Related papers: Target signatures for thin surfaces
We consider several intriguingly connected topics in the theory of wave propagation: geometrical characterizations of radiationless sources, non-radiating incident waves, interior transmission eigenfunctions, and their applications to…
Scanning tunnelling microscopy (STM) is a powerful technique for imaging surfaces with atomic resolution, providing insight into physical and chemical processes at the level of single atoms and molecules. A regular task of STM image…
A rigorous mathematical model and an efficient computational method are proposed to solving the inverse elastic surface scattering problem which arises from the near-field imaging of periodic structures. We demonstrate how an enhanced…
We are concerned with the inverse scattering problems associated with incomplete measurement data. It is a challenging topic of increasing importance in many practical applications. Based on a prototypical working model, we propose a…
It is well-known that classical optical cavities can exhibit localized phenomena associated to scattering resonances, leading to numerical instabilities in approximating the solution. This result can be established via the ``quasimodes to…
This work investigates the long time asymptotic behavior of some inhomogeneous non-linear Schr\"odinger type equations. We give sharp a threshold of scattering versus non-scattering of mass solutions, depending on the source term. This work…
We consider the 3D inverse scattering problem with non-over-determined scattering data. The data are the scattering amplitude $A(\beta, \alpha_0, k)$ for all $\beta \in S_\beta^2$, where $S_\beta^2$ is an open subset of the unit sphere…
We present a framework to solve the open problem of formulating the inverse scattering method (ISM) for an integrable PDE on a star-graph. The idea is to map the problem on the graph to a matrix initial-boundary value (IBV) problem and then…
We provide a new analytical and computational study of the transmission eigenvalues with a conductive boundary condition. These eigenvalues are derived from the scalar inverse scattering problem for an inhomogeneous material with a…
We study ground-penetrating synthetic aperture radar measurements of scattering by targets located below a rough air-soil interface. By considering the inherent space/angle limitations of this imaging modality, we introduce a simplified…
We present in this work a numerical model for characterizing the scattering properties of the human lens. After analyzing the scattering properties of two main scattering particles actually described in the literature through Finite Element…
This paper considers 3-D elastic scattering problems by penetrable obstacles with embedded objects. The well-posedness of transmission problem is proved by employing integral equation method. Then the Inverse Problems , which is to recover…
In this paper, we investigate two transmission eigenvalue problems associated with the scattering of a media with a coated boundary. In recent years, there has been a lot of interest in studying these eigenvalue problems. It can be shown…
Scattering problem for a self-adjoint integro-differential operator, which is the sum of the operator of second derivative and of a finite-dimensional self-adjoint operator, is studied. Jost solutions are found and it is shown that the…
Sensing and manipulating targets hidden under scattering media are universal problems that take place in applications ranging from deep-tissue optical imaging to laser surgery. A major issue in these applications is the shallow light…
We consider the scattering of time-harmonic electromagnetic waves by a penetrable thin tubular scattering object in three-dimensional free space. We establish an asymptotic representation formula for the scattered wave away from the thin…
We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…
Inverse wave scattering aims at determining the properties of an object using data on how the object scatters incoming waves. In order to collect information, sensors are put in different locations to send and receive waves from each other.…
Linear regression is a fundamental and primitive problem in supervised machine learning, with applications ranging from epidemiology to finance. In this work, we propose methods for speeding up distributed linear regression. We do so by…
We study an inverse source scattering problem for the Schr\"odinger equation with a quadratic nonlinearity. In general, uniqueness of inverse source problems can not be guaranteed at a fixed energy. Therefore, additional information is…