Related papers: Constraints on pure point diffraction on aperiodic…
Overlap coincidence in a self-affine tiling in $\R^d$ is equivalent to pure point dynamical spectrum of the tiling dynamical system. We interpret the overlap coincidence in the setting of substitution Delone set in $\R^d$ and find an…
We study compact polyhedral surfaces as Riemann surfaces and their discrete counterparts obtained through quadrilateral cellular decompositions and a linear discretization of the Cauchy-Riemann equation. By ensuring uniformly bounded…
In the present paper, the reducibility is derived for linear wave equation of finite smooth and time-quasi-periodic potential subject to Dirichlet boundary condition. Moreover, it is proved that the corresponding wave operator possesses the…
We generalize a recent model-independent form factor parameterization derived from rigorous dispersion relations to include constraints from data in the timelike region. These constraints dictate the convergence properties of the…
The diffraction of a scalar plane wave from a doubly-periodic surface on which either the Dirichlet or Neumann boundary condition is imposed is studied by means of a rigorous numerical solution of the Rayleigh equation for the amplitudes of…
We prove that a primitive substitution Delone set, which is pure point diffractive, is a Meyer set. This answers a question of J. C. Lagarias. We also show that for primitive substitution Delone sets, being a Meyer set is equivalent to…
The boundary problem of linear classical optics about the interaction of electromagnetic radiation with a thin dielectric film has been solved under explicit consideration of its discrete structure. The main attention has been paid to the…
We investigate the effect of spatial inhomogeneity on perfectly periodic, self-organized striped patterns in spatially extended systems. We demonstrate that inhomogeneities select a specific translate of the striped patterns and induce…
The pinwheel tiling is the paradigm for a substitution tiling with circular symmetry, in the sense that the corresponding autocorrelation is circularly symmetric. As a consequence, its diffraction measure is also circularly symmetric, so…
In an isotopically disordered harmonic chain, phonon transmission attenuates exponentially with distance because of multiple scattering by the isotopic defects. We propose a simple method, which is based on the static structure factor, for…
With the present and soon-to-be breakthrough of optical interferometry, countless objects shall be within reach of interferometers; yet, most of them are expected to remain only marginally resolved with hectometric baselines. In this paper,…
The scaling behaviour of the diffraction intensity near the origin is investigated for (partially) ordered systems, with an emphasis on illustrative, rigorous results. This is an established method to detect and quantify the fluctuation…
Random optical fields with two widely different correlation lengths generate far field speckle spots that are themselves highly speckled. We call such patterns speckled speckle, and study their critical points (singularities and stationary…
We study the boundary of the liquid region $\mathcal{L}$ in large random lozenge tiling models defined by uniform random interlacing particle systems with general initial configuration, which lies on the line $(x,1)$, $x\in\mathbb{R}\equiv…
The diffusive motion of overdamped Brownian particles in tilted piecewise linear pontentials is considered. It is shown that the enhancement of diffusion coefficient by an external static force is quite sensitive to the symmetry of periodic…
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…
For over a century diffraction theory has been thought to limit the resolution of focusing and imaging in the optical domain. The size of the smallest spot achievable is inversely proportional to the range of spatial wavevectors available.…
We review photonic band gap related properties of a simple periodic system of thin dielectric layers. Properties associated with forbidden and allowed bands of such one-dimensional photonic crystals are presented. A revision of forbidden…
For Euclidean pure point diffractive Delone sets of finite local complexity and with uniform patch frequencies it is well known that the patch counting entropy computed along the closed centred balls is zero. We consider such sets in the…
We determine the asymptotic behaviour of (bilateral) obstacle problems for fractional energies in rather general aperiodic settings via Gamma-convergence arguments. As further developments we consider obstacles with random sizes and shapes…