Related papers: Topics on mathematical crystallography
We study inverse problems of reconstructing static and dynamic discrete structures from tomographic data (with a special focus on the `classical' task of reconstructing finite point sets in $\mathbb{R}^d$). The main emphasis is on recent…
The fact that galaxy distribution exhibits fractal properties is well established since twenty years. Nowadays, the controversy concerns the range of the fractal regime, the value of the fractal dimension and the eventual presence of a…
Probabilistic cross-identification has been successfully applied to a number of problems in astronomy from matching simple point sources to associating stars with unknown proper motions and even radio observations with realistic morphology.…
The location of the beam focus when monochromatic x-ray radiation is diffracted by a thin bent crystal is predicted by "crystal lens equation". We derive this equation in a general form valid for Bragg and Laue geometries. This equation has…
The crystallographic texture is a key organization feature of many technical and biological materials. In these materials, especially hierarchically structured ones, the preferential alignment of the nano constituents is heavily influencing…
Ultrafast electron diffraction and time-resolved serial crystallography are the basis of the ongoing revolution in capturing at the atomic level of detail the structural dynamics of molecules. However, most experiments employ the classical…
Ballistic capture orbits offer safer Mars injection at longer transfer time. However, the search for such an extremely rare event is a computationally intensive process. Indeed, it requires the propagation of a grid sampling the whole…
Ice-templating is a simple materials processing and shaping route where the growth of crystals from a solvent template the porosity. Although the principles of ice-templating were established a long time ago, it has lured considerable…
Colloidal systems offer the ideal conditions to study the nucleation process, both from an experimental viewpoint, due to their relative large size and long time-scales, and from a modeling point of view, due to the tunability of their…
Systems as diverse as mechanical structures assembled from elastic components, and photonic metamaterials enjoy a common geometrical feature: a sublattice symmetry. This property realizes a chiral symmetry first introduced to characterize a…
We investigate to what extent the cosmic crystallographic methods aimed to detect the topology of the universe using catalogues of cosmic objects would be damaged by various observational uncertainties. We find that the topological…
Ten years ago, the new era of time crystals began. Time crystals are systems that behave in the time dimension like ordinary space crystals do in space dimensions. We present a brief history of a decade of research on time crystals,…
In (B-Gran, 2004), was given a categorical formulation of the Shifting Lemma which is a characterization of the Congruence Modular Varieties among all the variety of Universal Algebra, introduced in (Gumm, 1983). Starting from a…
The theory of fractional calculus is attracting a lot of attention from mathematicians as well as physicists. The fractional generalisation of the well-known ordinary calculus is being used extensively in many fields, particularly in…
Dislocations - linear defects within the crystal lattice of, e.g., metals - already have been directly observed and analyzed for nearly a century. While experimental characterization methods can nowadays reconstruct three-dimensional…
Experimental DSC and Avrami curves for the crystallization of metallic glasses demonstrate nucleation at grain boundaries and thus indicate their grain structure, which refutes the generally accepted idea of glass as a homogeneous frozen…
In recent years, the realm of crystalline materials has witnessed a surge in the development of generative models, predominantly aimed at the inverse design of crystals with tailored physical properties. However, spatial symmetry, which…
Identifying the three-dimensional (3D) crystal-plane and strain-field distributions of nanocrystals is essential for optical, catalytic, and electronic applications. Here, we developed a methodology for visualizing the 3D information of…
Crystallographic symmetry classifications from real-world images with periodicities in two dimensions (2D) are of interest to crystallographers and practitioners of computer vision studies alike. Currently, these classifications are…
Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to…