Numerical bifurcation study of superconducting patterns on a square

Authors

Schlömer, N., Avitabile, D. and Vanroose, W.

Abstract

This paper considers the extreme type-II Ginzburg–Landau 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.

DOI PDF

BibTeX

@article{schlomer2012numerical,
  title={Numerical bifurcation study of superconducting patterns on a square},
  author={Schl{\"o}mer, Nico and Avitabile, Daniele and Vanroose, Wim},
  journal={SIAM Journal on Applied Dynamical Systems},
  volume={11},
  number={1},
  pages={447--477},
  year={2012},
  publisher={SIAM}
}