Related papers: On the Solvability of Maxwell's Equations
The Inverse problem for an electromagnetic field produced by a dipole is solved. It is assumed that the field of an arbitrary changing dipole is known. Obtained formulae allow calculation of the position and dynamics of the dipole which…
We study, for times of order 1/h, solutions of Maxwell's equations in an O(h^2) modulation of an h-periodic medium. The solutions are of slowly varying amplitude type built on Bloch plane waves with wavelength of order h. We construct…
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…
In this paper we express the retarded fields of Maxwell's theory in terms of the instantaneous fields of a Galilei-invariant electromagnetic and we find the vector function whose spatial and temporal derivatives transform the instantaneous…
In a calculation that directly parallels the derivation of the Thomas precession, the first time derivative of the retarded potentials is derived. The solutions have to be integrated in time to obtain the potential solution. The Thomas…
In this paper we present a methodology for increasing the accuracy and accelerating the convergence of numerical methods for solution of Maxwell's equations in the frequency domain by taking into account the be-havior of the electromagnetic…
The intensity peak of a "flying focus" travels at a programmable velocity over many Rayleigh ranges while maintaining a near-constant profile. Assessing the extent to which these features can enhance laser-based applications requires an…
We prove Strichartz estimates for solutions to Maxwell equations in three dimensions with rough permittivities, which have less than three different eigenvalues. To this end, Maxwell equations are conjugated to half-wave equations in phase…
We considered the electromagnetic field of a charge moving with a constant acceleration along an axis. We found that this field obtained from the Li\'enard-Wiechert potentials does not satisfy Maxwell equations if one considers exclusively…
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…
We show that in the Maxwell-Lorentz theory of classical electrodynamics most initial values for fields and particles lead to an ill-defined dynamics, as they exhibit singularities or discontinuities along light-cones. This phenomenon…
Maxwell equations are solved in a layer comprising a finite number of homogeneous isotropic dielectric regions ended by anisotropic perfectly matched layers (PMLs). The boundary-value problem is solved and the dispersion relation inside the…
Nonlinear Maxwell equations are written up to the third-power deviations from a constant-field background, valid within any local nonlinear electrodynamics including QED with a Euler-Heisenberg (EH) effective Lagrangian. The linear electric…
We develop the method of vector-fields to further study Dispersive Wave Equations. Radial vector fields are used to get a-priori estimates such as the Morawetz estimate on solutions of Dispersive Wave Equations. A key to such estimates is…
The connection between the Lorentz invariance violation in the lagrangean context and the quantum theory of noncommutative fields is established for the U(1) gauge field. The modified Maxwell equations coincide with other derivations…
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…
There is a fundamental difference between the classical expression for the retarded electromagnetic potential and the corresponding retarded solution of the wave equation that governs the electromagnetic field. While the boundary…
In this paper we consider an abstract Cauchy problem for a Maxwell system modelling electromagnetic fields in the presence of an interface between optical media. The electric polarization is in general time-delayed and nonlinear, turning…
Starting from space-discretisation of Maxwell's equations, various classical formulations are proposed for the simulation of electromagnetic fields. They differ in the phenomena considered as well as in the variables chosen for…
The fact that electromagnetic effects propagate at the speed of light suggests how the Lorenz-gauge scalar and vector potentials of a uniformly moving point charge must be modified when the charge was initially at rest and then set suddenly…