The formation of the icosahedral phase (I-phase) as a secondary solidification phase in Mg–Zn–Y and Mg–Zn–Al base systems provides useful advantages in designing high performance wrought magnesium alloys. The strengthening in two-phase composites (I-phase + α-Mg) can be explained by dispersion hardening due to the presence of I-phase particles and by the strong bonding property at the I-phase/m...

Non-Hermitian quasicrystal forms a unique class of matter with symmetry-breaking, localization and topological transitions induced by gain loss or nonreciprocal effects. In this work, we introduce non-Abelian generalization non-Hermitian quasicrystal, in which the interplay between effects quasiperiodic potentials create mobility edges rich among extended, critical localized phases. These gener...

This paper develops a method for discrete computational Fourier analysis of functions defined on quasicrystals and other almost periodic sets. A key point is to build the analysis around the emerging theory of quasicrystals and diffraction in the setting on local hulls and dynamical systems. Numerically computed approximations arising in this way are built out of the Fourier module of the quasi...

The unrelated discoveries of quasicrystals and topological insulators have in turn challenged prevailing paradigms in condensed-matter physics. We find a surprising connection between quasicrystals and topological phases of matter: (i) quasicrystals exhibit nontrivial topological properties and (ii) these properties are attributed to dimensions higher than that of the quasicrystal. Specifically...

A meshless approximation and local integral equation (LIE) formulation are proposed for elastodynamic analysis of a hollow cylinder made of quasicrystal materials with decagonal quasicrystal properties. The cylinder is assumed to be under shock loading. Therefore, the general transient elastodynamic problem is considered for coupled phonon and phason displacements and stresses. The equations of...

One-dimensional quasiperiodic systems, such as the Harper model and the Fibonacci quasicrystal, have long been the focus of extensive theoretical and experimental research. Recently, the Harper model was found to be topologically nontrivial. Here, we derive a general model that embodies a continuous deformation between these seemingly unrelated models. We show that this deformation does not clo...

In 1962, Bienenstock and Ewald described the classification of crystalline space groups algebraically in the dual, or Fourier, space. Recently, the method has been applied to quasicrystals and modulated crystals. This paper phrases Bienenstock and Ewald’s definitions in terms of group cohomology. A Fourier quasicrystal is defined, along with its space group, without requiring that it come from ...