Related papers: Green's function for the wavized Maxwell fish-eye …
Kinsler and Favaro point out correctly that Blaikie's numerical solution of Maxwell's equations in Maxwell's fish eye is causal and hence valid, a solution where no perfect image is formed. It is wrong to conclude from the existence of a…
We have employed our recently developed Green's function formalism to study the dielectric behavior of a model membrane, formed by two periodic interfaces separating two media of different dielectric constants. The Maxwell's equations are…
We study three types of generalized partial fractional operators. An extension of Green's theorem, by considering partial fractional derivatives with more general kernels, is proved. New results are obtained, even in the particular case…
We discuss the imaging properties of uniaxial epsilon-near-zero metamaterial slabs with possibly tilted optical axis, analyzing their sub-wavelength focusing properties as a function of the design parameters. We derive in closed analytical…
Analytical solutions to the wave equation in spheroidal coordinates in the short wavelength limit are considered. The asymptotic solutions for the radial function are significantly simplified, allowing scalar spheroidal wave functions to be…
We compute a Green's function giving rise to the solution of the Cauchy problem for the source-free Maxwell's equations on a causal domain $\mathcal{D}$ contained in a geodesically normal domain of the Lorentzian manifold $AdS^5 \times…
In this paper we are interested in obtaining the exact expression and the study of the constant sign of the Green's function related to a second order perturbed periodic problem coupled with integral boundary conditions at the extremes of…
We consider a fractional Laplace equation and we give a self-contained elementary exposition of the representation formula for the Green function on the ball. In this exposition, only elementary calculus techniques will be used, in…
Energy functionals of the Green's function can simultaneously provide spectral and thermodynamic properties of interacting electrons' systems. Though powerful in principle, these formulations need to deal with dynamical…
We present a data-driven approach to mathematically model physical systems whose governing partial differential equations are unknown, by learning their associated Green's function. The subject systems are observed by collecting…
The Green-function technique, termed the irreducible Green functions (IGF) method, that is a certain reformulation of the equation-of motion method for double-time temperature dependent Green functions is presented. This method was…
In a recent series of scanning probe experiments, it became possible to visualize local electron flow in a two-dimensional electron gas. In this paper, a Green's function technique is presented that enables efficient calculation of the…
A first order differential equation of Green's Function, at the origin G(0), for the one- dimensional lattice is derived by simple recurrence relation. Green's Function at site (m)is then calculated in terms of G(0). A simple recurrence…
A new method is presented for Fourier decomposition of the Helmholtz Green Function in cylindrical coordinates, which is equivalent to obtaining the solution of the Helmholtz equation for a general ring source. The Fourier coefficients of…
Marchenko focusing functions are in their essence wavefields that satisfy the wave equation subject to a set of boundary, initial, and focusing conditions. Here, we show how Marchenko focusing functions can be modeled by finding the…
We establish the existence, uniqueness, and various estimates for Green functions of mixed Dirichlet-conormal derivative problems for the stationary Stokes system with measurable coefficients in a two-dimensional Reifenberg flat domain with…
We establish a local Harnack inequality in a neighborhood of an indecomposable singular point of a stationary integral varifold. Extending the method of Gr\"uter and Widman \cite{gruter1982green}, we construct the Green function on a…
Perfect imaging has been believed to rely on negative refraction, but here we show that an ordinary positively-refracting optical medium may form perfect images as well. In particular, we establish a mathematical proof that Maxwell's fish…
We present a general formula for the particular solution of an inhomogeneous linear difference equation with variable coefficients. The answer is expressed as a weighted sum of fundamental solutions of the associated linear difference…
In this review paper we stress the importance of the higher transcendental Wright functions of the second kind in the framework of Mathematical Physics.We first start with the analytical properties of the classical Wright functions of which…