Electronic Spectrum of a 2D Quasi-Crystal Related to the Octagonal Quasi-Periodic Tiling

Electronic Spectrum of a 2D Quasi-Crystal Related to the Octagonal Quasi-Periodic Tiling

Recently, a tiling derived from the well-known 2D quasi-periodic octagonal tiling has been introduced. In this letter, we show that in the framework of a tight-binding model, the electronic spectrum of this nontrivial tiling can be derived. The integrated density of state is singular and can be a devil staircase, there can be a finite or infinite number of gaps, whereas the measure of the spect...

Finite-Difference Time-Domain Simulation of Light Propagation in 2D Periodic and Quasi-Periodic Photonic Structures

Ultra-short pulse is a promising technology for achieving ultra-high data rate transmission which is required to follow the increased demand of data transport over an optical communication system. Therefore, the propagation of such type of pulses and the effects that it may suffer during its transmission through an optical waveguide has received a great deal of attention in the recent years. We...

Quasi - periodic Nonlinear Photonic Crystal

2 3 The second issue of SCE-Science opens up the aperture to a wider glance at the diverse and innovative research conducted at SCE-Sha-moon College of engineering. The articles brought here present just a small portion of the bustling activity of creation, cooperation, and study felt throughout our college. In this issue are represented some of our senior researchers as well as some of our lat...

Mathematics. Quasi-crystal conundrum opens a tiling can of worms.

Quasi-periodic Tiling with Multiplicity: A Lattice Enumeration Approach

The k-tiling problem is the problem of covering R with translates of a convex polytope P using a discrete multiset Λ of translation vectors. Thus, every point in R is covered exactly k times, except possibly for the boundary of P and its translates. In this paper, we study the k-tiling problem when the tiling set Λ is a finite union of translated lattices. This is motivated by the work of Kolou...