Related papers: Quasicrystals: A matter of definition
A novel way to create a band structure of the quasienergy spectrum for driven systems is proposed based on the discrete symmetry in phase space. The system, e.g., an ion or ultracold atom trapped in a potential, shows no spatial…
Complementarity is one of the main features of quantum physics that radically departs from classical notions. Here we consider the limitations that this principle imposes due to the unpredictability of measurement outcomes of incompatible…
We develop a rigorous framework for modelling the geometry equilibration of crystalline defects. We formulate the equilibration of crystal defects as a variational problems on a discrete energy space and establish qualitatively sharp…
A necessary and sufficient set of conditions for a quasisymmetric magnetic field in the form of constraint equations is derived from first principles. Without any assumption regarding the magnetohydrodynamic (MHD) equilibrium of the plasma,…
The discovery of quasicrystals with crystallographically forbidden rotational symmetries has changed the notion of the ordering in materials, yet little is known about the dynamical emergence of such exotic forms of order. Here we…
We propose a modification of the classical Vernam cipher based on properties of one-dimensional quasicrystals. The method uses the sequence of quasicrystal minimal distances as an one-time pad. The main advantages are strict aperiodicity of…
We argue that 2D dodecagonal spherical quasicrystalls (QCs) will be discovered in the nearest future and investigate how the planar QC order becomes compatible with the spherical geometry. We show that the appearance of curvature-induced…
We investigate the formation and stability of icosahedral quasicrytalline structures using a dynamic phase field crystal model. Nonlinear interactions between density waves at two length scales stabilize three-dimensional quasicrystals. We…
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…
Quasicrystals are one kind of space-filling structures. The traditional crystalline approximant method utilizes periodic structures to approximate quasicrystals. The errors of this approach come from two parts: the numerical discretization,…
Generic quantum interference effects occuring in 1D-quasicrystals are reviewed with emphasis on the joint effect of phason disorder on electronic localization and propagation modes. In close conjunction with properties of real materials,…
Since antiquity, the packing of convex shapes has been of great interest to many scientists and mathematicians. Recently, particular interest has been given to packings of three-dimensional tetrahedra. Dense packings of both crystalline and…
High massive compact stars have been reported recently in the literature, providing strong constraints on the properties of the ultradense matter beyond the saturation nuclear density. In view of these results, the calculations of quark…
We survey the recent developments in the theory of quasireg- ular mappings in metric spaces. In particular, we study the geometric porosity of the branch set of quasiregular mappings in general metric measure spaces, and then, introduce the…
We analytically model a one-dimensional lattice with periodic impurities representing a photonic crystal from first principles. We then investigate bound states in the continuum by computing the transmission and reflection coefficients. It…
An abstract indefinite least squares problem with a quadratic constraint is considered. This is a quadratic programming problem with one quadratic equality constraint, where neither the objective nor the constraint are convex functions.…
A quasicrystal is an ordered but non-periodic structure understood as a projection from a higher dimensional periodic structure. Some physical properties of quasicrystals are different from those of conventional solids. An anomalous…
Quasicrystals, structures that are ordered yet aperiodic, defy conventional band theory, confining most studies to finite-size real-space numerics. We overcome this limitation with a configuration-space framework that predicts and explains…
Quasi-symmetry of a steady magnetic field means integrability of first-order guiding-centre motion. Here we derive many restrictions on the possibilities for a quasi-symmetry. We also derive an analogue of the Grad-Shafranov equation for…
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…