Related papers: Aperiodic crystals and beyond
New aspects of a relation between lattice and dislocation structures are examined within a physically transparent theoretical scheme. Predicted features originating from the lattice discreteness include: (i) multiple core dislocation…
We consider partially ordered sets of combinatorial structures under consecutive orders, meaning that two structures are related when one embeds in the other such that `consecutive' elements remain consecutive in the image. Given such a…
Quasicrystals are metallic alloys that possess long-range, aperiodic structures with diffraction symmetries forbidden to conventional crystals. Since the discovery of quasicrystals by Schechtman et al. at 1984 (ref. 1), there has been…
We give a brief review of some generalized continuum theories applied to the crystals with complicated microscopic structure. Three different ways of generalization of the classical elasticity theory are discussed. One is the high-gradient…
In this short article, we overview a concept of electronic toroidal multipoles, and their ordering with associated physical properties in non-magnetic and magnetic materials. The toroidal multipoles are introduced as microscopic electronic…
In order to see the behavior of $\imath$canonical bases at $q = \infty$, we introduce the notion of $\imath$crystals associated to an $\imath$quantum group of certain quasi-split type. The theory of $\imath$crystals clarifies why…
Aperiodic tilings are non-periodic tilings defined by local rules. They are widely used to model quasicrystals, and a central question is to understand which of the non-periodic tilings are actually aperiodic. Among tilings, those by rhombi…
We consider a two-dimensional layer of dipolar particles in the regime of strong dipole moments. Here we can describe the system using classical methods and determine the crystal structure that minimizes the total energy. The dipoles are…
Crystal graphs are powerful combinatorial tools for working with the plactic monoid and symmetric functions. Quasi-crystal graphs are an analogous concept for the hypoplactic monoid and quasi-symmetric functions. This paper makes a…
Time crystals are many-body systems that spontaneously break time-translation symmetry, and thus exhibit long-range spatiotemporal order and robust periodic motion. Recent results have demonstrated how to build time-crystal phases in driven…
Linearly repetitive cut and project sets are mathematical models for perfectly ordered quasicrystals. In a previous paper we presented a characterization of linearly repetitive cut and project sets. In this paper we extend the classical…
We put forward a technique to unveil to which symmetry group a nonlinear crystal belongs, making use of nonlinear optics with structured light. We consider as example the process of spontaneous parametric down-conversion. The crystal, which…
A mixed lattice is a lattice-type structure consisting of a set with two partial orderings, and generalizing the notion of a lattice. Mixed lattice theory has previously been studied in various algebraic structures, such as groups and…
We confront existing definitions of chaos with the state of the art in topological dynamics. The article does not propose any new definition of chaos but, starting from several topological properties that can be reasonably called chaotic,…
We demonstrate a variety of ordered patterns, including hexagonal structures and chains, formed by colloidal particles (droplets) at the free surface of a nematic liquid crystal (LC). The surface placement introduces a new type of particle…
The bi-continuum model composed of two interpenetrating and dynamically coupled material continua is analysed as a simplified but relatively accurate way to describe some physical phenomena in crystalline solids. The essential novelty of…
This paper develops a new continuous approach to a similarity between periodic lattices of ideal crystals. Quantifying a similarity between crystal structures is needed to substantially speed up the Crystal Structure Prediction, because the…
An increasing variety of crystal structures has been observed in soft condensed matter over the past two decades, surpassing most expectations for the diversity of arrangements accessible through classical driving forces. Here, we survey…
The theory of magnetic symmetry in quasicrystals is used to characterize the nature of magnetic peaks, expected in elastic neutron diffraction experiments. It is established that there is no symmetry-based argument which forbids the…
Liquid crystals consisting of biaxial particles can exhibit a much richer phase behavior than their uniaxial counterparts. Usually, one has to rely on simulation results to understand the phase diagram of these systems, since very few…