the quasi-periodic order is a type of geometrical order in universe which is observed in the structure of quasi-crystals. this order was first introduced in mathematics in 1973 by roger penrose and then discovered in quasi-crystals in 1984 while spreading in mathematics, chemistry and physics. the paper professor james lu et al published in science magazine in 2007 illustrated that iranians wer...

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...

We use the subgraph replacement method to prove a simple product formula for the tilings of an octagonal counterpart of Propp’s quasi-hexagons (Problem 16 in New Perspectives in Geometric Combinatorics, Cambridge University Press, 1999), called quasi-octagon.

Neighborhoods and neighborhood sequences play important roles in several branches of pattern analysis. In earlier papers in Z only certain special (e.g. periodic or octagonal) sequences were investigated. In this paper we study neighborhood sequences which are either ultimately periodic or allow at every neighborhood to do nothing at no cost. We give finite procedures and descriptive theoretica...

In this paper, the periodic, quasi periodic and chaotic responses of rotational machines with a hexagonal centrifugal governor are studied. The external disturbance is assumed as a sinusoid effect. By using the forth order Rung-Kutta numerical integration method, bifurcation diagram, largest Lyapunov exponent and Lyapunov dimension are calculated and presented to detect the critical controlling...

quasicrystals are a group of materials with the quasi-periodic structure, and since their discovery in 1980 their specially interesting physical properties have attracted the attention of many researchers. the lack of translational periodicity makes the numerical calculations of their physical properties much more difficult than the crystalline solids. in this work we present a detailed numeric...