Related papers: A short guide to pure point diffraction in cut-and…
We discuss how the diffraction theory of a single translation bounded measure or a family of such measures can be understood within the framework of unitary group representations. This allows us to prove an orthogonality feature of measures…
Mathematical diffraction theory is concerned with the analysis of the diffraction measure of a translation bounded complex measure $\omega$. It emerges as the Fourier transform of the autocorrelation measure of $\omega$. The mathematically…
The contribution to diffraction dissociation of virtual photons due to quasi-elastic scattering of the $q$-$\bar q$ component is calculated in the framework of the QCD dipole picture. Both longitudinal and transverse components of the…
The shelling of crystals is concerned with counting the number of atoms on spherical shells of a given radius and a fixed centre. Its straight-forward generalization to quasicrystals, the so-called central shelling, leads to non-universal…
We introduce a construction to embed a quasiperiodic lattice of obstacles into a single unit cell of a higher-dimensional space, with periodic boundary conditions. This construction transparently shows the existence of channels in these…
Based on diffraction theory and the propagation of the light, Fourier optics is a powerful tool allowing the estimation of a visible-range imaging system to transfer the spatial frequency components of an object. The analyses of the imaging…
We introduce a topology ${\cal T}$ on the space $U$ of uniformly discrete subsets of the Euclidean space. Assume that $S$ in $U$ admits a unique autocorrelation measure. The diffraction measure of $S$ is purely atomic if and only if $S$ is…
In this paper, we study the mathematical imaging problem of diffraction tomography (DT), which is an inverse scattering technique used to find material properties of an object by illuminating it with probing waves and recording the…
Tilings based on the cut and project method are key model systems for the description of aperiodic solids. Typically, quantities of interest in crystallography involve averaging over large patches, and are well defined only in the…
We study random perturbations of quasi-periodic uniformly discrete sets in the $d$-dimensional euclidean space. By means of Diffraction Theory, we find conditions under which a quasi-periodic set $X$ can be almost surely recovered from its…
We generalize the notion of the Franhoufer diffraction from a single slit and a circular aperture to the case of partially temporal coherent and quasimonochromatic light. The problem is studied analytically and the effect of coherence…
The theory of magnetic symmetry in quasicrystals is used to characterize the nature of magnetic peaks, expected in elastic neutron diffraction experiments. It is established that there is no symmetry-based argument which forbids the…
Quasicrystals are characterized by quasi-periodic arrangements of atoms. The description of their mechanics involves deformation and a (so called phason) vector field accounting at macroscopic scale of local phase changes, due to atomic…
Hyperuniform systems, which include crystals, quasicrystals and special disordered systems, have attracted considerable recent attention, but rigorous analyses of the hyperuniformity of quasicrystals have been lacking because the support of…
In this work, we prove that if a uniformly separated sequence in $\mathbb{R}^d$ is uniformly quasicrystalline and converges rapidly enough to a discrete set $X$ in $\mathbb{R}^d$ having the same separation radius as the sequence, then $X$…
Dense forests are discrete subsets of Euclidean space which are uniformly close to all sufficiently long line segments. The degree of density of a dense forest is measured by its visibility function. We show that cut-and-project…
The diffraction pattern of a single non-periodic compact object, such as a molecule, is continuous and is proportional to the square modulus of the Fourier transform of that object. When arrayed in a crystal, the coherent sum of the…
A macroscopic characterization of fractals showing up a structural transition from dense to multibranched growth is made using optical diffraction theory. Such fractals are generated via the numerical solution of the 2D Poisson and…
At present, the theory of light diffraction only has the simple wave-optical approach. In this paper, we study light diffraction with the approach of relativistic quantum theory. We find that the slit length, slit width, slit thickness and…
The Fraunhofer diffraction of quantum particles from materials with sharp electron-density edges or symmetric bond structures is ubiquitous. In contrast, diffraction from atoms with characteristic asymptotically-diffused electron…