Related papers: Variations on the Maiani-Testa approach and the in…
In this paper we present a hybrid approach to numerically solve two-dimensional electromagnetic inverse scattering problems, whereby the unknown scatterer is hosted by a possibly inhomogeneous background. The approach is `hybrid' in that it…
A spherical tensor expansion is carried out to express the resonant inelastic scattering cross-section as a sum of products of fundamental spectra with tensors involving wavevectors and polarization vectors of incident and scattered…
This paper is concerned with a numerical method for a 3D coefficient inverse problem with phaseless scattering data. These are multi-frequency data generated by a single direction of the incident plane wave. Our numerical procedure consists…
A kinetic equation for Compton scattering is given that differs from the Kompaneets equation in several significant ways. By using an inverse differential operator this equation allows treatment of problems for which the radiation field…
We prove a fixed frequency inverse scattering result for the magnetic Schr\"odinger operator (or connection Laplacian) on surfaces with Euclidean ends. We show that, under suitable decaying conditions, the scattering matrix for the operator…
Inverse medium scattering is an ill-posed, nonlinear wave-based imaging problem arising in medical imaging, remote sensing, and non-destructive testing. Machine learning (ML) methods offer increased inference speed and flexibility in…
Given a compact Riemannian surface $M$, with Laplace-Beltrami operator $\Delta$, for $\lambda > 0$, let $P_{\lambda,\lambda^{-\frac{1}{3}}}$ be the spectral projector on the bandwidth $[\lambda-\lambda^{-\frac{1}{3}}, \lambda +…
Extended objects such as line or surface operators, interfaces or boundaries play an important role in conformal field theory. Here we propose a systematic approach to the relevant conformal blocks which are argued to coincide with the wave…
We study the query complexity of sampling from high-dimensional Gaussian distributions using gradient information. In the standard oracle model, exact gradients expose only matrix-vector products with the precision matrix, leading to…
We present first results on ultrafast X-ray scattering of strongly driven molecular Iodine and analysis of high-order anisotropic components of the scattering signal, up to four-photon absorption. We discuss the technical details of…
Within the framework of the Riemann-Hilbert problem, the theory of inverse scattering transform is established for the defocusing nonlinear Schr\"{o}dinger equation with local and nonlocal nonlinearities (which originates from the…
Methods from scattering theory are introduced to analyze random Schroedinger operators in one dimension by applying a volume cutoff to the potential. The key ingredient is the Lifshitz-Krein spectral shift function, which is related to the…
The time evolution of the scattering and spectral data is obtained for the differential operator $\displaystyle\frac{d^4}{dx^4} +\displaystyle\frac{d}{dx} u(x,t)\displaystyle\frac{d}{dx}+v(x,t),$ where $u(x,t)$ and $v(x,t)$ are real-valued…
Backward angle (u-channel) scattering provides complementary information for studies of hadron spectroscopy and structure, but has been less comprehensively studied than the corresponding forward angle case. As a result, the physics of…
Results are presented from numerical simulations of the flat-space nonlinear Maxwell-Klein-Gordon equations demonstrating deep inelastic scattering of $m=1$ vortices for a range of Ginzburg-Landau (or Abelian-Higgs) parameters ($\kappa$),…
Diffraction tomography aims to recover an object's scattering potential from measured wave fields. In the classical setting, the object is illuminated by plane waves from many directions, and the Fourier diffraction theorem provides a…
In this work we study the increasing resolution of linear inverse scattering problems at a large fixed frequency. We consider the problem of recovering the density of a Herglotz wave function, and the linearized inverse scattering problem…
Taking into account some likeness of moderate deviations (MD) and central limit theorems (CLT), we develop an approach, which made a good showing in CLT, for MD analysis of a family $$ S^\kappa_t=\frac{1}{t^\kappa}\int_0^tH(X_s)ds, \…
In many applications data are measured or defined on a spherical manifold; spherical harmonic transforms are then required to access the frequency content of the data. We derive algorithms to perform forward and inverse spin spherical…
An extended multi-hadron operator is developed to extract the spectra of irreducible representations in the finite volume. The irreducible representations of the cubic group are projected using a coordinate-space operator. The correlation…