Search Results (11)

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 through non-covalent hydrogen bonds when around FD-C₆₀ water layers are formed. SD-C₆₀ (Zeta potential is −43.29 mV) is much more stable than fullerol (Zeta potential is −25.85 mV), so agglomeration/fragmentation of the fullerol structure, due to instability, can cause toxic effects. When fullerol in solution was exposed to an oscillatory magnetic field with Re (real) part [250/−92 mT, H(ωt) = Acos(ωt)], water layers around FD-C₆₀ (fullerenol) are formed according to the Penrose process of 3D tiling formation, and the second derivative, SD-C₆₀ (or 3HFWC), is self-organized. However, when Im (imaginary) part [250/−92 mT, H(ωt) = Bisin (ωt)] of the external magnetic field is applied in addition to SD-C₆₀, ordered water chains and bubbling of water (“micelle”) are formed as a third derivative (TD-C₆₀). Fullerol (FD-C₆₀) interacts with biological structures biochemically, while the second (SD-C₆₀) and third (TD-C₆₀) derivatives act biophysically via non-covalent hydrogen bond oscillation. SD-C₆₀ and TD-C₆₀ significantly increased water solubility and reduced toxicity. The paper explains the synthesis of SD-C60 and TD-C60 from FD-C60 (fullerol) as a precursor by the influence of an oscillatory magnetic field (“Yin-Yang” principle) on hydrogen bonds in order to create water layers around fullerol. Examples of biomedical applications (cancer and Alzheimer’s) of this synergetic complex are given. This study shows that the “Yin-Yang” machinery, based on the nanophysics of C₆₀ molecules and non-covalent hydrogen bonds, is possible. The first attempt has been composed to synthesize nanomaterial for biophysical vibrational nanomedicine. Full article

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 particular emphasis on a mag-netic analog to the well-known confined states of a hopping Hamiltonian for independent electrons on a two-dimensional Penrose lattice. We present comprehensive calculations on the C_5v Penrose tiling in comparison with the C_8v Ammann–Beenker tiling, revealing their decagonal and octagonal antiferromagnetic microstructures. Their dynamic spin structure factors both exhibit linear soft modes emergent at magnetic Bragg wavevectors and have nearly or fairly flat scattering bands, signifying magnetic excitations localized in some way, at several different energies in a self-similar manner. In particular, the lowest-lying highly flat mode is distinctive of the Penrose lattice, which is mediated by its unique antiferromagnons confined within tricoordinated sites only, unlike their itinerant electron counterparts involving pentacoordinated, as well as tricoordinated, sites. Bringing harmonic antiferromagnons into higher-order quantum interaction splits, the lowest-lying nearly flat scattering band in two, each mediated by further confined antiferromagnons, which is fully demonstrated and throughly visualized in the perpendicular as well as real spaces. We disclose superconfined antiferromagnons on the two-dimensional Penrose lattice. Full article

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 optical fields, the two-dimensional quasi-periodicity is rarely considered. Here, we study the two-dimensional quasi-periodic diffraction properties of the scalar and vector optical fields based on the Penrose tiling, which is one of the most representative kinds of two-dimensional quasi-periodic patterns. We propose type-A and type-B Penrose tiling masks (PTMs) with phase modulation, and further show the diffraction properties of the optical fields passing through these masks. The intensity of the diffraction field holds a tenfold symmetry. It is proved that the iteration number n of the PTM shows the “weeding” function in the diffraction field, and this property is useful in filtering, shaping, and manipulating diffraction fields. Meanwhile, we also find that the diffraction patterns have the label of the Golden ratio, which can be applied in areas such as optical encryption and information transmission. Full article

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 mathematical properties of the Golden ratio are discussed before exploring where in nature it is claimed to appear; beginning at astronomical scales and progressing to smaller lengths, until reaching those of atomic and quantum physics. For each phenomenon discussed, the evidence for the presence of the Golden ratio is assessed. In making such a tour across length scales, it is illustrated just how prevalent this single number is within the natural universe. Full article

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 qubits with additional hardware-level protection against errors that could lead to the desired large-scale quantum computation. We propose quasicrystal materials as such a natural platform and show that they exhibit anyonic behavior that can be used for topological quantum computing. Different from anyons, quasicrystals are already implemented in laboratories. In particular, we study the correspondence between the fusion Hilbert spaces of the simplest non-abelian anyon, the Fibonacci anyons, and the tiling spaces of the one-dimensional Fibonacci chain and the two-dimensional Penrose tiling quasicrystals. A concrete encoding on these tiling spaces of topological quantum information processing is also presented by making use of inflation and deflation of such tiling spaces. While we outline the theoretical basis for such a platform, details on the physical implementation remain open. Full article

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 difficult phase problem of the structure factor must be solved. Diffraction patterns of quasicrystals consist of a periodic series of peaks, which can be reduced to a single envelope. Knowing the distribution of the diffraction image into series, it is possible to recover information about the phase of the structure factor without using time-consuming iterative methods. By the inverse Fourier transform, the structure factor can be obtained (enclosed in the shape of the average unit cell, or atomic surface) directly from the diffraction patterns. The method based on envelope function analysis was discussed in detail for a model 1D (Fibonacci chain) and 2D (Penrose tiling) quasicrystal. First attempts to apply this technique to a real Al-Cu-Rh decagonal quasicrystal were also made. Full article

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 uncertainty in the presence of symmetry elements from the group G in the given pattern. The informational measure of symmetry of the “ideal” pattern built of identical equilateral triangles is established as $H_{sym}\left(D_3\right)=$ 1.792. The informational measure of symmetry of the random, completely disordered pattern is zero, $H_{sym}=0$. The informational measure of symmetry is calculated for the patterns generated by the P3 Penrose tessellation. The informational measure of symmetry does not correlate with either the Voronoi entropy of the studied patterns nor with the continuous measure of symmetry of the patterns. Quantification of the “ordering” in 2D patterns performed solely with the Voronoi entropy is misleading and erroneous. Full article

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, vertices, and the centers of the edges of the Penrose rhombs are taken as the seed points (or nuclei). Voronoi diagrams keep the initial symmetry group of the Penrose tiling. We demonstrate that the continuous symmetry measure and the Voronoi entropy of the studied sets of points, generated by the Penrose tiling, do not necessarily correlate. Voronoi diagrams emerging from the centers of the edges of the Penrose rhombs, considered nuclei, deny the hypothesis that the continuous measure of symmetry and the Voronoi entropy are always correlated. The Voronoi entropy of this kind of tiling built of asymmetric convex quadrangles equals zero, whereas the continuous measure of symmetry of this pattern is high. Voronoi diagrams generate new types of Penrose tiling, which are different from the classical Penrose tessellation. Full article

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 triangles, and Danzer triangles to name a few. We point out that the symmetries representing the dihedral subgroup of order $2h$ involving the Coxeter element of order $h=n+1$ of the Coxeter–Weyl group $a_n$ play a crucial role for $h$ -fold symmetric tilings of the Coxeter plane. After setting the general scheme we give samples of patches with 4-, 5-, 6-, 7-, 8-, and 12-fold symmetries. The face centered cubic (f.c.c.) lattice described by the root lattice $A_3$ , whose Wigner–Seitz cell is the rhombic dodecahedron projects, as expected, onto a square lattice with an $h=4$ -fold symmetry. Full article

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 number of tiles at all distances, the empires. Considering the emperor and its local patch as a quasiparticle, in this case a glider, its empire represents its field and the interaction between quasiparticles can be modeled as the interaction between their empires. Following a set of rules, we model the walk of life in different setups and we present examples of self-interaction and two-particle interactions in several scenarios. This dynamic is influenced by both higher dimensional representations and local choice of hinge variables. We discuss our results in the broader context of particle physics and quantum field theory, as a first step in building a geometrical model that bridges together higher dimensional representations, quasicrystals and fundamental particles interactions. Full article

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 technique. Using Penrose tiling as an example, this method finds the forced tiles with the restrictions in the high dimensional lattice (the mother lattice) that can be cut-and-projected into the lower dimensional quasicrystal. We compare our method to the two existing methods, namely one method that uses the algorithm of the Fibonacci chain to force the Ammann bars in order to find the forced tiles of an empire and the method that follows the work of N.G. de Bruijn on constructing a Penrose tiling as the dual to a pentagrid. This new method is not only conceptually simple and clear, but it also allows us to calculate the empires of the vertex configurations in a defected quasicrystal by reversing the configuration of the quasicrystal to its higher dimensional lattice, where we then apply the restrictions. These advantages may provide a key guiding principle for phason dynamics and an important tool for self error-correction in quasicrystal growth. Full article