Related papers: Averaged shelling for quasicrystals
Atomic-scale mapping of the chemical elements in materials is now possible using aberration-corrected electron microscopes but delocalization and multiple scattering can confound image interpretation. Here we report atomic-resolution…
I provide analytical or semi-analytical expressions for the small-angle scattering of colloidal objects that can be described as curved plates. These models could help characterize a variety of inorganic or biological systems.
The method of fusion barrier distribution has been widely used to interpret the effect of nuclear structure on heavy-ion fusion reactions around the Coulomb barrier. We discuss a similar, but less well known, barrier distribution extracted…
We give mean square bounds for the remainder in the lattice point counting problem, counting the number of lattice points in a large ball in $\mathbb{R}^d$, when averaged over families of shears of the lattice.
We investigate theoretically the polarization properties of the quantum dot's optical emission from chiral photonic crystal structures made of achiral materials in the absence of external magnetic field at room temperature. The mirror…
We propose the theory which unifies the description of quasicrystal assembly thermodynamics and quasicrystal structure formation by combining the Landau theory of crystallization and the cluster approach to quasicrystals. The theory is…
Quasicrystals are ubiquitous in nature. Beyond crystalline solids, they can be created as optically induced or technologically fabricated structures in photonic and phononic systems, as potentials for cold atoms and Bose-Einstein…
We calculate Root Mean Square (RMS) deviations from equilibrium for atoms in a two dimensional crystal with local (e.g. covalent) bonding between close neighbors. Large scale Monte Carlo calculations are in good agreement with analytical…
Quasicrystals are solid structures with symmetry forbidden by crystallographic rules. Because of this some structural characteristics of quasicrystals, for instance, radial distribution function, can look similar to the ones of amorphous…
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…
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…
The Gauss circle problem asks for an approximation to the number of lattice points of $\mathbb{Z}^2$ contained in $B_r$, the disk of radius $r$ centered at the origin. Upper, lower, and average bounds have been established for this…
Closed-orbit theory provides a general approach to the semiclassical description of photo-absorption spectra of arbitrary atoms in external fields, the simplest of which is the hydrogen atom in an electric field. Yet, despite its apparent…
The extent to which the projected distribution of stars in a cluster is due to a large-scale radial gradient, and the extent to which it is due to fractal sub-structure, can be quantified -- statistically -- using the measure ${\cal Q} =…
The atomic lensing model has been proposed as a promising method facilitating atom-counting in heterogeneous nanocrystals [KHW van den Bos et. al, Phys. Rev. Lett. 116 (2016) 246101] Here, image simulations will validate the model, which…
The melting of the corner of a crystal is a classical, real-world, non-equilibrium statistical mechanics problem which has shown several connections with other branches of physics and mathematics. For a perfect, classical crystal in two and…
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…
The analysis of Coulomb crystallization is extended from one-component to two-component plasmas. Critical parameters for the existence of Coulomb crystals are derived for both classical and quantum crystals. In the latter case, a critical…
We provide integrated cross sections for quasielastic charged-current neutrino-nucleus scattering. Results evaluated using the phenomenological scaling function extracted from the analysis of experimental $(e,e')$ data are compared with…
We study the electronic structure of quasicrystals composed of incommensurate stacks of atomic layers. We consider two systems: a pair of square lattices with a relative twist angle of $\theta=45^\circ$ and a pair of hexagonal lattices with…