Non-Hermitian quasicrystals possess and metal–insulator transitions induced by gain loss or nonreciprocal effects. In this work, we uncover the nature of localization in a generalized Aubry–André–Harper model with dimerized hopping amplitudes complex onsite potential. By investigating spectrum, adjacent gap ratios inverse participation ratios, find an extended phase, localized phase mobility ed...

Design of some crystal and quasicrystal networks, based on rhombellane tiling,is presented. [1,1,1]Propellane,is a synthesized organic molecule; its hydrogenated form, the bicyclo[1.1.1]pentane,may be represented by the complete bipartite graph K2,3 which is the smallest rhombellane. Topology of translational and radial structures involving rhombellanes is described in terms of vertex symbol, c...

In this paper, the average unit cell for a quasicrystal is constructed by a statistical approach. For the Penrose tiling, it is shown that such a unit cell is fully equivalent to the oblique projection of the atomic surface onto physical space. The obtained statistical distributions can be easily extended to imperfect structures by using a Gaussian approximation. This leads to simple analytical...

Unique affine extensions H 2 , H 3 and H 4 are determined for the noncrystallographic Coxeter groups H2, H3 and H4. They are used for the construction of new mathematical models for quasicrystal fragments with 10-fold symmetry. The case of H 2 corresponding to planar point sets is discussed in detail. In contrast to the cutand-project scheme we obtain by construction finite point sets, which gr...

The shelling of crystals is concerned with counting the number of atoms on spherical shells of a given radius and a fixed centre. Its straight-forward generalization to quasicrystals, the so-called central shelling, leads to non-universal answers. As one way to cope with this situation, we consider shelling averages over all quasicrystal points. We express the averaged shelling numbers in terms...

We report the formation of a binary crystal of hard polyhedra due solely to entropic forces. Although the alternating arrangement of octahedra and tetrahedra is a known space-tessellation, it had not previously been observed in self-assembly simulations. Both known one-component phases - the dodecagonal quasicrystal of tetrahedra and the densest-packing of octahedra in the Minkowski lattice - a...

A molecular dynamics study on atomic self-diffusion in Frank-Kasper type dodecagonal quasicrystals is presented. It is found that the quasicrystal-specific flip mechanism for atomic diffusion, predicted by Kalugin and Katz, indeed occurs in this system. However, in order to be effective, this mechanism needs to be catalyzed by other defects, such as half-vacancies. For this reason, flip diffusi...

A molecular dynamics study of atomic self-diiusion in Frank-Kasper type do-decagonal quasicrystals is presented. It is found that the quasicrystal-speciic ip mechanism for atomic diiusion, predicted by Kalugin and Katz, indeed occurs in this system. However, in order to be eeective, this mechanism needs to be catalyzed by other defects, such as half-vacancies. For this reason, it is diicult to ...