Effective Dynamics of Magnetic Vortices

The Stability of Magnetic Vortices

We study the linearized stability of n-vortex solutions of the magnetic Ginzburg-Landau (or Abelian-Higgs) equations. We prove that the fundamental vortices (n=1,-1) are stable for all values of the coupling constant, k, and we prove that the higher-degree vortices (|n| > 1) are stable for k < 1 and unstable for k > 1. This resolves a long-standing conjecture.

Magnetic vortices for a Ginzburg-Landau type energy with discontinuous constraint. II

We study vortex nucleation for minimizers of a Ginzburg-Landau energy with discontinuous constraint. For applied magnetic fields comparable with the first critical field of vortex nucleation, we determine the limiting vorticities.

Magnetic vortices for a Ginzburg-Landau type energy with discontinuous constraint

This paper is devoted to an analysis of vortex-nucleation for a Ginzburg-Landau functional with discontinuous constraint. This functional has been proposed as a model for vortex-pinning, and usually accounts for the energy resulting from the interface of two superconductors. The critical applied magnetic field for vortex nucleation is estimated in the London singular limit, and as a by-product, results concerning vortex-pinning and boundary conditions on the interface are obtained.

Kinematic and dynamic vortices in a thin film driven by an applied current and magnetic field

Using a Ginzburg-Landau model, we study the vortex behavior of a rectangular thin film superconductor subjected to an applied current fed into a portion of the sides and an applied magnetic field directed orthogonal to the film. Through a center manifold reduction we develop a rigorous bifurcation theory for the appearance of periodic solutions in certain parameter regimes near the normal state. The leading order dynamics yield in particular a motion law for kinematic vortices moving up and down the center line of the sample. We also present computations that reveal the co-existence and period…

存在磁场时的边界涡旋

Boundary vortices in the presence of a magnetic field

本文研究外加面内恒定磁场下薄铁磁薄膜中边界涡旋主导的微磁能量行为，提出重整化能量的新定义并证明其二阶Γ收敛及能量集中现象，同时给出数值模拟验证。

Pinning by holes of multiple vortices in homogenization for Ginzburg-Landau problems

We consider a homogenization problem for magnetic Ginzburg-Landau functional in domains with large number of small holes. For sufficiently strong magnetic field, a large number of vortices is formed and they are pinned by the holes. We establish a scaling relation between sizes of holes and the magnitude of the external magnetic field when pinned vortices are multiple and their homogenized density is described by a hierarchy of variational problems. This stands in sharp contrast with homogeneous superconductors, where all vortices are known to be simple. The proof is based on $Γ$-convergence a…