Related papers: Bayesian Analysis Reveals the Key to Extracting Pa…
This paper is concerned with inverse acoustic scattering problem of inferring the position and shape of a sound-soft obstacle from phaseless far-field data. We propose the Bayesian approach to recover sound-soft disks, line cracks and…
A review of the author's results is given. Inversion formulas and stability estimates for the solutions to 3D inverse scattering problems with fixed-energy data are obtained. Inversions of exact and noisy data are stidied. The inverse…
This paper is concerned with uniqueness, phase retrieval and shape reconstruction methods for inverse elastic scattering problems with phaseless far field data. Systematically, we study two basic models, i.e., inverse scattering of plane…
Deep inelastic scattering is considered in a statistical model of the nucleon. This incorporates certain features which are absent in the standard parton model such as quantum statistical correlations which play a role in the propagation of…
The past decade or so has witnessed a large number of articles about water structure. The most incisive experiments involve radiation with a wavelength compatible with the observed inter-molecular separations found in water, of order $\sim…
In this work, we propose a linear machine learning force matching approach that can directly extract pair atomic interactions from ab initio calculations in amorphous structures. The local feature representation is specifically chosen to…
We consider a Bargmann-type rational parametrization of the nucleon scattering phase shifts. Applying Marchenko's method of quantum inverse scattering we show that the scattering data suggest a singular repulsive core of the potential of…
In an attempt to test the possibility of solving the inverse problem for liquid metals i.e. obtaining the effective pair potential from the experimental structure factor, we solve the modified Hypernetted-Chain Integral equation for liquid…
The inverse Henderson problem refers to the determination of the pair potential which specifies the interactions in an ensemble of classical particles in continuous space, given the density and the equilibrium pair correlation function of…
Neutrons and x-rays are coherent probes, and their coherent properties are used in scattering experiments. Only coherent scattering probes can elucidate collective molecular motions. While phonons in crystals were studied for half a century…
Nuclear density functional theory (DFT) is one of the main theoretical tools used to study the properties of heavy and superheavy elements, or to describe the structure of nuclei far from stability. While on-going efforts seek to better…
Bayesian filtering deals with computing the posterior distribution of the state of a stochastic dynamic system given noisy observations. In this paper, motivated by applications in counter-adversarial systems, we consider the following…
We define scattering data for the Newton equation in a potential $V\in C^2(\R^n,\R)$, $n\ge2$, that decays at infinity like $r^{-\alpha}$ for some $\alpha\in (0,1]$. We provide estimates on the scattering solutions and scattering data and…
We introduce a computational framework to statistically infer thermophysical properties of any given wall from in-situ measurements of air temperature and surface heat fluxes. The proposed framework uses these measurements, within a…
We consider a fixed angle inverse scattering problem in the presence of a known Riemannian metric. First, assuming a no caustics condition, we study the direct problem by utilizing the progressing wave expansion. Under a symmetry assumption…
Bayesian methods have been widely used in the last two decades to infer statistical properties of spatially variable coefficients in partial differential equations from measurements of the solutions of these equations. Yet, in many cases…
This investigation is concerned with the 2D acoustic scattering problem of a plane wave propagating in a non-lossy fluid host and soliciting a linear, isotropic, macroscopically-homogeneous, lossy, flat-plane layer in which the mass density…
The problem of recovering the asymptotics of a short range perturbation of the Euclidean metric on R^n from fixed energy scattering data is studied. It is shown that if two such metrics, g1, g2, have scattering data at some fixed energy…
Many inverse problems arising in engineering and applied sciences involve unknown quantities with pronounced spatial inhomogeneity, such as localized defects or spatially varying material properties, making reliable uncertainty…
The problem of mixed signals occurs in many different contexts; one of the most familiar being acoustics. The forward problem in acoustics consists of finding the sound pressure levels at various detectors resulting from sound signals…