Wiener-Hopf solution for impenetrable wedges at skew incidence

A new Wiener-Hopf approach for the solution of impenetrable wedges at skew incidence is presented. Mathematical aspects are described in a unified and consistent theory for angular region problems. Solutions are obtained using analytical and numerical-analytical approaches. Several numerical tests from the scientific literature validate the new technique, and new solutions for anisotropic surface impedance wedges are solved at skew incidence. The solutions are presented considering the geometrical and uniform theory of diffraction coefficients, total fields, and possible surface wave contribution

Generalized Wiener-Hopf Equations for Wedge problems involving arbitrary linear media

This paper provides new functional equations in angular regions that turn useful to study wedge problems in presence of arbitrary linear media. The enforcement of the boundary conditions on these equations reduces the wedge problems to Generalized Wiener-Hopf (GWHE) equations that can be approached with standard solution techniques. This procedure is briefly illustrated in this pape

Size-independent cylindrical resonator half-filled with DNG metamaterial

A circular cylindrical metallic resonator half filled with DPS material and half with DNG metamaterial is analyzed, in the frequency domain. The two materials are linear, lossless, homogeneous, and anti-isorefractive to each other. The electric field is assumed to be parallel to the cylinder axis. It is shown that the resonator performs independently of diameter size. Numerical results are presented and discussed for a resonator excited by a line source parallel to the axis

Riemann–Hilbert problems, Toeplitz operators and Q-classes

We generalize the notion of Q-classes C(Q1,Q2) , which was introduced in the context of Wiener–Hopf factorization, by considering very general 2 × 2 matrix functions Q1, Q2. This allows us to use a mainly algebraic approach to obtain several equivalent representations for each class, to study the intersections of Q-classes and to explore their close connection with certain non-linear scalar equations. The results are applied to various factorization problems and to the study of Toeplitz operators with symbol in a Q-class. We conclude with a group theoretic interpretation of some of the main results.Fundação para a Ciência e a Tecnologia (FCT/Portugal), through Project PTDC/MAT/121837/2010 and Project Est- C/MAT/UI0013/2011. The first author was also supported by the Center for Mathematical Analysis, Geometry, and Dynamical Systems and the second author was also supported by the Centre of Mathematics of the University of Minho through the FEDER Funds Programa Operacional Factores de Competitividade COMPET