30 citations · 69 across the 22 of their papers we have counts for
27 papers
Solving the Scattering Problem for Open Wave-Guide Networks, III: Radiation Conditions and Uniqueness
Charles L. Epstein, Rafe Mazzeo
This paper continues the analysis of the scattering problem for a network of open wave-guides started in [arXiv:2302.04353, arXiv:2310.05816]. In this part we present explicit, phy…
Solving the Scattering Problem for Open Wave-Guide Networks, I Fundamental Solutions and Integral Equations
Charles L. Epstein
We introduce a layer potential representation for the solution of the transmission problem defined by two dielectric channels, or open wave-guides, meeting along the straight-line…
Debye source representation for type-I superconductors, I
Charles L. Epstein, Manas Rachh
In this note, we analyze the classical magneto-static approach to the theory of type I superconductors, and a Debye source representation that can be used numerically to solve the…
Recovering missing data in coherent diffraction imaging
David Barmherzig, Alex B. Barnett, Charles L. Epstein +3
In coherent diffraction imaging (CDI) experiments, the intensity of the scattered wave impinging on an object is measured on an array of detectors. This signal can be interpreted a…
Explicit unconditionally stable methods for the heat equation via potential theory
Alex H. Barnett, Charles L. Epstein, Leslie Greengard +2
We study the stability properties of explicit marching schemes for second-kind Volterra integral equations that arise when solving boundary value problems for the heat equation by…
Geometry of the Phase Retrieval Problem
Alexander Barnett, Charles L. Epstein, Leslie Greengard +1
One of the most powerful approaches to imaging at the nanometer or subnanometer length scale is coherent diffraction imaging using X-ray sources. For amorphous (non-crystalline) sa…