The quad-curl problem arises in the study of the electromagnetic interior transmission problem and magnetohydrodynamics (MHD). In this paper, we study the quad-curl eigenvalue problem and propose a mixed method using edge elements. Assuming stringent regularity of the solution of the quadcurl source problem, we prove the convergence and show that the divergencefree condition can be bypassed.

The B (curl) mode of the correlation of galaxy ellipticities (shear) can be used to detect a stochastic gravitational wave background, such as that predicted by inflation. In this paper, we derive the tensor mode contributions to shear from both gravitational lensing and intrinsic alignments, using the gaugeinvariant, full-sky results of Schmidt and Jeong {arXiv:1204.3625 [Phys. Rev. D (to be p...

It is shown that the space of all vector elds with divergence and curl in L q ((), q 2 such that the normal-component vanishes one part of @ and the tangential-component vanishes on the other, is compactly imbedded in L 2 (().

Curling of knitted fabrics edges is one of the complicated problems of these structures. Therefore, study and measurement of curling in knitted fabrics is important. In this study, it is tried to model the three-dimensional wale wise curl of the fabric using finite element modelling. In this model the tensions in different parts of a knitted loop due to bending and torsional forces in knitting ...

This thesis deals with the higher-order Finite Element Method (FEM) for computational electromagnetics. The hp-version of FEM combines local mesh refinement (h) and local increase of the polynomial order of the approximation space (p). A key tool in the design and the analysis of numerical methods for electromagnetic problems is the de Rham Complex relating the function spaces H1(Ω), H(curl,Ω),...

For $10$ such that \[ \|{ P }\|_{L^p(\Omega,\mathbb{R}^{3\times3})}\leq c\,\left(\|{\operatorname{de...

Fractional curl operator has been used to derive solutions to the Maxwell equations for fractional rectangular cavity resonator. These solutions to the Maxwell equations may be regarded as fractional dual solutions. Behavior of field lines and surface current density in fractional cavity resonator have been investigated with respect to the fractional parameter. Fractional parameter describes th...

Finite element approximation to a decoupled formulation for the quad-curl problem is studied in this paper. The difficulty of constructing elements with certain conformity quad–curl problems has been greatly reduced. For convex domains, where regularity assumption holds Stokes equation, curl true solution quadratic order convergence and first energy norm. If shows singularity, an posterior erro...

Abstract We consider localized solutions of variants the semilinear curl-curl wave equation $$s(x) \partial _t^2 U +\nabla \times \nabla + q(x) \pm V(x) \vert ^{p-1} = 0$$ s ( x ) ∂ t 2</mml:m...