Related papers: Direct and inverse problems for the nonlinear time…
This paper considers the inverse problem of scattering of time-harmonic acoustic and electromagnetic plane waves by a bounded, inhomogeneous, penetrable obstacle with embedded objects inside. A new method is proposed to prove that the…
We study transverse magnetic (vector valued) wave-packets in the time dependent Kerr nonlinear Maxwell's equations at the interface of two inhomogeneous dielectrics with an instantaneous material response. The resulting model is…
We derive and interpret solutions of time-harmonic Maxwell's equations with a vertical and a horizontal electric dipole near a planar, thin conducting film, e.g. graphene sheet, lying between two unbounded isotropic and non-magnetic media.…
Analytical solutions are presented for the electromagnetic radiation by an arbitrary pulsed source into a homogeneous time-varying background medium. In the constant-impedance case an explicit radiation formula is obtained for the…
The inverse electromagnetic scattering problem for anisotropic media in general does not have a unique solution. A possible approach to this problem is through the use of appropriate "target signatures," i.e. eigenvalues associated with the…
We consider a linearised inverse conductivity problem for electromagnetic waves in a three dimensional bounded domain at a high time-harmonic frequency. Increasing stability bounds for the conductivity coefficient in the full Maxwell system…
A novel method to solve inverse problems for the wave equation is introduced. The method is a combination of the boundary control method and an iterative time reversal scheme, leading to adaptive imaging of coefficient functions of the wave…
We study the wave equation in a bounded domain or on a compact Riemannian manifold with boundary. Assume that we are given the hyperbolic Neumann-to-Dirichlet map on the boundary corresponding to physical boundary measurements. We consider…
The arrival time of electromagnetic signals traveling in chiral cosmic media is investigated in the context of Maxwell-Carroll-Field-Jackiw electrodynamics. Considering the interstellar medium (ISM) as a cold, ionized, chiral plasma, we…
We prove that, when linearized, the governing equations of an incompressible elastic continuum yield Maxwell's equations as corollaries. Through judicious distinction between the referential and local descriptions, the principle of material…
A Dirichlet problem is considered for the eikonal equation in an anisotropic medium. The nonlinear boundary value problem (BVP) formulated in the present work is the limit of the diffusion-reaction problem with a reaction parameter tending…
In this paper we consider the inverse electromagnetic scattering for a cavity surrounded by an inhomogeneous medium in three dimensions. The measurements are scattered wave fields measured on some surface inside the cavity, where such…
In this work we study linear Maxwell equations with time- and space-dependent matrix-valued permittivity and permeability on domains with a perfectly conducting boundary. This leads to an initial boundary value problem for a first order…
Nonlinear electrodynamics naturally arises in quantum field theory, where the electromagnetic vacuum behaves as an effective nonlinear optical medium, leading to phenomena such as vacuum birefringence and dichroism. Among the recently…
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,…
A quantum nature of vacuum is expected to affect electromagnetic fields in vacuum as a nonlinear correction, yielding nonlinear Maxwell's equations. We extend the finite-difference time-domain (FDTD) method in the case that the nonlinear…
The conventional description of time-varying media assumes that electromagnetic fields evolve according to fixed continuity conditions during parameter jumps. Here we reveal that these conditions are not physical constraints but tunable…
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…
We show that Maxwell's electromagnetism can be mapped into the Born-Infeld theory in a curved space-time, which depends only on the electromagnetic field in a specific way. This map is valid for any value of the two lorentz invariants $F$…
We study space-time noncommutativity applied to the hydrogen atom and the phenomenological aspects induced. We find that the noncommutative effects are similar to those obtained by considering the extended charged nature of the proton in…