Related papers: A note on measures whose diffraction is concentrat…
The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].
A new set of discrete ordinates is proposed for one-dimensional radiative transfer in spheres with central symmetry. The set is structured with un-normalized circular functions. This resulted in a conservative and closed set of discrete…
We study the high frequency limit for the dissipative Helmholtz equation when the source term concentrates on a submanifold of R^n. We prove that the solution has a unique semi-classical measure, which is precisely described in terms of the…
Minkowski's Theorem asserts that every centered measure on the sphere which is not concentrated on a great subsphere is the surface area measure of some convex body, and, moreover, the surface area measure determines a convex body uniquely.…
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…
This study describes both experimentally and theoretically an important hitherto undiscovered feature of the scattering of micron_sized spherical objects when illuminated with highly focused circularly polarized light. This is a regime of…
We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…
This paper provides a theoretical analysis of diffraction-limited superresolution, demonstrating that arbitrarily close point sources can be resolved in ideal situations. Precisely, we assume that the incoming signal is a linear combination…
It is known that the surface of a cone over the unit disc with large height has smaller distortion than the standard embedding of the 2-sphere in $\mathbb R^3$. In this note we show that distortion minimisers exist among convex embedded…
The Thue-Morse system is a paradigm of singular continuous diffraction in one dimension. Here, we consider a planar system, constructed by a bijective block substitution rule, which is locally equivalent to the squiral inflation rule. For…
The present work reports a general method for the calculation of t he polarizability of a truncated sphere on a substrate. A multipole ex pansion is used, where the multipoles are not necessarily localized in the center of the sphere but…
In the recent years, mater-wave interferometry has attracted growing attention due to its unique suitability for high-precision measurements and study of fundamental aspects of quantum theory. Diffraction and interference of matter waves…
The paradigm for singular continuous spectra in symbolic dynamics and in mathematical diffraction is provided by the Thue-Morse chain, in its realisation as a binary sequence with values in $\{\pm 1\}$. We revisit this example and derive a…
The disturbance of the transmission of light through a diffusive medium due to an object hidden in it can be expressed in terms of an effective charge and dipole moment. In the mesoscopic regime, beyond the diffusion approximation, we…
Consider time-harmonic acoustic scattering from a bounded penetrable obstacle $D\subset \mathbb R^N$ embedded in a homogeneous background medium. The index of refraction characterizing the material inside $D$ is supposed to be H\"older…
In this paper, we study an inverse problem of determining the cross section of an infinitely long cylindrical-like material structure from the transverse electromagnetic scattering measurement. We establish a sharp logarithmic stability…
We investigate dimension-theoretic properties of concentric topological spheres, which are fractal sets emerging both in pure and applied mathematics. We calculate the box dimension and Assouad spectrum of such collections, and use them to…
We extend the classical Douglas integral, which expresses the Dirichlet integral of a harmonic function on the unit disk in terms of its value on boundary, to the case of conservative symmetric diffusion in terms of Feller measure, by using…
In this article, for a two dimensional fractional diffusion equation, we study an inverse problem for simultaneous restoration of the fractional order and the source term from the sparse boundary measurements. By the adjoint system…
We formulate a general set of consistency requirements, which are expected to be satisfied by the scattering matrices in the presence of reflecting boundaries. In particular we derive an equivalent to the boostrap equation involving the…