Related papers: Tiling Billards on Triangle Tilings, and Interval …
The chapter contains a detailed presentation of the surface integral theory for modelling light diffraction by surface-relief diffraction gratings having a one-dimensional periodicity. Several different approaches are presented, leading…
Consider the incidence of a time-harmonic electromagnetic plane wave onto a biperiodic dielectric grating, where the surface is assumed to be a small and smooth perturbation of a plane. The diffraction is modeled as a transmission problem…
We investigate by direct numerical simulation Rayleigh-B\'enard convection in a rotating rectangular cell with rotation vector and gravity perpendicular to each other. The flow is two dimensional near the onset of convection with convection…
We study the structure of an interface in a three dimensional Ising system created by an external non-uniform field $H({\bf r},t)$. $H$ changes sign over a two dimensional plane of arbitrary orientation. When the field is pulled with…
We present the results of a set of Monte Carlo simulations of Dynamically Triangulated Random Surfaces embedded in three dimensions with an extrinsic curvature dependent action. We analyze several observables in the crossover regime and…
The transition from two-dimensional to three-dimensional flows in a finite circular cylinder driven by an axially oscillating sidewall is explored in detail. The complete symmetry group of this flow, including a spatio-temporal symmetry…
The orbital angular momentum conservation of light reveals different diffraction patterns univocally dependent on the topological charge of the incident light beam when passing through a triangular aperture. It is demonstrated that these…
This paper is about the tiling dynamical systems approach to the study of aperiodic order. We compare and contrast four related types of systems: ordinary (one-dimensional) symbolic systems, one-dimensional tiling systems, multidimensional…
When light travels through a medium in which the refractive index is rapidly changing with time, the light will undergo a shift in its frequency. Large frequency shifting effects have recently been reported for transparent conductive…
We analyze transmission of a layered photonic structure (a one-dimensional photonic crystal) consisting of alternating slabs of two materials with positive and negative refractive index. For the periodic structure with zero averaged…
A simple model for calculating the diffraction radiation characteristics from an ultrarelativistic charged particle moving close to a tilted ideally conducting strip is developed. Resonant diffraction radiation (RDR) is treated as a…
This paper is on tilings of polygons by rectangles. A celebrated physical interpretation of such tilings due to R.L. Brooks, C.A.B. Smith, A.H. Stone and W.T. Tutte uses direct-current circuits. The new approach of the paper is an…
We construct a microscopic model based on superexchange theory for a moir\'e bilayer in chromium trihalides (Cr$X_3$, $X=$Br, I). In particular, we derive analytically the interlayer Heisenberg exchange and the interlayer…
It is shown that tiling in icosahedral quasicrystals can also be properly described by cyclic twinning at the unit cell level. The twinning operation is applied on the primitive prolate golden rhombohedra, which can be considered a result…
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…
Recently Taylor and Socolar introduced an aperiodic mono-tile. The associated tiling can be viewed as a substitution tiling. We use the substitution rule for this tiling and apply the algorithm of \cite{AL} to check overlap coincidence. It…
We consider an optical diffraction grating in which the spatial distribution of open slits forms a fractal set. The Fraunhofer diffraction patterns through the fractal grating are obtained analytically for the simplest triad Cantor type and…
Consider the unit triangular lattice in the plane with origin $O$, drawn so that one of the sets of lattice lines is vertical. Let $l$ and $l'$ denote respectively the vertical and horizontal lines that intersect $O$. Suppose the plane…
A tiling is a decomposition of a polygon into finitely many non-overlapping triangles. We prove that if a regular n-gon, $n \geq 5$, $n \neq 28$, can be tiled with similar right triangles, then one of the angles of these triangles is in…
Recent studies of the tunnelling through two opaque barriers claim that the transit time is independent of the barrier widths and of the separation distance between the barriers. We observe, in contrast, that if multiple reflections are…