Related papers: Mathematical diffraction of aperiodic structures
It is shown that the diffraction on a polycrystal can be used for investigation and diagnostics of X-ray radiation emitted in a forward direction by relativistic charged particles moving in crystalline or other targets or fields. Methods…
We give an introduction into diffraction theory for aperiodic order. We focus on an approach via dynamical systems and the phenomenon of pure point diffraction. We review recent results and sketch proofs. We then present a new uniform…
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…
We present cut and project formalism based on measures and continuous weight functions of sufficiently fast decay. The emerging measures are strongly almost periodic. The corresponding dynamical systems are compact groups and homomorphic…
Topological properties of crystals and quasicrystals is a subject of recent and growing interest. This Letter reports an experiment where, for certain quasicrystals, these properties can be directly retrieved from diffraction. We directly…
Variation of the phase of the beam transmitted through a crystalline material as a function of the rocking angle is a well known dynamical effect in x-ray scattering. Unfortunately, it is not so easy to measure directly these phase…
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…
Preliminary results of extensive numerical experiments on a simple model specified by the smooth canonical strongly chaotic 2D-map with global virtual invariant curves (VICs) are presented and discussed. We focus on the statistics of the…
We develop a theory for the trajectory of an x ray in the presence of a crystal deformation. A set of equations of motion for an x-ray wave packet including the dynamical diffraction is derived, taking into account the Berry phase as a…
The advantages of convergent beam electron diffraction for symmetry determination at the scale of a few nm are well known. In practice, the approach is often limited due to the restriction on the angular range of the electron beam imposed…
The scattering from crystals can be divided into two parts: Bragg scattering and diffuse scattering. The analysis of Bragg diffraction data gives only information about the average structure of the crystal. The interpretation of diffuse…
We briefly review the diffraction of quasicrystals and then give an elementary alternative proof of the diffraction formula for regular cut-and-project sets, which is based on Bochner's theorem from Fourier analysis. This clarifies a common…
This paper considers some open questions related to the inverse problem of pure point diffraction, in particular, what types of objects may diffract, and which of these may exhibit the same diffraction. Some diverse objects with the same…
Two systems are homometric if they are indistinguishable by diffraction. We first make a distinction between Bragg and diffuse scattering homometry, and show that in the last case, coherent diffraction can allow the diffraction diagrams to…
Pinwheel patterns and their higher dimensional generalisations display continuous circular or spherical symmetries in spite of being perfectly ordered. The same symmetries show up in the corresponding diffraction images. Interestingly, they…
Predicting quasicrystal structures is a multifaceted problem that can involve predicting a previously unknown phase, predicting the structure of an experimentally observed phase, or predicting the thermodynamic stability of a given…
Using the FDTD method, we investigate the electromagnetic propagation in two-dimensional photonic crystals, formed by parallel air cylinders in a dielectric medium. The corresponding frequency band structure is computed using the standard…
This paper deals with certain dynamical systems built from point sets and, more generally, measures on locally compact Abelian groups. These systems arise in the study of quasicrystals and aperiodic order, and important subclasses of them…
Solving crystal structures from kinematical X-ray or electron diffraction patterns of single crystals requires many more diffracted beams to be recorded than there are atoms in the structure, since the phases of the structure factors can…
This introductory survey deals with mathematical and physical properties of discrete structures such as point sets and tilings. The emphasis is on proper generalizations of concepts and ideas from classical crystallography. In particular,…