Related papers: Substitution Delone Sets with Pure Point Spectrum …

We give a leisurely introduction into mathematical diffraction theory with a focus on pure point diffraction. In particular, we discuss various characterisations of pure point diffraction and common models arising from cut and project…

There are many examples for point sets in finite geometry, which behave "almost regularly" in some (well-defined) sense, for instance they have "almost regular" line-intersection numbers. In this paper we investigate point sets of a…

We study the interplay between different models of the same irreducible representation of the $F$-points of a reductive group over a local field.

In the present talk diffraction in deep inelastic scattering is discussed in the framework of the semiclassical approach. The main emphasis is on the possibility of a consistent semiclassical description of both hard and soft colour singlet…

This paper, in french, gives a new approach to the concept of Maximally Even Sets based on discrete Fourier transform, with several elementary but interesting and previously unpublished results. Maximally Even Sets have been invented by…

Sphere packings are essential to the development of physical models for powders, composite materials, and the atomic structure of the liquid state. There is a strong scientific need to be able to assess the fit of packing models to data,…

We describe the most general homogenous, planar, light-ray-direction-changing sheet that performs one-to-one imaging between object space and image space. This is a non-trivial special case (of the sheet being homogenous) of an earlier…

We consider topological dynamical systems over $\ZZ$ and, more generally, locally compact, $\sigma$-compact abelian groups. We relate spectral theory and diffraction theory. We first use a a recently developed general framework of…

By the algorithm implemented in the paper [2] by Akiyama-Lee and some of its predecessors, we have examined the pure discreteness of the spectrum for all irreducible Pisot substitutions of trace less than or equal to $2$, and some cases of…

Lebesgue curve is a space-filling curve that fills the unit square through linear interpolation. In this study, we generalise Lebesgue's construction to generate space-filling curves from any given planar substitution satisfying a mild…

We introduce a simple theoretical model that describes the interaction of light with optical metamaterials in terms of interfering optical plane waves. In this model, a metamaterial is considered to consist of planar arrays of densely…

In this letter, we study a nonlinear interferometric setup based on diffraction rather than beam combining. It consists of a nonlinear analogue of Young's double-slit experiment where a nonlinear material is placed exactly after one of the…

This paper explores the connection between dynamical system properties and statistical physics of ensembles of such systems. Simple models are used to give novel phase transitions; particularly for finite N particle systems with many…

The situation of the decay of the metastable phase on the several types of heterogeneous centers is described analytically. The total number of heterogeneous centers is supposed to be equal for different types. This description decomposes…

We discuss phase transitions in PT-symmetric optical systems. We show that due to frequency dispersion of the dielectric permittivity, an optical system can have PT-symmetry at isolated frequency points only. An assumption of the existence…

Cut and project sets are obtained by projecting an irrational slice through a lattice to a lower dimensional subspace. Under standard conditions, the resulting pattern has no translational periods even though it retains some regularity of…

We generalize Fulton's Residual Intersection Theorem for the Segre class and express the Segre classes of schemes with regularly embedded components in terms of the Chern classes of the normal bundles to the components and their…

Unlike the (classical) Kolakoski sequence on the alphabet {1,2}, its analogue on {1,3} can be related to a primitive substitution rule. Using this connection, we prove that the corresponding bi-infinite fixed point is a regular generic…

We construct examples of Delone sets of the plane (that is, discrete subsets that are uniformly separated and coarsely dense) that are repetitive (each patch of the set appears in every large-enough ball) though non-rectifiable (i.e. non…

The article presents a new perspective on the isomorphism problem for non-ergodic measure-preserving dynamical systems with discrete spectrum which is based on the connection between ergodic theory and topological dynamics constituted by…