Related papers: Identifying and Indexing Icosahedral Quasicrystals…
Machine learning algorithms based on artificial neural networks have proven very useful for a variety of classification problems. Here we apply them to a well-known problem in crystallography, namely the classification of X-ray diffraction…
Diffraction methods are at the heart of structure determination of solids. While Bragg-like scattering (pure point diffraction) is a characteristic feature of crystals and quasicrystals, it is not straightforward to interpret continuous…
We argue that 2D dodecagonal spherical quasicrystalls (QCs) will be discovered in the nearest future and investigate how the planar QC order becomes compatible with the spherical geometry. We show that the appearance of curvature-induced…
An algorithm for determining crystal structures from diffraction data is described which does not rely on the usual Fourier-space formulations of atomicity. The new algorithm implements atomicity constraints in real-space, as well as…
This paper continues our study of quasicrystals initiated in Part I. We propose a general mechanism for constructing quasicrystals, existing globally in time, in spatially-extended systems (partial differential equations with Euclidean…
Kinematic diffraction is well suited for a mathematical approach via measures, which has substantially been developed since the discovery of quasicrystals. The need for further insight emerged from the question of which distributions of…
Electron backscatter diffraction is a widely used technique for nano- to micro-scale analysis of crystal structure and orientation. Backscatter patterns produced by an alloy solid solution matrix and its ordered superlattice exhibit only…
The paper presents mathematical models of quasicrystals with particular attention given to cut-and-project sets. We summarize the properties of higher-dimensional quasicrystal models and then focus on the one-dimensional ones. For the…
We identify several new quasicrystal approximants in alloy systems in which quasicrystals have not been previously reported. Some occur in alloys with large size contrast between the constituent elements, either containing small Boron…
This paper introduces the use of pseudo-filters that optimize the detection/extraction of sources on a background. We assume as a first approach that such sources are described by a spherical (central) profile and that the background is…
Quasicrystals are long-range ordered and yet non-periodic. This interplay results in a wealth of intriguing physical phenomena, such as the inheritance of topological properties from higher dimensions, and the presence of non-trivial…
We demonstrate a smart laser-diffraction analysis technique for particle mixture identification. We retrieve information about the size, geometry, and ratio concentration of two-component heterogeneous particle mixtures with an efficiency…
The iso-frequency contours of a photonic crystal are important for predicting and understanding exotic optical phenomena that are not apparent from high-symmetry band structure visualizations. Here, we demonstrate a method to directly…
Multi-technique high resolution X-ray mapping enhanced by the recent advent of 4th generation synchrotron facilities can produce colossal datasets, challenging traditional analysis methods. Such difficulty is clearly materialized when…
The diffraction technique is widely used in the determination of crystal structures and is one of the bases for the modern science and technology. All related structure determination methods are based on the assumption that perfect single…
In a recent Letter we proposed a means to realize a quasicrystal with eight-fold symmetry by trapping particles in an optical potential created by four lasers. The quasicrystals obtained in this way, which are closely related to the…
We survey mathematical properties of quasicrystals, first from the point of view of harmonic analysis, then from the point of view of morphic and automatic sequences. Nous proposons un tour d'horizon de propri\'et\'es math\'ematiques des…
We report a promising InSiO film that allows simultaneous observation of sample morphology and Kikuchi patterns in raster scan mode of scanning electron microscopy. This new experimental observation suggests potential mechanism beyond…
The paper develops a method for discrete computational Fourier analysis of functions defined on quasicrystals and other almost periodic sets. A key point is to build the analysis around the emerging theory of quasicrystals and diffraction…
The primary consideration in developing new material platforms for quantum applications is to optimize coherence. Despite its importance, decoherence processes remains challenging to experimentally interrogate and quantify. In this…