Related papers: Wavelet Electrodynamics I
A new relativistic description of quantum electrodynamics is presented. Guideline of the theory is the Klein-Gordon equation, which is reformulated to consider spin effects. This is achieved by a representation of relativistic vectors with…
We investigate a class of localized, stationary, particular numerical solutions to the Maxwell-Dirac system of classical nonlinear field equations. The solutions are discrete energy eigenstates bound predominantly by the self-produced…
In this paper, we discuss the Maxwell equations in terms of differential forms, both in the 3-dimensional space and in the 4-dimensional space-time manifold. Further, we view the classical electrodynamics as the curvature of a line bundle,…
A process-theoretic approach to electrodynamics based on persistent Kac-type stochastic processes is developed. Finite-velocity stochastic propagation is taken as primary, while relativistic wave equations arise as emergent descriptions…
Motivated by previous investigations on the radiative effects of the electric dipoles embedded in structured cavities, localization of electromagnetic waves in two dimensions is studied {\it ab initio} for a system consisting of many…
This paper studies highly oscillatory solutions to a class of systems of semilinear hyperbolic equations with a small parameter, in a setting that includes Klein--Gordon equations and the Maxwell--Lorentz system. The interest here is in…
A reduction of the Dirac-Maxwell equations in the case of static cylindrical symmetry is performed. The behaviour of the resulting system of o.d.e.'s is examined analytically and numerical solutions presented. There are two classes of…
For the first time, complete source distributions for the emission and absorption of acoustic and electromagnetic wavelets are defined and computed, both in spacetime and Fourier space. The biggest surprise is the great simplicity of the…
An Electrodynamics solver for moving sources is introduced. The main challenges and formulation are highlighted. The solver enables the simulation of fields for sources undergoing arbitrary motion. Two examples of uniformly moving current…
Wavelets are a powerful new mathematical tool which offers the possibility to treat in a natural way quantities characterized by several length scales. In this article we will show how wavelets can be used to solve partial differential…
In order to extend the limits of classical theory application in the microworld some weak generalization of Maxwell electrodynamics is suggested. It is shown that slightly generalized classical Maxwell electrodynamics can describe the…
The present study deals with total internal reflection of a plane electromagnetic wave at an infinite plane boundary between a transparent medium and an amplifying or attenuating lower-index medium. Solutions of Maxwell's equations are…
This paper develops an explicit spectral representation for solutions of a one-dimensional linear wave equation with a constant time delay. The model is considered on a bounded interval with non-homogeneous Dirichlet boundary data and a…
The regularized Maxwell theory is a recently discovered theory of non-linear electrodynamics that admits many important gravitating solutions within the Einstein theory. Namely, it was originally derived as the unique non-linear…
A new class of exact solutions of the Einstein-Maxwell system is found in closed form. This is achieved by choosing a generalised form for one of the gravitational potentials and a particular form for the electric field intensity. For…
We present a mimetic finite-difference approach for solving Maxwell's equations in one and two spatial dimensions. After introducing the governing equations and the classical Finite-Difference Time-Domain (FDTD) method, we describe mimetic…
Many continuous wavelets are defined in the frequency domain and do not have analytical expressions in the time domain. Meyer wavelet is ordinarily defined in this way. In this note, we derive new straightforward analytical expressions for…
This article deals with the study of electromagnetic waves equations and the Lorentz condition, as emergent properties of Maxwell's system in the context of systems theory. To do this, the wave equations and the Helmholtz equation are first…
We construct representations of a q-oscillator algebra by operators on Fock space on positive matrices. They emerge from a multiresolution scaling construction used in wavelet analysis. The representations of the Cuntz Algebra arising from…
We develop a solution theory for a generalized electro-magneto static Maxwell system in an exterior domain with anisotropic coefficients converging at infinity with a certain rate towards the identity. Our main goal is to treat right hand…