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In this paper, we study the inverse source problem for the biharmonic wave equation. Mathematically, we characterize the radiating sources and non-radiating sources at a fixed wavenumber. We show that a general source can be decomposed into…
In a frame of quasi-crystal approximation the dispersion equations are obtained for the wave vector of a coherent electromagnetic wave propagating in a media which contains a random set of parallel dielectric cylinders with possible…
Quantitative phase analysis is one of the major applications of X-ray powder diffraction. The essential principle of quantitative phase analysis is that the diffraction intensity of a component phase in a mixture is proportional to its…
Determining the atomic-level structure of crystalline solids is critically important across a wide array of scientific disciplines. The challenges associated with obtaining samples suitable for single-crystal diffraction, coupled with the…
The routine atomic-resolution structure determination of single particles is expected to have profound implications for probing the structure-function relationship in systems ranging from energy materials to biological molecules.…
Change point detection has become an important part of the analysis of the single-particle tracking data, as it allows one to identify moments, in which the motion patterns of observed particles undergo significant changes. The segmentation…
An automated approach to reconstruct spherical Kikuchi maps from experimentally collected electron backscatter diffraction patterns and overlay each pattern onto its corresponding position on a simulated Kikuchi sphere is presented in this…
In a 2D rectangular microwave cavity dressed with one point-like scatterer, a semiclassical approach is used to analyze the spectrum in terms of periodic orbits and diffractive orbits. We show, both numerically and experimentally, how the…
A Python program for calculating the metrics necessary to perform information-theory based symmetry classifications and quantifications of transmission electron diffraction spot patterns is introduced. It is the first of its kind, in that…
Experimentally obtained X-ray diffraction (XRD) patterns can be difficult to solve, precluding the full characterization of materials, pharmaceuticals, and geological compounds. Herein, we propose a method based upon a multi-objective…
Crystalline materials used in technological applications are often complex assemblies composed of multiple phases and differently oriented grains. Robust identification of the phases and orientation relationships from these samples is…
This paper presents a new method for determining the diffusive properties of diffuse body waves, specifically diffusivity and dissipation, in concrete with multiple planar boundaries. Instead of relying on the analytical solution to the…
A simple model for calculating the diffraction radiation characteristics from an ultrarelativistic charged particle moving close to a tilted ideally conducting strip is developed. Resonant diffraction radiation (RDR) is treated as a…
A new approach for analyzing waveguide junctions containing conductive cylindrical objects is proposed. The algorithm is based on mode matching technique using local projection functions, which improves the numerical conditioning of the…
Phase is a fundamental resource for optical imaging but cannot be directly observed with intensity measurements. The existing methods to quantify a phase distribution rely on complex devices and structures. Here we experimentally…
The diffraction of a scalar plane wave from a doubly-periodic surface on which either the Dirichlet or Neumann boundary condition is imposed is studied by means of a rigorous numerical solution of the Rayleigh equation for the amplitudes of…
The scaling behaviour of the diffraction intensity near the origin is investigated for (partially) ordered systems, with an emphasis on illustrative, rigorous results. This is an established method to detect and quantify the fluctuation…
The reflecting features (reflected spectrum and phase) on the surface of pure-material plate depend on refractive index, extinction coefficient, incident angle, polarization direction and so on. The features, however, do not depend on a cut…
Grazing incidence X-ray diffraction (GIXD) is widely used for the structural characterization of thin films, particularly for analyzing phase composition and the orientation distribution of crystallites. While various tools exist for…
Distinguishing two objects or point sources located closer than the Rayleigh distance is impossible in conventional microscopy. Understandably, the task becomes increasingly harder with a growing number of particles placed in close…