We take the Gauss’ linking integral of two curves as a starting point to discuss the connection between the equation of continuity and the inhomogeneous Maxwell equations. Gauss’ formula has been discussed before, as being derivable from the line integral of a magnetic field generated by a steady current flowing through a loop. We argue that a purely geometrical result such as Gauss’ formula ca...

The interface problem describing the scattering of time-harmonic electromagnetic waves by a dielectric body is often formulated as a pair of coupled boundary integral equations for the electric and magnetic current densities on the interface Γ. In this paper, following an idea developed by Kleinman and Martin [19] for acoustic scattering problems, we consider methods for solving the dielectric ...

We derive equations modeling the resonant interaction of electric and magnetic components of light fields with metal nanostructures. This paired resonance was recently shown to produce negative refractive index. The model equations are a generalization of the well-known Maxwell–Lorentz model. We demonstrate that in the case of nonlinear polarization and linear magnetization, these equations are...

The structure of the Poincaré group gives, under all conditions, an equation of field helicity which reduces to the Maxwell equations and also gives cyclic relations between field components. If the underlying symmetry of special relativity is represented by the Poincaré group, it follows that the Maxwell equations and the cyclic equations are both products of special relativity itself, and bot...

Starting from the first principles of nonrelativistic QED we have developed the quantum theory of the interaction of a two-component ultracold atomic ensemble with the electromagnetic field of vacuum and laser photons. The main attention has been paid to the consistent consideration of dynamical dipole-dipole interactions in the radiation field. Taking into account local-field effects we have d...

In this paper we introduce a new method to study the influence of thermal conduction and viscous processes in anisotropic gravitational collapse. To this end we employ the HJR method to solve the Einstein equations. The Maxwell-Cattaneo type transport equations are used to find the temperature and bulk and shear viscous pressures. Under some conditions Maxwell-Cattaneo transport equations compl...

The most efficient solvers for finite element (fe) equations are certainly multigrid, or multilevel methods, and domain decomposition methods using local multigrid solvers. Typically, the multigrid convergence rate is independent of the mesh size parameter, and the arithmetical complexity grows linearly with the number of unknowns. However, the standard multigrid algorithms fail for the Maxwell...

We assemble the equations of general relativistic magnetohydrodynamics (MHD) in 3+1 form. These consist of the complete coupled set of Maxwell equations for the electromagnetic field, Einstein’s equations for the gravitational field, and the equations of relativistic MHD for a perfectly conducting ideal gas. The adopted form of the equations is suitable for evolving numerically a relativistic M...

in this paper vibration of ferromagnetic rectangular plates which are subjected to an inclined magnetic field is investigated based on classical plate theory and maxwell equations. levy type solution and finite element method using comsol software are used to obtain the frequency of the plate subjected to different boundary conditions, good agreements is obtained when computed results are compa...