Related papers: Spotlight Tiling
In this short paper we present a fluid dynamics video of the deformation of droplets when tilted on a motorized stage. This is a submission to the 2013 Gallery of Fluid Motion which is part of the 66th annual meeting of APS-DFD. The video…
In this paper, we study tilings of $\mathbb Z$, that is, coverings of $\mathbb Z$ by disjoint sets (tiles). Let $T=\{d_1,\ldots, d_s\}$ be a given multiset of distances. Is it always possible to tile $\mathbb Z$ by tiles, for which the…
Based on first-principles calculation we predict two new thermodynamically stable layered-phases of silicon, named as silicites, which exhibit strong directionality in the electronic and structural properties. As compared to silicon…
We introduce stripe-like quasi-nondiffracting lattices that can be generated via spatial spectrum engineering. The complexity of the spatial shapes of such lattices and the distance of their almost diffractionless propagation depend on the…
We study the dynamical evolution of the deposition interface using both discrete and continuous models for which shadowing effects are important. We explain why continuous and discrete models implying both only shadowing deposition do not…
This paper deals with iteration stable (STIT) tessellations, and, more generally, with a certain class of tessellations that are infinitely divisible with respect to iteration. They form a new, rich and flexible class of spatio-temporal…
Let P be an object such as tiling, Delone set and weighted Dirac comb. There corresponds a dynamical system to P, called the corresponding dynamical system. Such dynamical systems are geometric analogues of symbolic dynamics. It is…
Photonic crystal topological insulators host protected states at their edges. In the band structure these edge states appear as continuous bands crossing the photonic band gap. They allow light to propagate unidirectionally and without…
It has been seen recently that when probing a nanoscale object to determine, for example, size or position via light scattering, significant advantage in measurement precision can be gained from exploiting phase singularities in a…
In contrast to many known results concerning periodic tilings of the Euclidean plane with pentagons, here tilings with rotational symmetry are investigated. A certain class of convex pentagons is introduced. It can be shown that for any…
Fractal structures emerge from statistical and hierarchical processes in urban development or network evolution. In a class of efficient and robust geographical networks, we derive the size distribution of layered areas, and estimate the…
A new recipe for concealing objects from detection is suggested. Different with traditional cloak which deflects light around the core of the cloak to make the object inside invisible, our cloak guides the light to penetrate the core of the…
Given a collection of N rectangles such that the side ratio of each one is a quadratic irrationality, we find all rectangles which can be tiled by rectangles similar to one of the given ones. It means that each possible shape can be used…
Tilting modules over commutative rings were recently classified in [12]: they correspond bijectively to faithful Gabriel topologies of finite type. In this note we extend this classification by dropping faithfulness. The counterpart of an…
We describe a multispeckle dynamic light scattering technique capable of resolving the motion of scattering sites in cases that this motion changes systematically with time. The method is based on the visibility of the speckle pattern…
We show that tilting a model sandpile that has dynamic disorder leads to bistability and hysteresis at the angle of repose. Also the distribution of {\it local slopes} shows an interesting dependence on the amount of tilt - weakly tilted…
Congruent polygons are congruent in angles as well as in edge lengths. We concentrate on the angle aspect, and investigate how tilings of the sphere by congruent pentagons can be determined by the angle information only. We also investigate…
Concentrated colloidal suspensions are a well-tested model system which has a glass transition. Colloids are suspensions of small solid particles in a liquid, and exhibit glassy behavior when the particle concentration is high; the…
We review both theoretical and experimental advances in the recently emerged physics of modulated photonic lattices. Artificial periodic dielectric media, such as photonic crystals and photonic lattices, provide a powerful tool for the…
Metasurfaces represent a powerful paradigm of optical engineering that enables one to control the flow of light across material interfaces. We report on a discovery that metallic metasurfaces of a certain type respond differently to…