{"id":"https://openalex.org/W2063275453","doi":"https://doi.org/10.1137/040605916","title":"Energy Maximizers, Negative Temperatures, and Robust Symmetry Breaking in Vortex Dynamics on a Nonrotating Sphere","display_name":"Energy Maximizers, Negative Temperatures, and Robust Symmetry Breaking in Vortex Dynamics on a Nonrotating Sphere","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2063275453","doi":"https://doi.org/10.1137/040605916","mag":"2063275453"},"language":"en","primary_location":{"id":"doi:10.1137/040605916","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040605916","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077796426","display_name":"Chjan C. Lim","orcid":"https://orcid.org/0000-0003-4928-4780"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Chjan C. Lim","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5077796426"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.0626,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.85891898,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"65","issue":"6","first_page":"2093","last_page":"2106"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9998000264167786,"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/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9990000128746033,"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/T10255","display_name":"Oceanographic and Atmospheric Processes","score":0.9876999855041504,"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/enstrophy","display_name":"Enstrophy","score":0.9818986654281616},{"id":"https://openalex.org/keywords/vorticity","display_name":"Vorticity","score":0.6773833632469177},{"id":"https://openalex.org/keywords/vortex","display_name":"Vortex","score":0.6599793434143066},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.5990447402000427},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.572689414024353},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.497466117143631},{"id":"https://openalex.org/keywords/statistical-mechanics","display_name":"Statistical mechanics","score":0.4537435472011566},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.39302459359169006},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.38085293769836426},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3682563900947571},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3201741576194763},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21978476643562317},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.15198183059692383},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15158486366271973}],"concepts":[{"id":"https://openalex.org/C178944513","wikidata":"https://www.wikidata.org/wiki/Q1344391","display_name":"Enstrophy","level":4,"score":0.9818986654281616},{"id":"https://openalex.org/C200114574","wikidata":"https://www.wikidata.org/wiki/Q1143513","display_name":"Vorticity","level":3,"score":0.6773833632469177},{"id":"https://openalex.org/C140820882","wikidata":"https://www.wikidata.org/wiki/Q732722","display_name":"Vortex","level":2,"score":0.6599793434143066},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5990447402000427},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.572689414024353},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.497466117143631},{"id":"https://openalex.org/C99874945","wikidata":"https://www.wikidata.org/wiki/Q188715","display_name":"Statistical mechanics","level":2,"score":0.4537435472011566},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.39302459359169006},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.38085293769836426},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3682563900947571},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3201741576194763},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21978476643562317},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.15198183059692383},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15158486366271973}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/040605916","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040605916","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.8700000047683716}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1549629203","https://openalex.org/W1653619892","https://openalex.org/W1972379194","https://openalex.org/W1974667125","https://openalex.org/W1976526594","https://openalex.org/W1994619370","https://openalex.org/W1995299866","https://openalex.org/W2006204290","https://openalex.org/W2011810852","https://openalex.org/W2014217712","https://openalex.org/W2019364649","https://openalex.org/W2044111149","https://openalex.org/W2046093611","https://openalex.org/W2050353757","https://openalex.org/W2059502240","https://openalex.org/W2078247350","https://openalex.org/W2080676184","https://openalex.org/W2082717960","https://openalex.org/W2090844119","https://openalex.org/W2099743374","https://openalex.org/W2128467881","https://openalex.org/W2146181023","https://openalex.org/W2156362709","https://openalex.org/W2906548191","https://openalex.org/W3186605155","https://openalex.org/W3188897366","https://openalex.org/W4205293050","https://openalex.org/W4214856018","https://openalex.org/W4233882817","https://openalex.org/W4253608785"],"related_works":["https://openalex.org/W2016176385","https://openalex.org/W1994985469","https://openalex.org/W4323315934","https://openalex.org/W3099607407","https://openalex.org/W2064145476","https://openalex.org/W2036933802","https://openalex.org/W2001958875","https://openalex.org/W3198058640","https://openalex.org/W3100088679","https://openalex.org/W2258620507"],"abstract_inverted_index":{"This":[0],"paper":[1],"relates":[2],"the":[3,12,24,35,43,49,69,85,98,128,138],"existence":[4,117],"and":[5,105,118],"uniqueness":[6,119],"of":[7,14,23,30,34,72,97,120,127],"constrained":[8],"energy":[9,121],"maximizers":[10,122],"to":[11,56,112,143],"occurrence":[13],"negative":[15,44,103],"temperatures":[16],"in":[17,48,84,93,123],"a":[18,94,124,134],"recent":[19],"statistical":[20,99],"mechanics":[21],"model":[22,96,140],"energy-enstrophy":[25,100,130,141],"theory.":[26],"We":[27],"construct":[28],"examples":[29],"steady":[31],"state":[32],"solutions":[33],"vorticity":[36,46],"equation":[37],"which":[38,65],"break":[39],"SO(3)":[40],"symmetry":[41],"from":[42],"temperature":[45],"distributions":[47],"spherical":[50,95,139],"model.":[51],"These":[52],"vortex":[53],"states":[54,92],"correspond":[55],"solid-body":[57],"rotation":[58,61],"flows":[59],"at":[60,102,147],"rates":[62],"$\\Theta":[63,77],"$,":[64],"depend":[66],"only":[67],"on":[68],"fixed":[70],"value":[71],"enstrophy":[73],"$\\Gamma$,":[74],"that":[75,87],"is,":[76],"=\\sqrt{\\Gamma":[78],"/(4\\int_{S^2}\\cos^2\\theta\\,":[79],"dx)}$.":[80],"They":[81],"are":[82],"robust":[83],"sense":[86],"they":[88],"constitute":[89],"most":[90],"probable":[91],"theory":[101,131,142],"temperatures,":[104],"have":[106],"exponentially":[107],"large":[108],"Gibbs":[109],"probability":[110],"relative":[111],"any":[113],"other":[114],"macrostates.":[115],"The":[116],"variational":[125],"formulation":[126],"new":[129],"also":[132],"give":[133],"necessary":[135],"condition":[136],"for":[137],"be":[144],"well":[145],"defined":[146],"all":[148],"temperatures.":[149]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
