相关论文: Rhombic Tilings and Primordia Fronts of Phyllotaxi…
It is shown that tiling in icosahedral quasicrystals can also be properly described by cyclic twinning at the unit cell level. The twinning operation is applied on the primitive prolate golden rhombohedra, which can be considered a result…
We study single-flip dynamics in sets of three-dimensional rhombus tilings with fixed polyhedral boundaries. This dynamics is likely to be slowed down by so-called ``cycles'': such structures arise when tilings are encoded via the…
We have previously explored cylindrical packings of disks and their relation to sphere packings. Here we extend the analytical treatment of disk packings, analysing the rules for phyllotactic indices of related structures and the variation…
The purpose of this article is to view Penrose rhombus tilings from the perspective of symplectic geometry. We show that each thick rhombus in such a tiling can be naturally associated to a highly singular 4-dimensional compact symplectic…
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…
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…
The rhombus tilings of a simply connected domain of the Euclidean plane are known to form a flip-connected space (a flip is the elementary operation on rhombus tilings which rotates 180{\deg} a hexagon made of three rhombi). Motivated by…
In the realm of functional materials, the production of two-dimensional structures with tuneable porosity is of paramount relevance for many practical applications: surfaces with regular arrays of pores can be used for selective adsorption…
We study the covering of the plane by non-overlapping rhombus tiles, a problem well-studied only in the limiting case of dimer coverings of regular lattices. We go beyond this limit by allowing tiles to take any position and orientation on…
We investigate the properties of classical single flip dynamics in sets of two-dimensional random rhombus tilings. Single flips are local moves involving 3 tiles which sample the tiling sets {\em via} Monte Carlo Markov chains. We determine…
All edge-to-edge tilings of the sphere by congruent regular triangles and congruent rhombi are classified as: (1) a $1$-parameter family of protosets each admitting a unique $(2a^3,3a^4)$-tiling like a triangular prism; (2) a $1$-parameter…
This article introduces spotlight tiling, a type of covering which is similar to tiling. The distinguishing aspects of spotlight tiling are that the "tiles" have elastic size, and that the order of placement is significant. Spotlight…
Random tilings are interesting as idealizations of atomistic models of quasicrystals and for their connection to problems in combinatorics and algorithms. Of particular interest is the tiling entropy density, which measures the relation of…
Studies of periodically driven one-dimensional many-body systems have advanced our understanding of complex systems and stimulated promising developments in quantum simulation. It is hence of interest to go one step further, by…
We consider the evolution of the packing of disks (representing the position of buds) that are introduced at the top of a surface which has the form of a growing stem. They migrate downwards, while conforming to three principles, applied…
Aperiodic tiling is a well-know area of research. First developed by mathematicians for the mathematical challenge they represent and the beauty of their resulting patterns, they became a growing field of interest when their practical use…
The evolution of the interface propagation in a slowly rotating half-filled horizontal cylinder is studied using MRI. Initially, the cylinder contains two axially segregated bands of small and large particles with a sharp interface. The…
We classify the dihedral edge-to-edge tilings of the sphere by regular polygons with gonality at least 5 and rhombi.
We call "flippable tilings" of a constant curvature surface a tiling by "black" and "white" faces, so that each edge is adjacent to two black and two white faces (one of each on each side), the black face is forward on the right side and…
We classify the dihedral edge-to-edge tilings of the sphere by squares and rhombi.