Related papers: Inverse conductivity problem with one measurement:…
This paper extends the concept of generalized polarization tensors (GPTs), which was previously defined for inclusions with homogeneous conductivities, to inhomogeneous conductivity inclusions. We begin by giving two slightly different but…
This paper deals with numerical methods for reconstruction of inhomogeneous conductivities. We use the concept of Generalized Polarization Tensors, which were introduced in [3], to do reconstruction. Basic resolution and stability analysis…
This paper concerns the inverse problem of determining a planar conductivity inclusion. Our aim is to analytically recover from the generalized polarization tensors (GPTs), which can be obtained from exterior measurements, a homogeneous…
A conductivity inclusion, inserted in a homogeneous background, induces a perturbation in the background potential. This perturbation admits a multipole expansion whose coefficients are the so-called generalized polarization tensors (GPTs).…
This paper is concerned with the open problem proposed in Ammari et. al. Commun. Math.Phys, 2013. We first investigate the existence and uniqueness of Generalized Polarization Tensors (GPTs) vanishing structures locally in both two and…
We consider the shape reconstruction of a conductivity inclusion in two dimensions. We use the concept of Faber polynomials Polarization Tensors (FPTs) introduced in \cite{choi:2018:GME} to derive an exact shape recovery formula for an…
We investigate the problem of planar conductivity inclusion with imperfect interface conditions. We assume that the inclusion is simply connected. The presence of the inclusion causes a perturbation in the incident background field. This…
In this work, we propose a novel method for the detailed reconstruction of transparent objects by exploiting polarimetric cues. Most of the existing methods usually lack sufficient constraints and suffer from the over-smooth problem. Hence,…
We present new alternative complete asymptotic expansions for the time harmonic low--frequency magnetic field perturbation caused by the presence of a conducting permeable object as its size tends to zero for the eddy current approximation…
Perturbation theory (PT) is often used to model statistical observables capturing the translation and rotation-invariant information in cosmological density fields. PT produces higher-order corrections by integration over linear statistics…
The insulating state of matter can be probed by means of a ground state geometrical marker, which is closely related to the modern theory of polarization (based on a Berry phase). In the present work we show that this marker can be applied…
Polarization of radiation is a powerful tool to study cosmic magnetism and analysis of polarization can be used as a diagnostic tool for large-scale structures. In this paper, we present a solid theoretical foundation for using polarized…
To calculate the conductivity of a material having full knowledge of its composition is a reasonably simple task. To do the same in reverse, i.e., to find information about the composition of a device from its conductivity response alone,…
Electromagnetic linear-to-circular polarization converters with wide- and multi-band capabilities can simplify antenna systems where circular polarization is required. Multi-band solutions are attractive in satellite communication systems,…
We consider the inverse scattering problem of retrieving the structural parameters of a stratified medium consisting of dispersive materials, given knowledge of the complex reflection coefficient in a finite frequency range. It is shown…
We derive transformation formulas for the generalized polarization tensors under rigid motions and scaling in three dimensions, and use them to construct an infinite number of invariants under those transformations. These invariants can be…
The vectorial evolution of polarized light interaction with a medium can reveal its microstructure and anisotropy beyond what can be obtained from scalar light interaction. Anisotropic properties (diattenuation, retardance, and…
We study an inverse problem involving the unique recovery of several lower order anisotropic tensor perturbations of a polyharmonic operator in a bounded domain from the knowledge of the Dirichlet to Neumann map on a part of boundary. The…
Gravitational polarization is examined for equilibrium self-gravitating polytropic sheets perturbed by gravitational field due to test mass sheet. We find equilibrium solutions to the corresponding perturbed Lane-Emden equations for…
Using polarization measurements in remote sensing and optical studies allows retrieving more information. We consider relationship between the reflection coefficients of plane and rough surfaces for linearly polarized waves. Certain…