相关论文: The Ginzburg-Landau functional with vanishing magn…
We consider the Ginzburg-Landau functional with a variable applied magnetic field in a bounded and smooth two dimensional domain. We determine an accurate asymptotic formula for the minimizing energy when the Ginzburg-Landau parameter and…
We consider the Ginzburg-Landau functional defined over a bounded and smooth three dimensional domain. Supposing that the magnetic field is comparable with the second critical field and that the Ginzburg-Landau parameter is large, we…
We study the Ginzburg-Landau energy of a superconductor with a variable magnetic field and a pinning term in a bounded smooth two dimensional domain $\Omega$. Supposing that the Ginzburg-Landau parameter and the intensity of the magnetic…
The energy of a type II superconductor placed in a strong non-uniform, smooth and signed magnetic field is displayed via a universal characteristic function defined by means of a simplified two dimensional Ginzburg-Landau functional. We…
We consider the Ginzburg-Landau functional with a variable applied magnetic field in a bounded and smooth two dimensional domain. The applied magnetic field varies smoothly and is allowed to vanish non-degenerately along a curve. Assuming…
We study the minimizers of the Ginzburg-Landau energy functional with a constant magnetic field in a three dimensional bounded domain. The functional depends on two positive parameters, the Ginzburg-Landau parameter and the intensity of the…
We study the Ginzburg-Landau model of superconductivity in three dimensions and for strong external magnetic fields. For magnetic field strengths above the phenomenologically defined second critical field it is known from Physics that…
We consider the Ginzburg-Landau functional defined over a bounded and smooth three dimensional domain. Supposing that the strength of the applied magnetic field varies between the first and second critical fields, in such a way that…
We establish exponential bounds on the Ginzburg-Landau order parameter away from the curve where the applied magnetic field vanishes. In the units used in this paper, the estimates are valid when the parameter measuring the strength of the…
Superconductivity in the presence of a step magnetic field has been recently the focus of many works. This contribution examines the behavior of a two-dimensional superconducting domain, when superconductivity is lost in the whole domain…
We consider the two-dimensional Ginzburg-Landau functional with constant applied magnetic field. For applied magnetic fields close to the second critical field $H_{C_2}$ and large Ginzburg-Landau parameter, we provide leading order…
In this paper, we study the asymptotic behaviour of minimizing solutions of a Ginzburg-Landau type functional with a positive weight and with convex potential near $0$ and we estimate the energy in this case. We also generalize a lower…
We consider the Ginzburg-Landau functional, defined on a two-dimensional simply connected domain with smooth boundary, in the situation when the applied magnetic field is piecewise constant with a jump discontinuity along a smooth curve. In…
We prove that the lowest eigenvalue of the Laplace operator with a magnetic field having a self-intersecting zero set is a monotone function of the parameter defining the strength of the magnetic field, in a neighborhood of infinity. We…
Starting from the Bardeen-Cooper-Schrieffer (BCS) free energy functional, we derive the Ginzburg-Landau functional in the presence of a weak homogeneous magnetic field. We also provide an asymptotic formula for the BCS critical temperature…
This paper is concerned with spectrum properties of the magnetic Laplacian with a higher-order vanishing magnetic field in a bounded domain. We study the asymptotic behaviors of ground state energies for the Dirichlet Laplacian, the Neumann…
A new description is proposed for the low-field critical behavior of type-II superconductors. The starting point is the Ginzburg-Landau theory in presence of an external magnetic field H. A set of fictitious vortex variables and a singular…
Starting from the Ginzburg--Landau model in a planar simply connected domain, with a local compactly supported applied magnetic field, we derive an effective model in the strong field limit, defined on a non-simply connected domain. The…
We study the two-dimensional Ginzburg-Landau functional in a domain with corners for exterior magnetic field strengths near the critical field where the transition from the superconducting to the normal state occurs. We discuss and clarify…
We explore the relationship between two reference functions arising in the analysis of the Ginzburg-Landau functional. The first function describes the distribution of superconductivity in a type II superconductor subjected to a constant…