{"id":"https://openalex.org/W1489421437","doi":"https://doi.org/10.1007/0-387-33882-9_14","title":"Modelling and Fast Numerical Methods for Granular Flows","display_name":"Modelling and Fast Numerical Methods for Granular Flows","publication_year":2006,"publication_date":"2006-10-29","ids":{"openalex":"https://openalex.org/W1489421437","doi":"https://doi.org/10.1007/0-387-33882-9_14","mag":"1489421437"},"language":"en","primary_location":{"id":"doi:10.1007/0-387-33882-9_14","is_oa":true,"landing_page_url":"https://doi.org/10.1007/0-387-33882-9_14","pdf_url":"https://link.springer.com/content/pdf/10.1007/0-387-33882-9_14.pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IFIP International Federation for Information Processing","raw_type":"book-chapter"},"type":"conference-paper","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://link.springer.com/content/pdf/10.1007/0-387-33882-9_14.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036362276","display_name":"Elena Ferrari","orcid":"https://orcid.org/0000-0002-7312-6769"},"institutions":[{"id":"https://openalex.org/I201324441","display_name":"University of Ferrara","ror":"https://ror.org/041zkgm14","country_code":"IT","type":"education","lineage":["https://openalex.org/I201324441"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"E. Ferrari","raw_affiliation_strings":["Department of Mathematics, University of Ferrara, Ferrara, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Ferrara, Ferrara, Italy","institution_ids":["https://openalex.org/I201324441"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062399881","display_name":"Giovanni Naldi","orcid":"https://orcid.org/0000-0001-9191-6003"},"institutions":[{"id":"https://openalex.org/I189158943","display_name":"University of Milan","ror":"https://ror.org/00wjc7c48","country_code":"IT","type":"education","lineage":["https://openalex.org/I189158943"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"G. Naldi","raw_affiliation_strings":["Department of Mathematics, University of Milan, Milan, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Milan, Milan, Italy","institution_ids":["https://openalex.org/I189158943"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060753566","display_name":"Giuseppe Toscani","orcid":"https://orcid.org/0000-0003-4419-804X"},"institutions":[{"id":"https://openalex.org/I25217355","display_name":"University of Pavia","ror":"https://ror.org/00s6t1f81","country_code":"IT","type":"education","lineage":["https://openalex.org/I25217355"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"G. Toscani","raw_affiliation_strings":["Department of Mathematics, University of Pavia, Pavia, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Pavia, Pavia, Italy","institution_ids":["https://openalex.org/I25217355"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04140594,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"151","last_page":"161"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10615","display_name":"Granular flow and fluidized beds","score":1.0,"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":1.0,"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/T11751","display_name":"Lattice Boltzmann Simulation Studies","score":0.9997000098228455,"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/T12350","display_name":"Particle Dynamics in Fluid Flows","score":0.9986000061035156,"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/coefficient-of-restitution","display_name":"Coefficient of restitution","score":0.875985860824585},{"id":"https://openalex.org/keywords/inelastic-collision","display_name":"Inelastic collision","score":0.8044617176055908},{"id":"https://openalex.org/keywords/collision","display_name":"Collision","score":0.6613414883613586},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.6375496983528137},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.6157264113426208},{"id":"https://openalex.org/keywords/elastic-collision","display_name":"Elastic collision","score":0.5975596904754639},{"id":"https://openalex.org/keywords/boltzmann-constant","display_name":"Boltzmann constant","score":0.5940573215484619},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.5729836821556091},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.541390597820282},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5408945083618164},{"id":"https://openalex.org/keywords/boltzmann-equation","display_name":"Boltzmann equation","score":0.527198851108551},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.5214328169822693},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4761143624782562},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.45733126997947693},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.44590792059898376},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3755970895290375},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35651451349258423},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23092538118362427},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07592815160751343},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.07256248593330383}],"concepts":[{"id":"https://openalex.org/C5364694","wikidata":"https://www.wikidata.org/wiki/Q1143011","display_name":"Coefficient of restitution","level":2,"score":0.875985860824585},{"id":"https://openalex.org/C186647298","wikidata":"https://www.wikidata.org/wiki/Q2074917","display_name":"Inelastic collision","level":3,"score":0.8044617176055908},{"id":"https://openalex.org/C121704057","wikidata":"https://www.wikidata.org/wiki/Q352070","display_name":"Collision","level":2,"score":0.6613414883613586},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.6375496983528137},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.6157264113426208},{"id":"https://openalex.org/C52560446","wikidata":"https://www.wikidata.org/wiki/Q1044799","display_name":"Elastic collision","level":3,"score":0.5975596904754639},{"id":"https://openalex.org/C35304006","wikidata":"https://www.wikidata.org/wiki/Q5962","display_name":"Boltzmann constant","level":2,"score":0.5940573215484619},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.5729836821556091},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.541390597820282},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5408945083618164},{"id":"https://openalex.org/C165995430","wikidata":"https://www.wikidata.org/wiki/Q891653","display_name":"Boltzmann equation","level":2,"score":0.527198851108551},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.5214328169822693},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4761143624782562},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.45733126997947693},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.44590792059898376},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3755970895290375},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35651451349258423},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23092538118362427},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07592815160751343},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.07256248593330383},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C147120987","wikidata":"https://www.wikidata.org/wiki/Q2225","display_name":"Electron","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/0-387-33882-9_14","is_oa":true,"landing_page_url":"https://doi.org/10.1007/0-387-33882-9_14","pdf_url":"https://link.springer.com/content/pdf/10.1007/0-387-33882-9_14.pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IFIP International Federation for Information Processing","raw_type":"book-chapter"},{"id":"pmh:oai:sfera.unife.it:11392/526148","is_oa":false,"landing_page_url":"http://hdl.handle.net/11392/526148","pdf_url":null,"source":{"id":"https://openalex.org/S4306400369","display_name":"Institutional Research Information System University of Ferrara (University of Ferrara)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I201324441","host_organization_name":"University of Ferrara","host_organization_lineage":["https://openalex.org/I201324441"],"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":"info:eu-repo/semantics/conferenceObject"},{"id":"pmh:oai:zenodo.org:181986","is_oa":true,"landing_page_url":"https://www.openaccessrepository.it/record/181986","pdf_url":null,"source":{"id":"https://openalex.org/S4306402478","display_name":"INFM-OAR (INFN Catania)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210116497","host_organization_name":"Istituto Nazionale di Fisica Nucleare, Sezione di Catania","host_organization_lineage":["https://openalex.org/I4210116497"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/bookPart"},{"id":"doi:10.5281/zenodo.181986","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.181986","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Image"}],"best_oa_location":{"id":"doi:10.1007/0-387-33882-9_14","is_oa":true,"landing_page_url":"https://doi.org/10.1007/0-387-33882-9_14","pdf_url":"https://link.springer.com/content/pdf/10.1007/0-387-33882-9_14.pdf","source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IFIP International Federation for Information Processing","raw_type":"book-chapter"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1489421437.pdf","grobid_xml":"https://content.openalex.org/works/W1489421437.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W44278008","https://openalex.org/W177945435","https://openalex.org/W1537383557","https://openalex.org/W1584425277","https://openalex.org/W1612701840","https://openalex.org/W1973004342","https://openalex.org/W1998759078","https://openalex.org/W2013626271","https://openalex.org/W2036898921","https://openalex.org/W2051358691","https://openalex.org/W2054527546","https://openalex.org/W2058205543","https://openalex.org/W2070616503","https://openalex.org/W2124532861","https://openalex.org/W2130062345","https://openalex.org/W2132065774","https://openalex.org/W2182274314","https://openalex.org/W3101662299","https://openalex.org/W3122950674","https://openalex.org/W4255612286","https://openalex.org/W6632102023"],"related_works":["https://openalex.org/W1997635098","https://openalex.org/W2106057630","https://openalex.org/W1489421437","https://openalex.org/W2365339277","https://openalex.org/W4200258835","https://openalex.org/W2985110030","https://openalex.org/W1980222575","https://openalex.org/W2060757356","https://openalex.org/W2087359588","https://openalex.org/W2898786072"],"abstract_inverted_index":{"In":[0,23,56],"this":[1],"work":[2],"we":[3],"discuss":[4],"the":[5,11,16,26,45,50,54,57,60,66,88],"development":[6],"of":[7,19,41,53,68,87],"fast":[8],"algorithms":[9],"for":[10],"inelastic":[12,33],"Boltzmann":[13,71],"equation":[14],"describing":[15],"collisional":[17],"motion":[18],"a":[20,39,74,83],"granular":[21,61],"gas.":[22],"such":[24],"systems":[25],"collisions":[27],"between":[28],"particles":[29],"occur":[30],"in":[31,44],"an":[32,69],"way":[34],"and":[35,73],"are":[36,91],"characterized":[37],"by":[38,65],"coefficient":[40],"restitution":[42],"which":[43],"general":[46],"case":[47],"depends":[48],"on":[49,82],"relative":[51],"velocity":[52],"collision.":[55],"quasi-elastic":[58],"approximation":[59],"operator":[62,72],"is":[63],"replaced":[64],"sum":[67],"elastic":[70],"nonlinear":[75],"friction":[76],"term.":[77],"Fast":[78],"numerical":[79],"methods":[80],"based":[81],"suitable":[84],"spectral":[85],"representation":[86],"approximated":[89],"model":[90],"then":[92],"presented.":[93]},"counts_by_year":[],"updated_date":"2026-08-12T21:12:35.861297","created_date":"2025-10-10T00:00:00"}