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It is shown that the set of equations known as Maxwell's equations perfectly describe two very different systems: (1) the usual electromagnetic phenomena in vacuum or in the matter and (2) the deformation of isotropic solid lattices,…
Maxwell's equations for the time-dependent electromagnetic field in a homogeneous chiral medium are reduced to a single quaternionic equation. Its fundamental solution satisfying the causality principle is obtained which allows us to solve…
This paper treats the time-harmonic electro-magnetic scattering or radiation problem governed by Maxwell's equations in an exterior weak Lipschitz domain divided into two disjoint weak Lipschitz parts We will present a solution theory using…
The problem of finding the elastic strains arising due to the converse flexoelectric effect is solved for a case of uniformly polarized ball of isotropic dielectric material. The strains occurs due to the fact that, as shown in a previous…
A close examination of the Maxwell-Lorentz theory of electrodynamics reveals that polarization and magnetization of material media need not be treated as local averages over small volumes - volumes that nevertheless contain a large number…
We prove area inequalities for stable marginally outer trapped surfaces in Einstein-Maxwell-dilaton theory. Our inspiration comes on the one hand from a corresponding upper bound for the area in terms of the charges obtained recently by…
We discuss the radiation problem of total reflection for a time-harmonic generalized Maxwell system in a non-smooth exterior domain with non-smooth inhomogeneous, anisotropic coefficients converging near infinity with a certain rate towards…
By the extinction theorem we explore the Brewster effect in the external and internal reflections of electromagnetic wave associated with an anisotropic material that is both dielectric and magnetic, including metamaterials. We obtain…
We consider a coupled system of Maxwell's equations and the equations of elasticity, which is commonly used to model piezo-electric material behavior. The boundary influence is encoded as a separate dynamics on the boundary data spaces…
We show that axions interacting with abelian gauge fields obtain a potential from loops of magnetic monopoles. This is a consequence of the Witten effect: the axion field causes the monopoles to acquire an electric charge and alters their…
The magnetoelectric coupling of electrons in a three-dimensional solid can be effectively described by axion electrodynamics. Here we report the discovery of the fractional magnetoelectric effect in chiral anomalous semimetals of the…
In relation to the BSSN formulation of the Einstein equations, we write down the boundary conditions that result from the vanishing of the projection of the Einstein tensor normally to a timelike hypersurface. Furthermore, by setting up a…
A self-consistent theory for the classical description of the interaction of light and matter at the nano-scale is presented, which takes into account spatial dispersion. Up to now, the Maxwell equations in nanostructured materials with…
We study the local effects of an external time-dependent magnetic field on axion-like particles assuming they are all the dark matter of the universe. We find that under suitable conditions the amplitude of the dark matter field can…
The surface tension of quark matter in a strong magnetic field is investigated using a geometric approach. The interface between the hadronic phase and quark phase is determined by the Maxwell construction of the first-order transition.…
We study the constraints imposed on the electromagnetic response of general media by microcausality (commutators of local fields vanish outside the light cone) and positivity of the imaginary parts (the medium can only absorb energy from…
We are interested in the uniqueness of solutions to Maxwell's equations when the magnetic permeability $\mu$ and the permittivity $\varepsilon$ are symmetric positive definite matrix-valued functions in $\mathbb{R}^{3}$. We show that a…
In a bounded domain $\mathcal{O}\subset\mathbb{R}^3$ of class $C^{1,1}$, we consider a stationary Maxwell system with the perfect conductivity boundary conditions. It is assumed that the dielectric permittivity and the magnetic permeability…
We consider mathematical aspects of the axion electrodynamics in application to the problem of evolution of geomagnetic and terrestrial electric fields, which are coupled by relic axions born in the early Universe and (hypothetically)…
It is shown that in rather strong magnetic field the interlayer electron conductivity is exponentially damped by the Coulomb barrier arising from the formation of polaron around each localized electron state. The theoretical model is…