Asymptotic analysis of a secondary bifurcation of the one-dimensional Ginzburg-Landau equations of superconductivity
The bifurcation of asymmetric superconducting solutions from the normal solution is considered for the one-dimensional Ginzburg--Landau equations by the methods of formal asymptotics. The behavior of the bifurcating branch depends on the parameters d, the size of the superconducting slab, and $\kapp...
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| Формат: | Journal article |
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2000
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| _version_ | 1826295529133309952 |
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| author | Aftalion, A Chapman, S |
| author_facet | Aftalion, A Chapman, S |
| author_sort | Aftalion, A |
| collection | OXFORD |
| description | The bifurcation of asymmetric superconducting solutions from the normal solution is considered for the one-dimensional Ginzburg--Landau equations by the methods of formal asymptotics. The behavior of the bifurcating branch depends on the parameters d, the size of the superconducting slab, and $\kappa$, the Ginzburg--Landau parameter. The secondary bifurcation in which the asymmetric solution branches reconnect with the symmetric solution branch is studied for values of $(\kappa,d)$ for which it is close to the primary bifurcation from the normal state. These values of $(\kappa,d)$ form a curve in the $\kappa d$-plane, which is determined. At one point on this curve, called the quintuple point, the primary bifurcations switch from being subcritical to supercritical, requiring a separate analysis. The results answer some of the conjectures of [A. Aftalion and W. C. Troy, Phys. D, 132 (1999), pp. 214--232]. |
| first_indexed | 2024-03-07T04:02:26Z |
| format | Journal article |
| id | oxford-uuid:c50af85a-0a79-47bd-8f82-b47b6c2091f4 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T04:02:26Z |
| publishDate | 2000 |
| record_format | dspace |
| spelling | oxford-uuid:c50af85a-0a79-47bd-8f82-b47b6c2091f42022-03-27T06:28:03ZAsymptotic analysis of a secondary bifurcation of the one-dimensional Ginzburg-Landau equations of superconductivityJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:c50af85a-0a79-47bd-8f82-b47b6c2091f4Mathematical Institute - ePrints2000Aftalion, AChapman, SThe bifurcation of asymmetric superconducting solutions from the normal solution is considered for the one-dimensional Ginzburg--Landau equations by the methods of formal asymptotics. The behavior of the bifurcating branch depends on the parameters d, the size of the superconducting slab, and $\kappa$, the Ginzburg--Landau parameter. The secondary bifurcation in which the asymmetric solution branches reconnect with the symmetric solution branch is studied for values of $(\kappa,d)$ for which it is close to the primary bifurcation from the normal state. These values of $(\kappa,d)$ form a curve in the $\kappa d$-plane, which is determined. At one point on this curve, called the quintuple point, the primary bifurcations switch from being subcritical to supercritical, requiring a separate analysis. The results answer some of the conjectures of [A. Aftalion and W. C. Troy, Phys. D, 132 (1999), pp. 214--232]. |
| spellingShingle | Aftalion, A Chapman, S Asymptotic analysis of a secondary bifurcation of the one-dimensional Ginzburg-Landau equations of superconductivity |
| title | Asymptotic analysis of a secondary bifurcation of the one-dimensional Ginzburg-Landau equations of superconductivity |
| title_full | Asymptotic analysis of a secondary bifurcation of the one-dimensional Ginzburg-Landau equations of superconductivity |
| title_fullStr | Asymptotic analysis of a secondary bifurcation of the one-dimensional Ginzburg-Landau equations of superconductivity |
| title_full_unstemmed | Asymptotic analysis of a secondary bifurcation of the one-dimensional Ginzburg-Landau equations of superconductivity |
| title_short | Asymptotic analysis of a secondary bifurcation of the one-dimensional Ginzburg-Landau equations of superconductivity |
| title_sort | asymptotic analysis of a secondary bifurcation of the one dimensional ginzburg landau equations of superconductivity |
| work_keys_str_mv | AT aftaliona asymptoticanalysisofasecondarybifurcationoftheonedimensionalginzburglandauequationsofsuperconductivity AT chapmans asymptoticanalysisofasecondarybifurcationoftheonedimensionalginzburglandauequationsofsuperconductivity |