相关论文: Discrete quasiperiodic sets with predefined coveri…
The architecture of infinite structures with non-crystallographic symmetries can be modeled via aperiodic tilings, but a systematic construction method for finite structures with non-crystallographic symmetry at different radial levels is…
The relative stability of three-dimensional icosahedral quasicrystals in multi-component systems has been investigated based on a coupled-mode Swift-Hohenberg model with two-length-scales. A recently developed projection method, which…
Tiling models can reveal unexpected ways in which local constraints give rise to exotic long-range spatial structure. The recently discovered Hat monotile (and its mirror image) has been shown to be aperiodic~[Smith et al., arXiv:2303.10798…
Exotic tiling patterns of quasicrystals have gotten a lot of attention for unique quantum phenomena such as critical state and multifractality. In this regard, finding new quasi-periodic tiling patterns and the relevant quantum states is…
We show that diffraction features of $1D$ quasicrystals can be retrieved from a single topological quantity, the \v{C}ech cohomology group, $\check{H}^{1}\cong\mathbb{Z}^2$, which encodes all relevant combinatorial information of tilings.…
We compute the Parisi overlap distribution for paperfolding sequences. It turns out to be discrete, and to live on the dyadic rationals. Hence it is a pure point measure whose support is the full interval [-1; +1]. The space of paperfolding…
We extend so-called slit-slide-sew bijections to constellations and quasiconstellations. We present an involution on the set of hypermaps given with an orientation, one distinguished corner, and one distinguished edge leading away from the…
We devise an ideal 3-dimensional octagonal quasicrystal that is based upon the 2-dimensional Ammann-Beenker tiling and that is potentially suitable for realization with patchy particles. Based on an analysis of its local environments we…
A new scheme for producing semidiscrete self-trapped vortices (\textquotedblleft swirling photon droplets\textquotedblright ) in photonic crystals with competing quadratic ($\chi ^{(2)}$) and self-defocusing cubic ($\chi ^{(3)}$)…
This paper introduces {\em fusion subspace clustering}, a novel method to learn low-dimensional structures that approximate large scale yet highly incomplete data. The main idea is to assign each datum to a subspace of its own, and minimize…
We study random perturbations of quasi-periodic uniformly discrete sets in the $d$-dimensional euclidean space. By means of Diffraction Theory, we find conditions under which a quasi-periodic set $X$ can be almost surely recovered from its…
Metasurfaces are extremely useful for controlling and manipulating electromagnetic waves. Full-wave numerical simulation is highly desired for their design and optimization, but it is notoriously difficult, even for two-dimensional…
The description of almost periodic or quasiperiodic structures has a long tradition in mathematical physics, in particular since the discovery of quasicrystals in the early 80's. Frequently, the modelling of such structures leads to…
Cut and project sets are obtained by projecting an irrational slice through a lattice to a lower dimensional subspace. Under standard conditions, the resulting pattern has no translational periods even though it retains some regularity of…
Superconducting circuits are an extremely versatile platform to realize quantum information hardware and to emulate topological materials. We here show how a simple arrangement of capacitors and conventional…
We study the properties of a quasi-one dimensional superconductor which consists of an alternating array of two inequivalent chains. This model is a simple charicature of a locally striped high temperature superconductor, and is more…
We find explicit subdivision rules for all special cubulated groups. A subdivision rule for a group produces a sequence of tilings on a sphere which encode all quasi-isometric information for a group. We show how these tilings detect…
Metasurface, a kind of two-dimensional structured medium, represents a novel platform to manipulate the propagation of light at subwavelength scale. In linear optical regime, many interesting topics such as planar metalens, metasurface…
We show that generalized Penrose tilings can be obtained by the projection of a cut plane of a 5-dimensional lattice into two dimensions, while 3-d quasiperiodic lattices with overlapping unit cells are its projections into 3d. The…
This paper continues our study of quasicrystals initiated in Part I. We propose a general mechanism for constructing quasicrystals, existing globally in time, in spatially-extended systems (partial differential equations with Euclidean…