{"id":"https://openalex.org/W2945554820","doi":"https://doi.org/10.3390/e21050522","title":"An Expression for Velocity Lag in Sediment-Laden Open-Channel Flows Based on Tsallis Entropy Together with the Principle of Maximum Entropy","display_name":"An Expression for Velocity Lag in Sediment-Laden Open-Channel Flows Based on Tsallis Entropy Together with the Principle of Maximum Entropy","publication_year":2019,"publication_date":"2019-05-23","ids":{"openalex":"https://openalex.org/W2945554820","doi":"https://doi.org/10.3390/e21050522","mag":"2945554820","pmid":"https://pubmed.ncbi.nlm.nih.gov/33267236"},"language":"en","primary_location":{"id":"doi:10.3390/e21050522","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21050522","pdf_url":"https://www.mdpi.com/1099-4300/21/5/522/pdf?version=1559043276","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/21/5/522/pdf?version=1559043276","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5045437724","display_name":"Zhongfan Zhu","orcid":"https://orcid.org/0000-0003-0579-608X"},"institutions":[{"id":"https://openalex.org/I25254941","display_name":"Beijing Normal University","ror":"https://ror.org/022k4wk35","country_code":"CN","type":"education","lineage":["https://openalex.org/I25254941"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhongfan Zhu","raw_affiliation_strings":["Beijing Key Laboratory of Urban Hydrological Cycle and Sponge City Technology, College of Water Sciences, Beijing Normal University, Beijing 100875, China"],"raw_orcid":"https://orcid.org/0000-0003-0579-608X","affiliations":[{"raw_affiliation_string":"Beijing Key Laboratory of Urban Hydrological Cycle and Sponge City Technology, College of Water Sciences, Beijing Normal University, Beijing 100875, China","institution_ids":["https://openalex.org/I25254941"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069570565","display_name":"Jingshan Yu","orcid":null},"institutions":[{"id":"https://openalex.org/I25254941","display_name":"Beijing Normal University","ror":"https://ror.org/022k4wk35","country_code":"CN","type":"education","lineage":["https://openalex.org/I25254941"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jingshan Yu","raw_affiliation_strings":["Beijing Key Laboratory of Urban Hydrological Cycle and Sponge City Technology, College of Water Sciences, Beijing Normal University, Beijing 100875, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing Key Laboratory of Urban Hydrological Cycle and Sponge City Technology, College of Water Sciences, Beijing Normal University, Beijing 100875, China","institution_ids":["https://openalex.org/I25254941"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103127563","display_name":"Jie Dou","orcid":"https://orcid.org/0000-0001-5930-199X"},"institutions":[{"id":"https://openalex.org/I85922643","display_name":"Nagaoka University of Technology","ror":"https://ror.org/00ys1hz88","country_code":"JP","type":"education","lineage":["https://openalex.org/I85922643"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Jie Dou","raw_affiliation_strings":["Department of Civil and Environmental Engineering, Nagaoka University of Technology 1603-1, Kami-Tomioka, Nagaoka 940-2188, Japan"],"raw_orcid":"https://orcid.org/0000-0001-5930-199X","affiliations":[{"raw_affiliation_string":"Department of Civil and Environmental Engineering, Nagaoka University of Technology 1603-1, Kami-Tomioka, Nagaoka 940-2188, Japan","institution_ids":["https://openalex.org/I85922643"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055361370","display_name":"Dingzhi Peng","orcid":"https://orcid.org/0000-0003-2118-5174"},"institutions":[{"id":"https://openalex.org/I25254941","display_name":"Beijing Normal University","ror":"https://ror.org/022k4wk35","country_code":"CN","type":"education","lineage":["https://openalex.org/I25254941"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Dingzhi Peng","raw_affiliation_strings":["Beijing Key Laboratory of Urban Hydrological Cycle and Sponge City Technology, College of Water Sciences, Beijing Normal University, Beijing 100875, China"],"raw_orcid":"https://orcid.org/0000-0003-2118-5174","affiliations":[{"raw_affiliation_string":"Beijing Key Laboratory of Urban Hydrological Cycle and Sponge City Technology, College of Water Sciences, Beijing Normal University, Beijing 100875, China","institution_ids":["https://openalex.org/I25254941"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5055361370"],"corresponding_institution_ids":["https://openalex.org/I25254941"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.7612,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.71969611,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"21","issue":"5","first_page":"522","last_page":"522"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10577","display_name":"Hydrology and Sediment Transport Processes","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/2303","display_name":"Ecology"},"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/T10577","display_name":"Hydrology and Sediment Transport Processes","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/2303","display_name":"Ecology"},"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/T11186","display_name":"Hydrology and Drought Analysis","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/2306","display_name":"Global and Planetary Change"},"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/T12022","display_name":"Hydraulic flow and structures","score":0.9728000164031982,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/tsallis-entropy","display_name":"Tsallis entropy","score":0.8810058832168579},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.6061611175537109},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5941451787948608},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.5459328293800354},{"id":"https://openalex.org/keywords/lag","display_name":"Lag","score":0.5375997424125671},{"id":"https://openalex.org/keywords/binary-entropy-function","display_name":"Binary entropy function","score":0.5361338257789612},{"id":"https://openalex.org/keywords/maximum-entropy-probability-distribution","display_name":"Maximum entropy probability distribution","score":0.4951895773410797},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.4447680115699768},{"id":"https://openalex.org/keywords/maximum-entropy-thermodynamics","display_name":"Maximum entropy thermodynamics","score":0.4431363046169281},{"id":"https://openalex.org/keywords/open-channel-flow","display_name":"Open-channel flow","score":0.4213123321533203},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3083256781101227},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.25928956270217896},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1922619342803955},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.17122066020965576},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.1488470733165741},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11828917264938354}],"concepts":[{"id":"https://openalex.org/C117521176","wikidata":"https://www.wikidata.org/wiki/Q7849341","display_name":"Tsallis entropy","level":3,"score":0.8810058832168579},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.6061611175537109},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5941451787948608},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5459328293800354},{"id":"https://openalex.org/C75778745","wikidata":"https://www.wikidata.org/wiki/Q342626","display_name":"Lag","level":2,"score":0.5375997424125671},{"id":"https://openalex.org/C44415725","wikidata":"https://www.wikidata.org/wiki/Q4913893","display_name":"Binary entropy function","level":3,"score":0.5361338257789612},{"id":"https://openalex.org/C60507348","wikidata":"https://www.wikidata.org/wiki/Q6795892","display_name":"Maximum entropy probability distribution","level":3,"score":0.4951895773410797},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.4447680115699768},{"id":"https://openalex.org/C49775889","wikidata":"https://www.wikidata.org/wiki/Q6795896","display_name":"Maximum entropy thermodynamics","level":4,"score":0.4431363046169281},{"id":"https://openalex.org/C180925781","wikidata":"https://www.wikidata.org/wiki/Q514096","display_name":"Open-channel flow","level":3,"score":0.4213123321533203},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3083256781101227},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.25928956270217896},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1922619342803955},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.17122066020965576},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.1488470733165741},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11828917264938354},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e21050522","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21050522","pdf_url":"https://www.mdpi.com/1099-4300/21/5/522/pdf?version=1559043276","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:33267236","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33267236","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:323a5abf515346b08085b188b99940ab","is_oa":true,"landing_page_url":"https://doaj.org/article/323a5abf515346b08085b188b99940ab","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 21, Iss 5, p 522 (2019)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/21/5/522/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e21050522","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:7515011","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7515011","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e21050522","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e21050522","pdf_url":"https://www.mdpi.com/1099-4300/21/5/522/pdf?version=1559043276","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.4300000071525574,"id":"https://metadata.un.org/sdg/14","display_name":"Life below water"}],"awards":[{"id":"https://openalex.org/G5153751377","display_name":null,"funder_award_id":"51509004","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W2945554820.pdf"},"referenced_works_count":40,"referenced_works":["https://openalex.org/W1483542850","https://openalex.org/W1508677930","https://openalex.org/W1590483699","https://openalex.org/W1983874169","https://openalex.org/W2018490621","https://openalex.org/W2025857893","https://openalex.org/W2032558547","https://openalex.org/W2033349742","https://openalex.org/W2042852466","https://openalex.org/W2045890360","https://openalex.org/W2059613502","https://openalex.org/W2062306054","https://openalex.org/W2062652302","https://openalex.org/W2072618914","https://openalex.org/W2080124689","https://openalex.org/W2082216427","https://openalex.org/W2087284375","https://openalex.org/W2087520990","https://openalex.org/W2093981043","https://openalex.org/W2098610027","https://openalex.org/W2116551930","https://openalex.org/W2120999731","https://openalex.org/W2121281480","https://openalex.org/W2136080925","https://openalex.org/W2140425410","https://openalex.org/W2153607407","https://openalex.org/W2155086759","https://openalex.org/W2188820641","https://openalex.org/W2333612398","https://openalex.org/W2513246207","https://openalex.org/W2770292949","https://openalex.org/W2809566242","https://openalex.org/W2901144471","https://openalex.org/W2914090065","https://openalex.org/W2918843854","https://openalex.org/W4252028749","https://openalex.org/W4256415651","https://openalex.org/W4302499807","https://openalex.org/W6672319979","https://openalex.org/W6756387705"],"related_works":["https://openalex.org/W2034921015","https://openalex.org/W3021846434","https://openalex.org/W2064875109","https://openalex.org/W2889261288","https://openalex.org/W32935261","https://openalex.org/W2053566994","https://openalex.org/W2042719478","https://openalex.org/W20961974","https://openalex.org/W2176894780","https://openalex.org/W3103154033"],"abstract_inverted_index":{"In":[0,39],"the":[1,20,37,47,57,63,72,85,107,114,126,130,137,143,147,156,169,182,187,198,201,205,207,211,216,223,230,233,239,246,254],"context":[2],"of":[3,65,78,90,136,155,176,200,204,232,241],"river":[4],"dynamics,":[5],"some":[6],"experimental":[7,94,103,127,149],"results":[8],"have":[9],"shown":[10],"that":[11,154],"particle":[12,208,252],"velocity":[13,18,29,34,48,73,91,203,217,248],"is":[14],"different":[15],"from":[16,93,106],"fluid":[17,256],"along":[19],"stream-wise":[21,247],"direction":[22],"for":[23,45,133,146,173,181],"uniform":[24],"sediment-laden":[25,258],"open-channel":[26,51,259],"flows;":[27],"this":[28,40],"difference":[30],"has":[31],"been":[32],"termed":[33],"lag":[35,49,74,92,218,249],"in":[36,50,257],"literature.":[38],"study,":[41],"an":[42],"analytical":[43],"expression":[44,70,98,164],"estimating":[46],"flows":[52],"was":[53,99,151],"derived":[54,69,97],"based":[55,221],"on":[56,84,215,222],"Tsallis":[58,120,162,224,234],"entropy":[59,81,235,243],"theory":[60,236],"together":[61,237],"with":[62,109,125,238],"principle":[64,240],"maximum":[66,88,242],"entropy.":[67],"The":[68,96,119],"represents":[71],"as":[75],"a":[76,79,192,251],"function":[77],"non-dimensional":[80],"parameter":[82],"depending":[83],"average":[86],"and":[87,113,142,210,253],"values":[89],"measurements.":[95],"tested":[100],"against":[101],"twenty-two":[102,138],"datasets":[104,128,150],"collected":[105],"literature":[108],"three":[110],"deterministic":[111,131],"models":[112,132],"developed":[115,157],"Shannon":[116,158,170,188],"entropy-based":[117,121,159,163,171,189,225],"model.":[118,226],"model":[122,160,172,190],"agreed":[123,165],"better":[124,167],"than":[129,168],"eighteen":[134,148,177],"out":[135,175],"total":[139],"real":[140],"cases,":[141,179,186],"prediction":[144,195],"accuracy":[145],"comparable":[152],"to":[153,244],"(the":[161],"slightly":[166,193],"twelve":[174],"test":[178,185],"whereas":[180],"other":[183],"six":[184],"had":[191],"higher":[194],"accuracy).":[196],"Finally,":[197],"effects":[199],"friction":[202],"flow,":[206],"diameter,":[209],"particles'":[212],"specific":[213],"gravity":[214],"were":[219],"analyzed":[220],"This":[227],"study":[228],"shows":[229],"potential":[231],"predict":[245],"between":[250],"surrounding":[255],"flows.":[260]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}