3 citations · 3 across the 9 of their papers we have counts for
11 papers
Scattering of plane waves and a modified Pompeiu criterion
Narek Hovsepyan, Michael S. Vogelius
In this paper we prove that plane waves always scatter from bounded, strictly convex planar inhomogeneities with constant material parameters. Our approach involves the introductio…
On the potential lack of response in a model of second-harmonic generation. A computer-assisted proof
Miguel Ayala, Dominic Blanco, Fioralba Cakoni +2
This paper provides a rigorous computer-assisted proof of the existence of generalized transmission eigenvalues arising in nonlinear optics in the context of high-order harmonic ge…
Regularity and non-degeneracy of implies regularity of the fixed boundary
Henrik Garde, Michael S. Vogelius
For a diffeomorphism of a domain onto itself, which is the identity on , we prove that local regularity of the push-forward implies local regul…
Limiting Absorption Principle and Radiation Condition for the Fractional Helmholtz Equation
Dana Zilberberg, Fioralba Cakoni, Michael S. Vogelius
We investigate elliptic fractional equations in the whole space, involving zero order perturbations of the fractional Laplacian , . Our main objective is to determin…
Transmission Eigenvalues and Non-scattering
Fioralba Cakoni, Michael S. Vogelius
In this paper we survey some recent results concerning scattering and non-scattering in the context of the linear Helmholtz equation and inhomogeneities of nontrivial contrast. We…
Scattering of plane waves
Narek Hovsepyan, Michael S. Vogelius
We formulate a problem that can be viewed as a natural variation of the so-called Pompeiu or Schiffer problem in the context of scattering of plane waves for the Linear Helmholtz e…
Scattering from analytic and piecewise analytic inhomogeneities
Narek Hovsepyan, Michael S. Vogelius
We study scattering for the linear Helmholtz operator in two dimensions and develop a technique, which can be used to ascertain scattering of a given incident wave from very regula…
Perfectly matched layers in time domain. A simple two-dimensional error analysis
Kurt Bryan, Michael S. Vogelius
Perfectly Matched Layers (PML) has become a very common method for the numerical approximation of wave and wave-like equations on unbounded domains. This technique allows one to ob…
Finiteness Results for Non-Scattering Herglotz Waves: The case of inhomogeneities obtained by very general perturbations of disks
Michael S. Vogelius, Jingni Xiao
We study non-scattering phenomena associated with the time-harmonic Helmholtz equation in two dimensions. For very general classes of star-shaped domains, we show that there are at…
On the lack of external response of a nonlinear medium in the second-harmonic generation process
Fioralba Cakoni, Narek Hovsepyan, Matti Lassas +1
This paper concerns the scattering problem for a nonlinear medium of compact support, , with second-harmonic generation. Such a medium, when probed with monochromatic light beam…
Singularities Almost Always Scatter: Regularity Results for Non-scattering Inhomogeneities
Fioralba Cakoni, Michael S. Vogelius
In this paper we examine necessary conditions for an inhomogeneity to be non-scattering, or equivalently, by negation, sufficient conditions for it to be scattering. These conditio…