Related papers: A short guide to pure point diffraction in cut-and…
The recently developed information-theoretic approach to crystallographic symmetry classifications and quantifications in two dimensions (2D) from digital transmission electron and scanning probe microscope images is adapted for the…
In this paper, based on the analysis of the formula (2.2) for calculating the elastic scattering diagrams of microparticles on a multilayer crystal surface, derived by the author in the article [3], it is shown that the stochastic approach…
We show that for multi-colored Delone point sets with finite local complexity and uniform cluster frequencies the notions of pure point diffraction and pure point dynamical spectrum are equivalent.
Based on the seminal work by John T. Sheridan [1] we discuss the usefulness and validity of simple diffraction theories frequently used to determine and characterize optical holographic gratings. Experimental investigations obtained in…
Diffraction is a fundamental property of light propagation. Owing to this phenomenon,light diffracts out in all directions when it passes through a subwavelength slit.This imposes a fundamental limit on the transverse size of a light beam…
We extend a modal theory of diffraction by a set of parallel fibers to deal with the case of a hard boundary: that is a structure made for instance of air-holes inside a dielectric matrix. Numerical examples are given concerning some…
Motivated by applications to acoustic imaging, the present work establishes a framework to analyze scattering for the one-dimensional wave, Helmholtz, Schr\"odinger and Riccati equations that allows for coefficients which are more singular…
A theoretical approach for uniformly extracting light propagating through a light guide plate is developed here. Typically, liquid crystal display modalities utilize a backlit lighting system illuminated from the edge with light emitting…
In this article we present an analytic solution of the famous problem of diffraction and interference of electrons through one and two slits (for simplicity, only the one-dimensional case is considered). In addition to exact formulas, we…
This article considers the problem of diffraction by a wedge consisting of two semi-infinite periodic arrays of point scatterers. The solution is obtained in terms of two coupled systems, each of which is solved using the discrete…
We build an effective field theory (EFT) for quasicrystals -- aperiodic incommensurate lattice structures -- at finite temperature, entirely based on symmetry arguments and a well-define action principle. By means of Schwinger-Keldysh…
Modulated crystals and quasicrystals can simultaneously be described as modulated quasicrystals, a class of point sets introduced by de Bruijn in 1987. With appropriate modulation functions, modulated quasicrystals themselves constitute a…
Determining the atomic-level structure of crystalline solids is critically important across a wide array of scientific disciplines. The challenges associated with obtaining samples suitable for single-crystal diffraction, coupled with the…
Very short pulses of x-ray free-electron lasers opened the way to obtain diffraction signal from single particles beyond the radiation dose limit. For 3D structure reconstruction many patterns are recorded in the object's unknown…
We consider the problem of extraction and validation of matching rules, directly from the phased diffraction data of a quasicrystal, and propose an algorithmic procedure to produce the rules of the shortest possible range. We have developed…
Bochner's theorem gives the necessary and sufficient conditions on a function such that its Fourier transform corresponds to a true probability density function. In the Wigner phase space picture, quantum Bochner's theorem gives the…
A common way of speeding up powder diffraction measurements is the use of one or two dimensional detectors. This usually goes along with worse resolution and asymmetric peak profiles. In this work the influence of a straight linear detector…
We present a molecular dynamics study on atomic self-diffusion in Frank-Kasper type dodecagonal quasicrystals. It is found that the quasicrystal-specific flip mechanism for atomic diffusion as predicted by Kalugin and Katz, indeed occurs in…
We consider temperate distributions on Euclidean spaces with uniformly discrete support and locally finite spectrum. We find conditions on coefficients of distributions under which they are finite sum of derivatives of generalized lattice…
We develop a wavepacket approach to the diffraction of charged particles by a thin material target and we use the de Broglie-Bohm quantum trajectories to study various phenomena in this context. We find the form of the separator, i.e.the…