相关论文: Proof of Aperiodicity of hat tile using the Golden…

This paper describes the celebrated aperiodic hat tiling by Smith et al. [Comb. Theory 8 (2024), 6] as generated by an overlapping iterated function system. We briefly introduce and study infinite sequences of iterated function systems that…

This paper is devoted to the first systematic investigation of manifolds that are Einstein for a connection with skew symmetric torsion. We derive the Einstein equation from a variational principle and prove that, for parallel torsion, any…

Architected materials achieve unique mechanical properties through precisely engineered microstructures that minimize material usage. However, a key challenge of low-density materials is balancing high stiffness with stable deformability up…

This paper explores ``black hole'' solutions of various Einstein-wave matter systems admitting an isometry of their domain of outer communications taking every point to its future. In the first two parts, it is shown that such solutions,…

Tilings based on the cut and project method are key model systems for the description of aperiodic solids. Typically, quantities of interest in crystallography involve averaging over large patches, and are well defined only in the…

Manifolds endowed with torsion and nonmetricity are interesting both from the physical and the mathematical points of view. In this paper, we generalize some results presented in the literature. We study Einstein manifolds (i.e., manifolds…

We obtain structural results on translational tilings of periodic functions in $\mathbb{Z}^d$ by finite tiles. In particular, we show that any level one tiling of a periodic set in $\mathbb{Z}^2$ must be weakly periodic (the disjoint union…

Our understanding of physical properties of quasicrystals owes a great deal to studies of tight-binding models constructed on quasiperiodic tilings. Among the large number of possible quasiperiodic structures, two dimensional tilings are of…

We consider a homogeneous fibration $G/L \to G/K$, with symmetric fiber and base, where $G$ is a compact connected semisimple Lie group and $L$ has maximal rank in $G$. We suppose the base space $G/K$ is isotropy irreducible and the fiber…

The Einstein-Straus spacetime describes a nonrotating black hole immersed in a matter-dominated cosmology. It is constructed by scooping out a spherical ball of the dust and replacing it with a vacuum region containing a black hole of the…

Constructing an accurate approximation to nonadiabatic rate theory which is valid for arbitrary values of the electronic coupling has been a long-standing challenge in theoretical chemistry. Ring-polymer instanton theories offer a very…

We give a criterion which allows to prove non-ergodicity for certain infinite periodic billiards and directional flows on Z-periodic translation surfaces. Our criterion applies in particular to a billiard in an infinite band with…

Quasicrystals are aperiodically ordered solids that exhibit long-range order without translational periodicity, bridging the gap between crystalline and amorphous materials. Due to their lack of translational periodicity, information on…

The top of the attractor $A$ of a hyperbolic iterated function system $\left\{ f_{i}:\mathbb{R}^{n}\rightarrow\mathbb{R}^{n}|i=1,2,\dots,M\right\} $ is defined and used to extend self-similar tilings to overlapping systems. The theory…

A finite set of integers $A$ tiles the integers by translations if $\mathbb{Z}$ can be covered by pairwise disjoint translated copies of $A$. Restricting attention to one tiling period, we have $A\oplus B=\mathbb{Z}_M$ for some…

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…

Classifications of symmetry-protected topological (SPT) phases provide a framework to systematically understand the physical properties and potential applications of topological systems. While such classifications have been widely explored…

Quantum Hall phases have recently emerged as a platform to investigate non-Hermitian topology in condensed-matter systems. This platform is particularly interesting due to its tunability, which allows to modify the properties and topology…

Consider a periodic tiling of a plane by equal triangles obtained from the equilateral tiling by a linear transformation. We study a following tiling billiard: a ball follows straight segments and bounces of the boundaries of the tiles into…

With the help of AdS/CFT correspondence, the Einstein ring of a charged black hole in conformal gravity has been studied. Imposing an oscillating Gauss source on one side of the AdS boundary which propagates in the bulk, we derive the…