ترغب بنشر مسار تعليمي؟ اضغط هنا

Effective Maxwells equations in general periodic microstructures

76   0   0.0 ( 0 )
 نشر من قبل Maik Urban
 تاريخ النشر 2017
  مجال البحث
والبحث باللغة English
 تأليف Ben Schweizer




اسأل ChatGPT حول البحث

We study the time harmonic Maxwell equations in a meta-material consisting of perfect conductors and void space. The meta-material is assumed to be periodic with period $eta > 0$; we study the behaviour of solutions $(E^{eta}, H^{eta})$ in the limit $eta to 0$ and derive an effective system. In geometries with a non-trivial topology, the limit system implies that certain components of the effective fields vanish. We identify the corresponding effective system and can predict, from topological properties of the meta-material, whether or not it permits the propagation of waves.



قيم البحث

اقرأ أيضاً

This paper provides a view of Maxwells equations from the perspective of complex variables. The study is made through complex differential forms and the Hodge star operator in $mathbb{C}^2$ with respect to the Euclidean and the Minkowski metrics. It shows that holomorphic functions give rise to nontrivial solutions, and the inner product between the electric and the magnetic fields is considered in this case. Further, it obtains a simple necessary and sufficient condition regarding harmonic solutions to the equations. In the end, the paper gives an interpretation of the Lorenz gauge condition in terms of the codifferential operator.
In this work, we are interested in the analysis of time-harmonic Maxwells equations in presence of a conical tip of a material with negative dielectric constants. When these constants belong to some critical range, the electromagnetic field exhibits strongly oscillating singularities at the tip which have infinite energy. Consequently Maxwells equations are not well-posed in the classical $L^2$ framework. The goal of the present work is to provide an appropriate functional setting for 3D Maxwells equations when the dielectric permittivity (but not the magnetic permeability) takes critical values. Following what has been done for the 2D scalar case, the idea is to work in weighted Sobolev spaces, adding to the space the so-called outgoing propagating singularities. The analysis requires new results of scalar and vector potential representations of singular fields. The outgoing behaviour is selected via the limiting absorption principle.
Let $V(t) = e^{tG_b},: t geq 0,$ be the semigroup generated by Maxwells equations in an exterior domain $Omega subset {mathbb R}^3$ with dissipative boundary condition $E_{tan}- gamma(x) ( u wedge B_{tan}) = 0, gamma(x) > 0, forall x in Gamma = parti al Omega.$ We study the case when $Omega = {x in {mathbb R^3}:: |x| > 1}$ and $gamma eq 1$ is a constant. We establish a Weyl formula for the counting function of the negative real eigenvalues of $G_b.$
70 - Yanli Chen , Peijun Li , Xu Wang 2020
This paper is concerned with the mathematical analysis of the time-domain electromagnetic scattering problem in an infinite rectangular waveguide. A transparent boundary condition is developed to reformulate the problem into an equivalent initial bou ndary value problem in a bounded domain. The well-posedness and stability are obtained for the reduced problem. The perfectly matched layer method is studied to truncate the waveguide. It is shown that the truncated problem attains a unique solution. Moreover, an explicit error estimate is given between the solutions of the original scattering problem and the truncated problem. Based on the estimate, the stability and exponential convergence are established for the truncated problem. The optimal bound is achieved for the error with explicit dependence on the parameters of the perfectly matched layer.
We study the homogenization of elliptic systems of equations in divergence form where the coefficients are compositions of periodic functions with a random diffeomorphism with stationary gradient. This is done in the spirit of scalar stochastic homog enization by Blanc, Le Bris and P.-L. Lions. An application of the abstract result is given for Maxwells equations in random dissipative bianisotropic media.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا