{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T07:51:05Z","timestamp":1777449065956,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"1-2","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Asymptotic Analysis"],"published-print":{"date-parts":[[2013,7]]},"abstract":"<jats:p>\n                    We consider singular limits of the three-dimensional Ginzburg\u2013Landau functional for a superconductor with thin-film geometry, in a constant external magnetic field. The superconducting domain has characteristic thickness on the scale \u03b5&gt;0, and we consider the simultaneous limit as the thickness \u03b5\u21920 and the Ginzburg\u2013Landau parameter \u03ba\u2192\u221e. We assume that the applied field is strong (on the order of \u03b5\n                    <jats:sup>\u22121<\/jats:sup>\n                    in magnitude) in its components tangential to the film domain, and of order log\u2009\u03ba in its dependence on \u03ba. We prove that the Ginzburg\u2013Landau energy \u0393-converges to an energy associated with a two-obstacle problem, posed on the planar domain which supports the thin film. The same limit is obtained regardless of the relationship between \u03b5 and \u03ba in the limit. Two illustrative examples are presented, each of which demonstrating how the curvature of the film can induce the presence of both (positively oriented) vortices and (negatively oriented) antivortices coexisting in a global minimizer of the energy.\n                  <\/jats:p>","DOI":"10.3233\/asy-2012-1155","type":"journal-article","created":{"date-parts":[[2019,11,29]],"date-time":"2019-11-29T19:27:51Z","timestamp":1575055671000},"page":"127-156","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["Singular limits for thin film superconductors in strong magnetic fields"],"prefix":"10.1177","volume":"83","author":[{"given":"Stan","family":"Alama","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, McMaster University, Hamilton, ON, Canada. E-mails: {alama, bronsard}@mcmaster.ca"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lia","family":"Bronsard","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, McMaster University, Hamilton, ON, Canada. E-mails: {alama, bronsard}@mcmaster.ca"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bernardo","family":"Galv\u00e3o-Sousa","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Toronto, Toronto, ON, Canada. E-mail: beni@math.toronto.edu"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2013,1,1]]},"container-title":["Asymptotic Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2012-1155","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/ASY-2012-1155","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T12:39:54Z","timestamp":1777379994000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/ASY-2012-1155"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,1,1]]},"references-count":0,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2013,7]]}},"alternative-id":["10.3233\/ASY-2012-1155"],"URL":"https:\/\/doi.org\/10.3233\/asy-2012-1155","relation":{},"ISSN":["0921-7134","1875-8576"],"issn-type":[{"value":"0921-7134","type":"print"},{"value":"1875-8576","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,1,1]]}}}