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This work applies the contact formalism of classical mechanics and classical field theory, introduced by Herglotz and later developed in the context of contact geometry, to describe electromagnetic systems with dissipation. In particular,…
We argue that the classical theory of electromagnetism is based on Maxwell's macroscopic equations, an energy postulate, a momentum postulate, and a generalized form of the Lorentz law of force. These seven postulates constitute the…
Recent proposals suggest using magnetically trapped superconducting spheres in the Meissner state to create low-loss mechanical oscillators with long coherence times. In these proposals the derivation of the force on the superconducting…
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 present a method developed to deal with electromagnetic wave propagation inside a material medium that reacts, in general, non-linearly to the field strength. We work in the context of Maxwell' s theory in the low frequency limit and…
This paper aims to present an elaborate view on the motivation and realization of the idea to extend Maxwell's electrodynamics to Extended Electrodynamics in a reasonable and appropriate way in order to make it possible to describe…
The macroscopic equations of Maxwell combined with a generalized form of the Lorentz law are a complete and consistent set; not only are these five equations fully compatible with the special theory of relativity, they also conform with the…
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…
We use Maxwell's equations in a sourceless, inhomogeneous medium with continuous permeability $\mu (\mathbf{r}) $ and permittivity $% \epsilon (\mathbf{r}) $ to study the wave propagation. The general form of the wave equation is derived…
In this letter we describe a new and simple approach for modulating the electromagnetic wave propagating in a dielectric medium in the form of solitons by considering the torque developed between the induced dipoles in the medium and…
We study the Helmholtz equation with electromagnetic-type perturbations, in the exterior of a domain, in dimension $n\geq3$. We prove, by multiplier techniques in the sense of Morawetz, a family of a priori estimates from which the limiting…
We present a Ginzburg-Landau theory of inhomogeneous polyelectrolytes with a polar solvent. First, we take into account the molecular (solvation) interaction among the ions, the charged monomers, the uncharged monomers, and the solvent…
We study the limiting absorption principle and the well-posedness of Maxwell equations with anisotropic sign-changing coefficients in the time-harmonic domain. The starting point of the analysis is to obtain Cauchy problems associated with…
The Maxwell equations for an homogeneous medium in which electric currents are composed of Ohmic, diffusive and impressed currents are written in the static approximation in which displacements currents are neglected. Closed exact…
By modeling a linear, anisotropic and inhomogeneous magnetodielectric medium with two independent set of harmonic oscillators, electromagnetic field is quantized in such a medium. The electric and magnetic polarizations of the medium are…
This paper suggests an axiomatic approach to Maxwell's equations. The basis of this approach is a theorem formulated for two sets of functions localized in space and time. If each set satisfies a continuity equation then the theorem…
This paper presents a brief review of the newly developed \emph{Extended Electrodynamics}. The relativistic and non-relativistic approaches to the extension of Maxwell equations are considered briefly, and the further study is carried out…
This paper formulates a new particle-in-cell method for the Vlasov-Maxwell system. Under the Lorenz gauge condition, Maxwell's equations for the electromagnetic fields can be written as a collection of scalar and vector wave equations. The…
A framework for premetric p-form electrodynamics is proposed. Independently of particular constitutive relations, the corresponding Maxwell equations are derived as a special case of stress theory in geometric continuum mechanics.…
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…