{"id":"https://openalex.org/W2232537544","doi":"https://doi.org/10.1137/15m103844x","title":"A Finite Element Method for Nematic Liquid Crystals with Variable Degree of Orientation","display_name":"A Finite Element Method for Nematic Liquid Crystals with Variable Degree of Orientation","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2232537544","doi":"https://doi.org/10.1137/15m103844x","mag":"2232537544"},"language":"en","primary_location":{"id":"doi:10.1137/15m103844x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m103844x","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1601.00037","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040883953","display_name":"Ricardo H. Nochetto","orcid":"https://orcid.org/0009-0002-8895-1144"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ricardo H. Nochetto","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037361022","display_name":"Shawn W. Walker","orcid":"https://orcid.org/0000-0002-8027-5789"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shawn W. Walker","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5029100440","display_name":"Wujun Zhang","orcid":"https://orcid.org/0000-0003-4066-8534"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wujun Zhang","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5040883953"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6175,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.82035844,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"55","issue":"3","first_page":"1357","last_page":"1386"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"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/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9677000045776367,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9553999900817871,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/liquid-crystal","display_name":"Liquid crystal","score":0.6990500092506409},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6719902157783508},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6650484204292297},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5764663219451904},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.5755159854888916},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.5572150349617004},{"id":"https://openalex.org/keywords/orientation","display_name":"Orientation (vector space)","score":0.49501723051071167},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.49434518814086914},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.47857335209846497},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.44143572449684143},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.4244599938392639},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.28561532497406006},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.249171644449234},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.14567464590072632},{"id":"https://openalex.org/keywords/condensed-matter-physics","display_name":"Condensed matter physics","score":0.09460625052452087}],"concepts":[{"id":"https://openalex.org/C13274807","wikidata":"https://www.wikidata.org/wiki/Q203989","display_name":"Liquid crystal","level":2,"score":0.6990500092506409},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6719902157783508},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6650484204292297},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5764663219451904},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.5755159854888916},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.5572150349617004},{"id":"https://openalex.org/C16345878","wikidata":"https://www.wikidata.org/wiki/Q107472979","display_name":"Orientation (vector space)","level":2,"score":0.49501723051071167},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.49434518814086914},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.47857335209846497},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.44143572449684143},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.4244599938392639},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.28561532497406006},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.249171644449234},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.14567464590072632},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.09460625052452087},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/15m103844x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m103844x","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1601.00037","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1601.00037","pdf_url":"https://arxiv.org/pdf/1601.00037","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":"pmh:oai:repository.lsu.edu:mathematics_pubs-2796","is_oa":false,"landing_page_url":"https://repository.lsu.edu/mathematics_pubs/1794","pdf_url":null,"source":{"id":"https://openalex.org/S4210169993","display_name":"Civil War Book Review","issn_l":"1528-6592","issn":["1528-6592"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310315936","host_organization_name":"Louisiana State University","host_organization_lineage":["https://openalex.org/P4310315936"],"host_organization_lineage_names":["Louisiana State University"],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty Publications","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1601.00037","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1601.00037","pdf_url":"https://arxiv.org/pdf/1601.00037","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":[{"score":0.41999998688697815,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[{"id":"https://openalex.org/G1681180284","display_name":null,"funder_award_id":"DMS-1411808","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4816005617","display_name":null,"funder_award_id":"1411808","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5681886212","display_name":"Numerical Analysis and Methods for Simulating Moving Interfaces and Controlling Shape","funder_award_id":"1418994","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6993189578","display_name":"CAREER:   Numerical Methods For Liquid Crystals And Their Optimal Design","funder_award_id":"1555222","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7709308483","display_name":null,"funder_award_id":"DMS-1418994","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G88013652","display_name":null,"funder_award_id":"DMS-1555222","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/F4320310578","display_name":"University of Maryland","ror":"https://ror.org/01r0c1p88"},{"id":"https://openalex.org/F4320321516","display_name":"Centre Elile Borel, Institut Henri-Poincar\u00e9","ror":"https://ror.org/05dfxeg46"},{"id":"https://openalex.org/F4320328291","display_name":"Institut Henri Poincar\u00e9","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W1569061876","https://openalex.org/W1968731434","https://openalex.org/W1972001314","https://openalex.org/W1997775923","https://openalex.org/W1997972181","https://openalex.org/W2013377070","https://openalex.org/W2015660465","https://openalex.org/W2019798593","https://openalex.org/W2025043986","https://openalex.org/W2025664518","https://openalex.org/W2029449803","https://openalex.org/W2034029678","https://openalex.org/W2034174857","https://openalex.org/W2035427049","https://openalex.org/W2036523872","https://openalex.org/W2039925534","https://openalex.org/W2040456154","https://openalex.org/W2045933447","https://openalex.org/W2050863519","https://openalex.org/W2050969603","https://openalex.org/W2052084709","https://openalex.org/W2058578329","https://openalex.org/W2063041321","https://openalex.org/W2064050389","https://openalex.org/W2065357863","https://openalex.org/W2071700284","https://openalex.org/W2084889427","https://openalex.org/W2087755793","https://openalex.org/W2088152649","https://openalex.org/W2110203116","https://openalex.org/W2123896152","https://openalex.org/W2124673822","https://openalex.org/W2130641059","https://openalex.org/W2131368873","https://openalex.org/W2146329425","https://openalex.org/W2156201971","https://openalex.org/W3100841396"],"related_works":["https://openalex.org/W2069570482","https://openalex.org/W2080612831","https://openalex.org/W2018581211","https://openalex.org/W4226524568","https://openalex.org/W2915257559","https://openalex.org/W3157084023","https://openalex.org/W2094386919","https://openalex.org/W2018289167","https://openalex.org/W2123791017","https://openalex.org/W1982804439"],"abstract_inverted_index":{"We":[0,78,112,129,151],"consider":[1],"the":[2,37,54,58,85,97,123,161,173,179],"simplest":[3],"one-constant":[4],"model,":[5],"put":[6],"forward":[7],"by":[8,25],"J.":[9],"Ericksen,":[10],"for":[11,57,65,69,135,178],"nematic":[12],"liquid":[13,86,182],"crystals":[14],"with":[15,89],"variable":[16],"degree":[17,32],"of":[18,33,44,84,115,175,181,191],"orientation.":[19],"The":[20,168],"equilibrium":[21,138],"state":[22],"is":[23,108],"described":[24],"a":[26,42,48,61,80,131,145],"director":[27],"field":[28],"$\\mathbf{n}\\mathbf{n}$":[29],"and":[30,47,71,103,110,140,156,189],"its":[31],"orientation":[34],"$s$,":[35],"where":[36],"pair":[38],"$(s,":[39],"\\mathbf{n})$":[40],"minimizes":[41],"sum":[43],"Frank-like":[45],"energies":[46],"double":[49],"well":[50],"potential.":[51],"In":[52],"particular,":[53],"Euler--Lagrange":[55],"equations":[56],"minimizer":[59],"contain":[60],"degenerate":[62,98],"elliptic":[63,99],"equation":[64],"$\\mathbf{n}$,":[66],"which":[67],"allows":[68],"line":[70],"plane":[72],"defects":[73],"to":[74,119,127,159,164],"have":[75],"finite":[76,92],"energy.":[77],"present":[79,152],"structure":[81],"preserving":[82],"discretization":[83],"crystal":[87,183],"energy":[88,148],"piecewise":[90],"linear":[91],"elements":[93],"that":[94,106,142],"can":[95],"handle":[96,165],"part":[100],"without":[101],"regularization,":[102],"we":[104],"show":[105],"it":[107,143],"consistent":[109],"stable.":[111],"prove":[113,141],"$\\Gamma$-convergence":[114],"discrete":[116,137],"global":[117],"minimizers":[118],"continuous":[120],"ones":[121],"as":[122],"mesh":[124],"size":[125],"goes":[126],"zero.":[128],"develop":[130],"quasi-gradient":[132],"flow":[133],"scheme":[134],"computing":[136],"solutions":[139],"has":[144],"strictly":[146],"monotone":[147],"decreasing":[149],"property.":[150],"simulations":[153],"in":[154],"two":[155],"three":[157],"dimensions":[158],"illustrate":[160],"method's":[162],"ability":[163],"nontrivial":[166],"defects.":[167],"following":[169],"online":[170],"video":[171],"illustrates":[172],"role":[174],"numerical":[176],"analysis":[177],"simulation":[180],"phenomena:":[184],"[Walker,":[185],"Shawn.":[186],"\u201cMathematical":[187],"Modeling":[188],"Simulation":[190],"Nematic":[192],"Liquid":[193],"Crystals":[194],"(A":[195],"Montage).\u201d":[196],"YouTube":[197],"video,":[198],"04:13.":[199],"Posted":[200],"March":[201],"6,":[202],"2016.":[203],"http://www.youtube.com/watch?v=pWWw7_6cQ-U].":[204]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2020-11-23T00:00:00"}
