Related papers: Aperiodic order and spherical diffraction, III: Th…
Partially coherent light is abundant in many physical systems, and its propagation properties are well understood. Here we extend current theory of propagation of partially coherent light beams to the field of coherent diffusion. Based on a…
This study describes both experimentally and theoretically an important hitherto undiscovered feature of the scattering of micron_sized spherical objects when illuminated with highly focused circularly polarized light. This is a regime of…
We put forward a method that allows the experimental determination of the entire spatial mode spectrum of any arbitrary monochromatic wave field in a plane normal to its propagation direction. For coherent optical fields, our spatial…
We give an introduction into diffraction theory for aperiodic order. We focus on an approach via dynamical systems and the phenomenon of pure point diffraction. We review recent results and sketch proofs. We then present a new uniform…
The non-linear transformations incurred by the rays in an optical system can be suitably described by matrices to any desired order of approximation. In systems composed of uniform refractive index elements, each individual ray refraction…
We introduce orthogonal ring patterns in the 2-sphere and in the hyperbolic plane, consisting of pairs of concentric circles, which generalize circle patterns. We show that their radii are described by a discrete integrable system. This is…
The diffraction trace formula ({\em Phys. Rev. Lett.} {\bf 73}, 2304 (1994)) and spectral determinant are tested on the open three disk scattering system. The system contains a generic and exponentially growing number of diffraction…
We examine the diffraction properties of lattice dynamical systems of algebraic origin. It is well-known that diverse dynamical properties occur within this class. These include different orders of mixing (or higher-order correlations), the…
A consolidated mathematical formulation of the spherically symmetric mass-transfer problem is presented, with the quasi-stationary approximating equations derived from a perturbation point of view for the leading-order effect. For the…
This work discusses the homogenization analysis for diffusion processes on scale-free metric graphs, using weak variational formulations. The oscillations of the diffusion coefficient along the edges of a metric graph induce internal…
Given a self-adjoint operator H, a self-adjoint trace class operator V and a fixed Hilbert-Schmidt operator F with trivial kernel and co-kernel, using limiting absorption principle an explicit set of full Lebesgue measure is defined such…
The present state of mathematical diffraction theory for systems with continuous spectral components is reviewed and extended. We begin with a discussion of various characteristic examples with singular or absolutely continuous diffraction,…
We develop a modal method that solves Maxwell's equations in the presence of the linearized hydrodynamic correction. Using this approach, it is now possible to calculate the full diffraction for structures with period of the order of the…
We derive the transmission coefficient, $T(\omega)$, for grazing incidence of crystals with spatial dispersion accounting for the excitation of multiple modes with different wave vectors ${\bf k}$ for a given frequency $\omega$. The…
In the presence of crystalline symmetries, topological phases of matter acquire a host of invariants leading to non-trivial quantized responses. Here we study a particular invariant, the discrete shift $\mathscr{S}$, for the square lattice…
Diffraction images with continuous rotation symmetry arise from amorphous systems, but also from regular crystals when investigated by powder diffraction. On the theoretical side, pinwheel patterns and their higher dimensional…
The mutual shadow area of pairs of surface regions is used for guiding the study of the spectral components and rank of their wave interaction, as captured by the corresponding moment matrix blocks. It is demonstrated that the mutual shadow…
In this paper we show that the Fourier transform induces an isomorphism between the coorbit spaces defined by Feichtinger and Gr\"ochenig of the mixed, weighted Lebesgue spaces $L_{v}^{p,q}$ with respect to the quasi-regular representation…
Aerosols' impact on the performance of a clear-sky solar irradiance model is often evaluated from the perspective of the overall accuracy of estimates. This study assesses the aerosol role in clear-sky solar irradiance modelling from a…
The scattering theory of the integrable statistical models can be generalized to the case of systems with extended lines of defect. This is done by adding the reflection and transmission amplitudes for the interactions with the line of…