{"id":"https://openalex.org/W3088944539","doi":"https://doi.org/10.3390/e22111241","title":"Geometric Aspects of the Isentropic Liquid Dynamics and Vorticity Invariants","display_name":"Geometric Aspects of the Isentropic Liquid Dynamics and Vorticity Invariants","publication_year":2020,"publication_date":"2020-10-31","ids":{"openalex":"https://openalex.org/W3088944539","doi":"https://doi.org/10.3390/e22111241","mag":"3088944539","pmid":"https://pubmed.ncbi.nlm.nih.gov/33287009"},"language":"en","primary_location":{"id":"doi:10.3390/e22111241","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e22111241","pdf_url":"https://www.mdpi.com/1099-4300/22/11/1241/pdf?version=1604488122","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":"review","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/22/11/1241/pdf?version=1604488122","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091025769","display_name":"Alexander Balinsky","orcid":"https://orcid.org/0000-0002-8151-4462"},"institutions":[{"id":"https://openalex.org/I79510175","display_name":"Cardiff University","ror":"https://ror.org/03kk7td41","country_code":"GB","type":"education","lineage":["https://openalex.org/I79510175"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Alexander A. Balinsky","raw_affiliation_strings":["School of Mathematics, Cardiff University, Cardiff CF24 4AG, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Cardiff University, Cardiff CF24 4AG, UK","institution_ids":["https://openalex.org/I79510175"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003281118","display_name":"Denis Blackmore","orcid":"https://orcid.org/0000-0003-3524-9538"},"institutions":[{"id":"https://openalex.org/I118118575","display_name":"New Jersey Institute of Technology","ror":"https://ror.org/05e74xb87","country_code":"US","type":"education","lineage":["https://openalex.org/I118118575"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Denis Blackmore","raw_affiliation_strings":["Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ 07102, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ 07102, USA","institution_ids":["https://openalex.org/I118118575"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074802886","display_name":"R. A. Kycia","orcid":"https://orcid.org/0000-0002-6390-4627"},"institutions":[{"id":"https://openalex.org/I24881138","display_name":"Cracow University of Technology","ror":"https://ror.org/00pdej676","country_code":"PL","type":"education","lineage":["https://openalex.org/I24881138"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Rados\u0142aw Kycia","raw_affiliation_strings":["Faculty of Physics, Mathematics and Computer Science, Cracow University of Technology, 31-155 Krak\u00f3w, Poland"],"raw_orcid":"https://orcid.org/0000-0002-6390-4627","affiliations":[{"raw_affiliation_string":"Faculty of Physics, Mathematics and Computer Science, Cracow University of Technology, 31-155 Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I24881138"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112459338","display_name":"Anatolij K. Prykarpatski","orcid":"https://orcid.org/0000-0001-5124-5890"},"institutions":[{"id":"https://openalex.org/I24881138","display_name":"Cracow University of Technology","ror":"https://ror.org/00pdej676","country_code":"PL","type":"education","lineage":["https://openalex.org/I24881138"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Anatolij K. Prykarpatski","raw_affiliation_strings":["Department of Physics, Mathematics and Computer Science, Cracov University of Technology, 31-155 Krak\u00f3w, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics, Mathematics and Computer Science, Cracov University of Technology, 31-155 Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I24881138"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5112459338"],"corresponding_institution_ids":["https://openalex.org/I24881138"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.1333,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.45296614,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"22","issue":"11","first_page":"1241","last_page":"1241"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9976000189781189,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9976000189781189,"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/T10025","display_name":"Black Holes and Theoretical Physics","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy 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/T11965","display_name":"Quantum, superfluid, helium dynamics","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/poisson-bracket","display_name":"Poisson bracket","score":0.7446138858795166},{"id":"https://openalex.org/keywords/diffeomorphism","display_name":"Diffeomorphism","score":0.6255502700805664},{"id":"https://openalex.org/keywords/phase-space","display_name":"Phase space","score":0.5890654921531677},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5886071920394897},{"id":"https://openalex.org/keywords/lie-group","display_name":"Lie group","score":0.5331016778945923},{"id":"https://openalex.org/keywords/semidirect-product","display_name":"Semidirect product","score":0.48615285754203796},{"id":"https://openalex.org/keywords/isentropic-process","display_name":"Isentropic process","score":0.4309196472167969},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.4197835922241211},{"id":"https://openalex.org/keywords/symplectic-geometry","display_name":"Symplectic geometry","score":0.41877883672714233},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3736805319786072},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3623524308204651},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.35848313570022583},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.34024518728256226},{"id":"https://openalex.org/keywords/lie-algebra","display_name":"Lie algebra","score":0.33865422010421753},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.18700289726257324},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1591198742389679}],"concepts":[{"id":"https://openalex.org/C188845816","wikidata":"https://www.wikidata.org/wiki/Q1052775","display_name":"Poisson bracket","level":3,"score":0.7446138858795166},{"id":"https://openalex.org/C47556283","wikidata":"https://www.wikidata.org/wiki/Q1058314","display_name":"Diffeomorphism","level":2,"score":0.6255502700805664},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.5890654921531677},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5886071920394897},{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.5331016778945923},{"id":"https://openalex.org/C75066664","wikidata":"https://www.wikidata.org/wiki/Q291126","display_name":"Semidirect product","level":3,"score":0.48615285754203796},{"id":"https://openalex.org/C172959903","wikidata":"https://www.wikidata.org/wiki/Q907271","display_name":"Isentropic process","level":2,"score":0.4309196472167969},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4197835922241211},{"id":"https://openalex.org/C168619227","wikidata":"https://www.wikidata.org/wiki/Q2190991","display_name":"Symplectic geometry","level":2,"score":0.41877883672714233},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3736805319786072},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3623524308204651},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.35848313570022583},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.34024518728256226},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.33865422010421753},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.18700289726257324},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1591198742389679},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.3390/e22111241","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e22111241","pdf_url":"https://www.mdpi.com/1099-4300/22/11/1241/pdf?version=1604488122","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:33287009","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/33287009","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:https://orca.cardiff.ac.uk:136077","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306401195","display_name":"ORCA Online Research @Cardiff (Cardiff University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79510175","host_organization_name":"Cardiff University","host_organization_lineage":["https://openalex.org/I79510175"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:doaj.org/article:d279f969da8e4dfa80287c8e92711dfb","is_oa":true,"landing_page_url":"https://doaj.org/article/d279f969da8e4dfa80287c8e92711dfb","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 22, Iss 11, p 1241 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/22/11/1241/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e22111241","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 22; Issue 11; Pages: 1241","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:7712039","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/7712039","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/e22111241","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e22111241","pdf_url":"https://www.mdpi.com/1099-4300/22/11/1241/pdf?version=1604488122","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":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3088944539.pdf","grobid_xml":"https://content.openalex.org/works/W3088944539.grobid-xml"},"referenced_works_count":50,"referenced_works":["https://openalex.org/W437609271","https://openalex.org/W1534305016","https://openalex.org/W1588860486","https://openalex.org/W1921530130","https://openalex.org/W1966368036","https://openalex.org/W1979713244","https://openalex.org/W1984533458","https://openalex.org/W1986077531","https://openalex.org/W1994088960","https://openalex.org/W2001215954","https://openalex.org/W2006266826","https://openalex.org/W2009541625","https://openalex.org/W2010392208","https://openalex.org/W2012393256","https://openalex.org/W2018760935","https://openalex.org/W2028724137","https://openalex.org/W2033360875","https://openalex.org/W2047062138","https://openalex.org/W2057455674","https://openalex.org/W2070077284","https://openalex.org/W2090924180","https://openalex.org/W2092272609","https://openalex.org/W2104241561","https://openalex.org/W2106477228","https://openalex.org/W2121581155","https://openalex.org/W2130006697","https://openalex.org/W2480162062","https://openalex.org/W2593529653","https://openalex.org/W2962757225","https://openalex.org/W2974342273","https://openalex.org/W3010257371","https://openalex.org/W3013347551","https://openalex.org/W3024151287","https://openalex.org/W3090235204","https://openalex.org/W3100972644","https://openalex.org/W3101290746","https://openalex.org/W3102966011","https://openalex.org/W3106117827","https://openalex.org/W4205727720","https://openalex.org/W4213170058","https://openalex.org/W4229672964","https://openalex.org/W4234144990","https://openalex.org/W4244308380","https://openalex.org/W4245017101","https://openalex.org/W4248008043","https://openalex.org/W4292023748","https://openalex.org/W6615272508","https://openalex.org/W6623084272","https://openalex.org/W6640064158","https://openalex.org/W6676009748"],"related_works":["https://openalex.org/W2038056514","https://openalex.org/W1940683986","https://openalex.org/W2964299164","https://openalex.org/W4300636709","https://openalex.org/W2379640127","https://openalex.org/W3102972417","https://openalex.org/W2003243206","https://openalex.org/W2099519649","https://openalex.org/W2261037252","https://openalex.org/W1951894854"],"abstract_inverted_index":{"We":[0,33,97,116],"review":[1],"a":[2,59,65,100,109],"modern":[3],"differential":[4],"geometric":[5],"description":[6],"of":[7,13,47,68,102,108,121,146,149,188],"fluid":[8,54],"isentropic":[9,122],"motion":[10,55,130],"and":[11,64,127,135,160,185],"features":[12],"it":[14],"including":[15],"diffeomorphism":[16],"group":[17,180],"structure,":[18],"modelling":[19],"the":[20,29,35,42,45,48,53,69,78,83,87,103,118,132,158,170,189],"related":[21,49,129,136],"dynamics,":[22,38],"as":[23,25,58],"well":[24],"its":[26,74,128],"compatibility":[27],"with":[28,174],"quasi-stationary":[30],"thermodynamical":[31],"constraints.":[32],"analyze":[34],"adiabatic":[36],"liquid":[37,114,167],"within":[39,131],"which,":[40],"following":[41],"general":[43],"approach,":[44],"nature":[46],"Poissonian":[50],"structure":[51,72,120],"on":[52,73,82,169],"phase":[56,125,171],"space":[57,76,85,126,172],"semidirect":[60,89],"Banach":[61],"groups":[62],"product,":[63],"natural":[66],"reduction":[67],"canonical":[70,190],"symplectic":[71],"cotangent":[75],"to":[77,86,176],"classical":[79],"Lie-Poisson":[80,191],"bracket":[81,193],"adjoint":[84],"corresponding":[88],"Lie":[90],"algebras":[91],"product":[92],"are":[93],"explained":[94],"in":[95,106,157],"detail.":[96],"also":[98,183],"present":[99],"modification":[101],"Hamiltonian":[104,133],"analysis":[105,134],"case":[107],"flow":[110],"governed":[111],"by":[112],"isothermal":[113],"dynamics.":[115],"study":[117],"differential-geometric":[119,163],"magneto-hydrodynamic":[123,151],"superfluid":[124],"invariant":[137,173],"theory.":[138],"In":[139],"particular,":[140],"we":[141],"construct":[142],"an":[143,177],"infinite":[144],"hierarchy":[145],"different":[147],"kinds":[148],"integral":[150],"invariants,":[152],"generalizing":[153],"those":[154],"previously":[155],"constructed":[156],"literature,":[159],"analyzing":[161],"their":[162],"origins.":[164],"A":[165],"charged":[166],"dynamics":[168],"respect":[175],"abelian":[178],"gauge":[179],"transformation":[181],"is":[182,194],"investigated,":[184],"some":[186],"generalizations":[187],"type":[192],"presented.":[195]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
