This book shows how the concept of geometrical frustration can be used to elucidate the
structure and properties of nonperiodic materials such as metallic glasses, quasicrystals …

The first quasicrystal (QC) structure was observed in 1984. QCs possess long-range
orientational and translational order while lacking the periodicity of crystals. An overview is …

Random tilings that comprise squares and equilateral triangles can model quasicrystals with
twelvefold symmetry. A (phason) elastic theory for such tilings is constructed, whose order …

We investigate the phase diagram of two-dimensional binary mixtures of hard dises. There
are two parameters in the problem, the ratio r of the radii of the two dises, and the …

Using computer simulations, we study the phase behavior of a model system of colloidal
hard disks with a diameter σ and a soft corona of width 1.4σ. The particles interact with a …

Dislocations in crystals naturally break the symmetry of the bulk, introducing local atomic
configurations with symmetries such as fivefold rings. But dislocations do not usually …

Using Monte Carlo simulations and free-energy calculations, we study the phase behaviour
of a two-dimensional system of particles interacting with a hard core of diameter σ HD and a …

Random tiling models cover the plane with a set of rigid tiles without gaps between tiles and
without overlap. This paper considers tilings of the plane by squares and equilateral …

We map the ground-state ensemble of antiferromagnetic Ising model of spin-S on a
triangular lattice to an interface model whose entropic fluctuations are proposed to be …

We introduce a concept for random tilings which, comprising the conventional one, is also
applicable to tiling ensembles without height representation. In particular, we focus on the …