Related papers: Some comments on pinwheel tilings and their diffra…

We obtain tilings with a singular point by applying conformal maps on regular tilings of the Euclidean plane, and determine its symmetries. The resulting tilings are then symmetrically colored by applying the same conformal maps on…

Diffraction is a manifestation of light at edge due to its wavelike nature. The well-known diffraction phenomena are Fresnel and Fraunhofer, they find variety of applications individually. But the synergy of two phenomena is not studied and…

We investigate the structural and spectral properties of deterministic aperiodic arrays designed from the statistically isotropic pinwheel tiling. By studying the scaling of the cumulative integral of its structure factor in combination…

We argue that diffraction (Pomeron) contribution is present in the pp spin-flip amplitude. RHIC polarization will be able to prove (or disprove) this conjecture.

A basic assumption of tiling theory is that adjacent tiles can meet in only a finite number of ways, up to rigid motions. However, there are many interesting tiling spaces that do not have this property. They have "fault lines", along which…

An extension of the Gutzwiller trace formula is given that includes diffraction effects due to hard wall scatterers or other singularities. The new trace formula involves periodic orbits which have arcs on the surface of singularity and…

We construct optical appearance and profiled spectral lines of Keplerian discs with inner edge at the innermost circular geodesic located on both sides of the reflection-symmetric Simpson-Visser wormhole, in dependence on its parameter and…

We derive from first principles the expression for the angular/wavelength distribution of the intensity diffracted by a blazed reflective grating, according to a scalar theory of diffraction. We considered the most common case of a groove…

A description of an algorithm for a rather general modal grating calculation is presented. Arbitrary profiles, depth, and permittivity are allowed. Gratings built up from sub-gratings are allowed, as are coatings on the sidewalls of lines,…

We consider tilings of Euclidean spaces by polygons or polyhedra, in particular, tilings made by a substitution process, such as the Penrose tilings of the plane. We define an isomorphism invariant related to a subgroup of rotations and…

In this paper, we use the theory of symmetric Dirichlet forms to give a probabilistic interpretation of Calder\'{o}n's inverse conductivity problem in terms of reflecting diffusion processes and their corresponding boundary trace processes.

We show that diffraction features of $1D$ quasicrystals can be retrieved from a single topological quantity, the \v{C}ech cohomology group, $\check{H}^{1}\cong\mathbb{Z}^2$, which encodes all relevant combinatorial information of tilings.…

The edge diffraction of a homogeneously polarized light beam is studied theoretically based on the paraxial optics and Fresnel-Kirchhoff approximation, and the dependence of the diffracted beam pattern of the incident beam polarization is…

Every simple quadrangulation of the sphere is generated by a graph called a pseudo-double wheel with two local expansions (Brinkmann et al. "Generation of simple quadrangulations of the sphere." Discrete Math., Vol. 305, No. 1-3, pp. 33-54,…

Scattering matrices with block symmetry, which corresponds to scattering process on cavities with geometrical symmetry, are analyzed. The distribution of transmission coefficient is computed for different number of channels in the case of a…

We find explicit optimal vertex, edge and face coulourings for the chair tiling, the Ammann--Beenker tiling, the rational pinwheel tiling and the pinwheel tiling.

In this paper we give a classification of tilings of the sphere by congruent quadrilaterals with exactly two equal edges. The tilings are the earth map tilings, $(p,q)$-earth map tilings and their flip modifications, and quadrilateral…

We consider a particle that is subject to a constant force and scatters inelastically on a vibrating periodically corrugated floor. At small friction and small radius of the circular scatterers the dynamics is dominated by resonances…

Diffuse two-dimensional integer-valued arrays are demonstrated that have delta-like aperiodic autocorrelation and, simultaneously, the array sums form delta-like projections along several directions. The delta-projected views show a single…

The diffraction spectrum of coherent waves scattered from fractal supports is calculated exactly. The fractals considered are of the class generated iteratively by successive dilations and translations, and include generalizations of the…