Related papers: Quaternionic equation for electromagnetic fields i…
By using the energy-type inequality, we obtain, in this paper, the result on propagation of Gevrey regularity for the solution of the spatially homogeneous Landau equation in the cases of Maxwellian molecules and hard potential.
The Duffin-Kemmer form of massless vector field (Maxwell field) is extended to the case of arbitrary pseudo-Riemannian space-time in accordance with the tetrad recipe of Tetrode-Weyl-Fock-Ivanenko. In this approach, the Maxwell equations…
After giving an outline of the quantization scheme based on the microscopic Hopfield model of a dielectric bulk material, we show how the classical phenomenological Maxwell equations of the electromagnetic field in the presence of…
This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The…
The Riemann -- Silberstein -- Majorana -- Oppenheimer approach to the Maxwell electrodynamics in presence of electrical sources and arbitrary media is investigated within the matrix formalism. The symmetry of the matrix Maxwell equation…
We look for travelling wave fields $$ E(x,y,z,t)= U(x,y) \cos(kz+\omega t)+ \widetilde U(x,y)\sin(kz+\omega t),\quad (x,y,z)\in\mathbb{R}^3,\, t\in\mathbb{R} $$ satisfying Maxwell's equations in a nonlinear medium which is not necessarily…
We present a collection of well-conditioned integral equation methods for the solution of electrostatic, acoustic or electromagnetic scattering problems involving anisotropic, inhomogeneous media. In the electromagnetic case, our approach…
Rotations on the 3-dimensional Euclidean vector-space can be represented by real quaternions, as was shown by Hamilton. Introducing complex quaternions allows us to extend the result to elliptic and hyperbolic rotations on the Minkowski…
Applications of the covariant theory of drive-forms are considered for a class of perfectly insulating media. The distinction between the notions of "classical photons" in homogeneous bounded and unbounded stationary media and in stationary…
Superluminal electromagnetic fields of dyons are described in T^{4}- space and Quaternion formulation of various quantum equations is derived. It is shown that on passing from subluminal to superluminal realm via quaternion the theory of…
A new mathematical and computational technique for calculating quantum vacuum expectation values of energy and momentum densities associated with electromagnetic fields in bounded domains containing inhomogeneous media is discussed. This…
In this paper, we present an accurate numerical method for the time-harmonic Maxwell's equations for bi-periodic multilayered media with quasi-periodic incident waves using the Method of Fundamental Solutions in conjunction with a…
We show how to use the quasi-Maxwell formalism to obtain solutions of Einstein's field equations corresponding to homogeneous cosmologies - namely Einstein's universe, Godel's universe and the Ozsvath-Farnsworth-Kerr class I solutions -…
Maxwell's equations hold in inertial reference frames in uniform translational motion relative to one another. In conjunction with the Lorentz coordinate transformation equations, the transformation equations for the electric and magnetic…
We generalize Maxwell equations which describe the vacuum of quantum electrodynamics into the quantum form. This nontraditional approach is different from the widely used theory|-Quantum Electrodynamics. From another viewpoint, it could be…
A unified treatment for the propagation of classical waves in inhhomogeneous media is proposed. We deal with four kinds of waves, they are the acoustic wave in fluid, the elastic shear wave in two diemnsional solid, and the E- and…
In this paper we discuss global existence of the solution of the Maxwell and Newton system of equations, describing the interaction of a rigid charge distribution with the electromagnetic field it generates. A unique solution is proved to…
We consider for the time-dependent Maxwell's equations the inverse problem of identifying locations and certain properties of small electromagnetic inhomogeneities in a homogeneous background medium from dynamic measurements of the…
Let us consider a reference frame for which the pseudo-Euclidean geometry is valid (prefered frame). The equations of Maxwell in empty space have a simple form and are derived from a Lagrangian. In a medium magnetic permeability and…
We derive the essential space-time spectrum of the Maxwell equations in linear isotropic inhomogeneous media together with the corresponding essential modes. These modes represent the collapse of the electromagnetic field into a single…