{"id":"https://openalex.org/W2505138721","doi":"https://doi.org/10.3390/e18080283","title":"A Critical Reassessment of the Hess\u2013Murray Law","display_name":"A Critical Reassessment of the Hess\u2013Murray Law","publication_year":2016,"publication_date":"2016-08-05","ids":{"openalex":"https://openalex.org/W2505138721","doi":"https://doi.org/10.3390/e18080283","mag":"2505138721"},"language":"en","primary_location":{"id":"doi:10.3390/e18080283","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e18080283","pdf_url":"https://www.mdpi.com/1099-4300/18/8/283/pdf?version=1470391692","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"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/18/8/283/pdf?version=1470391692","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043152045","display_name":"Enrico Sciubba","orcid":"https://orcid.org/0000-0003-2220-1762"},"institutions":[{"id":"https://openalex.org/I861853513","display_name":"Sapienza University of Rome","ror":"https://ror.org/02be6w209","country_code":"IT","type":"education","lineage":["https://openalex.org/I861853513"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Enrico Sciubba","raw_affiliation_strings":["Department of Mechanical and Aerospace Engineering, University of Roma Sapienza, 00185 Roma, Italy"],"raw_orcid":"https://orcid.org/0000-0003-2220-1762","affiliations":[{"raw_affiliation_string":"Department of Mechanical and Aerospace Engineering, University of Roma Sapienza, 00185 Roma, Italy","institution_ids":["https://openalex.org/I861853513"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5043152045"],"corresponding_institution_ids":["https://openalex.org/I861853513"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.3405,"has_fulltext":false,"cited_by_count":21,"citation_normalized_percentile":{"value":0.61821737,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"18","issue":"8","first_page":"283","last_page":"283"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10466","display_name":"Meteorological Phenomena and Simulations","score":0.7508999705314636,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"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/T10466","display_name":"Meteorological Phenomena and Simulations","score":0.7508999705314636,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.73580002784729,"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/T10255","display_name":"Oceanographic and Atmospheric Processes","score":0.6772000193595886,"subfield":{"id":"https://openalex.org/subfields/1910","display_name":"Oceanography"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4579239785671234},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.40271323919296265},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.34688085317611694},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.33986377716064453},{"id":"https://openalex.org/keywords/theoretical-physics","display_name":"Theoretical physics","score":0.3346109092235565},{"id":"https://openalex.org/keywords/political-science","display_name":"Political science","score":0.24133777618408203}],"concepts":[{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4579239785671234},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.40271323919296265},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.34688085317611694},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.33986377716064453},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.3346109092235565},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.24133777618408203}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e18080283","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e18080283","pdf_url":"https://www.mdpi.com/1099-4300/18/8/283/pdf?version=1470391692","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":"pmh:oai:doaj.org/article:4a23835343774bf18c71243bff6aa56f","is_oa":true,"landing_page_url":"https://doaj.org/article/4a23835343774bf18c71243bff6aa56f","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 18, Iss 8, p 283 (2016)","raw_type":"article"},{"id":"pmh:oai:iris.uniroma1.it:11573/970977","is_oa":false,"landing_page_url":"http://hdl.handle.net/11573/970977","pdf_url":null,"source":{"id":"https://openalex.org/S4377196107","display_name":"IRIS Research product catalog (Sapienza University of Rome)","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:mdpi.com:/1099-4300/18/8/283/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e18080283","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; Volume 18; Issue 8; Pages: 283","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e18080283","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e18080283","pdf_url":"https://www.mdpi.com/1099-4300/18/8/283/pdf?version=1470391692","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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W2505138721.pdf"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W985366881","https://openalex.org/W1908884897","https://openalex.org/W1968553256","https://openalex.org/W1970635916","https://openalex.org/W1971810557","https://openalex.org/W1975495747","https://openalex.org/W1985242491","https://openalex.org/W1996884577","https://openalex.org/W1998978018","https://openalex.org/W2002933529","https://openalex.org/W2042131650","https://openalex.org/W2044948463","https://openalex.org/W2046322851","https://openalex.org/W2057824330","https://openalex.org/W2068730021","https://openalex.org/W2080843536","https://openalex.org/W2084535563","https://openalex.org/W2092868937","https://openalex.org/W2102340376","https://openalex.org/W2117184765","https://openalex.org/W2134071028","https://openalex.org/W2146538081","https://openalex.org/W2150447796","https://openalex.org/W2152825691","https://openalex.org/W2154066255","https://openalex.org/W2185476616","https://openalex.org/W2235431484","https://openalex.org/W2315729882","https://openalex.org/W2786372830","https://openalex.org/W3092084256","https://openalex.org/W6625807372","https://openalex.org/W6639922905","https://openalex.org/W6686146830","https://openalex.org/W6783920417"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2935759653","https://openalex.org/W3105167352","https://openalex.org/W54078636","https://openalex.org/W2954470139","https://openalex.org/W1501425562","https://openalex.org/W2902782467","https://openalex.org/W3084825885","https://openalex.org/W2298861036","https://openalex.org/W3148032049"],"abstract_inverted_index":{"The":[0,52],"Hess\u2013Murray":[1,176,295],"law":[2,40,53,130,177,250,296],"is":[3,54,67,131,278],"a":[4,70,75,125,188,195,216,219,262],"correlation":[5,105],"between":[6,215],"the":[7,21,39,44,57,113,117,121,135,140,149,175,181,192,209,223,237,246,249,265,283,294],"radii":[8],"of":[9,78,86,103,116,128,139,142,144,166,191,211,222,225,239,248,264,285,293],"successive":[10],"branchings":[11],"in":[12,15,30,37,50,64,112,229,236,282,303],"bi/trifurcated":[13],"vessels":[14,137],"biological":[16,306],"tissues.":[17],"First":[18],"proposed":[19],"by":[20,43,69],"Swiss":[22],"physiologist":[23,46],"and":[24,35,109,120,201,213,218,231,241,251,258,305],"Nobel":[25],"laureate":[26],"Walter":[27],"Rudolf":[28],"Hess":[29],"his":[31],"1914":[32],"doctoral":[33],"thesis":[34],"published":[36],"1917,":[38],"was":[41,185],"\u201crediscovered\u201d":[42],"American":[45],"Cecil":[47],"Dunmore":[48],"Murray":[49],"1926.":[51],"based":[55],"on":[56],"assumption":[58],"that":[59,197,253],"blood":[60],"or":[61,233],"lymph":[62],"circulation":[63],"living":[65],"organisms":[66],"governed":[68],"\u201cwork":[71],"minimization\u201d":[72],"principle":[73],"that\u2014under":[74,124],"certain":[76],"set":[77],"specified":[79],"conditions\u2014leads":[80],"to":[81,158,170,204,273],"an":[82,286,290,300],"\u201coptimal":[83,206],"branching":[84],"ratio\u201d":[85],"r":[87,91],"i":[88,92],"+":[89],"1":[90,94],"=":[93,97],"2":[95],"3":[96],"0.7937":[98],".":[99],"This":[100,243],"\u201ccubic":[101],"root":[102],"2\u201d":[104],"underwent":[106],"extensive":[107],"theoretical":[108],"experimental":[110],"reassessment":[111],"second":[114],"half":[115],"20th":[118],"century,":[119],"results":[122],"indicate":[123],"well-defined":[126],"series":[127],"conditions\u2014the":[129],"sufficiently":[132],"accurate":[133],"for":[134,148,208,255,259],"smallest":[136],"(r":[138],"order":[141],"fractions":[143],"millimeter)":[145],"but":[146],"fails":[147],"larger":[150],"ones;":[151],"moreover,":[152],"it":[153,184],"cannot":[154],"be":[155],"successfully":[156],"extended":[157],"turbulent":[159],"flows.":[160],"Recent":[161],"comparisons":[162],"with":[163],"numerical":[164],"investigations":[165],"branched":[167],"flows":[168,257],"led":[169],"similar":[171],"conclusions.":[172],"More":[173],"recently,":[174],"came":[178],"back":[179],"into":[180],"limelight":[182],"when":[183],"taken":[186],"as":[187],"founding":[189],"paradigm":[190],"Constructal":[193],"Law,":[194],"theory":[196],"employs":[198],"physical":[199],"intuition":[200],"mathematical":[202],"reasoning":[203],"derive":[205],"paths\u201d":[207],"transport":[210],"matter":[212],"energy":[214],"source":[217],"sink,":[220],"regardless":[221],"mode":[224],"transportation":[226,238],"(continuous,":[227],"like":[228,235],"convection":[230],"conduction,":[232],"discrete,":[234],"goods":[240],"people).":[242],"paper":[244],"examines":[245],"foundation":[247],"argues":[252],"both":[254],"natural":[256],"engineering":[260,304],"designs,":[261],"minimization":[263],"irreversibility":[266],"under":[267],"physically":[268],"sound":[269],"boundary":[270],"conditions":[271],"leads":[272],"somewhat":[274],"different":[275],"results.":[276],"It":[277],"also":[279],"shown":[280],"that,":[281],"light":[284],"exergy-based":[287],"resource":[288],"analysis,":[289],"amended":[291],"version":[292],"may":[297],"still":[298],"hold":[299],"important":[301],"position":[302],"sciences.":[307]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}