Related papers: Generalized Snell's law and Maxwell equations
We present a short overview of the recent results in the theory of diffusion and wave equations with generalised derivative operators. We give generic examples of such generalised diffusion and wave equations, which include time-fractional,…
We investigate the one-dimensional propagation of waves in the Anderson localization regime, for a single-mode, surface disordered waveguide. We make use of both an analytical formulation and rigorous numerical simulation calculations. The…
We consider an interface with surface tension that separates a perfectly conducting inviscid fluid from a vacuum. The fluid flow is governed by the equations of ideal compressible magnetohydrodynamics (MHD), while the electric and magnetic…
We study the variational problem of finding the fastest path between two points that belong to different anisotropic media, each with a prescribed speed profile and a common interface. The optimal curves are Finsler geodesics that are…
In the first sections of this article, we discuss two variations on Maxwell's equations that have been introduced in earlier work--a class of nonlinear Maxwell theories with well-defined Galilean limits (and correspondingly generalized…
We establish the well-posedness, the finite speed propagation, and a regularity result for Maxwell's equations in media consisting of dispersive (frequency dependent) metamaterials. Two typical examples for such metamaterials are materials…
We express Maxwell's equations as a single equation, first using the divergence of a special type of matrix field to obtain the four current, and then the divergence of a special matrix to obtain the Electromagnetic field. These two…
We present exact solutions to the Einstein-Maxwell system of equations in spherically symmetric gravitational fields with a specified form of the electric field intensity. The condition of pressure isotropy yields a difference equation with…
The ultraconfined light of plasmonic modes put their effective wavelength close to the mean free path of electrons inside the metal electron gas. The Drude model, which can not take the repulsive interactions of electrons into account, then…
The existence of twisted light may be inferred from modern quantum concepts and experimental data. These waves possess energy, impulse and angular momentum. However, the Maxwell's four-dimensional theory of electromagnetism does not imply…
Two methods are explained to exactly solve Maxwell's equations where permittivity, permeability and conductivity may vary in space. In the constitutive relations, retardation is regarded. If the material properties depend but on one…
This paper is devoted to the complete convergence study of the finite-element approximation of Maxwell's equations in the case where the magnetic permeability is constant. Standard linear finite elements for the space discretization are…
The form of Maxwell's theory is well known in the framework of general relativity, a fact that is related to the applicability of the principle of equivalence to electromagnetic phenomena. We pose the question whether this form changes if…
The dynamics of an electron driven by arbitrary plane wave laser radiation is formulated as a relativistically and mathematically exact refraction process based on an exact index of refraction. This reformulation leads to that index as an…
There is considerable interest in the application of quantum information science to advance computations in plasma physics. Many of the topics in fusion plasma physics are classical in nature. In order to implement them on quantum computers…
This paper aims to present an elaborate view on the motivation and realization of the idea to extend Maxwell's electrodynamics to Extended Electrodynamics in a reasonable and appropriate way in order to make it possible to describe…
In this paper, asymptotic expansions of the distributions and densities of powered extremes for Maxwell samples are considered. The results show that the convergence speeds of normalized partial maxima relies on the powered index.…
In this paper, we present some geometric properties of the maximum entropy (MaxEnt) Tsallis- distributions under energy constraint. In the case q > 1, these distributions are proved to be marginals of uniform distributions on the sphere; in…
We will display the fundamental structure of classical electrodynamics. Starting from the axioms of (1) electric charge conservation, (2) the existence of a Lorentz force density, and (3) magnetic flux conservation, we will derive Maxwell's…
In this work, we have discussed the Maxwell's electrodynamics in non-linear forms in FRW universe. The energy density and pressure for non-linear electrodynamics have been written in the electro-magnetic universe. The Einstein's field…