Related papers: Mathematical diffraction of aperiodic structures
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…
Crystals are paradigms of ordered structures. While order was once seen as synonymous with lattice periodic arrangements, the discoveries of incommensurate crystals and quasicrystals led to a more general perception of crystalline order,…
We study the diffraction produced by a $PT$-symmetric volume Bragg grating that combines modulation of refractive index and gain/loss of the same periodicity with a quarter-period shift between them. Such a complex grating has a directional…
The convergence problem for scattering states is studied in detail within the framework of the Algebraic Model, a representation of the Schrodinger equation in an L^2 basis. The dynamical equations of this model are reformulated featuring…
Diffusion preserves the positivity of concentrations, therefore, multicomponent diffusion should be nonlinear if there exist non-diagonal terms. The vast variety of nonlinear multicomponent diffusion equations should be ordered and special…
Visualization of internal deformation fields in crystalline materials helps bridge the gap between theoretical models and practical applications. Applying Bragg coherent diffraction imaging under X-ray dynamical diffraction conditions…
By a rigorous numerical simulation based on the standard multiple scattering theory, we investigate the optical transmission in photonic crystal structures, formed by dielectric cylinders embedded in parallel in a uniform medium. In…
The question of the relative importance of coherent structures and waves has for a long time attracted a great deal of interest in astrophysical plasma turbulence research, with a more recent focus on kinetic scale dynamics. Here we utilize…
We give a generalization of Lagarias' formula for diffraction by ideal crystals, and we apply it to the lattice case, in preparation for addressing the problem of quasicrystals and complex dimensions posed by Lapidus and van Frankenhuijsen…
Emerging coherent X-ray scattering patterns of single particles have shown dominant morphological signatures in agreement with predictions of the scattering model used for conventional protein crystallography. The key question is if and to…
This article deals with pure point diffraction and its connection to various notions of almost periodicity. We explain why the Fibonacci chain does not fit into the classical class of Bohr almost periodicity and how it fits into the classes…
In the framework of the approximation of slowly varying amplitudes a multiwave dynamical theory of neutron diffraction on a moving phase grating was developed. The influence of the velocity of the grating, its period and height of the slits…
In the recent years, mater-wave interferometry has attracted growing attention due to its unique suitability for high-precision measurements and study of fundamental aspects of quantum theory. Diffraction and interference of matter waves…
Bragg scattering in sinusoidal PT-symmetric complex crystals of finite thickness is theoretically investigated by the derivation of exact analytical expressions for reflection and transmission coefficients in terms of modified Bessel…
It is well known that a positive proportion of all points in a $d$-dimensional lattice is visible from the origin, and that these visible lattice points have constant density in $\mathbb{R}^d$. In the present paper we prove an analogous…
The axial propagation of circularly polarized light in an optically active structurally chiral medium is exactly solved via full electromagnetic analysis. Some symmetries of the system's characteristic matrix reveal new insights, which are…
The paper develops a method for discrete computational Fourier analysis of functions defined on quasicrystals and other almost periodic sets. A key point is to build the analysis around the emerging theory of quasicrystals and diffraction…
We survey the distributional properties of progressively dilating sets under projection by covering maps, focusing on manifolds of constant sectional curvature. In the Euclidean case, we review previously known results and formulate some…
We investigate the dynamics of a kicked particle in an infinite square well undergoing frequent measurements of energy. For a large class of periodic kicking force, constant diffusion is found in such a non-KAM system. The influence of…
Liquids in systems with spherically symmetric interactions are not thermodynamically stable when the range of the attraction is reduced sufficiently. However, these metastable liquids have lifetimes long enough that they are readily…