{"id":"https://openalex.org/W1985309651","doi":"https://doi.org/10.1137/130935963","title":"The Ginzburg--Landau Order Parameter near the Second Critical Field","display_name":"The Ginzburg--Landau Order Parameter near the Second Critical Field","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W1985309651","doi":"https://doi.org/10.1137/130935963","mag":"1985309651"},"language":"en","primary_location":{"id":"doi:10.1137/130935963","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130935963","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":"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/A5103511976","display_name":"Ayman Kachmar","orcid":null},"institutions":[{"id":"https://openalex.org/I911468752","display_name":"Lebanese International University","ror":"https://ror.org/034agrd14","country_code":"LB","type":"education","lineage":["https://openalex.org/I911468752"]},{"id":"https://openalex.org/I160368002","display_name":"Lebanese University","ror":"https://ror.org/05x6qnc69","country_code":"LB","type":"education","lineage":["https://openalex.org/I160368002"]}],"countries":["LB"],"is_corresponding":true,"raw_author_name":"Ayman Kachmar","raw_affiliation_strings":["Lebanese International University, Beirut, Lebanon","Department of Mathematics, Lebanese University, Hadat, Lebanon; School of Arts and Sciences,"],"affiliations":[{"raw_affiliation_string":"Lebanese International University, Beirut, Lebanon","institution_ids":["https://openalex.org/I911468752"]},{"raw_affiliation_string":"Department of Mathematics, Lebanese University, Hadat, Lebanon; School of Arts and Sciences,","institution_ids":["https://openalex.org/I160368002"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5103511976"],"corresponding_institution_ids":["https://openalex.org/I160368002","https://openalex.org/I911468752"],"apc_list":null,"apc_paid":null,"fwci":4.4822,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.94206316,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"46","issue":"1","first_page":"572","last_page":"587"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10037","display_name":"Physics of Superconductivity and Magnetism","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter 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/T10382","display_name":"Quantum and electron transport phenomena","score":0.998199999332428,"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/ginzburg\u2013landau-theory","display_name":"Ginzburg\u2013Landau theory","score":0.6816108822822571},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6717347502708435},{"id":"https://openalex.org/keywords/superconductivity","display_name":"Superconductivity","score":0.5834884643554688},{"id":"https://openalex.org/keywords/landau-theory","display_name":"Landau theory","score":0.5565318465232849},{"id":"https://openalex.org/keywords/landau-quantization","display_name":"Landau quantization","score":0.4883134067058563},{"id":"https://openalex.org/keywords/magnetic-field","display_name":"Magnetic field","score":0.47721701860427856},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4723050594329834},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.450487345457077},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4321085512638092},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4183422923088074},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.41805386543273926},{"id":"https://openalex.org/keywords/infinity","display_name":"Infinity","score":0.413896769285202},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3258068561553955},{"id":"https://openalex.org/keywords/condensed-matter-physics","display_name":"Condensed matter physics","score":0.3232540786266327},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2967161536216736},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.21472376585006714},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.08147883415222168},{"id":"https://openalex.org/keywords/phase-transition","display_name":"Phase transition","score":0.08123290538787842}],"concepts":[{"id":"https://openalex.org/C163192330","wikidata":"https://www.wikidata.org/wiki/Q900905","display_name":"Ginzburg\u2013Landau theory","level":3,"score":0.6816108822822571},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6717347502708435},{"id":"https://openalex.org/C54101563","wikidata":"https://www.wikidata.org/wiki/Q124131","display_name":"Superconductivity","level":2,"score":0.5834884643554688},{"id":"https://openalex.org/C201144084","wikidata":"https://www.wikidata.org/wiki/Q1626812","display_name":"Landau theory","level":3,"score":0.5565318465232849},{"id":"https://openalex.org/C50899005","wikidata":"https://www.wikidata.org/wiki/Q277967","display_name":"Landau quantization","level":3,"score":0.4883134067058563},{"id":"https://openalex.org/C115260700","wikidata":"https://www.wikidata.org/wiki/Q11408","display_name":"Magnetic field","level":2,"score":0.47721701860427856},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4723050594329834},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.450487345457077},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4321085512638092},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4183422923088074},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.41805386543273926},{"id":"https://openalex.org/C7321624","wikidata":"https://www.wikidata.org/wiki/Q205","display_name":"Infinity","level":2,"score":0.413896769285202},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3258068561553955},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.3232540786266327},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2967161536216736},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.21472376585006714},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.08147883415222168},{"id":"https://openalex.org/C149288129","wikidata":"https://www.wikidata.org/wiki/Q185357","display_name":"Phase transition","level":2,"score":0.08123290538787842},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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":1,"locations":[{"id":"doi:10.1137/130935963","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130935963","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322377","display_name":"Universit\u00e9 Libanaise","ror":"https://ror.org/05x6qnc69"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1980654830","https://openalex.org/W2018427797","https://openalex.org/W2018449838","https://openalex.org/W2023851009","https://openalex.org/W2036304670","https://openalex.org/W2070831463","https://openalex.org/W2089799684","https://openalex.org/W2495411885"],"related_works":["https://openalex.org/W1969590470","https://openalex.org/W2280449994","https://openalex.org/W2950014500","https://openalex.org/W4301437198","https://openalex.org/W2962941236","https://openalex.org/W2078828991","https://openalex.org/W2019416042","https://openalex.org/W2068177783","https://openalex.org/W1978673548","https://openalex.org/W2029653893"],"abstract_inverted_index":{"In":[0,24],"the":[1,6,11,21,28,31,38,44,48,56,69],"Ginzburg--Landau":[2,49,70],"theory":[3],"of":[4,10,30,60],"superconductivity,":[5],"density":[7],"and":[8,42],"location":[9],"superconducting":[12],"electrons":[13],"are":[14],"measured":[15],"by":[16],"a":[17,53],"complex-valued":[18],"wave":[19],"function,":[20],"order":[22,45,58],"parameter.":[23],"this":[25],"paper,":[26],"when":[27,43],"intensity":[29],"applied":[32],"magnetic":[33],"field":[34],"is":[35,66],"close":[36],"to":[37,73],"second":[39],"critical":[40],"field,":[41],"parameter":[46,71],"minimizes":[47],"functional":[50],"defined":[51],"over":[52],"two-dimensional":[54],"domain,":[55],"leading":[57],"approximation":[59],"its":[61],"$L^2$-norm":[62],"in":[63],"\u201csmall\u201d":[64],"squares":[65],"given":[67],"as":[68],"tends":[72],"infinity.":[74]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
