ﻻ يوجد ملخص باللغة العربية
We establish the well-posedness, the finite speed propagation, and a regularity result for Maxwells equations in media consisting of dispersive (frequency dependent) metamaterials. Two typical examples for such metamaterials are materials obeying Drudes and Lorentz models. The causality and the passivity are the two main assumptions and play a crucial role in the analysis. It is worth noting that by contrast the well-posedness in the frequency domain is not ensured in general. We also provide some numerical experiments using the Drudes model to illustrate its dispersive behaviour.
Surveys on wave propagation in dispersive media have been limited since the pioneering work of Sommerfeld [Ann. Phys. 349, 177 (1914)] by the presence of branches in the integral expression of the wave function. In this article, a method is proposed
We consider quantum walks with position dependent coin on 1D lattice $mathbb{Z}$. The dispersive estimate $|U^tP_c u_0|_{l^infty}lesssim (1+|t|)^{-1/3} |u_0|_{l^1}$ is shown under $l^{1,1}$ perturbation for the generic case and $l^{1,2}$ perturbation
We study the behavior of wave propagation in materials for which not all of the principle elements of the permeability and permittivity tensors have the same sign. We find that a wide variety of effects can be realized in such media, including negati
The extreme magnetoelectric medium (EME medium) is defined in terms of two medium dyadics, $alpha$, producing electric polarization by the magnetic field and $beta$, producing magnetic polarization by the electric field. Plane-wave propagation of tim
In arXiv:1201.4067 and arXiv:1611.08030, Eyink and Shi and Chibbaro et al., respectively, formally derived an infinite, coupled hierarchy of equations for the spectral correlation functions of a system of weakly interacting nonlinear dispersive waves