Related papers: Designing aperiodic to periodic interfaces
We present a novel variant of a planar quasiperiodic tiling with tenfold symmetry, employing the same thick and thin rhombuses as the celebrated rhombic Penrose tiling. Despite its distinct visual appearance, this new tiling shares several…
We present aperiodic sets of prototiles whose shapes are based on the well-known Penrose rhomb tiling. Some decorated prototiles lead to an exact Penrose rhomb tiling without any matching rules. We also give an approximate solution to an…
Anisotropic acoustic metamaterials have been proved very useful for their high potential in guiding and manipulating sound energy. In this paper, we further develop the idea by using periodically layered structures for transformational…
A recursive scheme relying on decagons is used to generate Penrose-like sublattices or tilings. Its relevance for understanding structures with non-crystallographic symmetry is discussed.
Topological mechanical metamaterials are artificial structures whose unusual properties are protected very much like their electronic and optical counterparts. Here, we present an experimental and theoretical study of an active metamaterial…
We propose a new simple construction of an aperiodic tile set based on self-referential (fixed point) argument. People often say about some discovery that it appeared "ahead of time", meaning that it could be fully understood only in the…
Periodic frameworks with crystallographic symmetry are investigated from the perspective of a general deformation theory of periodic bar-and-joint structures in $R^d$. It is shown that natural parametrizations provide affine section…
We demonstrate a new method of achieving topologically protected states in a discrete hexagonal lattice by attaching gyroscopic spinners, which bring chirality to the system. Dispersive features of this medium are investigated in detail…
We determine the topology of the moduli space of periodic tilings of the plane by parallelograms. To each such tiling, we associate combinatorial data via the zone curves of the tiling. We show that all tilings with the same combinatorial…
Some combinatorial properties of fixed boundary rhombus random tilings with octagonal symmetry are studied. A geometrical analysis of their configuration space is given as well as a description in terms of discrete dynamical systems, thus…
Periodic configurations have dominated the design of phononic and elastic-acoustic metamaterial structures for the past decades. Unlike periodic crystals, quasicrystals lack translational symmetry but are unrestricted in rotational…
Can the entire plane be paved with a single tile that forces aperiodicity? This is known as the ein Stein problem (in German, ein Stein means one tile). This paper presents a monotile that delivers aperiodic tiling by design. It is based on…
The modular design of planar phased array antennas with hexagonal apertures is addressed by means of innovative diamond-shaped tiling techniques. Both tiling configuration and subarray coefficients are optimized to fit user-defined…
A combinatorial tiling of the sphere is naturally given by an embedded graph. We study the case that each tile has exactly five edges, with the ultimate goal of classifying combinatorial tilings of the sphere by geometrically congruent…
Symmetries are known to dictate important physical properties and can be used as a design principle in particular in wave physics, including wave structures and the resulting propagation dynamics. Local symmetries, in the sense of a…
We explore the macroscopic elastic behavior of the aperiodic but hyperuniform (single tile) tiling.
We introduce a square tiling/tetragonal strip representation to the P, D, and G triply periodic minimal surfaces. This approach is useful in identifying mixtures and grain boundaries of these surfaces that might be useful for material…
The steady state structure of an interface in an Ising system on a square lattice placed in a {\em non-uniform} external field, shows a commensurate -incommensurate transition driven by the velocity of the interface. The non-uniform field…
By reformulating Wang tiles with tensors, we propose a natural generalization to the probabilistic and quantum setting. In this new framework, we introduce notions of tilings and periodicity directly extending their classical counterparts.…
The quest for novel designs for lightweight phononic crystals and elastic metamaterials with wide lowfrequency band gaps has proven to be a significant challenge in recent years. In this context, lattice-type materials represent a promising…