Related papers: Wide-angle x-ray diffraction theory versus classic…
A case for the teaching of classical thermodynamics with an explicit time variable, with phenomena involving changes in time, is made by presenting and solving a exercise in textbook style, and pointing out that a solution accords with…
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…
Fourier transforms are ubiquitous mathematical tools in basic and applied sciences. We here report classical and quantum optical realizations of the discrete fractional Fourier transform, a generalization of the Fourier transform. In the…
The symmetry reduction of dynamical systems that are invariant under changes of global scale is well-understood for classical theories of particles, and fields. The excision of the superfluous degree of freedom generating such rescalings…
The first part of the paper is devoted to diffraction phenomena that can be expressed by fractional Fourier transforms whose orders are real numbers. According to a scalar theory, diffraction acts on the amplitude of the electric field as…
We review some applications of fractional calculus developed by the author (partly in collaboration with others) to treat some basic problems in continuum and statistical mechanics. The problems in continuum mechanics concern mathematical…
We show that the nonlinear interactions between x rays and longer wavelengths in crystals depend strongly on the band structure and related properties. Consequently, these types of interactions can be used as a powerful probe for…
The nonlinear quantum interaction of a linearly polarized x-ray probe beam with a focused intense standing laser wave is studied theoretically. Because of the tight focusing of the standing laser pulse, diffraction effects arise for the…
We present a simplified model for dynamical diffraction of particles through a periodic thick perfect crystal based on repeated application of a coherent beam splitting unitary at coarse-grained lattice sites. By demanding translational…
I present new comparisons of AGN optical, UV, and X-ray variations. These reveal complex relationships between the different passbands that can change with time in a given object. While there is evidence from several objects that X-ray and…
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…
Dark-field X-ray microscopy is a new full-field imaging technique that nondestructively maps the structure and local strain inside deeply embedded crystalline elements in three dimensions. Placing an objective lens in the diffracted beam…
A simple method for presenting a dynamic transition between Fresnel and Fraunhofer diffraction zones is considered. Experiments are conducted on different apertures and diffraction patterns are photographed at various distances between the…
An intriguing feature of the Standard Model is that the representations of the unbroken gauge symmetries are vector-like whereas those of the spontaneously broken gauge symmetries are chiral. Here we provide a toy model which shows that a…
We present a quantum theory for the dynamic structure factors in non-equilibrium, correlated, two-component systems such as plasmas or warm dense matter. Using this general framework, we derive expressions for effective local field…
We present an algorithm to evaluate the large deviation functions associated to history-dependent observables. Instead of relying on a time discretisation procedure to approximate the dynamics, we provide a direct continuous-time algorithm,…
A fractional diffusion equation based on Riemann-Liouville fractional derivatives is solved exactly. The initial values are given as fractional integrals. The solution is obtained in terms of $H$-functions. It differs from the known…
We describe a diffraction microscopy technique based on refractive optics to study structural variations in crystals. The X-ray beam diffracted by a crystal was magnified by beryllium parabolic refractive lenses on a 2D X-ray camera. The…
The localization length for classical waves in two dimensional random media is calculated exactly, and is compared with the theoretical prediction from the previous analytic theory. Significant discrepancies are observed. It is also shown…
Conventional X-ray methods use incoming plane waves and result in discrete diffraction patterns when scattered at crystals. Here we find, by a systematic method, incoming waveforms which exhibit discrete diffraction patterns when scattered…