Related papers: Wavelet Electrodynamics I
The representation of solutions of Maxwell's equations as superpositions of scalar wavelets with vector coefficients developed earlier is generalized to wavelets with polarization, which are matrix-valued. The construction proceeds in four…
In this paper we extend for the case of Maxwell equations the "X-shaped" solutions previously found in the case of scalar (e.g., acoustic) wave equations. Such solutions are localized in theory, i.e., diffraction-free and particle-like…
An integral representation of solutions of the wave equation as a superposition of other solutions of this equation is built. The solutions from a wide class can be used as building blocks for the representation. Considerations are based on…
New solutions of relativistic wave equations are obtained in a unified manner from generating functions of spinorial variables. The choice of generating functions as Gaussians leads to representations in the form of generalized fractional…
This paper investigates an adaptive wavelet collocation time domain method for the numerical solution of Maxwell's equations. In this method a computational grid is dynamically adapted at each time step by using the wavelet decomposition of…
A representation of solutions of the wave equation with two spatial coordinates in terms of localized elementary ones is presented. Elementary solutions are constructed from four solutions with the help of transformations of the affine…
Methods to solve the relativistic hydrodynamic equations are a key computational kernel in a large number of astrophysics simulations and are crucial to understanding the electromagnetic signals that originate from the merger of…
New elliptic cylindrical wavelets are introduced, which exploit the relationship between analysing filters and Floquet's solution of Mathieu differential equations. It is shown that the transfer function of both multiresolution filters is…
In the first part of this article the various experimental sectors of physics in which Superluminal motions seem to appear are briefly mentioned, after a sketchy theoretical introduction. In particular, a panoramic view is presented of the…
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 field is expanded in a wavelet series and the wavelet coefficients are varied in a simulation of the 2D $\phi^4$ field theory. The drastically reduced autocorrelations result in a substantial decrease of computing requirements, compared…
The main result of this paper is the proof that there are local electric and magnetic field configurations expressed in terms of field lines on an arbitrary hyperbolic manifold. This electromagnetic field is described by (dual) solutions of…
The robustness of XRD methods for the determination of the lattice parameters of crystals is well established. These methods have been extended to helical atomic structures using twisted x-rays \cite{friesecke_twisted_2016}. Building on an…
The paper formulates Maxwell's equations in 4-dimensional Euclidean space by embedding the electromagnetic vector potential in the frame vector $g_0$. Relativistic electrodynamics is the first problem tackled; in spite of using a geometry…
We present the exact solution to the linearized Maxwell equations in space-time slightly curved by a gravitational wave. We show that in general, even dealing with a first-order theory in the strength of the gravitational field, the…
Particle physics has for some time made extensive use of extended field configuations such as solitons, instantons, and sphalerons. However, no direct use has yet been made of the quite extensive literature on ``localized wave''…
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…
The notion of wavelets is defined. It is briefly described {\it what} are wavelets, {\it how} to use them, {\it when} we do need them, {\it why} they are preferred and {\it where} they have been applied. Then one proceeds to the…
We study a class of localized solutions of the wave equation, called eigenwavelets, obtained by extending its fundamental solutions to complex spacetime in the sense of hyperfunctions. The imaginary spacetime variables y, which form a…
We present the applications of variation -- wavelet analysis to polynomial/rational approximations for orbital motion in transverse plane for a single particle in a circular magnetic lattice in case when we take into account multipolar…