Hyperuniform point patterns are characterized by vanishing infinitewavelength density fluctuations and encompass all crystal structures, certain quasiperiodic systems, and special disordered point patterns (Torquato and Stillinger 2003 Phys. Rev. E 68 041113). This paper generalizes the notion of hyperuniformity to include also two-phase random heterogeneous media. Hyperuniform random media do ...

We classify a quasiperiodic flow as either algebraic or transcendental. For an algebraic quasiperiodic flow φ on the n-torus, Tn, we prove that an absolute invariant of the smooth conjugacy class of φ, known as the multiplier group, is a subgroup of the group of units of the ring of integers in a real algebraic number field F of degree n over Q. We also prove that for any real algebraic number ...

A quasiperiodic word is, here, a finite or infinite word that can be obtained by concatenations or overlaps of a given finite word, called a quasiperiod of the whole word. For instance, aba is a quasiperiod of the Fibonacci word. It is an immediate observation that any quasiperiodic word contains an overlap. Thus its critical exponent is greater than 2. What is the minimal critical exponent of ...

Ag films on GaAs(110) exhibit a one-dimensional quasiperiodic modulation, resulting in a Fibonacci sequence of parallel stripes with two different widths. Valence level photoemission shows that the Ag electronic states acquire a unique character along the quasiperiodic direction, distinctively manifested by a hierarchy of energy level replicas and avoided crossings at characteristic intervals i...

Frank-Kasper phases are tetrahedrally packed structures occurring in numerous materials, from elements to intermetallics to self-assembled soft materials. They exhibit complex manifolds of Wigner-Seitz cells with many-faceted polyhedra, forming an important bridge between the simple close-packed periodic and quasiperiodic crystals. The recent discovery of the Frank-Kasper σ-phase in diblock and...

We study the properties of wavefunctions and the wavepacket dynamics in quasiperiodic tight-binding models in one, two, and three dimensions. The atoms in the one-dimensional quasiperiodic chains are coupled by weak and strong bonds aligned according to the Fibonacci sequence. The associated d-dimensional quasiperiodic tilings are constructed from the direct product of d such chains, which yiel...

Scattering problems for periodic structures have been studied a lot in the past few years. A main idea for numerical solution methods is to reduce such problems to one periodicity cell. In contrast to periodic settings, scattering from locally perturbed periodic surfaces is way more challenging. In this paper, we introduce and analyze a new numerical method to simulate scattering from locally p...