation","display_name":"The Nonclassical Boltzmann Equation and DIffusion-Based Approximations to the Boltzmann Equation","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W1933192240","doi":"https://doi.org/10.1137/140999451","mag":"1933192240"},"language":"en","primary_location":{"id":"doi:10.1137/140999451","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140999451","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1412.1000","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Martin Frank","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Martin Frank","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Kai Krycki","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kai Krycki","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Edward W. Larsen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Edward W. Larsen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Richard Vasques","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Richard Vasques","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":2.068,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.84781815,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"75","issue":"3","first_page":"1329","last_page":"1345"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.7168999910354614,"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"}},"topics":[{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.7168999910354614,"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.029500000178813934,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10558","display_name":"Advancements in Semiconductor Devices and Circuit Design","score":0.017500000074505806,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/boltzmann-equation","display_name":"Boltzmann equation","score":0.843999981880188},{"id":"https://openalex.org/keywords/direct-simulation-monte-carlo","display_name":"Direct simulation Monte Carlo","score":0.7764999866485596},{"id":"https://openalex.org/keywords/boltzmann-constant","display_name":"Boltzmann constant","score":0.5406000018119812},{"id":"https://openalex.org/keywords/truncation","display_name":"Truncation (statistics)","score":0.4885999858379364},{"id":"https://openalex.org/keywords/lattice-boltzmann-methods","display_name":"Lattice Boltzmann methods","score":0.4839000105857849},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.4706000089645386},{"id":"https://openalex.org/keywords/diffusion-equation","display_name":"Diffusion equation","score":0.4514000117778778},{"id":"https://openalex.org/keywords/heavy-traffic-approximation","display_name":"Heavy traffic approximation","score":0.4359000027179718},{"id":"https://openalex.org/keywords/boltzmann-distribution","display_name":"Boltzmann distribution","score":0.42660000920295715}],"concepts":[{"id":"https://openalex.org/C165995430","wikidata":"https://www.wikidata.org/wiki/Q891653","display_name":"Boltzmann equation","level":2,"score":0.843999981880188},{"id":"https://openalex.org/C164916747","wikidata":"https://www.wikidata.org/wiki/Q4382753","display_name":"Direct simulation Monte Carlo","level":4,"score":0.7764999866485596},{"id":"https://openalex.org/C35304006","wikidata":"https://www.wikidata.org/wiki/Q5962","display_name":"Boltzmann constant","level":2,"score":0.5406000018119812},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5027999877929688},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.4885999858379364},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4853000044822693},{"id":"https://openalex.org/C21821499","wikidata":"https://www.wikidata.org/wiki/Q1807064","display_name":"Lattice Boltzmann methods","level":2,"score":0.4839000105857849},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.4706000089645386},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.4514000117778778},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.439300000667572},{"id":"https://openalex.org/C193290586","wikidata":"https://www.wikidata.org/wiki/Q17022030","display_name":"Heavy traffic approximation","level":2,"score":0.4359000027179718},{"id":"https://openalex.org/C193999330","wikidata":"https://www.wikidata.org/wiki/Q834200","display_name":"Boltzmann distribution","level":2,"score":0.42660000920295715},{"id":"https://openalex.org/C102727969","wikidata":"https://www.wikidata.org/wiki/Q4901423","display_name":"Bhatnagar\u2013Gross\u2013Krook operator","level":5,"score":0.41769999265670776},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4153999984264374},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.41519999504089355},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.39239999651908875},{"id":"https://openalex.org/C33932047","wikidata":"https://www.wikidata.org/wiki/Q375553","display_name":"Boltzmann's entropy formula","level":3,"score":0.37610000371932983},{"id":"https://openalex.org/C193386753","wikidata":"https://www.wikidata.org/wiki/Q1130396","display_name":"Approximations of \u03c0","level":2,"score":0.3702999949455261},{"id":"https://openalex.org/C17456955","wikidata":"https://www.wikidata.org/wiki/Q343279","display_name":"Convection\u2013diffusion equation","level":2,"score":0.3578999936580658},{"id":"https://openalex.org/C109757611","wikidata":"https://www.wikidata.org/wiki/Q901009","display_name":"Poisson\u2013Boltzmann equation","level":3,"score":0.33379998803138733},{"id":"https://openalex.org/C183960323","wikidata":"https://www.wikidata.org/wiki/Q4455915","display_name":"Statistical weight","level":2,"score":0.3100999891757965},{"id":"https://openalex.org/C69123182","wikidata":"https://www.wikidata.org/wiki/Q891766","display_name":"Fokker\u2013Planck equation","level":3,"score":0.3098999857902527},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.29280000925064087},{"id":"https://openalex.org/C203809815","wikidata":"https://www.wikidata.org/wiki/Q634965","display_name":"Maxwell\u2013Boltzmann distribution","level":3,"score":0.2865999937057495},{"id":"https://openalex.org/C107665910","wikidata":"https://www.wikidata.org/wiki/Q4940270","display_name":"Boltzmann relation","level":5,"score":0.2847999930381775},{"id":"https://openalex.org/C68710425","wikidata":"https://www.wikidata.org/wiki/Q5275442","display_name":"Diffusion process","level":3,"score":0.2831999957561493},{"id":"https://openalex.org/C146651103","wikidata":"https://www.wikidata.org/wiki/Q7201780","display_name":"Plasma modeling","level":3,"score":0.27219998836517334},{"id":"https://openalex.org/C70985411","wikidata":"https://www.wikidata.org/wiki/Q2380676","display_name":"Integro-differential equation","level":4,"score":0.2565999925136566},{"id":"https://openalex.org/C192576344","wikidata":"https://www.wikidata.org/wiki/Q194706","display_name":"Boltzmann machine","level":3,"score":0.2531000077724457}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/140999451","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140999451","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:arXiv.org:1412.1000","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1412.1000","pdf_url":"https://arxiv.org/pdf/1412.1000","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1412.1000","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1412.1000","pdf_url":"https://arxiv.org/pdf/1412.1000","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1844244698","https://openalex.org/W1995692708","https://openalex.org/W2029532347","https://openalex.org/W2035079782","https://openalex.org/W2073901367","https://openalex.org/W2081489139","https://openalex.org/W2107648085","https://openalex.org/W2962964462"],"related_works":[],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2],"several":[3],"diffusion-based":[4,41],"approximations":[5,42],"(classical":[6],"diffusion":[7],"or":[8],"$SP_1$,":[9],"$SP_2$,":[10],"$SP_3$)":[11],"to":[12,38,43],"the":[13,44],"linear":[14],"Boltzmann":[15,45],"equation":[16,46],"can":[17],"(for":[18],"an":[19],"infinite,":[20],"homogeneous":[21],"medium)":[22],"be":[23],"represented":[24],"exactly":[25],"by":[26],"a":[27,32,36],"nonclassical":[28],"transport":[29],"equation.":[30],"As":[31],"consequence,":[33],"we":[34],"indicate":[35],"method":[37],"solve":[39],"these":[40],"via":[47],"Monte":[48],"Carlo":[49],"methods,":[50],"with":[51],"only":[52],"statistical":[53],"errors---no":[54],"truncation":[55],"errors.":[56]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2016-06-24T00:00:00"}