Related papers: Periodicity and ergodicity in the trihexagonal til…
We study the optic control for birefringence of a polarized light by an atomic ensemble with a tripod configuration, which is mediated by the electromagnetically induced transparency with a spatially inhomogeneous laser. The atom ensemble…
We show that a rectangle triangle random tiling with a tenfold symmetric phase is solvable by Bethe Ansatz. After the twelvefold square triangle and the eightfold rectangle triangle random tiling, this is the third example of a rectangle…
We know that tilesets that can tile the plane always admit a quasi-periodic tiling [4, 8], yet they hold many uncomputable properties [3, 11, 21, 25]. The quasi-periodicity function is one way to measure the regularity of a quasi-periodic…
Crystallization and radiation of accelerator beams is considered. For the first time it is shown that crystallization conditions for charged particle beams differs from those of plasma. Crystallization conditions of charged relativistic…
The hexagon is the least-perimeter tile in the Euclidean plane. On hyperbolic surfaces, the isoperimetric problem differs for every given area. Cox conjectured that a regular $k$-gonal tile with 120-degree angles is isoperimetric for its…
We consider two dimensional and three dimensional semi-infinite tubes made of "Lambertian" material, so that the distribution of the direction of a reflected light ray has the density proportional to the cosine of the angle with the normal…
The complete sets of irreducible triangulations are known for the orientable surfaces with genus of 0, 1, or 2 and for the nonorientable surfaces with genus of 1, 2, 3, or 4. By examining these sets we determine some of the properties of…
A recent "hidden symmetry" conjecture of B. Gin-ge Chen et al is resolved, concerning the dimension of the mechanical modes of a generic $2$-periodic triangulated surface $O$ in $R^3$ whose structure graph corresponds to a triangular tiling…
Depinning of two-dimensional liquid ridges and three-dimensional drops on an inclined substrate is studied within the lubrication approximation. The structures are pinned to wetting heterogeneities arising from variations of the strength of…
In this paper, we turn our attention to light propagation in three-dimensional electrodynamics. More specifically, we investigate the behavior of light rays in a continuous bi-dimensional hypothetical medium living in a three-dimensional…
An example of a teleparallel texture is given by an appropriate choice of torsion components in the tetrad frame.In the light cone limit the metric is not globally Euclidean and the spherical angles depend on torsion similarly to what…
We study dynamics and bifurcations of two-dimensional reversible maps having non-transversal heteroclinic cycles containing symmetric saddle periodic points. We consider one-parameter families of reversible maps unfolding generally the…
We study electronic properties as a function of the six types of local environments found in the octagonal tiling. The density of states has six characteristic forms, although the detailed structure differs from site to site since no two…
The dynamics of three soft interacting particles on a ring is shown to correspond to the motion of one particle inside a soft triangular billiard. The dynamics inside the soft billiard depends only on the {\it masses ratio} between…
Congruent polygons are congruent in angles as well as in edge lengths. We concentrate on the angle aspect, and investigate how tilings of the sphere by congruent pentagons can be determined by the angle information only. We also investigate…
We study semi-dynamical systems associated to delay differential equations. We give a simple criteria to obtain weak and strong persistence and provide sufficient conditions to guarantee uniform persistence. Moreover, we show the existence…
We study ray optics in the context of double mirror systems, in the limit as the two mirrors approach one another (thin films). This leads to a novel set of differential equations on a mirror surface which have interesting structure as seen…
Limit periodic point sets are aperiodic structures with pure point diffraction supported on a countably, but not finitely generated Fourier module that is based on a lattice and certain integer multiples of it. Examples are cut and project…
The motion, settling, and dispersion of microplastics in the ocean are determined by their rotational dynamics. We present experiments on elongated, large aspect ratio, and mildly curved plastic fibers slightly longer than the Kolmogorov…
We investigate the behavior of the solutions of the ray equation in isotropic media. We discuss local and global transversals and wavefronts and give examples of rays without wavefronts.