相关论文: Quaternionic equation for electromagnetic fields i…
Using octonions, more specifically, using a 4 x 4 matrix representation of octonions obtained with the help of algebraic properties of quaternions, we obtain the fully symmetric Maxwell's equations (Maxwell's equations with electric and…
A modified Faraday's law of electromagnetic induction in media is put forward.
The classification of exact solutions of Maxwell vacuum equations for the case when the electromagnetic fields and metrics of homogeneous spaces are invariant with respect to the motion group G(VII) is completed. All non-equivalent exact…
The aim of this article is to investigate the well-posedness, stability and convergence of solutions to the time-dependent Maxwell's equations for electric field in conductive media in continuous and discrete settings. The situation we…
In curved spacetime, Maxwell's equations can be expressed in forms valid in Minkowski background, with the effect of the metric (gravity) appearing as effective polarizations and magnetizations. The electric and magnetic (EM) fields depend…
We show that the Maxwell equations describing an electromagnetic wave are a mathematical consequence of the Einstein equations for the same wave. This fact is significant for the problem of the Einsteinian metrics corresponding to the…
Dual electrodynamics and corresponding Maxwell's equations (in the presence of monopole only) are revisited from dual symmetry and accordingly the quaternionic reformulation of field equations and equation of motion is developed in simple,…
We propose a new class of fundamental solutions for the numerical analysis of boundary value problems for the Maxwell equations. We prove completeness of systems of such fundamental solutions in appropriate Sobolev spaces on a smooth…
This note offers a conceptually straightforward and efficient way to formulate and solve problems in the electromagnetics of moving media based on a representation of Maxwell's equations in terms of differential forms on spacetime together…
The differential form of the Maxwell's equations was first derived based on an assumption that the media are stationary, which is the foundation for describing the electro-magnetic coupling behavior of a system. For a general case in which…
Quaternion analysis of time dependent Maxwell's equations in presence of electric and magnetic charges has been developed and the solutions for the classical problem of moving charges (electric and magnetic) are obtained in unique, simple…
A quantization scheme for the phenomenological Maxwell theory of the full electromagnetic field in an inhomogeneous three-dimensional, dispersive and absorbing dielectric medium is developed. The classical Maxwell equations with spatially…
In this note, we propose an exegesis of the Maxwell equations for electromagnetism. We begin with an analogy between the homogeneous Maxwell equations and the equations needed to describe the vorticity field of an incompressible inviscid…
The classical macroscopic Maxwell equations are approximated. They are a corollary of the multipole expansion of the local electrostatic potential up to dipolar terms. But quadrupolarization of the medium should not be neglected if the…
Spatially dispersive (also known as non-local) electromagnetic media are considered where the parameters defining the permittivity relation vary periodically. Maxwell's equations give rise to a difference equation corresponding to the…
Two known, alternative to each other, forms of the Maxwell's electromagnetic equations in a moving uniform media are investigated and discussed. Approach commonly used after Minkowski is based on the two tensors: H^{ab} = (D, H /c) and…
In the recent decades, it became more and more popular for engineers, physicists, and mathematicians alike to put the Maxwell equations into a generally covariant form. This is particularly useful for understanding the fundamental structure…
We derive a new eight dimensional matrix representation of the Maxwell equations for a linear homogeneous medium and extend it to the case of a linear inhomogneous medium. This derivation starts ab initio with the Maxwell equations and uses…
In this paper, using the Newman-Penrose formalism, we find the Maxwell equations in NUT space and after separation into angular and radial components solve them analytically. All the angular equations are solved in terms of Jaccobi…
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…