Related papers: Quasicrystals: Atomic coverings and windows are du…
Recent studies of holographic tensor network models defined on regular tessellations of hyperbolic space have not yet addressed the underlying discrete geometry of the boundary. We show that the boundary degrees of freedom naturally live on…
We show that quasicrystals exhibit anyonic behavior that can be used for topological quantum computing. In particular, we study a correspondence between the fusion Hilbert spaces of the simplest non-abelian anyon, the Fibonacci anyons, and…
We present a new complementary strategy to quasicrystalline structure determination: The local atomic structure of simple icosahedral (si) Ho11Mg15Zn74 [a(6D)=5.144(3)A] in a sphere of up to r=17A was refined using the atomic pair…
Starting from the classical results of Shubnikov and Zamorzayev, computer models of shapes are implemented, which allow to visualize the action of discrete subgroups of continuous topological groups. The action is visualize by performing…
Relying on rays, we search for submodules of a module V over a supertropical semiring on which a given anisotropic quadratic form is quasilinear. Rays are classes of a certain equivalence relation on V, that carry a notion of convexity,…
We argue that 2D dodecagonal spherical quasicrystalls (QCs) will be discovered in the nearest future and investigate how the planar QC order becomes compatible with the spherical geometry. We show that the appearance of curvature-induced…
Optical interference holography has been proved to be a useful technique in fabricating periodic photonic crystals in which electromagnetic waves are forbidden in certain frequency bandgaps. Compared to periodic crystals quasicrystals,…
We report a degenerate quasicrystal in Monte Carlo simulations of hard triangular bipyramids each composed of two regular tetrahedra sharing a single face. The dodecagonal quasicrystal is similar to that recently reported for hard…
A tile Hamiltonian (TH) replaces the actual atomic interactions in a quasicrystal with effective interactions between and within tiles. We study Al-Co-Ni and Al-Co-Cu decagonal quasicrystals described as decorated Hexagon-Boat-Star (HBS)…
With the rapid development of topological states in crystals, the study of topological states has been extended to quasicrystals in recent years. In this review, we summarize the recent progress of topological states in quasicrystals,…
Quasicrystals remain among the most intriguing materials in physics and chemistry. Their structure results in many unusual properties including anomalously low friction as well as poor electrical and thermal conductivity but it also…
On the example of exceptional families of viruses we i) show the existence of a completely new type of matter organization in nanoparticles, in which the regions with a chiral pentagonal quasicrystalline order of protein positions are…
We study the phase behaviour of a quasi-two dimensional cholesteric liquid crystal shell. We characterise the topological phases arising close to the isotropic-cholesteric transition, and show that they differ in a fundamental way from…
Quasicrystals are ubiquitous in nature. Beyond crystalline solids, they can be created as optically induced or technologically fabricated structures in photonic and phononic systems, as potentials for cold atoms and Bose-Einstein…
We study the cohomology and hence $K$-theory of the aperiodic tilings formed by the so called 'cut and project' method, i.e., patterns in $d$ dimensional Euclidean space which arise as sections of higher dimensional, periodic structures.…
The projections of the lattices, may be used as models of quasicrystals, and the particular affine extension of the $H_2$ symmetry as a subgroup of $A_4$, discussed in the work, presents a different perspective to 5-fold symmetric…
We present an icosahedral quasicrystal as a modification of the icosagrid, a multigrid with 10 plane sets that are arranged with icosahedral symmetry. We use the Fibonacci chain to space the planes, thereby obtaining a quasicrystal with…
Two well-known methods for the design of quasicrystal models are used to create novel nonlinear optical devices. These devices are useful for efficient three-wave mixing of several different processes, and therefore offer greater…
We describe the structure of quasiflats in two-dimensio\-nal Artin groups. We rely on the notion of metric systolicity developed in our previous work. Using this weak form of non-positive curvature and analyzing in details the combinatorics…
We introduce a construction to embed a quasiperiodic lattice of obstacles into a single unit cell of a higher-dimensional space, with periodic boundary conditions. This construction transparently shows the existence of channels in these…