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A complete and consistent inversion technique is proposed to derive an accurate interaction potential from an effective-range function for a given partial wave in the neutral case. First, the effective-range function is Taylor or Pad\'e…
We are concerned with the acoustic scattering problem, at a frequency $\kappa$, by many small obstacles of arbitrary shapes with impedance boundary condition. These scatterers are assumed to be included in a bounded domain $\Omega$ in…
This work studies a posteriori error estimates and their use for time-dependent acoustic scattering problems, formulated as a time-dependent boundary integral equation based on a single-layer ansatz. The integral equation is discretized by…
Accurate spectral analysis of high-energy astrophysical sources often relies on comparing observed data to incident spectral models convolved with the instrument response. However, for Gamma-Ray Bursts and other high-energy transient events…
The high energy physics unfolding problem is an important statistical inverse problem in data analysis at the Large Hadron Collider (LHC) at CERN. The goal of unfolding is to make nonparametric inferences about a particle spectrum from…
We discuss a time-harmonic inverse scattering problem for the Helmholtz equation with compactly supported penetrable and possibly inhomogeneous scattering objects in an unbounded homogeneous background medium, and we develop a monotonicity…
This paper gives a remark on the Enclosure Method by considering inverse obstacle scattering problems with a single incident wave whose governing equation is given by the Helmholtz equation in two dimensions. It is concerned with the…
We show that spectral synthesis thresholds are governed by a quantitative spectral complexity parameter, the Fourier Ratio, in addition to the geometric size of the Fourier support. In the Euclidean setting, we prove that if a compactly…
Radiative transfer (RT) problems in which the source function includes a scattering-like integral are typical two-points boundary problems. Their solution via differential equations implies to make hypotheses on the solution itself, namely…
This paper proposes four new methods to decontaminate spectra of stars and galaxies resulting from slitless spectroscopy used in many space missions such as Euclid. These methods are based on two distinct approaches and simultaneously take…
To identify some way to measure the quark transversity, this thesis analyzes one-particle and two-particle inclusive deep inelastic scattering, where one and two of the outgoing hadrons are detected in coincidence with the electron. It is…
The $N^*(1535)$ can be dynamically generated in the chiral unitary approach with the coupled channels, $K^0 \Sigma^+, K^+ \Sigma^0, K^+ \Lambda$ and $\eta p$. In this work we evaluate the correlation functions for every channel and face the…
This work investigates both direct and inverse problems of the variable-exponent sub-diffusion model, which attracts increasing attentions in both practical applications and theoretical aspects. Based on the perturbation method, which…
Neutrino-electron scattering is a purely leptonic fundamental interaction and therefore provides an important channel to test the Standard Model, especially at the low energy-momentum transfer regime. We derived constraints on neutrino…
This paper addresses the inverse obstacle scattering problem of simultaneously reconstructing the obstacle geometry and boundary conditions from multi-frequency near-field backscattering data. We first establish rigorous high-frequency…
This paper is concerned with time domain forward scattering and inverse scattering problems with a single moving point source as the emitter. Approximate solutions are provided for the forward scattering problem with a moving emitter.…
We present a new expression of the scattering amplitude, valid for spherical absorbing objects, which leads to an improved version of the eikonal method outside the diffraction region. Limitations of this method are discussed and numerical…
The simulation of light scattering by particles on a substrate with the $T$-matrix method relies on the expansion of the scattered field in spherical waves, followed by a plane wave expansion to allow the evaluation of the reflection from…
A recently re-discovered variant of the Backus-Gilbert algorithm for spectral reconstruction enables the controlled determination of smeared spectral densities from lattice field theory correlation functions. A particular advantage of this…
We propose a non-perturbative numerical approach to calculate the spectrum of a many-body Hamiltonian with time and momentum resolution by exactly recreating a scattering event using the time-dependent Schr\"odinger equation. Akin an actual…