Related papers: Hyperuniform properties of the square-triangle til…
We investigate magnetic properties of the ferromagnetic Ising model on square-triangle tilings to explore how the hyperuniformity, which characterizes long-range behavior of the point pattern, influences critical phenomena where long-range…
We consider the scaling properties characterizing the hyperuniformity (or anti-hyperuniformity) of long wavelength fluctuations in a broad class of one-dimensional substitution tilings. We present a simple argument that predicts the…
Hyperuniform point patterns can be classified by the hyperuniformity scaling exponent $\alpha > 0$, that characterizes the power-law scaling behavior of the structure factor $S(\mathbf{k})$ as a function of wavenumber $k\equiv|\mathbf{k}|$…
Square-triangle-rhombus ($\mathcal{STR}$) tilings are encountered in various self-organized multi-component systems. They exhibit a rich structural diversity, encompassing both periodic tilings and long-range ordered quasicrystals,…
One well studied way to construct quasicrystalline tilings is via inflate-and-subdivide (a.k.a. substitution) rules. These produce self-similar tilings--the Penrose, octagonal, and pinwheel tilings are famous examples. We present a…
Hyperuniformity, the suppression of density fluctuations at large length scales, is observed across a wide variety of domains, from cosmology to condensed matter and biological systems. Although the standard definition of hyperuniformity…
A growth mechanism for a perfect one-dimensional (1D) quasiperiodic structure is presented with a local covering rule. We use rectangular tiles with two different types of string decorations. The string position in a tile is allowed to move…
Hyperuniformity is a property of certain heteroneous media in which density fluctuations in the long wavelength range decay to zero. In reciprocal space this behavior translates into a decay of Fourier intensities in the range near small…
Hyperuniformity refers to the suppression of density fluctuations at large scales. Typical for ordered systems, this property also emerges in several disordered physical and biological systems, where it is particularly relevant to…
In this work we present a study on the characterization of ordered and disordered hyperuniform point distributions on spherical surfaces. In spite of the extensive literature on disordered hyperuniform systems in Euclidean geometries, to…
Let U be a multiply-connected region in R^2 with smooth boundary. Let P_epsilon be a polyomino in epsilon Z^2 approximating U as epsilon tends to 0. We show that, for certain boundary conditions on P_epsilon, the height distribution on a…
We consider the construction of point processes from tilings, with equal volume tiles, of d-dimensional Euclidean space. We show that one can generate, with simple algorithms ascribing one or more points to each tile, point processes which…
A construction as a growth process for sampling of the uniform infinite planar triangulation (UIPT), defined in a previous paper, is given. The construction is algorithmic in nature, and is an efficient method of sampling a portion of the…
A general construction principle of inflation rules for decagonal quasiperiodic tilings is proposed. The prototiles are confined to be polygons with unit edges. An inflation rule for a tiling is the combination of an expansion and a…
We provide large deviations estimates for the upper tail of the number of triangles in scale-free inhomogeneous random graphs where the degrees have power law tails with index $-\alpha, \alpha \in (1,2)$. We show that upper tail…
Given a graph $G$ and collection of subgraphs $T$ (called tiles), we consider covering $G$ with copies of tiles in $T$ so that each vertex $v\in G$ is covered with a predetermined multiplicity. The multinomial tiling model is a natural…
We know that tilesets that can tile the plane always admit a quasi-periodic tiling [4, 8], yet they hold many uncomputable properties [3, 11, 21, 25]. The quasi-periodicity function is one way to measure the regularity of a quasi-periodic…
We review an approach which aims at studying discrete (pseudo-)manifolds in dimension $d\geq 2$ and called random tensor models. More specifically, we insist on generalizing the two-dimensional notion of $p$-angulations to higher…
We study tilings of the plane that combine strong properties of different nature: combinatorial and algorithmic. We prove existence of a tile set that accepts only quasiperiodic and non-recursive tilings. Our construction is based on the…
We study hyperuniform properties in various two-dimensional periodic and quasiperiodic point patterns. Using the histogram of the two-point distances, we develop an efficient method to calculate the hyperuniformity order metric, which…