{"id":"https://openalex.org/W1926161541","doi":"https://doi.org/10.1137/15m1028960","title":"Branched Microstructures in the Ginzburg--Landau Model of Type-I Superconductors","display_name":"Branched Microstructures in the Ginzburg--Landau Model of Type-I Superconductors","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W1926161541","doi":"https://doi.org/10.1137/15m1028960","mag":"1926161541"},"language":"en","primary_location":{"id":"doi:10.1137/15m1028960","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1028960","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":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1507.00836","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086193278","display_name":"Sergio Conti","orcid":"https://orcid.org/0000-0001-7987-9174"},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Sergio Conti","raw_affiliation_strings":["University of Bonn"],"affiliations":[{"raw_affiliation_string":"University of Bonn","institution_ids":["https://openalex.org/I135140700"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073872018","display_name":"F\u00e9lix Otto","orcid":"https://orcid.org/0000-0002-2327-5950"},"institutions":[{"id":"https://openalex.org/I149899117","display_name":"Max Planck Society","ror":"https://ror.org/01hhn8329","country_code":"DE","type":"nonprofit","lineage":["https://openalex.org/I149899117"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Felix Otto","raw_affiliation_strings":["Max Planck Institute for Mathematics in the Sciences#TAB#"],"affiliations":[{"raw_affiliation_string":"Max Planck Institute for Mathematics in the Sciences#TAB#","institution_ids":["https://openalex.org/I149899117"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112203717","display_name":"Sylvia Serfaty","orcid":null},"institutions":[{"id":"https://openalex.org/I4210091327","display_name":"Max Planck Institute for Mathematics in the Sciences","ror":"https://ror.org/00ez2he07","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210091327"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Sylvia Serfaty","raw_affiliation_strings":["MPI-MiS - Max-Planck-Institut f\u00fcr Mathematik in den Naturwissenschaften (Inselstra\u00dfe 22, 04103 Leipzig, Deutschland - Germany)"],"affiliations":[{"raw_affiliation_string":"MPI-MiS - Max-Planck-Institut f\u00fcr Mathematik in den Naturwissenschaften (Inselstra\u00dfe 22, 04103 Leipzig, Deutschland - Germany)","institution_ids":["https://openalex.org/I4210091327"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5086193278"],"corresponding_institution_ids":["https://openalex.org/I135140700"],"apc_list":null,"apc_paid":null,"fwci":1.6236,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.82222848,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"48","issue":"4","first_page":"2994","last_page":"3034"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.9994999766349792,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9993000030517578,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9991000294685364,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/ansatz","display_name":"Ansatz","score":0.7447801828384399},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.72834712266922},{"id":"https://openalex.org/keywords/superconductivity","display_name":"Superconductivity","score":0.6765909194946289},{"id":"https://openalex.org/keywords/magnetic-field","display_name":"Magnetic field","score":0.6219912767410278},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5739547610282898},{"id":"https://openalex.org/keywords/condensed-matter-physics","display_name":"Condensed matter physics","score":0.5612072944641113},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5109983682632446},{"id":"https://openalex.org/keywords/slab","display_name":"Slab","score":0.5068774819374084},{"id":"https://openalex.org/keywords/energy-functional","display_name":"Energy functional","score":0.5058512687683105},{"id":"https://openalex.org/keywords/type-ii-superconductor","display_name":"Type-II superconductor","score":0.4703417420387268},{"id":"https://openalex.org/keywords/perpendicular","display_name":"Perpendicular","score":0.46174269914627075},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.44496867060661316},{"id":"https://openalex.org/keywords/ginzburg\u2013landau-theory","display_name":"Ginzburg\u2013Landau theory","score":0.42015182971954346},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4172390103340149},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3261576294898987},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3258799910545349},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.27285951375961304},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1584797501564026}],"concepts":[{"id":"https://openalex.org/C130979935","wikidata":"https://www.wikidata.org/wiki/Q568954","display_name":"Ansatz","level":2,"score":0.7447801828384399},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.72834712266922},{"id":"https://openalex.org/C54101563","wikidata":"https://www.wikidata.org/wiki/Q124131","display_name":"Superconductivity","level":2,"score":0.6765909194946289},{"id":"https://openalex.org/C115260700","wikidata":"https://www.wikidata.org/wiki/Q11408","display_name":"Magnetic field","level":2,"score":0.6219912767410278},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5739547610282898},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.5612072944641113},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5109983682632446},{"id":"https://openalex.org/C113740112","wikidata":"https://www.wikidata.org/wiki/Q5904738","display_name":"Slab","level":2,"score":0.5068774819374084},{"id":"https://openalex.org/C191640071","wikidata":"https://www.wikidata.org/wiki/Q5377056","display_name":"Energy functional","level":2,"score":0.5058512687683105},{"id":"https://openalex.org/C124932887","wikidata":"https://www.wikidata.org/wiki/Q4919231","display_name":"Type-II superconductor","level":3,"score":0.4703417420387268},{"id":"https://openalex.org/C199631012","wikidata":"https://www.wikidata.org/wiki/Q205034","display_name":"Perpendicular","level":2,"score":0.46174269914627075},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.44496867060661316},{"id":"https://openalex.org/C163192330","wikidata":"https://www.wikidata.org/wiki/Q900905","display_name":"Ginzburg\u2013Landau theory","level":3,"score":0.42015182971954346},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4172390103340149},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3261576294898987},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3258799910545349},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.27285951375961304},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1584797501564026},{"id":"https://openalex.org/C8058405","wikidata":"https://www.wikidata.org/wiki/Q46255","display_name":"Geophysics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/15m1028960","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1028960","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:1507.00836","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1507.00836","pdf_url":"https://arxiv.org/pdf/1507.00836","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":"","raw_type":"text"},{"id":"pmh:oai:HAL:hal-01377811v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01377811","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Mathematical Analysis, 2016","raw_type":"Journal articles"},{"id":"pmh:oai:edoc.mpg.de:729148","is_oa":false,"landing_page_url":"http://edoc.mpg.de/729148","pdf_url":null,"source":{"id":"https://openalex.org/S4406922265","display_name":"Max Planck Institute for Plasma Physics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Mathematical Analysis, v.48, 2994-3034 (2016)","raw_type":"Article"},{"id":"doi:10.48550/arxiv.1507.00836","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1507.00836","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:1507.00836","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1507.00836","pdf_url":"https://arxiv.org/pdf/1507.00836","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":"","raw_type":"text"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.47999998927116394}],"awards":[{"id":"https://openalex.org/G3501886293","display_name":null,"funder_award_id":"Sonderforschungsbereich 1060","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320322893","display_name":"Institut Universitaire de France","ror":"https://ror.org/055khg266"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1497769420","https://openalex.org/W1966779513","https://openalex.org/W1976263579","https://openalex.org/W1978865327","https://openalex.org/W1994473330","https://openalex.org/W1996873638","https://openalex.org/W2001428881","https://openalex.org/W2004860839","https://openalex.org/W2015233417","https://openalex.org/W2019382745","https://openalex.org/W2036304670","https://openalex.org/W2039902237","https://openalex.org/W2062546867","https://openalex.org/W2066181993","https://openalex.org/W2072679197","https://openalex.org/W2078123722","https://openalex.org/W2085818229","https://openalex.org/W2090852002","https://openalex.org/W2092688833","https://openalex.org/W2109846132","https://openalex.org/W2125821539","https://openalex.org/W2150401053","https://openalex.org/W2163055580","https://openalex.org/W2171154348","https://openalex.org/W2963322755","https://openalex.org/W2964027309","https://openalex.org/W3102087632","https://openalex.org/W3104343180","https://openalex.org/W3106058975"],"related_works":["https://openalex.org/W2004947065","https://openalex.org/W2052662779","https://openalex.org/W793000188","https://openalex.org/W3028180257","https://openalex.org/W2031172429","https://openalex.org/W2273072181","https://openalex.org/W2549759121","https://openalex.org/W2048498236","https://openalex.org/W2116167311","https://openalex.org/W2015233417"],"abstract_inverted_index":{"We":[0,33],"consider":[1],"the":[2,10,31,35,40,46,49,52,60,87,90,101,104,115,118,121,126],"Ginzburg--Landau":[3],"energy":[4,42],"for":[5],"a":[6],"type-I":[7],"superconductor":[8],"in":[9,43,117],"shape":[11],"of":[12,39,45,48,89],"an":[13,21,75,108],"infinite":[14],"three-dimensional":[15],"slab,":[16],"with":[17,20,96],"two-dimensional":[18],"periodicity,":[19],"applied":[22,53],"magnetic":[23,54,111],"field":[24,55,112],"which":[25,79],"is":[26,56,68],"uniform":[27,110],"and":[28,59,74,82],"perpendicular":[29],"to":[30,107,125],"slab.":[32],"determine":[34],"optimal":[36,65],"scaling":[37,66,98],"law":[38,67],"minimal":[41],"terms":[44],"parameters":[47],"problem":[50],"when":[51],"sufficiently":[57,62],"small":[58],"sample":[61],"thick.":[63],"This":[64],"proven":[69],"via":[70],"ansatz-free":[71],"lower":[72],"bounds":[73],"explicit":[76],"branching":[77,105],"construction":[78],"refines":[80],"further":[81,83],"as":[84],"one":[85,120],"approaches":[86],"surface":[88],"sample.":[91],"Two":[92],"different":[93,97],"regimes":[94],"appear,":[95],"exponents.":[99],"In":[100],"first":[102],"regime,":[103],"leads":[106],"almost":[109],"pattern":[113],"on":[114],"boundary;":[116],"second":[119],"inhomogeneity":[122],"survives":[123],"up":[124],"boundary.":[127]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3}],"updated_date":"2026-03-25T23:56:10.502304","created_date":"2016-06-24T00:00:00"}
