On multiply connected mesoscopic superconducting structures
On quantum fields and systems with ordered ground state.
On some sufficient conditions for the blow-up solutions of the nonlinear Ginzburg-Landau-Schrödinger evolution equation.
On the double critical-state model for type-II superconductivity in 3D
In this paper we mathematically analyse an evolution variational inequality which formulates the double critical-state model for type-II superconductivity in 3D space and propose a finite element method to discretize the formulation. The double critical-state model originally proposed by Clem and Perez-Gonzalez is formulated as a model in 3D space which characterizes the nonlinear relation between the electric field, the electric current, the perpendicular component of the electric current...
On the Ginzburg-Landau and related equations
We describe qualitative behaviour of solutions of the Gross-Pitaevskii equation in 2D in terms of motion of vortices and radiation. To this end we introduce the notion of the intervortex energy. We develop a rather general adiabatic theory of motion of well separated vortices and present the method of effective action which gives a fairly straightforward justification of this theory. Finally we mention briefly two special situations where we are able to obtain rather detailed picture of the vortex...
On the Ginzburg-Landau energy with weight
On the Ginzburg–Landau model of a superconducting ball in a uniform field
On the Lawrence–Doniach model of superconductivity: magnetic fields parallel to the axes
We consider periodic minimizers of the Lawrence–Doniach functional, which models highly anisotropic superconductors with layered structure, in the simultaneous limit as the layer thickness tends to zero and the Ginzburg–Landau parameter tends to infinity. In particular, we consider the properties of minimizers when the system is subjected to an external magnetic field applied either tangentially or normally to the superconducting planes. For normally applied fields, our results show that the resulting...
On the minimizers of the Ginzburg-Landau energy for high kappa : the axially symmetric case
On the regularity of a free boundary for a nonlinear obstacle problem arising in superconductor modelling
Optimal feedback control of Ginzburg-Landau equation for superconductivity via differential inclusion
Slightly below the transition temperatures, the behavior of superconducting materials is governed by the Ginzburg-Landau (GL) equation which characterizes the dynamical interaction of the density of superconducting electron pairs and the exited electromagnetic potential. In this paper, an optimal control problem of the strength of external magnetic field for one-dimensional thin film superconductors with respect to a convex criterion functional is considered. It is formulated as a nonlinear coefficient...