Related papers: Pinwheel patterns and powder diffraction

Diffraction images with continuous rotation symmetry arise from amorphous systems, but also from regular crystals when investigated by powder diffraction. On the theoretical side, pinwheel patterns and their higher dimensional…

The pinwheel tiling is the paradigm for a substitution tiling with circular symmetry, in the sense that the corresponding autocorrelation is circularly symmetric. As a consequence, its diffraction measure is also circularly symmetric, so…

Two new series of substitution tilings are introduced in which the tiles appear in infinitely many orientations. It is shown that several properties of the well-known pinwheel tiling do also hold for these new examples, and, in fact, for…

The diffraction of stochastic point sets, both Bernoulli and Markov, and of random tilings with crystallographic symmetries is investigated in rigorous terms. In particular, we derive the diffraction spectrum of 1D random tilings, of…

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…

We introduce a fractal version of the pinwheel substitution tiling. There are thirteen basic prototiles, all of which have fractal boundaries. These tiles, along with their reflections and rotations, create a tiling space which is mutually…

We introduce a new family of nonperiodic tilings, based on a substitution rule that generalizes the pinwheel tiling of Conway and Radin. In each tiling the tiles are similar to a single triangular prototile. In a countable number of cases,…

As in the available literature there are still misconceptions about powder diffraction phenomena observed for small nanocrystals ($D<10$ nm), we propose here a systematic and concise review of the involved issues that can be approached by…

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…

Friedel's law guarantees an inversion-symmetric diffraction pattern for thin, light materials where a kinematic approximation or a single-scattering model holds. Typically, breaking Friedel symmetry is ascribed to multiple scattering events…

The large amount of powder diffraction data for which the corresponding crystal structures have not yet been identified suggests the existence of numerous undiscovered, physically relevant crystal structure prototypes. In this paper, we…

We present a scheme to identify quasicrystals based on powder diffraction data and to provide a standardized indexing. We apply our scheme to a large catalog of powder diffraction patterns, including natural minerals, to look for new…

An extension of the Gutzwiller trace formula is given that includes diffraction effects due to hard wall scatterers or other singularities. The new trace formula involves periodic orbits which have arcs on the surface of singularity and…

Mathematical diffraction theory is concerned with the diffraction image of a given structure and the corresponding inverse problem of structure determination. In recent years, the understanding of systems with continuous and mixed spectra…

There is a growing body of results in the theory of discrete point sets and tiling systems giving conditions under which such systems are pure point diffractive. Here we look at the opposite direction: what can we infer about a discrete…

Mathematical diffraction theory is concerned with the analysis of the diffraction image of a given structure and the corresponding inverse problem of structure determination. In recent years, the understanding of systems with continuous and…

Diffusion-driven patterns appear on curved surfaces in many settings, initiated by unstable modes of an underlying Laplacian operator. On a flat surface or perfect sphere, the patterns are degenerate, reflecting translational/rotational…

The Fourier-based diffraction approach is an established method to extract order and symmetry propertiesfrom a given point set. We want to investigate a different method for planar sets which works in direct spaceand relies on reduction of…

The superstructure spots that appear in diffraction patterns of tilted perovskites are well documented and easily calculated using crystallographic software. Here, by considering a distortion mode as a perturbation of the prototype…

Metasurfaces enable powerful control of electromagnetic waves using subwavelength planar structures, but their deeply subwavelength periodicity typically suppresses propagating diffraction orders, which limits the number of available…