{"id":"https://openalex.org/W2809457558","doi":"https://doi.org/10.3390/e20070492","title":"Analytical and Numerical Treatments of Conservative Diffusions and the Burgers Equation","display_name":"Analytical and Numerical Treatments of Conservative Diffusions and the Burgers Equation","publication_year":2018,"publication_date":"2018-06-25","ids":{"openalex":"https://openalex.org/W2809457558","doi":"https://doi.org/10.3390/e20070492","mag":"2809457558","pmid":"https://pubmed.ncbi.nlm.nih.gov/33265582"},"language":"en","primary_location":{"id":"doi:10.3390/e20070492","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e20070492","pdf_url":"https://www.mdpi.com/1099-4300/20/7/492/pdf?version=1530010720","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/1099-4300/20/7/492/pdf?version=1530010720","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010053128","display_name":"Dimiter Prodanov","orcid":"https://orcid.org/0000-0001-8694-0535"},"institutions":[{"id":"https://openalex.org/I4210114974","display_name":"IMEC","ror":"https://ror.org/02kcbn207","country_code":"BE","type":"nonprofit","lineage":["https://openalex.org/I4210114974"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"Dimiter Prodanov","raw_affiliation_strings":["Department of Environment, Health and Safety, Imec, 3001 Leuven, Belgium"],"raw_orcid":"https://orcid.org/0000-0001-8694-0535","affiliations":[{"raw_affiliation_string":"Department of Environment, Health and Safety, Imec, 3001 Leuven, Belgium","institution_ids":["https://openalex.org/I4210114974"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5010053128"],"corresponding_institution_ids":["https://openalex.org/I4210114974"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.444,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.61398048,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"20","issue":"7","first_page":"492","last_page":"492"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9991999864578247,"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9991000294685364,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9955000281333923,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/fokker\u2013planck-equation","display_name":"Fokker\u2013Planck equation","score":0.7598848342895508},{"id":"https://openalex.org/keywords/langevin-equation","display_name":"Langevin equation","score":0.6892529129981995},{"id":"https://openalex.org/keywords/burgers-equation","display_name":"Burgers' equation","score":0.6889641880989075},{"id":"https://openalex.org/keywords/stochastic-differential-equation","display_name":"Stochastic differential equation","score":0.6483269929885864},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.6124987006187439},{"id":"https://openalex.org/keywords/probability-density-function","display_name":"Probability density function","score":0.47991594672203064},{"id":"https://openalex.org/keywords/statistical-mechanics","display_name":"Statistical mechanics","score":0.476066529750824},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4666585624217987},{"id":"https://openalex.org/keywords/diffusion-equation","display_name":"Diffusion equation","score":0.4520813822746277},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4497414529323578},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.44338011741638184},{"id":"https://openalex.org/keywords/geodesic","display_name":"Geodesic","score":0.41397497057914734},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4112856686115265},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.30652502179145813}],"concepts":[{"id":"https://openalex.org/C69123182","wikidata":"https://www.wikidata.org/wiki/Q891766","display_name":"Fokker\u2013Planck equation","level":3,"score":0.7598848342895508},{"id":"https://openalex.org/C2777577648","wikidata":"https://www.wikidata.org/wiki/Q584537","display_name":"Langevin equation","level":2,"score":0.6892529129981995},{"id":"https://openalex.org/C129747778","wikidata":"https://www.wikidata.org/wiki/Q1014918","display_name":"Burgers' equation","level":3,"score":0.6889641880989075},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.6483269929885864},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.6124987006187439},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.47991594672203064},{"id":"https://openalex.org/C99874945","wikidata":"https://www.wikidata.org/wiki/Q188715","display_name":"Statistical mechanics","level":2,"score":0.476066529750824},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4666585624217987},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.4520813822746277},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4497414529323578},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.44338011741638184},{"id":"https://openalex.org/C165818556","wikidata":"https://www.wikidata.org/wiki/Q213488","display_name":"Geodesic","level":2,"score":0.41397497057914734},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4112856686115265},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30652502179145813},{"id":"https://openalex.org/C136264566","wikidata":"https://www.wikidata.org/wiki/Q159810","display_name":"Economy","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C2780378061","wikidata":"https://www.wikidata.org/wiki/Q25351891","display_name":"Service (business)","level":2,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.3390/e20070492","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e20070492","pdf_url":"https://www.mdpi.com/1099-4300/20/7/492/pdf?version=1530010720","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:33265582","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33265582","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:lirias2repo.kuleuven.be:20.500.12942/788787","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/20.500.12942/788787","pdf_url":null,"source":{"id":"https://openalex.org/S7407055369","display_name":"Lirias","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","license_id":"https://openalex.org/licenses/cc-by","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Entropy, vol. 20 (7), Art.No. ARTN 492","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:96f9ffeb3bdd4b248b02bc842f337ef4","is_oa":true,"landing_page_url":"https://doaj.org/article/96f9ffeb3bdd4b248b02bc842f337ef4","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 7, p 492 (2018)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/20/7/492/","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/e20070492","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:7513018","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7513018","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/e20070492","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e20070492","pdf_url":"https://www.mdpi.com/1099-4300/20/7/492/pdf?version=1530010720","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":[],"awards":[{"id":"https://openalex.org/G883652272","display_name":null,"funder_award_id":"VS.097.16N","funder_id":"https://openalex.org/F4320321730","funder_display_name":"Fonds Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320306689","display_name":"Fetzer Institute","ror":"https://ror.org/02t1yaf39"},{"id":"https://openalex.org/F4320321730","display_name":"Fonds Wetenschappelijk Onderzoek","ror":"https://ror.org/03qtxy027"},{"id":"https://openalex.org/F4320327336","display_name":"Vlaamse regering","ror":null},{"id":"https://openalex.org/F4320332999","display_name":"Horizon 2020 Framework Programme","ror":"https://ror.org/00k4n6c32"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2809457558.pdf","grobid_xml":"https://content.openalex.org/works/W2809457558.grobid-xml"},"referenced_works_count":57,"referenced_works":["https://openalex.org/W60850999","https://openalex.org/W1524941116","https://openalex.org/W1965311453","https://openalex.org/W1965929587","https://openalex.org/W1970652246","https://openalex.org/W1977225660","https://openalex.org/W1977360274","https://openalex.org/W1985382297","https://openalex.org/W1992651842","https://openalex.org/W2012421353","https://openalex.org/W2016135784","https://openalex.org/W2017578770","https://openalex.org/W2021808187","https://openalex.org/W2023418334","https://openalex.org/W2037835420","https://openalex.org/W2038259289","https://openalex.org/W2045384647","https://openalex.org/W2051767463","https://openalex.org/W2054800656","https://openalex.org/W2058976606","https://openalex.org/W2067625009","https://openalex.org/W2069647600","https://openalex.org/W2076272146","https://openalex.org/W2088090305","https://openalex.org/W2127519480","https://openalex.org/W2143588546","https://openalex.org/W2161953807","https://openalex.org/W2172846583","https://openalex.org/W2223094112","https://openalex.org/W2319919424","https://openalex.org/W2326651233","https://openalex.org/W2479823038","https://openalex.org/W2527988682","https://openalex.org/W2565432921","https://openalex.org/W2586773123","https://openalex.org/W2594084774","https://openalex.org/W2617211606","https://openalex.org/W2617905331","https://openalex.org/W2756137296","https://openalex.org/W2783007365","https://openalex.org/W2799637418","https://openalex.org/W2963822527","https://openalex.org/W3098273576","https://openalex.org/W3098972213","https://openalex.org/W3102507613","https://openalex.org/W3102597530","https://openalex.org/W3103363953","https://openalex.org/W3123098901","https://openalex.org/W4232486802","https://openalex.org/W4238187298","https://openalex.org/W4240986989","https://openalex.org/W4245732230","https://openalex.org/W4246997062","https://openalex.org/W4248755160","https://openalex.org/W4388167314","https://openalex.org/W6782398337","https://openalex.org/W7024292067"],"related_works":["https://openalex.org/W1536424668","https://openalex.org/W1511221904","https://openalex.org/W2085044856","https://openalex.org/W826125831","https://openalex.org/W3126582067","https://openalex.org/W2044768923","https://openalex.org/W1999755075","https://openalex.org/W2083610184","https://openalex.org/W2036007974","https://openalex.org/W1964238656"],"abstract_inverted_index":{"The":[0,121],"present":[1],"work":[2],"is":[3,27,161],"concerned":[4],"with":[5,80],"the":[6,17,30,33,36,42,47,55,58,70,73,81,84,98,106,108,126,130,134,145,150,157,169],"study":[7,82],"of":[8,20,32,35,44,46,57,83,105,129,133,144,156],"a":[9,93,118,153],"generalized":[10],"Langevin":[11,37,109],"equation":[12,38,96,110,128],"and":[13,23,75],"its":[14],"link":[15],"to":[16,61,168],"physical":[18],"theories":[19],"statistical":[21,123],"mechanics":[22,77],"scale":[24],"relativity.":[25],"It":[26],"demonstrated":[28],"that":[29],"form":[31],"coefficients":[34],"depends":[39],"critically":[40],"on":[41,149],"assumption":[43],"continuity":[45],"reconstructed":[48],"trajectory.":[49],"This":[50,66],"in":[51,64,88,117],"turn":[52],"demands":[53],"for":[54,97],"fluctuations":[56],"diffusion":[59],"term":[60],"be":[62,139],"discontinuous":[63],"time.":[65],"paper":[67],"further":[68,101],"investigates":[69],"connection":[71],"between":[72],"scale-relativistic":[74],"stochastic":[76,94,164],"approaches,":[78],"respectively,":[79],"Burgers":[85],"equation,":[86],"which":[87,137],"this":[89],"case":[90],"appears":[91],"as":[92],"geodesic":[95],"drift.":[99],"By":[100],"demanding":[102],"time":[103],"reversibility":[104],"drift,":[107],"can":[111,138],"also":[112],"describe":[113],"equivalent":[114],"quantum-mechanical":[115],"systems":[116],"path-wise":[119],"manner.":[120],"resulting":[122],"description":[124],"obeys":[125],"Fokker-Planck":[127,151],"probability":[131,159],"density":[132],"differential":[135],"system,":[136],"readily":[140],"estimated":[141],"from":[142],"simulations":[143,165],"random":[146],"paths.":[147],"Based":[148],"formalism,":[152],"new":[154],"derivation":[155],"transient":[158],"densities":[160],"presented.":[162],"Finally,":[163],"are":[166],"compared":[167],"theoretical":[170],"results.":[171]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":2}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}
