相关论文: Diffraction of the Dart-Rhombus Random Tiling
De-diffraction (DD), a new procedure to totally cancel diffraction effects from wave-fields is presented, whereby the full field from an aperture is utilized and a truncated geometrical field is obtained, allowing infinitely sharp focusing…
Diffusion is the result of repeated random scattering. It governs a wide range of phenomena from Brownian motion, to heat flow through window panes, neutron flux in fuel rods, dispersion of light in human tissue, and electronic conduction.…
We consider the spectral response of moving diffraction gratings, in which the incident light extends over a broad angular range and where the diffracted light is observed from a specific angle. We show that the dispersion relation between…
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…
Decorating the Spectre tile with hexagons reveals triangular hexagonal clusters whose structure we study. In the process we reprove that the Spectre tilings exist and are uniquely hierarchical. The proof is not computer-assisted.
We study statistical properties of a class of band random matrices which naturally appears in systems of interacting particles. The local spectral density is shown to follow the Breit-Wigner distribution in both localized and delocalized…
We introduce a new dynamical system that we call "tiling billiards," where trajectories refract through planar tilings. This system is motivated by a recent discovery of physical substances with negative indices of refraction. We…
An intermittent nonlinear map generating subdiffusion is investigated. Computer simulations show that the generalized diffusion coefficient of this map has a fractal, discontinuous dependence on control parameters. An amended continuous…
We study the behavior of a point particle incident from the left on a slab of a randomly diluted triangular array of circular scatterers. Various scattering properties, such as the reflection and transmission probabilities and the…
In computational optics, numerical modeling of diffraction between arbitrary planes offers unparalleled flexibility. However, existing methods suffer from the trade-off between computational accuracy and efficiency. To resolve this dilemma,…
Letting $T$ denote an ergodic transformation of the unit interval and letting $f \colon [0,1)\to \mathbb{R}$ denote an observable, we construct the $f$-weighted return time measure $\mu_y$ for a reference point $y\in[0,1)$ as the weighted…
A phenomenological theory of luminescence properties of one-dimensional resonant photonic crystals is developed within the framework of classical Maxwell equations with fluctuating polarization terms representing non-coherent sources of…
We numerically calculate the reliability with which one can optically determine the presence or absence of an individual scatterer in a randomly occupied 3D array of well-localized, coherently radiating scatterers. The reliability depends…
Tomography is the three-dimensional reconstruction of an object from images taken at different angles. The term classical tomography is used, when the imaging beam travels in straight lines through the object. This assumption is valid for…
The spectral gap is estimated for measure-valued diffusion processes induced by the intrinsic/extrinsic derivatives on the space of finite measures over a Riemannian manifold. This provides explicit exponential convergence rate for these…
A popular pedagogical approach for introducing diffraction is to assume normal incidence of light on a single slit or a plane transmission grating. Interesting cases of diffraction from a grating at orientations other than normal incidence…
Standard statistical mechanical or condensed matter arguments tell us that bulk properties of a physical system do not depend too much on boundary conditions. Random tilings of large regions provide counterexamples to such intuition, as…
Random matrix theory (RMT) universality is the defining property of quantum mechanical chaotic systems, and can be probed by observables like the spectral form factor (SFF). In this paper, we describe systematic deviations from RMT…
Diffraction microtomography in coherent light is foreseen as a promising technique to image transparent living samples in three dimensions without staining. Contrary to conventional microscopy with incoherent light, which gives…
The spectrum of a weighted Dirac comb on the Thue-Morse quasicrystal is investigated, and characterized up to a measure zero set, by means of the Bombieri-Taylor conjecture, for Bragg peaks, and of another conjecture that we call…