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Data encoded as symmetric positive definite (SPD) matrices frequently arise in many areas of computer vision and machine learning. While these matrices form an open subset of the Euclidean space of symmetric matrices, viewing them through…
An algorithm for determining crystal structures from diffraction data is described which does not rely on the usual Fourier-space formulations of atomicity. The new algorithm implements atomicity constraints in real-space, as well as…
Characterizing crystal structures and interfaces down to the atomic level is an important step for designing advanced materials. Modern electron microscopy routinely achieves atomic resolution and is capable to resolve complex arrangements…
Convergent-beam electron diffraction (CBED) is a well-established probe for spatial symmetries of crystalline samples, mainly exploiting the well-defined mapping between the diffraction groups (symmetry group of CBED patterns) and the…
Adaptive finite elements are the method of choice for accurate simulations of optical components. However as shown recently by Bienstman et al. many finite element mode solvers fail to compute the propagation constant's imaginary part of a…
Space group theory is pivotal in the design of nanophotonics devices, enabling the characterization of periodic optical structures such as photonic crystals. The aim of this study is to extend the application of nonsymmorphic space groups…
Group Theory techniques can aid greatly the determination of magnetic structures. The integration of their calculations into new and existing refinement programs is an ongoing development that will simplify and make more rigorous the…
We present a procedure for fitting an ellipse to powder diffraction patterns recorded on a planar 2D detector, which uses the peak intensities as weights. This procedure works for complete and spotty diffraction rings. We outline all the…
Generating novel crystalline materials has the potential to lead to advancements in fields such as electronics, energy storage, and catalysis. The defining characteristic of crystals is their symmetry, which plays a central role in…
3D photoelectron angular distributions (PADs) are measured from an atomic target ionized by ultrafast, elliptical fields of opposite handedness. Comparing these PADs to one another and to numeric simulations, a difficult to avoid systematic…
Electron microscopy is a powerful tool for studying the properties of materials down to their atomic structure. In many cases, the quantitative interpretation of images requires simulations based on atomistic structure models. These…
It is shown that the diffraction on a polycrystal can be used for investigation and diagnostics of X-ray radiation emitted in a forward direction by relativistic charged particles moving in crystalline or other targets or fields. Methods…
We have developed a symmetry-adapted modeling procedure for molecules and crystals. By using the completeness of multipoles to express spatial and time-reversal parity-specific anisotropic distributions, we can generate systematically the…
We report on a new algorithm for detection of crystallographic information in 3D, as retained in Atom Probe Tomography (APT), with improved robustness and signal detection performance. The algorithm is underpinned by 1D distribution…
In this thesis we investigate high throughput computational methods for processing large quantities of data collected from synchrotrons and their application to spectral analysis of powder diffraction data. We also present the main product…
In this paper we observe that information theoretical concepts are valuable tools for extracting information from images and, in particular, information on image symmetries. It is shown that the problem of detecting reflectional and…
The quaternion Bingham distribution has been used to model preferred crystallographic orientation, or crystallographic texture, in polycrystalline materials in the materials science and geological communities. A primary difficulty in…
We study the problem of supervised learning a metric space under discriminative constraints. Given a universe $X$ and sets ${\cal S}, {\cal D}\subset {X \choose 2}$ of similar and dissimilar pairs, we seek to find a mapping $f:X\to Y$, into…
We introduce a Python framework designed to automate the most common tasks associated with the extraction and upscaling of the statistics of single-impact crater functions to inform coefficients of continuum equations describing surface…
We propose a novel scheme for asymmetric light diffraction of a weak probe field into a one-dimensional (1D) and two-dimensional (2D) lattice occupied with cold atoms. The atoms are driven into the double lambda-type configuration by a…