Related papers: Aperiodic crystals and beyond
Due to the lack of long-range order, it remains challenging to characterize the structure of disordered solids and understand the nature of the glass transition. Here we propose a new structural order parameter by taking into account…
The present work is dedicated to searching parameters, alternative to entropy, applicable for description of highly organized systems. The general concept has been offered, in which the system complexity and order are functions of the order…
We consider the possibility that classical dynamical systems display motion in their lowest energy state, forming a time analogue of crystalline spatial order. Challenges facing that idea are identified and overcome. We display arbitrary…
With the rapid development of topological states in crystals, the study of topological states has been extended to quasicrystals in recent years. In this review, we summarize the recent progress of topological states in quasicrystals,…
Disordered systems like liquids, gels, glasses, or granular materials are not only ubiquitous in daily life and in industrial applications but they are also crucial for the mechanical stability of cells or the transport of chemical and…
The radial distribution function is a characteristic geometric quantity of a point set in Euclidean space that reflects itself in the corresponding diffraction spectrum and related objects of physical interest. The underlying combinatorial…
Liquid crystals in two dimensions undergo a first-order isotropic-to-quasi-nematic transition, provided the particle interactions are sufficiently ``sharp and narrow''. This implies phase coexistence between isotropic and quasi-nematic…
A discrete set in the Euclidian space is almost periodic, if the measure with the unite masses at points of the set is almost periodic in the weak sense. We prove the following result: if A is a discrete almost periodic set and the set A-A…
Aperiodic crystals constitute a fascinating class of materials that includes incommensurate (IC) modulated structures and quasicrystals (QCs). Although these two categories share a common foundation in the concept of superspace, the…
Photonic crystals are characterized by a spatial modulation of the dielectric constant on the length scale of the wavelength of light giving rise to energy ranges where light cannot propagate through the crystal - the photonic band gap.…
Finding an optimal match between two different crystal structures underpins many important materials science problems, including describing solid-solid phase transitions, developing models for interface and grain boundary structures. In…
This monograph introduces key concepts and problems in the new research area of Periodic Geometry and Topology for materials applications.Periodic structures such as solid crystalline materials or textiles were previously classified in…
Twisting and stacking two copies of a 2D crystal can produce a long-wavelength periodic interference pattern known as a moir\'e pattern. Performing the same procedure with an aperiodic structure instead generates a single moir\'e spot at…
Unlike atoms, colloidal particles are not identical, but can only be synthesised within a finite size tolerance. Colloids are therefore polydisperse, i.e. mixtures of infinitely many components with sizes drawn from a continuous…
Topological properties of crystals and quasicrystals is a subject of recent and growing interest. This Letter reports an experiment where, for certain quasicrystals, these properties can be directly retrieved from diffraction. We directly…
It is show that in group representation by non-traditionally determining by the Maxwell equations, instead of wave, linear differential operator of momentous type from the common point of view the transformation of electromagnetic and…
The concept of the order parameter is extremely useful in physics. Here, I discuss extensions of this concept to cases when the order parameter is no longer a constant but fluctuates or oscillates in space and time. This allows one to…
Periodicity is usually assumed to be the necessary and sufficient condition for the formation of band gaps, i.e., energy bands with a suppressed density of states. Here, we check this premise by analyzing the band gap properties of three…
In glass physics, order parameters have long been used in the thermodynamic description of glasses, but the nature is not yet clear. The difficulty is how to find order in disordered systems. The usual treatment of glass as an exceptional…
Liquid crystals are the prototype of the so-called soft condensed matter. In simple terms they are "structured liquids" that historically have received a lot of interest because they help to generate new concepts and knowledge in Physics,…