Title
Numerical bifurcation study of superconducting patterns on a square Numerical bifurcation study of superconducting patterns on a square
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
Philadelphia, Pa ,
Subject
Mathematics
Physics
Source (journal)
SIAM journal on applied dynamical systems. - Philadelphia, Pa
Volume/pages
11(2012) :1 , p. 447-477
ISSN
1536-0040
ISI
000302237300016
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
This paper considers the extreme type-II GinzburgLandau equations that model vortex patterns in superconductors. The nonlinear PDEs are solved using Newton's method, and properties of the Jacobian operator are highlighted. Specifically, this paper illustrates how the operator can be regularized using an appropriate phase condition. For a two-dimensional square sample, the numerical results are based on a finite-difference discretization with link variables that preserves the gauge invariance. For two exemplary sample sizes, a thorough bifurcation analysis is performed using the strength of the applied magnetic field as a bifurcation parameter and focusing on the symmetries of this system. The analysis gives new insight into the transitions between stable and unstable states, as well as the connections between stable solution branches.
Full text (open access)
https://repository.uantwerpen.be/docman/irua/3cdc04/3953.pdf
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