Related papers: Periodic diffraction patterns for 1D quasicrystals
6-d polyhedral models give a periodic description of aperiodic quasicrystals. There are powerful tools to describe their structural surface properties. Basis of the model for icosahedral quasicrystals are given. This description is further…
Inspired by recent advances in the manipulation of atoms trapped near 1D waveguides and pro- posals to use surface acoustic waves on piezoelectric substrates for the same purpose, we show the potential of two-dimensional platforms. We…
A method is presented for calculating the frequencies of non-retarded surface plasmons propagating on a semi-inifinite medium with a surface profile described by a one-dimension quasiperiodic function. The profiles are generated, in analogy…
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…
We show that diffraction features of $1D$ quasicrystals can be retrieved from a single topological quantity, the \v{C}ech cohomology group, $\check{H}^{1}\cong\mathbb{Z}^2$, which encodes all relevant combinatorial information of tilings.…
We investigate the iterative construction of discrete Laplacians on 2D square lattices, revealing emergent fractal-like patterns shaped by modular arithmetic. While classical 2222-style iterations reproduce known structures such as the…
In this work, we consider m-bonacci chains, unidimensional quasicrystals obtained by general classes of Rauzy substitutions. Motivated by applications in spectrography and diffraction patterns of some quasicrystals, we pose the problem of…
This paper is concerned with analysis of coupled fractional reaction-diffusion equations. It provides analytical comparison for the fractional and regular reaction-diffusion systems. As an example, the reaction-diffusion model with cubic…
A brief summary of recent developments in mathematical diffraction theory is given. Particular emphasis is placed on systems with aperiodic order and continuous spectral components. We restrict ourselves to some key results and refer to the…
We experimentally probe complex bio-photonic architecture of microstructures on the transparent insect wings by a simple, non-invasive, real time optical technique. A stable and reproducible far-field diffraction pattern in transmission was…
Quasi-periodic structures of quasicrystals yield novel effects in diverse systems. However, there is little investigation on employing quasi-periodic structures in the morphology control. Here, we show the use of quasi-periodic surface…
We present a theoretical justification for a method of extracting of supplementary information for the phase retrieval procedure taken from diffraction of fs-pulses from X-ray Free Electron Laser facilities. The approach is based on…
We develop a general framework to study hyperuniformity of various mathematical models of quasicrystals. Using this framework we provide examples of non-hyperuniform quasicrystals which unlike previous examples are not limit-quasiperiodic.…
Crystal structure determination from powder diffraction patterns is a complex challenge in materials science, often requiring extensive expertise and computational resources. This study introduces DiffractGPT, a generative pre-trained…
Based on the rigorous generalized Mie theory solution of Maxwell's equations for dielectric cylinders we theoretically investigate the optical properties of two-dimensional deterministic structures based on the Fibonacci, Thue-Morse and…
We present a semi-analytic method to calculate the dispersion curves and the group velocity of photonic crystal waveguide modes in two-dimensional geometries. We model the waveguide as a homogenous strip, surrounded by photonic crystal…
This paper is devoted to the mathematical analysis of a time-domain electromagnetic scattering by periodic structures which are known as diffraction gratings. The scattering problem is reduced equivalently into an initial-boundary value…
Optical interference holography has been proved to be a useful technique in fabricating periodic photonic crystals in which electromagnetic waves are forbidden in certain frequency bandgaps. Compared to periodic crystals quasicrystals,…
We investigate the influence of diffraction on the statistics of energy levels in quantum systems with a chaotic classical limit. By applying the geometrical theory of diffraction we show that diffraction on singularities of the potential…
Redundancies are pointed out in the widely used extension of the crystallographic concept of Bravais class to quasiperiodic materials. Such pitfalls can be avoided by abandoning the obsolete paradigm that bases ordinary crystallography on…