Related papers: A compactness result for Landau state in thin-film…
We consider an asymptotic regime for two-dimensional ferromagnetic films that is consistent with the formation of transition layers (N\'eel walls). We first establish compactness of S2-valued magnetizations in the energetic regime of N\'eel…
This paper considers minimizers of the Ginzburg-Landau energy functional in special multiscale spaces that are based on finite elements. The spaces are constructed by localized orthogonal decomposition techniques and their usage for solving…
We consider a Ginzburg-Landau type energy with a piecewise constant pinning term $a$ in the potential $(a^2 - |u|^2)^2$. The function $a$ is different from 1 only on finitely many disjoint domains, called the {\it pinning domains}. These…
A central focus of Ginzburg-Landau theory is the understanding and characterization of vortex configurations. On a bounded domain $\Omega\subseteq \mathbb{R}^2,$ global minimizers, and critical states in general, of the corresponding energy…
We prove some improved estimates for the Ginzburg-Landau energy (with or without magnetic field) in two dimensions, relating the asymptotic energy of an arbitrary configuration to its vortices and their degrees, with possibly unbounded…
We study a variational model which combines features of the Ginzburg-Landau model in 2D and of the Mumford-Shah functional. As in the classical Ginzburg-Landau theory, a prescribed number of point vortices appear in the small energy regime;…
Ferromagnetic materials are governed by a variational principle which is nonlocal, nonconvex and multiscale. The main object is given by a unit-length three-dimensional vector field, the magnetization, that corresponds to the stable states…
Motivated by recent experiments on fermionic rings, we study the asymptotic behaviour of minimizers of the Ginzburg-Landau (GL) energy in an annulus with a Dirichlet data which depends on the GL parameter on the outer boundary. We show that…
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…
In this work, we study discrete minimizers of the Ginzburg-Landau energy in finite element spaces. Special focus is given to the influence of the Ginzburg-Landau parameter $\kappa$. This parameter is of physical interest as large values can…
We study the Ginzburg-Landau equations in order to describe a two-dimensional superconductor in a bounded domain. Using the properties of a particular integrability point ($\kappa = 1/ \sqrt2$) of these nonlinear equations which allows…
The vortex states in a thin mesoscopic disk are investigated within the phenomenological Ginzburg-Landau theory in the presence of different ''model'' magnetic field profiles with zero average field which may result from a ferromagnetic…
In this review article, we provide an overview of recent advances in the numerical approximation of minimizers of the Ginzburg-Landau energy in multiscale spaces. Such minimizers represent the most stable states of type-II superconductors…
We consider a two-dimensional Ginzburg-Landau problem on an arbitrary domain with a finite number of vanishingly small circular holes. A special choice of scaling relation between the material and geometric parameters (Ginzburg-Landau…
We present the first fully microscopic, self-consistent, and self-contained theory of superconducting weakly coupled periodic multilayers with tunnel barriers in the presence of externally applied parallel magnetic fields, in the local…
We study the Ginzburg-Landau energy of superconductors with a term $a_\ep$ modelling the pinning of vortices by impurities in the limit of a large Ginzburg-Landau parameter $\kappa=1/\ep$. The function $a_\ep$ is oscillating between 1/2 and…
We analyse two variants of a nonconvex variational model from micromagnetics with a nonlocal energy functional, depending on a small parameter $\epsilon > 0$. The model gives rise to transition layers, called N\'eel walls, and we study…
The problem of the giant vortex state around a magnetic dot which is embedded in a superconducting film is investigated. The full non-linear, self-consistent Ginzburg-Landau equations are solved numerically in order to calculate the free…
We study minimizers of the Lawrence--Doniach energy, which describes equilibrium states of superconductors with layered structure, assuming Floquet-periodic boundary conditions. Specifically, we consider the effect of a constant magnetic…
We study tensor-valued minimizers of the Landau-de Gennes energy functional on a simply-connected planar domain $\Omega$ with non-contractible boundary data. Here the tensorial field represents the second moment of a local orientational…