11 Results Found

A continuous measure of symmetry and the Voronoi entropy of 2D patterns representing Voronoi diagrams emerging from the Penrose tiling were calculated. A given Penrose tiling gives rise to a diversity of the Voronoi diagrams when the centers, vertice...

The notion of the informational measure of symmetry is introduced according to: $H_{sym}\left(G\right)=-{{\displaystyle \sum }}_{i=1}^{k}P\left(G_i\right)lnP\left(G_i\right)$, where $P\left(G_i\right)$ is the probability of appearance of the symmetry operation $G_i$ within the given 2D pattern. $H_{sym}\left(G\right)$ is interpreted as an averaged u...

Employing the spin-wave formalism within and beyond the harmonic-oscillator approx-imation, we study the dynamic structure factors of spin-${\displaystyle \frac{1}{2}}$ nearest-neighbor quantum Heisenberg antiferromagnets on two-dimensional quasiperiodic lattices with particul...

The Golden ratio is an irrational number that has a tendency to appear in many different scientific and artistic fields. It may be found in natural phenomena across a vast range of length scales; from galactic to atomic. In this review, the mathemati...

This paper reviews the empire problem for quasiperiodic tilings and the existing methods for generating the empires of the vertex configurations in quasicrystals, while introducing a new and more efficient method based on the cut-and-project techniqu...

As is known, quasi-periodicity attracts great attention in many scientific regions. For instance, the discovery of the quasicrystal was rewarded the Nobel Prize in 2011, leading to a series of its applications. However, in the area of manipulating op...

The concrete realization of topological quantum computing using low-dimensional quasiparticles, known as anyons, remains one of the important challenges of quantum computing. A topological quantum computing platform promises to deliver more robust qu...

The orthogonal projections of the Voronoi and Delone cells of root lattice $A_n$ onto the Coxeter plane display various rhombic and triangular prototiles including thick and thin rhombi of Penrose, Amman–Beenker tiles, Robinson triangle...

On a two-dimensional quasicrystal, a Penrose tiling, we simulate for the first time a game of life dynamics governed by non-local rules. Quasicrystals have inherently non-local order since any local patch, the emperor, forces the existence of a large...

Quasicrystals have attracted a growing interest in material science because of their unique properties and applications. Proper determination of the atomic structure is important in designing a useful application of these materials, for which a diffi...

To overcome the negative effects of the biochemical application of nano-substances in medicine (toxicity problem), using the example of fullerene C₆₀’s first derivative (fullerenol, FD-C₆₀), we show that their biophysical effect is possible thr...