Related papers: Robust minimal matching rules for quasicrystals
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…
Dodecagonal bilayer graphene quasicrystal has 12-fold rotational order but lacks translational symmetry which prevents the application of band theory. In this paper, we study the electronic and optical properties of graphene quasicrystal…
Quasicrystals possess long-range order but lack the translational symmetry of crystalline solids. In solid state physics, periodicity is one of the fundamental properties that prescribes the electronic band structure in crystals. In the…
Recent quasi-optimal error estimates for the finite element approximation of total-variation regularized minimization problems require the existence of a Lipschitz continuous dual solution. We discuss the validity of this condition and…
The strict geometric rules that define aperiodic tilings lead to the unique spectral and transport properties of quasicrystals, but also limit our ability to design them. In this Letter, we explore a novel example of a continuously tunable…
Quasi steady state assumptions are often used to simplify complex systems of ordinary differential equations in modelling of biochemical processes. The simplified system is designed to have the same qualitative properties as the original…
We show that atomic Fermi mixtures with density and mass imbalance exhibit a rich diversity of scaling laws for the quasiparticle decay rate beyond the quadratic energy and temperature dependence of conventional Fermi liquids. For certain…
Quasiperiodic potentials can be used to interpolate between localization and delocalization in one dimension. With the rise of optical platforms engineering dipolar interactions, a key question is the stability of quasicrystalline phases…
We study decorated one-dimensional quasicrystal obtained by a non-standard projection of a part of two-dimensional lattice. We focus on the impact of varying relative positions of decorated sites. First, we give general expression for the…
We study semi-dynamical systems associated to delay differential equations. We give a simple criteria to obtain weak and strong persistence and provide sufficient conditions to guarantee uniform persistence. Moreover, we show the existence…
Freezing of charge-stabilized colloidal suspensions and relative stabilities of crystals and quasicrystals are studied using thermodynamic perturbation theory. Macroion interactions are modelled by effective pair potentials combining…
To understand an aperiodic tiling (or a quasicrystal modeled on an aperiodic tiling), we construct a space of similar tilings, on which the group of translations acts naturally. This space is then an (abstract) dynamical system. Dynamical…
Adaptive quasicontinuum (QC) methods are important methodologies in molecular mechanics for the simulations of materials with defects, intending to achieve the optimal balance of accuracy and efficiency on the fly. In this study, we propose…
We give a simple computational approach to mathematical quasicrystals, combining cut-and-project methods with self-similarity. Starting with a Pisot unit $\beta$ and an iterated function system $g_k(z)=\beta z +z_k, \ k=1,...,m$ in a…
We show that one can employ well-established numerical continuation methods to efficiently calculate the phase diagram for thermodynamic systems. In particular, this involves the determination of lines of phase coexistence related to first…
Determining crystal structures from X-ray diffraction data is fundamental across diverse scientific fields, yet remains a significant challenge when data is limited to low resolution. While recent deep learning models have made…
Quasiperiodic arrangements of the constitutive materials in composites result in effective properties with very unusual electromagnetic and elastic properties. The paper discusses the cut-and-projection method that is used to characterize…
Automatic crystal orientation determination and orientation mapping are important tools for research on polycrystalline materials. The most common methods of automatic orientation determination rely on detecting and indexing individual…
Discrete time crystals (DTCs) are nonequilibrium phases of matter with exotic observable dynamics. Among their remarkable features is their response to a periodic drive at a fraction of its frequency. Current successful experiments are…
Self-similar quasicrystals (like the famous Penrose and Ammann-Beenker tilings) are exceptional geometric structures in which long-range order, quasiperiodicity, non-crystallographic orientational symmetry, and discrete scale invariance are…