Related papers: Vortex-capturing multiscale spaces for the Ginzbur…
We present and analyze a pollution-free Petrov-Galerkin multiscale finite element method for the Helmholtz problem with large wave number $\kappa$ as a variant of [Peterseim, ArXiv:1411.1944, 2014]. We use standard continuous $Q_1$ finite…
Motivated by some variational problems from a nonlocal model of mechanics, this work presents a set of sufficient conditions that guarantee a compact inclusion in the function space of $L^{p}$ vector fields defined on a domain $\Omega$ that…
We consider minimizers $u_\varepsilon$ of the Ginzburg-Landau energy with quadratic divergence penalization on a simply-connected two-dimensional domain $\Omega$. On the boundary, strong tangential anchoring is imposed. We prove that…
The extended Painlev\'e P.D.E. system $\Delta y -x_1 y - 2 |y|^2y=0$, $(x_1,\ldots,x_n)\in \mathbb{R}^n$, $y:\mathbb{R}^n\to\mathbb{R}^m$, is obtained by multiplying by $-x_1$ the linear term of the Ginzburg-Landau equation $\Delta…
Various applications ranging from spintronic devices, giant magnetoresistance sensors, and magnetic storage devices, include magnetic parts on very different length scales. Since the consideration of the Landau-Lifshitz-Gilbert equation…
We study spatially localized optical vortices created by self-trapping of partially incoherent light with a phase dislocation in a biased photorefractive crystal. In a contrast to the decay of coherent self-trapped vortex beams due to the…
We study computationally dynamics of quantised vortices in two-dimensional superfluid Bose-Einstein condensates confined in highly oblate power-law traps. We have found that the formation of large scale Onsager vortex clusters prevalent in…
This paper develops a geometric and analytical extension of the Finsler--Ginzburg--Landau framework by introducing a distributed control field acting as a translation in the tangent bundle. Within this formulation, the classical Tonelli…
In this work we study the interaction between vortices and nematic domain walls within the framework of a Ginzburg Landau approach. The free energy of the system is written in terms of a complex order parameter characteristic of $s$-wave…
We develop a Finsler Ginzburg--Landau framework for the analysis of vortex interactions in anisotropic superconductors. Within this setting, the Finsler structure encodes directional dependence of the condensate energy, yielding a…
We prove existence of Abrikosov vortex lattice solutions of the Ginzburg-Landau equations in two dimensions, for magnetic fields larger than but close to the first critical magnetic field.
The theory of vortex motion in a dilute superfluid of inhomogeneous density demands a boundary layer approach, in which different approximation schemes are employed close to and far from the vortex, and their results matched smoothly…
Results are presented from numerical simulations of the flat-space nonlinear Maxwell-Klein-Gordon equations demonstrating deep inelastic scattering of $m=1$ vortices for a range of Ginzburg-Landau (or Abelian-Higgs) parameters ($\kappa$),…
We consider extreme type-II superconductors modeled by the Ginzburg--Landau energy with a pinning term $a_\varepsilon(x)$, which we assume to be a bounded measurable function such that $b\leq a_\varepsilon(x)\leq 1$ for some constant $b>0$.…
We analyze space-time finite element methods for the numerical solution of distributed parabolic optimal control problems with energy regularization in the Bochner space $L^2(0,T;H^{-1}(\Omega))$. By duality, the related norm can be…
We provide a construction of the moduli spaces of framed Hitchin pairs and their master spaces. These objects have come to interest as algebraic versions of solutions of certain coupled vortex equations by work of Lin and Stupariu. Our…
In this paper, we provide the constraint energy minimization generalized multiscale finite element method (CEM-GMsFEM) to solve Helmholtz equations in heterogeneous medium. This novel multiscale method is specifically designed to overcome…
We are concerned with $L^2$-constraint minimizers for the Kirchhoff functional $$ E_b(u)=\int_{\Omega}|\nabla u|^2\mathrm{d}x+\frac{b}{2}\left(\int_\Omega|\nabla u|^2\mathrm{d}x\right)^2+\int_\Omega…
We study a nonlocal perimeter functional inspired by the Minkowski content, whose main feature is that it interpolates between the classical perimeter and the volume functional. This problem is related by a generalized coarea formula to a…
We introduce a GPU-accelerated variational framework with exact projection onto the Lowest Landau Level to probe vortex patterns in rapidly rotating two-dimensional Bose-Einstein condensates. For repulsive interactions, our approach…