Related papers: Robust matching rules for real quasicrystals
Quasicrystals lack translational symmetry, but can still exhibit long-ranged order, promoting them to candidates for unconventional physics beyond the paradigm of crystals. Here, we apply a real-space functional renormalization group…
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…
The detailed atomic structure of quasicrystals has been an open question for decades. Here, we present a quasilattice-conserved optimization method (quasiOPT), with particular quasiperiodic boundary conditions. As the atomic coordinates…
Robust estimation is much more challenging in high dimensions than it is in one dimension: Most techniques either lead to intractable optimization problems or estimators that can tolerate only a tiny fraction of errors. Recent work in…
A combination of classical density-functional theory and thermodynamic perturbation theory is applied to a survey of finite-temperature trends in the relative stabilities of one-component crystals and quasicrystals interacting via effective…
This letter reports theory of elasticity and hydrodynamics of quasicrystals with 7-, 14-, 9- and 18-fold symmetries in solid phase, in which the 6-dimensional embedding space concept is used. Based on the concept and the Landau-Anderson…
Quasicrystals and their periodic approximants are complex phases, which have by now been observed in many metallic alloys, soft matter systems, and particle simulations. In recent experiments of thin-film perovskites on solid substrates,…
Atomic-resolution electron microscope images show that a quasicrystal is a quasiperiodic packing of clusters. The outer atomic shells of multi-shell clusters occuring in quasicrystals are highly symmetric and rather robust, but some…
The growth of quasicrystals, i.e., aperiodic structures with long-range order, seeded from the melt is investigated using a dynamical phase field crystal model. Depending on the thermodynamic conditions, two different growth modes are…
A simple model of 1D structure based on a Fibonacci sequence with variable atomic spacings is proposed. The model allows for observation of the continuous transition between periodic and non-periodic diffraction patterns. The diffraction…
Persistent homology is a popular method for computing topological features of (metric) data. Standard approaches based on the \v{C}ech or Rips filtration are stable under small perturbations of the data, but highly sensitive to outliers.…
Quasicrystals whose building blocks are of mesoscopic rather than atomic scale have recently been discovered in several soft-matter systems. Contrary to metallurgic quasicrystals whose source of stability remains a question of great debate…
In this article, we discuss the stability of soft quasicrystalline phases in a coupled-mode Swift-Hohenberg model for three-component systems, where the characteristic length scales are governed by the positive-definite gradient terms.…
Topological phases of matter have sparked an immense amount of activity in recent decades. Topological materials are classified by topological invariants that act as a non-local order parameter for any symmetry and condition. As a result,…
The field of mathematical morphology offers well-studied techniques for image processing. In this work, we view morphological operations through the lens of persistent homology, a tool at the heart of the field of topological data analysis.…
We consider a 1D periodic atomistic model, for which we formulate and analyze an adaptive variant of a quasicontinuum method. We establish a posteriori error estimates for the energy norm and for the energy, based on a posteriori residual…
Despite an artificial intelligence-assisted modeling of disordered crystals is a widely used and well-tried method of new materials design, the issues of its robustness, reliability, and stability are still not resolved and even not…
This paper rigorously solves the challenging problem of recognizing periodic patterns under rigid motion in Euclidean geometry. The 3-dimensional case is practically important for justifying the novelty of solid crystalline materials…
We investigate a quasicontinuum method by means of analytical tools. More precisely, we compare a discrete-to-continuum analysis of an atomistic one-dimensional model problem with a corresponding quasicontinuum model. We consider next and…
We introduce a topology ${\cal T}$ on the space $U$ of uniformly discrete subsets of the Euclidean space. Assume that $S$ in $U$ admits a unique autocorrelation measure. The diffraction measure of $S$ is purely atomic if and only if $S$ is…