Related papers: The density of superconductivity in the bulk regim…
In Ginzburg-Landau Theory of superconductivity, the density and location of the superconducting electrons are measured by a complex-valued wave function, the order parameter. In this paper, when the intensity of the applied magnetic field…
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…
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 compute the $L^2$-norm of the minimizer of the Ginzburg-Landau functional in a planar domain with a finite number of corners. Our computations are valid for a uniform applied magnetic field, large Ginzburg-Landau parameter and in the…
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…
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 2D Ginzburg-Landau theory for a type-II superconductor in an applied magnetic field varying between the second and third critical value. In this regime the order parameter minimizing the GL energy is concentrated along the…
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 study the distribution of bulk superconductivity in presence of an applied magnetic field, supposed to be a step function, modeled by the Ginzburg-Landau theory. Our results are valid for the minimizers of the two-dimensional…
We present new estimates on the two-dimensional Ginzburg-Landau energy of a type-II superconductor in an applied magnetic field varying between the second and third critical fields. In this regime, superconductivity is restricted to a thin…
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…
We formulate a spectral problem related to the onset of superconductivity for a generalized Ginzburg-Landau model, where the order parameter and the magnetic potential are defined in the whole space. This model is devoted to the `proximity…
Superconductivity for Type II superconductors in external magnetic fields of magnitude between the second and third critical fields is known to be restricted to a narrow boundary region. The profile of the superconducting order parameter in…
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 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…
A numerical approach to Ginzburg-Landau (GL) theory is demonstrated and we review its applications to several examples of current interest in the research on superconductivity. This analysis also shows the applicability of the…
We consider superconductors of Type II near the transition from the 'bulk superconducting' to the 'surface superconducting' state. We prove a new $L^{\infty}$ estimate on the order parameter in the bulk, i.e. away from the boundary. This…
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…
The Ginzburg-Landau (GL) theory is recast using a Hamiltonian involving the complete kinetic energy density which requires that the surface energy must contain a term \nabla |\psi|^2 to support superconducting (SC) states. The GL equations…
The purpose of this research is to study the upper critical field (Hc2) of two-band superconductors by two-band Ginzburg - Landau approach. The analytical formula of Hc2 included anisotropy of order parameter and anisotropy of…