Vector spherical harmonic analyses have been used successfully to solve laminar and mean-field magnetohydrodynamic dynamo problems with interactions, such as the laminar induction term, anisotropic alpha-effects and anisotropic diffusion, which are difficult to analyse spectrally in spherical geometries. Spectral forms of the non-linear rotating Boussinesq and anelastic momentum, magnetic field...

We present a scheme for the determination of the vector nature of an electric field by optical second-harmonic generation. We demonstrate the technique by mapping the two-dimensional electric-field vector of a biased transmission line structure on silicon with a spatial resolution of ~10mum .

This paper introduces the reader to electric and magnetic fields, particularly those fields produced by electric power systems and other sources using frequencies in the power-frequency range. Electric fields are produced by electric charges; a magnetic field also is produced if these charges are in motion. Electric fields exert forces on other charges; if in motion, these charges will experien...

This paper presents a new numerical method for div-curl systems with the normal boundary condition by using finite element technique known as primal-dual weak Galerkin (PDWG). The PDWG scheme system has two prominent features in that it offers not only an accurate and reliable solution to under low Hα-regularity (α>0) assumption true solution, but also effective approximation of harmonic vector...

We derive a lower bound for energies of harmonic maps of convex polyhedra in R 3 to the unit sphere S, with tangent boundary conditions on the faces. We also establish that C maps, satisfying tangent boundary conditions, are dense with respect to the Sobolev norm, in the space of continuous tangent maps of finite energy. Mathematics Subject Classifications (2000). 58E20, 35J55.

‎in this paper‎, ‎we introduce the structure of a groupoid associated to a vector field‎ ‎on a smooth manifold‎. ‎we show that in the case of the $1$-dimensional manifolds‎, ‎our‎ ‎groupoid has a‎ ‎smooth structure such that makes it into a lie groupoid‎. ‎using this approach‎, ‎we associated to‎ ‎every vector field an equivalence‎ ‎relation on the lie algebra of all vector fields on the smooth...