相关论文: A Note on Shelling

The shelling of crystals is concerned with counting the number of atoms on spherical shells of a given radius and a fixed centre. Its straight-forward generalization to quasicrystals, the so-called central shelling, leads to non-universal…

This review revolves around the question which general distribution of scatterers (in a Euclidean space) results in a pure point diffraction spectrum. Firstly, we treat mathematical diffration theory and state conditions under which such a…

Quasicrystals are solid structures with symmetry forbidden by crystallographic rules. Because of this some structural characteristics of quasicrystals, for instance, radial distribution function, can look similar to the ones of amorphous…

The distribution function of particles over clusters is proposed for a system of identical intersecting spheres, the centres of which are uniformly distributed in space. Consideration is based on the concept of the rank number of clusters,…

Regular model sets, describing the point positions of ideal quasicrystallographic tilings, are mathematical models of quasicrystals. An important result in mathematical diffraction theory of regular model sets, which are defined on locally…

We introduce a construction to embed a quasiperiodic lattice of obstacles into a single unit cell of a higher-dimensional space, with periodic boundary conditions. This construction transparently shows the existence of channels in these…

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…

When expressing a distribution in Euclidean space in spherical co-ordinates, derivation with respect to the radial and angular co-ordinates is far from trivial. Exploring the possibilities of defining a radial derivative of the…

A detailed analysis is given of the angular distribution of an charged particle moving along the arc of a circle. The areas of different angular distribution behavior are highlighted and studied.

Quantum theory is proposed of high energy electrons scattering in ultrathin crystals. This theory is based upon a special representation of the scattering amplitude in the form of the integral over the surface surrounding the crystal, and…

In this paper, we propose a general mechanism for the existence of quasicrystals in spatially extended systems (partial differential equations with Euclidean symmetry). We argue that the existence of quasicrystals with higher order…

Crystals are paradigms of ordered structures. While order was once seen as synonymous with lattice periodic arrangements, the discoveries of incommensurate crystals and quasicrystals led to a more general perception of crystalline order,…

Tilings based on the cut and project method are key model systems for the description of aperiodic solids. Typically, quantities of interest in crystallography involve averaging over large patches, and are well defined only in the…

Scattering is a ubiquitous phenomenon which is observed in a variety of physical systems which span a wide range of length scales. The scattering matrix is the key quantity which provides a complete description of the scattering process.…

- An algorithm for calculating the radiation field of a charged point particle performing a spiral motion in an infinite cylindrical waveguide with a multilayer side wall is found. The number of layers and their filling is arbitrary. The…

A simple model of 1D structure based on a Fibonacci sequence with variable atomic spacings is proposed. The model allows for observation of the continuous transition between periodic and non-periodic diffraction patterns. The diffraction…

Using a measure of clustering derived from the nearest neighbour distribution and the void probability function we are able to distinguish between regular and clustered structures. With an example we show that regularity is a property of a…

Several combinatorial problems of (quasi-)crystallography are reviewed with special emphasis on a unified approach, valid for both crystals and quasicrystals. In particular, we consider planar sublattices, similarity sublattices,…

The quasi-channeling of positive and negative relativistic particles in a bent crystal is studied using the classical deflection function. It was shown that the potential scattering in a central field of bounded ring-like potentials may…

The fundamental issues of symmetry related to chirality are discussed and applied to simple situations relevant to liquid crystals. We show that any chiral measure of a geometric object is a pseudoscalar (invariant under proper rotations…