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We prove that a positive-definite measure in $\mathbb{R}^n$ with uniformly discrete support and discrete closed spectrum, is representable as a finite linear combination of Dirac combs, translated and modulated. This extends our recent…
In this paper, we study the structure of the set of tilings produced by any given tile-set. For better understanding this structure, we address the set of finite patterns that each tiling contains. This set of patterns can be analyzed in…
Transformation-based cylindrical cloaks and concentrators are illuminated with non-monochromatic waves and unusual effects are observed with interesting potential applications. The transient responses of the devices are studied numerically…
We give an introduction into diffraction theory for aperiodic order. We focus on an approach via dynamical systems and the phenomenon of pure point diffraction. We review recent results and sketch proofs. We then present a new uniform…
Transport properties of a single-mode waveguide with rough boundary are studied by discrimination between two mechanisms of surface scattering, the amplitude and square-gradient ones. Although these mechanisms are generically mixed, we show…
Self-similar solutions of the coherent diffusion equation are derived and measured. The set of real similarity solutions is generalized by the introduction of a nonuniform phase surface, based on the elegant Gaussian modes of optical…
We theoretically study the effect of stripe-like superconducting inclusions on the non-linear resistivity in single crystals. Even when the stripe orientation varies throughout the sample between two orthogonal directions due to twinning,…
We develop a systematic study about the spectrality of measures supported on piecewise smooth curves by studying the support of the tempered distributions arising from the tiling equation of some singular spectral measures. In doing so, we…
A theory of light diffraction from planar quasicrystalline lattice with resonant scatterers is presented. Rich structure, absent in the periodic case, is found in specular reflection spectra, and interpreted as a specific kind of Wood…
We present mathematical theory for understanding the transmission spectra of heterogeneous materials formed by generalised Fibonacci tilings. Our results, firstly, characterise super band gaps, which are spectral gaps that exist for any…
The effect of dispersion or diffraction on zero-velocity solitons is studied for the generalized massive Thirring model describing a nonlinear optical fiber with grating or parallel-coupled planar waveguides with misaligned axes. The…
It is well known that certain special classes of self-gravitating point-like defects, such as global (non gauged) monopoles, give rise to non-asymptotically flat space-times characterized by solid angle deficits, whose size depends on the…
We say that a tiling separates discs of a packing in the Euclidean plane, if each tile contains exactly one member of the packing. It is a known elementary geometric problem to show that for each locally finite packing of circular discs,…
Problem solutions in area of diffraction and of scattering theory are considered from one point of view. The method common for them is based on approximate orthogonality of solution constituents, which oscillate on a body long frontier.…
This paper presents a study of acoustic scattering by a cylinder of either infinite or finite length near a flat pressure-release surface. A novel self-consistent method is developed to describe the multiple scattering interactions between…
We formulate simple graphical rules which allow explicit calculation of nonperturbative $c=1$ $S$-matrices. This allows us to investigate the constraint of nonperturbative unitarity, which indeed rules out some theories. Nevertheless, we…
We classify the dihedral edge-to-edge tilings of the sphere by regular polygons and quadrilaterals with equal opposite edges (edge configuration xyxy).
Classical results on aperiodic tilings are rather complicated and not widely understood. Below, an alternative approach is discussed in hope to provide additional intuition not apparent in classical works.
Two novel classes of spherical invisibility cloaks based on nonlinear transformation have been studied. The cloaking characteristics are presented by segmenting the nonlinear transformation based spherical cloak into concentric isotropic…
In this article we show that in a three dimensional (3D) optical field there can exist two types of hidden singularities, one is spin density (SD) phase singularity and the other is SD vector singularity, which are both unique to 3D fields.…