{"id":"https://openalex.org/W2773814169","doi":"https://doi.org/10.1137/18m1178360","title":"A Ginzburg--Landau-Type Problem for Highly Anisotropic Nematic Liquid Crystals","display_name":"A Ginzburg--Landau-Type Problem for Highly Anisotropic Nematic Liquid Crystals","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2773814169","doi":"https://doi.org/10.1137/18m1178360","mag":"2773814169"},"language":"en","primary_location":{"id":"doi:10.1137/18m1178360","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1178360","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1712.00493","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005239381","display_name":"Dmitry Golovaty","orcid":"https://orcid.org/0000-0003-0696-2211"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Dmitry Golovaty","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033685679","display_name":"Peter Sternberg","orcid":"https://orcid.org/0000-0002-5955-5612"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Peter Sternberg","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5077917583","display_name":"Raghavendra Venkatraman","orcid":"https://orcid.org/0009-0002-7667-7598"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Raghavendra Venkatraman","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5005239381"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.00057411,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"51","issue":"1","first_page":"276","last_page":"320"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10306","display_name":"Liquid Crystal Research Advancements","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2504","display_name":"Electronic, Optical and Magnetic Materials"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10306","display_name":"Liquid Crystal Research Advancements","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2504","display_name":"Electronic, Optical and Magnetic Materials"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9905999898910522,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9894999861717224,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/nabla-symbol","display_name":"Nabla symbol","score":0.7659450769424438},{"id":"https://openalex.org/keywords/liquid-crystal","display_name":"Liquid crystal","score":0.7407904863357544},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.680785596370697},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.6597250699996948},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5657181739807129},{"id":"https://openalex.org/keywords/anisotropy","display_name":"Anisotropy","score":0.49951887130737305},{"id":"https://openalex.org/keywords/dirichlet-boundary-condition","display_name":"Dirichlet boundary condition","score":0.46300697326660156},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.45663338899612427},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.4483658969402313},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4157765507698059},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.35944366455078125},{"id":"https://openalex.org/keywords/condensed-matter-physics","display_name":"Condensed matter physics","score":0.3008173704147339},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.21710675954818726},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.21477776765823364}],"concepts":[{"id":"https://openalex.org/C54207081","wikidata":"https://www.wikidata.org/wiki/Q937750","display_name":"Nabla symbol","level":3,"score":0.7659450769424438},{"id":"https://openalex.org/C13274807","wikidata":"https://www.wikidata.org/wiki/Q203989","display_name":"Liquid crystal","level":2,"score":0.7407904863357544},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.680785596370697},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6597250699996948},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5657181739807129},{"id":"https://openalex.org/C85725439","wikidata":"https://www.wikidata.org/wiki/Q466686","display_name":"Anisotropy","level":2,"score":0.49951887130737305},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.46300697326660156},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.45663338899612427},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.4483658969402313},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4157765507698059},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.35944366455078125},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.3008173704147339},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.21710675954818726},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.21477776765823364},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"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/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/18m1178360","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1178360","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1712.00493","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1712.00493","pdf_url":"https://arxiv.org/pdf/1712.00493","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"mag:2773814169","is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/1712.00493","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1712.00493","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1712.00493","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1712.00493","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1712.00493","pdf_url":"https://arxiv.org/pdf/1712.00493","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G288238064","display_name":null,"funder_award_id":"DMS-1729538","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6423680530","display_name":null,"funder_award_id":"DMS-1362879","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7854329968","display_name":null,"funder_award_id":"DMS-1101290","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309291","display_name":"Indiana University","ror":"https://ror.org/01kg8sb98"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2773814169.pdf","grobid_xml":"https://content.openalex.org/works/W2773814169.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W1485178947","https://openalex.org/W1503076391","https://openalex.org/W1518472176","https://openalex.org/W1600845614","https://openalex.org/W1970240635","https://openalex.org/W1997753603","https://openalex.org/W2005216696","https://openalex.org/W2013381870","https://openalex.org/W2017962183","https://openalex.org/W2025562870","https://openalex.org/W2039925534","https://openalex.org/W2041681101","https://openalex.org/W2056402155","https://openalex.org/W2073030855","https://openalex.org/W2076582418","https://openalex.org/W2078155977","https://openalex.org/W2095409038","https://openalex.org/W2142981887","https://openalex.org/W2153365756","https://openalex.org/W2325300816","https://openalex.org/W2346459980","https://openalex.org/W2595348797","https://openalex.org/W2963083408"],"related_works":["https://openalex.org/W2902931628","https://openalex.org/W2932570839","https://openalex.org/W2612441315","https://openalex.org/W2951288866","https://openalex.org/W1992313030","https://openalex.org/W2963561905","https://openalex.org/W2089211776","https://openalex.org/W3117331192","https://openalex.org/W3191167316","https://openalex.org/W3010362608","https://openalex.org/W3035074531","https://openalex.org/W3105834505","https://openalex.org/W3102108215","https://openalex.org/W2898534283","https://openalex.org/W3135776917","https://openalex.org/W1753889080","https://openalex.org/W1502197581","https://openalex.org/W2992120299","https://openalex.org/W3207801893","https://openalex.org/W2963057656"],"abstract_inverted_index":{"We":[0,78,116,153,174],"carry":[1],"out":[2],"an":[3,97],"asymptotic":[4],"analysis":[5],"of":[6,14,76,90,104,111,138,147,167,178,185],"a":[7,54,64,72,80,88,91,130,136,165],"variational":[8,139],"problem":[9],"relevant":[10],"in":[11,107],"the":[12,25,83,102,105,108,112,118,123,156,176],"studies":[13],"nematic":[15,114],"liquid":[16],"crystalline":[17],"films":[18],"when":[19],"one":[20],"elastic":[21],"constant":[22],"dominates":[23],"over":[24],"others,":[26],"namely,":[27],"$":[28,47,62],"\\inf":[29],"E_\\varepsilon(u)$,":[30],"where":[31],"$E_\\varepsilon(u)":[32],":=":[33],"\\frac{1}{2}\\int_\\Omega":[34],"\\left\\{\\varepsilon\\,|\\nabla":[35],"u|^2":[36],"+":[37,42],"\\frac{1}{\\varepsilon}":[38],"\\,(|u|^2":[39],"-":[40],"1)^2":[41],"L":[43],"\\,(\\mathrm{div}\\,":[44],"u)^2\\right\\}":[45],"\\,dx.":[46],"Here":[48],"$u:":[49],"\\Omega":[50],"\\to":[51],"\\mathbb{R}^2$":[52],"is":[53,63,71,87],"vector":[55],"field,":[56],"$0":[57],"<":[58],"\\varepsilon":[59],"\\ll":[60],"1":[61],"small":[65],"parameter,":[66],"and":[67,96,121,150],"$L":[68],">":[69],"0$":[70],"fixed":[73],"constant,":[74],"independent":[75],"$\\varepsilon$.":[77],"identify":[79],"candidate":[81,128],"for":[82,126,141,159],"$\\Gamma$-limit":[84],"$E_0$,":[85],"which":[86],"sum":[89],"bulk":[92],"term":[93],"penalizing":[94],"divergence":[95],"Aviles--Giga-type":[98],"wall":[99],"energy":[100],"involving":[101],"cube":[103],"jump":[106],"tangential":[109],"component":[110],"$\\mathbb{S}^1$-valued":[113],"director.":[115],"establish":[117],"lower":[119],"bound":[120],"provide":[122],"recovery":[124],"sequence":[125],"this":[127],"within":[129],"restricted":[131],"class.":[132],"Then":[133],"we":[134,188],"consider":[135],"set":[137],"problems":[140],"$E_0$":[142,160,186],"arising":[143],"from":[144],"various":[145],"choices":[146],"domain":[148],"geometry":[149],"boundary":[151],"conditions.":[152],"demonstrate":[154],"that":[155,171,187],"criticality":[157],"conditions":[158],"can":[161],"be":[162],"expressed":[163],"as":[164],"pair":[166],"scalar":[168],"conservation":[169],"laws":[170],"share":[172],"characteristics.":[173],"use":[175],"method":[177],"characteristics":[179],"to":[180],"analytically":[181],"construct":[182],"critical":[183],"points":[184],"observe":[189],"numerically.":[190]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2022-09-26T00:00:00"}
