{"id":"https://openalex.org/W2116036133","doi":"https://doi.org/10.1137/080733759","title":"A Catastrophe-Theoretic Approach to Tricritical Points with Application to Liquid Crystals","display_name":"A Catastrophe-Theoretic Approach to Tricritical Points with Application to Liquid Crystals","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2116036133","doi":"https://doi.org/10.1137/080733759","mag":"2116036133"},"language":"en","primary_location":{"id":"doi:10.1137/080733759","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080733759","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/A5087345400","display_name":"Livio Gibelli","orcid":"https://orcid.org/0000-0002-0104-828X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Livio Gibelli","raw_affiliation_strings":["School of Engineering"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Engineering","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030749427","display_name":"Stefano Turzi","orcid":"https://orcid.org/0000-0003-1245-3800"},"institutions":[{"id":"https://openalex.org/I43439940","display_name":"University of Southampton","ror":"https://ror.org/01ryk1543","country_code":"GB","type":"education","lineage":["https://openalex.org/I43439940"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Stefano Turzi","raw_affiliation_strings":["Univ Southampton, University of Southampton"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Univ Southampton, University of Southampton","institution_ids":["https://openalex.org/I43439940"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2754,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.55894777,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"70","issue":"1","first_page":"63","last_page":"76"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10306","display_name":"Liquid Crystal Research Advancements","score":0.9977999925613403,"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":0.9977999925613403,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9890000224113464,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10474","display_name":"Material Dynamics and Properties","score":0.9455999732017517,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/tricritical-point","display_name":"Tricritical point","score":0.8503795862197876},{"id":"https://openalex.org/keywords/phase-diagram","display_name":"Phase diagram","score":0.6870368719100952},{"id":"https://openalex.org/keywords/catastrophe-theory","display_name":"Catastrophe theory","score":0.6406595706939697},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.49205273389816284},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4795498549938202},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.4463644027709961},{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.4435860514640808},{"id":"https://openalex.org/keywords/liquid-crystal","display_name":"Liquid crystal","score":0.43664878606796265},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4137551784515381},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.38756245374679565},{"id":"https://openalex.org/keywords/theoretical-physics","display_name":"Theoretical physics","score":0.36875462532043457},{"id":"https://openalex.org/keywords/condensed-matter-physics","display_name":"Condensed matter physics","score":0.21140840649604797},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.12842422723770142},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.06545644998550415}],"concepts":[{"id":"https://openalex.org/C70850613","wikidata":"https://www.wikidata.org/wiki/Q7841310","display_name":"Tricritical point","level":4,"score":0.8503795862197876},{"id":"https://openalex.org/C85906118","wikidata":"https://www.wikidata.org/wiki/Q186693","display_name":"Phase diagram","level":3,"score":0.6870368719100952},{"id":"https://openalex.org/C33474566","wikidata":"https://www.wikidata.org/wiki/Q1345659","display_name":"Catastrophe theory","level":2,"score":0.6406595706939697},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.49205273389816284},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4795498549938202},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.4463644027709961},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.4435860514640808},{"id":"https://openalex.org/C13274807","wikidata":"https://www.wikidata.org/wiki/Q203989","display_name":"Liquid crystal","level":2,"score":0.43664878606796265},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4137551784515381},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.38756245374679565},{"id":"https://openalex.org/C33332235","wikidata":"https://www.wikidata.org/wiki/Q18362","display_name":"Theoretical physics","level":1,"score":0.36875462532043457},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.21140840649604797},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.12842422723770142},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.06545644998550415},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C187320778","wikidata":"https://www.wikidata.org/wiki/Q1349130","display_name":"Geotechnical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/080733759","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080733759","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.314.4734","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.314.4734","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0808.3555v1.pdf","raw_type":"text"},{"id":"pmh:oai:re.public.polimi.it:11311/564059","is_oa":false,"landing_page_url":"http://hdl.handle.net/11311/564059","pdf_url":null,"source":{"id":"https://openalex.org/S4306400312","display_name":"Virtual Community of Pathological Anatomy (University of Castilla La Mancha)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79189158","host_organization_name":"University of Castilla-La Mancha","host_organization_lineage":["https://openalex.org/I79189158"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W102651561","https://openalex.org/W576014789","https://openalex.org/W1508391401","https://openalex.org/W1596149888","https://openalex.org/W1600845614","https://openalex.org/W1970215649","https://openalex.org/W1971719711","https://openalex.org/W1977605213","https://openalex.org/W1982100316","https://openalex.org/W2001473712","https://openalex.org/W2004191588","https://openalex.org/W2010651006","https://openalex.org/W2013837726","https://openalex.org/W2016295415","https://openalex.org/W2031498546","https://openalex.org/W2054080979","https://openalex.org/W2056448664","https://openalex.org/W2057874652","https://openalex.org/W2064459010","https://openalex.org/W2082185883","https://openalex.org/W2090258588","https://openalex.org/W2095132758","https://openalex.org/W2123407750"],"related_works":["https://openalex.org/W2364546904","https://openalex.org/W2366891651","https://openalex.org/W1985925153","https://openalex.org/W2961079112","https://openalex.org/W1989855437","https://openalex.org/W2028098186","https://openalex.org/W2051116168","https://openalex.org/W2115581514","https://openalex.org/W1965011582","https://openalex.org/W2033077683"],"abstract_inverted_index":{"A":[0],"criterion":[1,12],"to":[2,32,67],"locate":[3],"tricritical":[4,53],"points":[5,54],"in":[6,15,28],"phase":[7],"diagrams":[8],"is":[9,13,71],"proposed.":[10],"The":[11],"formulated":[14],"the":[16,25],"framework":[17],"of":[18],"elementary":[19],"catastrophe":[20],"theory":[21],"and":[22],"encompasses":[23],"all":[24],"existing":[26],"criteria":[27],"that":[29,52],"it":[30],"applies":[31],"systems":[33],"described":[34],"by":[35,58],"a":[36],"generally":[37],"nonsymmetric":[38],"free":[39,59],"energy":[40],"which":[41,61],"can":[42],"depend":[43],"on":[44],"one":[45],"or":[46],"more":[47],"order":[48],"parameters.":[49],"We":[50],"show":[51],"are":[55,62],"necessarily":[56],"given":[57],"energies":[60],"not":[63],"4-determined.":[64],"An":[65],"application":[66],"smectic-C":[68],"liquid":[69],"crystals":[70],"briefly":[72],"discussed.":[73]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
