Vortex patterns in a superconducting cube with magnetic core

Numerical parameter continuation results for a cubic extreme-type-II superconductor with a spherical cavity at its center. The cavity contains a magnetic dipole which is switched off initially. The parameter $\mu$ cotnrols the strength of the dipole. The left hand sides of the plots show the Gibbs energy of the system as a function of the control parameter. The right hand sides show the complex-valued order parameter $\psi$: $arg(\psi)$ is highlighted at the back sides of the cube, and the isosurface $|\psi|^2 = 0.1$ is shown. As $\mu$ increases, the typical vortex loops are showing.