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We interpret the forward Maxwell equation with up to third order induced polarizations and get so called nonlinear wave equation in frequency domain (NWEF), which is based on Maxwell wave equation and using slowly varying spectral amplitude…
We propose a novel scheme to normalize scattering modes of the electromagnetic field. By relying on analytical solutions for Maxwell's equations in the homogenous medium outside the scatterer, we derive normalization conditions that only…
The analogy between electromagnetism and gravitation was achieved by linearizing the tensorial gravitational equations of general relativity and converting them into a vector form corresponding to Maxwell's electromagnetic equations. On…
This paper encompasses a set of stellar equations that administer the formation and evolution of self-gravitating, dissipative spherically symmetric fluid distributions having anisotropic stresses in the presence of electromagnetic field.…
Incompressibility is established for three-dimensional and two-dimensional deformations of an anisotropic linearly elastic material, as conditions to be satisfied by the elastic compliances. These conditions make it straightforward to…
In this letter we introduce a particular solution for parallel electric and magnetic fields, in a gravitational background, which satisfy free-wave equations and the phenomenology suggested by astrophysical plasma physics. These free-wave…
We show that arbitrary 3D electromagnetic fields are transient solutions to Maxwell's equations and provide a simple equation to find how the field evolves over time. Multiple 3D fields can be realized at different times by superposing with…
We classify (1+3)-dimensional Pauli equations for a spin-1/2 particle interacting with the electro-magnetic field, that are solvable by the method of separation of variables. As a result, we obtain the eleven classes of vector-potentials of…
In this article we have illustrated how is possible to formulate Maxwell's equations in vacuum in an independent form of the usual systems of units. Maxwell's equations, are then specialized to the most commonly used systems of units:…
An asymptotic investigation of monochromatic electromagnetic fields in a layered periodic medium is carried out under the assumption that the wave frequency is close to the frequency of a stationary point of the dispersion surface. We find…
This paper discusses the use of the Riemann-Silberstein vector to solve the source-free Maxwell's equations and obtains novel analytical solutions. The solving process naturally leads to the spinor form of the source-free Maxwell's…
The electric and magnetic fields of a spatio-temporally varying electric current loop are calculated using the Jefimenko equations. The radiation and the nonradiation parts of the electromagnetic fields are derived in the framework of…
The theoretical description and experimental verification of resonant phenomena in electromagnetic fields generated in the near zone of all-dielectric rectangular thin sub wavelength frames, subjected to an incident microwave, is…
The boundary-value problem for the perturbation of an electric potential by a homogeneous anisotropic dielectric sphere in vacuum was formulated. The total potential in the exterior region was expanded in series of radial polynomials and…
This paper provides a rigorous analysis of boundary element methods for the magnetic field integral equation on Lipschitz polyhedra. The magnetic field integral equation is widely used in practical applications to model electromagnetic…
We present a domain decomposition method (DDM) devoted to the iterative solution of time-harmonic electromagnetic scattering problems, involving large and resonant cavities. This DDM uses the electric field integral equation (EFIE) for the…
An inverse obstacle scattering problem for the electromagnetic wave governed by the Maxwell system over a finite time interval is considered. It is assumed that the wave satisfies the Leontovich boundary condition on the surface of an…
We prove that the electromagnetic fields in dielectric media whose susceptibility follows a fractional power-law dependence in a wide frequency range can be described by differential equations with time derivatives of noninteger order. We…
We prove that in contrast to the free wave equation in $\R^3$ there are no incoming solutions of Maxwell's equations in the form of spherical or modulated spherical waves. We construct solutions which are corrected by lower order incoming…
This work studies time-dependent electromagnetic scattering from obstacles whose interaction with the wave is fully determined by a nonlinear boundary condition. In particular, the boundary condition studied in this work enforces a power…