{"id":"https://openalex.org/W2899761918","doi":"https://doi.org/10.3390/e20110845","title":"A Simple Explicit Expression for the Flocculation Dynamics Modeling of Cohesive Sediment Based on Entropy Considerations","display_name":"A Simple Explicit Expression for the Flocculation Dynamics Modeling of Cohesive Sediment Based on Entropy Considerations","publication_year":2018,"publication_date":"2018-11-04","ids":{"openalex":"https://openalex.org/W2899761918","doi":"https://doi.org/10.3390/e20110845","mag":"2899761918","pmid":"https://pubmed.ncbi.nlm.nih.gov/33266569"},"language":"en","primary_location":{"id":"doi:10.3390/e20110845","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e20110845","pdf_url":"https://www.mdpi.com/1099-4300/20/11/845/pdf?version=1542608519","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/1099-4300/20/11/845/pdf?version=1542608519","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":true,"raw_author_name":"Zhongfan Zhu","raw_affiliation_strings":["College of Water Sciences, Beijing Normal University, Xinjiekouwai Street 19, Beijing 100875, China"],"raw_orcid":"https://orcid.org/0000-0003-0579-608X","affiliations":[{"raw_affiliation_string":"College of Water Sciences, Beijing Normal University, Xinjiekouwai Street 19, Beijing 100875, China","institution_ids":["https://openalex.org/I25254941"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5045437724"],"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":1.4585,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.7884058,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"20","issue":"11","first_page":"845","last_page":"845"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10647","display_name":"Coastal and Marine Dynamics","score":0.9819999933242798,"subfield":{"id":"https://openalex.org/subfields/1904","display_name":"Earth-Surface Processes"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10647","display_name":"Coastal and Marine Dynamics","score":0.9819999933242798,"subfield":{"id":"https://openalex.org/subfields/1904","display_name":"Earth-Surface Processes"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10779","display_name":"Coastal wetland ecosystem dynamics","score":0.9688000082969666,"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/T11188","display_name":"Coagulation and Flocculation Studies","score":0.9664000272750854,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/flocculation","display_name":"Flocculation","score":0.7579847574234009},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.6331294178962708},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5846362113952637},{"id":"https://openalex.org/keywords/tsallis-entropy","display_name":"Tsallis entropy","score":0.5162965655326843},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4827355742454529},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.4697202742099762},{"id":"https://openalex.org/keywords/turbulence","display_name":"Turbulence","score":0.46118977665901184},{"id":"https://openalex.org/keywords/binary-entropy-function","display_name":"Binary entropy function","score":0.4531148672103882},{"id":"https://openalex.org/keywords/sigmoid-function","display_name":"Sigmoid function","score":0.44812625646591187},{"id":"https://openalex.org/keywords/expression","display_name":"Expression (computer science)","score":0.4451347291469574},{"id":"https://openalex.org/keywords/siltation","display_name":"Siltation","score":0.4192183315753937},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4152621328830719},{"id":"https://openalex.org/keywords/sediment","display_name":"Sediment","score":0.3686860203742981},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.34958845376968384},{"id":"https://openalex.org/keywords/environmental-science","display_name":"Environmental science","score":0.28963929414749146},{"id":"https://openalex.org/keywords/principle-of-maximum-entropy","display_name":"Principle of maximum entropy","score":0.27376168966293335},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23898908495903015},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.2276347577571869},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2113669216632843},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.20478975772857666},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.19966024160385132},{"id":"https://openalex.org/keywords/environmental-engineering","display_name":"Environmental engineering","score":0.1289615035057068},{"id":"https://openalex.org/keywords/geomorphology","display_name":"Geomorphology","score":0.08208316564559937}],"concepts":[{"id":"https://openalex.org/C148815931","wikidata":"https://www.wikidata.org/wiki/Q900689","display_name":"Flocculation","level":2,"score":0.7579847574234009},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.6331294178962708},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5846362113952637},{"id":"https://openalex.org/C117521176","wikidata":"https://www.wikidata.org/wiki/Q7849341","display_name":"Tsallis entropy","level":3,"score":0.5162965655326843},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4827355742454529},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.4697202742099762},{"id":"https://openalex.org/C196558001","wikidata":"https://www.wikidata.org/wiki/Q190132","display_name":"Turbulence","level":2,"score":0.46118977665901184},{"id":"https://openalex.org/C44415725","wikidata":"https://www.wikidata.org/wiki/Q4913893","display_name":"Binary entropy function","level":3,"score":0.4531148672103882},{"id":"https://openalex.org/C81388566","wikidata":"https://www.wikidata.org/wiki/Q526668","display_name":"Sigmoid function","level":3,"score":0.44812625646591187},{"id":"https://openalex.org/C90559484","wikidata":"https://www.wikidata.org/wiki/Q778379","display_name":"Expression (computer science)","level":2,"score":0.4451347291469574},{"id":"https://openalex.org/C206700591","wikidata":"https://www.wikidata.org/wiki/Q1408124","display_name":"Siltation","level":3,"score":0.4192183315753937},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4152621328830719},{"id":"https://openalex.org/C2816523","wikidata":"https://www.wikidata.org/wiki/Q180184","display_name":"Sediment","level":2,"score":0.3686860203742981},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.34958845376968384},{"id":"https://openalex.org/C39432304","wikidata":"https://www.wikidata.org/wiki/Q188847","display_name":"Environmental science","level":0,"score":0.28963929414749146},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.27376168966293335},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23898908495903015},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.2276347577571869},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2113669216632843},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.20478975772857666},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.19966024160385132},{"id":"https://openalex.org/C87717796","wikidata":"https://www.wikidata.org/wiki/Q146326","display_name":"Environmental engineering","level":1,"score":0.1289615035057068},{"id":"https://openalex.org/C114793014","wikidata":"https://www.wikidata.org/wiki/Q52109","display_name":"Geomorphology","level":1,"score":0.08208316564559937},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e20110845","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e20110845","pdf_url":"https://www.mdpi.com/1099-4300/20/11/845/pdf?version=1542608519","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:33266569","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33266569","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:2012bd45a8924a8b9ddca243c6a01ccf","is_oa":true,"landing_page_url":"https://doaj.org/article/2012bd45a8924a8b9ddca243c6a01ccf","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 20, Iss 11, p 845 (2018)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/20/11/845/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e20110845","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:7512407","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7512407","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/e20110845","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e20110845","pdf_url":"https://www.mdpi.com/1099-4300/20/11/845/pdf?version=1542608519","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":[{"display_name":"Life below water","id":"https://metadata.un.org/sdg/14","score":0.8600000143051147}],"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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2899761918.pdf","grobid_xml":"https://content.openalex.org/works/W2899761918.grobid-xml"},"referenced_works_count":64,"referenced_works":["https://openalex.org/W1896394914","https://openalex.org/W1900152434","https://openalex.org/W1963642114","https://openalex.org/W1967021498","https://openalex.org/W1971060127","https://openalex.org/W1980017789","https://openalex.org/W1980457672","https://openalex.org/W1983359531","https://openalex.org/W1983874169","https://openalex.org/W1990966649","https://openalex.org/W1991406135","https://openalex.org/W1995875735","https://openalex.org/W1997925903","https://openalex.org/W1998275876","https://openalex.org/W2000781232","https://openalex.org/W2008212951","https://openalex.org/W2008689207","https://openalex.org/W2010453193","https://openalex.org/W2018490621","https://openalex.org/W2018658913","https://openalex.org/W2018968906","https://openalex.org/W2024623951","https://openalex.org/W2025329525","https://openalex.org/W2026580727","https://openalex.org/W2032558547","https://openalex.org/W2034133710","https://openalex.org/W2037577616","https://openalex.org/W2039904045","https://openalex.org/W2054443626","https://openalex.org/W2059613502","https://openalex.org/W2061597763","https://openalex.org/W2070191765","https://openalex.org/W2078399286","https://openalex.org/W2082676852","https://openalex.org/W2086773195","https://openalex.org/W2094135014","https://openalex.org/W2096113645","https://openalex.org/W2112907615","https://openalex.org/W2113025165","https://openalex.org/W2121322905","https://openalex.org/W2123134918","https://openalex.org/W2136080925","https://openalex.org/W2144658364","https://openalex.org/W2145747436","https://openalex.org/W2155086759","https://openalex.org/W2163603242","https://openalex.org/W2261991651","https://openalex.org/W2287281516","https://openalex.org/W2301773334","https://openalex.org/W2333612398","https://openalex.org/W2507882493","https://openalex.org/W2565795088","https://openalex.org/W2741359985","https://openalex.org/W2742794306","https://openalex.org/W2746722116","https://openalex.org/W2762843800","https://openalex.org/W2770292949","https://openalex.org/W2774807654","https://openalex.org/W2891344701","https://openalex.org/W4252028749","https://openalex.org/W4256415651","https://openalex.org/W6639760674","https://openalex.org/W6654876234","https://openalex.org/W6664185776"],"related_works":["https://openalex.org/W2047083630","https://openalex.org/W2113282606","https://openalex.org/W1986828803","https://openalex.org/W2097585984","https://openalex.org/W2945554820","https://openalex.org/W2005137334","https://openalex.org/W4221032372","https://openalex.org/W4379780488","https://openalex.org/W3164805786","https://openalex.org/W2132024773"],"abstract_inverted_index":{"The":[0,90],"flocculation":[1,49,60,82,102,143],"of":[2,33,62,67,103,142,163,203,230,244,249,271],"cohesive":[3,63,104],"sediment":[4,23,64,105],"plays":[5],"an":[6,97,125,286],"important":[7],"role":[8],"in":[9,19,25,36,87,106,232],"affecting":[10],"morphological":[11],"changes":[12],"to":[13,16,22,30,45,59,79,95,134,151,180,234,284],"coastal":[14],"areas,":[15],"dredging":[17],"operations":[18],"navigational":[20],"canals,":[21],"siltation":[24],"reservoirs":[26],"and":[27,29,119,174,196,217,251,255],"lakes,":[28],"the":[31,81,88,101,129,147,152,159,171,175,181,185,194,197,214,226,235,240,247,260,268,291],"variation":[32],"water":[34],"quality":[35],"estuarine":[37],"waters.":[38],"Many":[39],"studies":[40],"have":[41],"been":[42],"conducted":[43],"recently":[44],"formulate":[46,80],"a":[47,53,76,107,136,140,156,221,275],"turbulence-induced":[48],"model":[50,83,248,257],"(described":[51],"by":[52,65,145],"characteristic":[54,130],"floc":[55,131,164,264,272],"size":[56,265,273],"with":[57,190,201,213,290],"respect":[58],"time)":[61],"virtue":[66],"theoretical":[68],"analysis,":[69],"numerical":[70],"modeling,":[71],"and/or":[72],"experimental":[73,191,215,245],"observation.":[74],"However,":[75],"probability":[77],"study":[78,123],"is":[84],"still":[85],"lacking":[86],"literature.":[89],"present":[91],"study,":[92],"therefore,":[93],"aims":[94],"derive":[96],"explicit":[98,126],"expression":[99,127,187],"for":[100,128,225,239,263],"turbulent":[108],"fluid":[109],"environment":[110],"based":[111],"on":[112],"two":[113],"common":[114],"entropy":[115,118,148,173,177],"theories:":[116],"Shannon":[117,172],"Tsallis":[120,176],"entropy.":[121],"This":[122],"derives":[124],"size,":[132],"assumed":[133],"be":[135,259],"random":[137],"variable,":[138],"as":[139],"function":[141,149,162],"time":[144],"maximizing":[146],"subject":[150],"constraint":[153],"equation":[154],"using":[155],"hypothesis":[157],"regarding":[158],"cumulative":[160],"distribution":[161],"size.":[165],"It":[166],"was":[167,188,282],"found":[168,283],"that":[169,208,218],"both":[170],"theories":[178],"lead":[179],"same":[182],"expression.":[183],"Furthermore,":[184],"derived":[186],"tested":[189],"data":[192,216,231],"from":[193],"literature":[195],"results":[198],"were":[199],"compared":[200],"those":[202],"existing":[204],"deterministic":[205],"models,":[206,237],"showing":[207],"it":[209,219],"has":[210,220],"good":[211],"agreement":[212],"better":[222,261],"prediction":[223],"accuracy":[224],"logarithmic":[227],"growth":[228,242],"pattern":[229,243],"comparison":[233],"other":[236],"whereas,":[238],"sigmoid":[241],"data,":[246],"Keyvani":[250],"Strom":[252],"or":[253],"Son":[254],"Hsu":[256],"could":[258],"choice":[262],"prediction.":[266],"Finally,":[267],"maximum":[269],"capacity":[270],"growth,":[274],"key":[276],"parameter":[277],"incorporated":[278],"into":[279],"this":[280],"expression,":[281],"exhibit":[285],"empirical":[287],"power":[288],"relationship":[289],"flow":[292],"shear":[293],"rate.":[294]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}