Related papers: A $\Gamma$-convergence result for 2D type-I superc…
A classical result in the study of Ginzburg-Landau equations is that, for Dirichlet or Neumann boundary conditions, if a sequence of functions has energy uniformly bounded on a logarithmic scale then we can find a subsequence whose…
We prove a $\Gamma$-convergence result for a class of Ginzburg-Landau type functionals with $\mathcal{N}$-well potentials, where $\mathcal{N}$ is a closed and $(k-2)$-connected submanifold of $\mathbb{R}^m$, in arbitrary dimension. This…
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…
It is shown that within the Ginzburg-Landau (GL) approximation the order parameters Delta1(r, T) and Delta2(r, T) in two-band superconductors vary on the same length scale, the difference in the zero-T coherence lengths xi0_i…
We study the variational convergence of a family of two-dimensional Ginzburg-Landau functionals arising in the study of superfluidity or thin-film superconductivity, as the Ginzburg-Landau parameter epsilon tends to 0. In this regime and…
In this paper we generalize to arbitrary dimensions a one-dimensional equicoerciveness and $\Gamma$-convergence result for a second derivative perturbation of Perona-Malik type functionals. Our proof relies on a new density result in the…
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…
We study the $\Gamma$-convergence of a family of non-local, non-convex functionals in $L^p(I)$ for $p \ge 1$, where $I$ is an open interval. We show that the limit is a multiple of the $W^{1, p}(I)$ semi-norm to the power $p$ when $p>1$…
Let $\Omega$ be an open subset of a Stein manifold $\Sigma$ and let $M$ be its boundary. It is well known that $M$ inherits a natural contact structure. In this paper we consider a family of variational functionals $F_\varepsilon$ defined…
In this paper we consider the asymptotic behavior of the Ginzburg- Landau model for superconductivity in 3-d, in various energy regimes. We rigorously derive, through an analysis via {\Gamma}-convergence, a reduced model for the vortex…
We study the Ginzburg-Landau model of type-I superconductors in the regime of small external magnetic fields. We show that, in an appropriate asymptotic regime, flux patterns are described by a simplified branched transportation functional.…
We study Gamma-convergence of graph based Ginzburg-Landau functionals, both the limit for zero diffusive interface parameter epsilon->0 and the limit for infinite nodes in the graph m -> infinity. For general graphs we prove that in the…
We present a semi-perturbative approach which yields an infrared-stable fixed point in the Ginzburg-Landau for N=2, where $N/2$ is the number of complex components. The calculations are done in $d=3$ dimensions and below $T_c$, where 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 prove that certain non-local functionals defined on measurable sets Gamma-converge to the perimeter in the sense of De Giorgi.
We prove that, on a planar regular domain, suitably scaled functionals of Ginzburg-Landau type, given by the sum of quadratic fractional Sobolev seminorms and a penalization term vanishing on the unitary sphere, $\Gamma$-converge to…
We prove compactness with respect to $\Gamma$-convergence for a general class of non-local energies modelled after the ones considered in [Gobbino, CPAM (1998)]. We give an integral representation result for the limits, which are free…
Basing on self-consistent solution of non-linear GL-equations, the phase boundary is found, which divides the regions of I- and II-order phase transitions of a superconducting cylinder in magnetic field to normal state. This boundary is a…
In this paper we achieve some $\Gamma$-compactness results for suitable classes of integral functionals depending on a given family of Lipschitz vector fields, with respect to both the strong $L^p-$topology and the strong…
In this study we consider the $\Gamma$-limit of a highly oscillatory Riemannian metric length functional as its period tends to 0. The metric coefficient takes values in either $\{1,\infty\}$ or $\{1,\beta \varepsilon^{-p}\}$ where…