Related papers: A Note on the Justification of the Eddy Current Mo…
We discuss the well-posedness of the 'transient eddy current' magneto-quasistatic approximation of Maxwell's initial value problem with bounded and measurable conductivity, with sources, on a domain. We prove existence and uniqueness of…
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…
An analysis of the concept of orientation used in electrodynamics is presented. At least two different versions are encountered in the literature. Both are clearly identified and comparisons are made.
For low-frequency electromagnetic problems, where wave-propagation effects can be neglected, eddy current formulations are commonly used as a simplification of the full Maxwell's equations. In this setup, time-domain simulations, needed to…
An integral equation reformulation of the Maxwell transmission problem is presented. The reformulation uses techniques such as tuning of free parameters and augmentation of close-to-rank-deficient operators. It is designed for the eddy…
We present an abstract framework for parabolic type equations which possibly degenerate on certain spatial regions. The degeneracies are such that the equations under investigation may admit a type change ranging from parabolic to elliptic…
Motivated by various applications, this article develops the notion of boundary control for Maxwell's equations in the frequency domain. Surface curl is shown to be the appropriate regularization in order for the optimal control problem to…
The constraint equations in Maxwell theory are investigated. In analogy with some recent results on the constraints of general relativity it is shown, regardless of the signature and dimension of the ambient space, that the "divergence of a…
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…
We are concerned with increasing stability in the inverse source problems for the time-dependent Maxwell equations in R^3 , where the source term is compactly supported in both time and spatial variables. By using the Fourier transform,…
We outline a regular way for solving Maxwell's equations. We take, as the starting point, the notion of vector potentials. The rationale for introducing this notion in electrodynamics is that the set of Maxwell's equations is seemingly…
A simple model of eddy currents in which current is computed solely from magnetic forces acting on electrons proves accessible to introductory students and gives a good qualitative account of eddy current forces. However, this model cannot…
Expectation values of the electromagnetic field and the electric current are introduced at space-time resolution which belongs to the quantum domain. These allow us to approach some key features of classical electrodynamics from the…
Advanced electromagnetic potentials are indigenous to the classical Maxwell theory. Generally however they are deemed undesirable and are forcibly excluded, destroying the theory's inherent time-symmetry. We investigate the reason for this,…
We refine the understanding of continuous dependence on coefficients of solution operators under the nonlocal $H$-topology viz Schur topology in the setting of evolutionary equations in the sense of Picard. We show that certain components…
This paper is concerned with the derivation of computable and guaranteed upper and lower bounds of the difference between the exact and the approximate solution of a boundary value problem for static Maxwell equations. Our analysis is based…
Maxwell's equations describe the relation of charge and electric force almost perfectly even though electrons and permanent charge were not in his equations, as he wrote them. For Maxwell, all charge depended on electric field. Charge was…
The spatial discretization of the magnetic vector potential formulation of magnetoquasistatic field problems results in an infinitely stiff differential-algebraic equation system. It is transformed into a finitely stiff ordinary…
It is commonly asserted that the electromagnetic current is conserved and therefore is not renormalized. Within QED we show (a) that this statement is false, (b) how to obtain the renormalization of the current to all orders of perturbation…
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…