Publication: Limiting behavior of the ginzburg-landau functional
dc.contributor.coauthor | Jerrard, Robert L. | |
dc.contributor.department | Department of Mathematics | |
dc.contributor.kuauthor | Soner, Halil Mete | |
dc.contributor.schoolcollegeinstitute | College of Sciences | |
dc.date.accessioned | 2024-11-09T23:12:33Z | |
dc.date.issued | 2002 | |
dc.description.abstract | We continue our study of the functional E-0(u) := integral(0)1/2\delu\(2) + 1/4epsilon(2) (1 - \u\(2))(2) dx, for u is an element of H-1(U;R-2), where U is a bounded, open subset of R-2. Compactness results for the scaled Jacobian of u(E) are proved under the assumption that E, (u(r)) is bounded uniformly by a function of epsilon. In addition, the Gamma limit of E(u(r))/(ln epsilon)(2) is shown to be E(upsilon) := 1/2parallel toupsilonparallel to(2)(2) + parallel todel x upsilonparallel to(.H), where upsilon is the limit of j(u(0))/\ln epsilon\, j(u(0)) = u(0) x Du(0), and parallel to(.)parallel to(.H) is the total variation of a Radon measure. These results are applied to the Ginzburg-Landau functional F-0(u,A;h(ext)) := integral(upsilon)1/2 \del(A)u\(2) + 1/4epsilon(2) (1 - \u\(2))(2) + 1/2\del x A - h(ext)\ dx, with external magnetic field h(ext) approximate to H\ln epsilon\. The Gamma limit of F-0/(ln epsilon)(2) is calculated to be F(upsilon, a; H) := 1/2[parallel toupsilon - aparallel to(2)(2) +parallel todel x upsilonparallel to(.H) + parallel todel x a - Hparallel to(2)(2)], where upsilon is as before, and a is the limit of A(p)/\ln epsilon\. (C) Elsevier Science (USA). | |
dc.description.indexedby | WOS | |
dc.description.indexedby | Scopus | |
dc.description.issue | 2 | |
dc.description.openaccess | YES | |
dc.description.publisherscope | International | |
dc.description.sponsoredbyTubitakEu | N/A | |
dc.description.volume | 192 | |
dc.identifier.doi | 10.1006/jfan.2001.3906 | |
dc.identifier.eissn | 1096-0783 | |
dc.identifier.issn | 0022-1236 | |
dc.identifier.quartile | Q1 | |
dc.identifier.scopus | 2-s2.0-0037055182 | |
dc.identifier.uri | https://doi.org/10.1006/jfan.2001.3906 | |
dc.identifier.uri | https://hdl.handle.net/20.500.14288/9837 | |
dc.identifier.wos | 178011500011 | |
dc.keywords | Gamma limit | |
dc.keywords | Ginzburg-landau functional | |
dc.keywords | BnV | |
dc.keywords | Compactness | |
dc.language.iso | eng | |
dc.publisher | Elsevier | |
dc.relation.ispartof | Journal of Functional Analysis | |
dc.subject | Mathematics | |
dc.title | Limiting behavior of the ginzburg-landau functional | |
dc.type | Journal Article | |
dspace.entity.type | Publication | |
local.contributor.kuauthor | Soner, Halil Mete | |
local.publication.orgunit1 | College of Sciences | |
local.publication.orgunit2 | Department of Mathematics | |
relation.isOrgUnitOfPublication | 2159b841-6c2d-4f54-b1d4-b6ba86edfdbe | |
relation.isOrgUnitOfPublication.latestForDiscovery | 2159b841-6c2d-4f54-b1d4-b6ba86edfdbe | |
relation.isParentOrgUnitOfPublication | af0395b0-7219-4165-a909-7016fa30932d | |
relation.isParentOrgUnitOfPublication.latestForDiscovery | af0395b0-7219-4165-a909-7016fa30932d |