相关论文: Local growth of icosahedral quasicrystalline tilin…
Recent studies of holographic tensor network models defined on regular tessellations of hyperbolic space have not yet addressed the underlying discrete geometry of the boundary. We show that the boundary degrees of freedom naturally live on…
After providing a concise overview on quasicrystals and their discovery more than a quarter of a century ago, I consider the unexpected interplay between nanotechnology and quasiperiodic crystals. Of particular relevance are efforts to…
The theory of integral quadratic constraints (IQCs) allows verification of stability and gain-bound properties of systems containing nonlinear or uncertain elements. Gain bounds often imply exponential stability, but it can be challenging…
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…
We investigate the self-assembly of two-dimensional dodecagonal quasicrystals driven by cyclic shear, effectively replacing thermal fluctuations with plastic rearrangements. Using particles interacting via a smoothed square-shoulder…
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…
The unitary coupled cluster (UCC) approximation is one of the more promising wave-function ans\"atze for electronic structure calculations on quantum computers via the variational quantum eigensolver algorithm. However, for large systems…
For many years, quasicrystals were observed only as solid-state metallic alloys, yet current research is now actively exploring their formation in a variety of soft materials, including systems of macromolecules, nanoparticles and colloids.…
Motivated by recent experimental findings, we investigate the possible occurrence and characteristics of quasicrystalline order in two-dimensional mixtures of point dipoles with two sorts of dipole moments. Despite the fact that the dipolar…
A new type of long-range ordering in the absence of translational symmetry gives rise to drastic revolution of our common knowledge in condensed matter physics. Quasicrystal, as such unconventional system, became a plethora to test our…
As the size $n$ of datasets become massive, many commonly-used clustering algorithms (for example, $k$-means or hierarchical agglomerative clustering (HAC) require prohibitive computational cost and memory. In this paper, we propose a…
We consider the problem of extraction and validation of matching rules, directly from the phased diffraction data of a quasicrystal, and propose an algorithmic procedure to produce the rules of the shortest possible range. We have developed…
The incipient infinite cluster (IIC) measure is the percolation measure at criticality conditioned on the cluster of the origin to be infinite. Using the lace expansion, we construct the IIC measure for high-dimensional percolation models…
Using molecular dynamics simulations, we study computational self-assembly of one-component three-dimensional dodecagonal (12-fold) quasicrystals in systems with two-length-scale potentials. Existing criteria for three-dimensional…
In many modern applications, there is interest in analyzing enormous data sets that cannot be easily moved across computers or loaded into memory on a single computer. In such settings, it is very common to be interested in clustering.…
We propose a simple phenomenological model to analyze vibrational characteristics of quasicrystals (QCs). The interpretation of the obtained recently data is based on the existence of almost dispersionless optical modes most probably…
\kmeans clustering is a fundamental problem in many scientific and engineering domains. The optimization problem associated with \kmeans clustering is nonconvex, for which standard algorithms are only guaranteed to find a local optimum.…
Depending on the pH value and salt concentration of Al2O3 suspensions different microstructures can form. Especially the clustered one is of major interest for industrial purposes as found in the production of ceramics. In this paper we…
We report a new algorithm to generate Laplacian Growth Patterns using iterated conformal maps. The difficulty of growing a complete layer with local width proportional to the gradient of the Laplacian field is overcome. The resulting growth…
We propose a unified framework for dealing with matching rules of quasiperiodic patterns, relevant for both tiling models and real world quasicrystals. The approach is intended for extraction and validation of a minimal set of matching…