Related papers: Symmetric functions and the phase problem in cryst…
Explicit structure constants are calculated for certain Lie algebras of vectorfields on 2-dimensional compact manifolds.
The transformation of the path integral measure under the reduction procedure in the dynamical systems with a symmetry is considered. The investigation is carried out in the case of the Wiener--type path integrals that are used for…
At modern X-ray sources, such as synchrotrons and X-ray Free-Electron Lasers (XFELs), it is important to measure the absolute value of the photon energy directly. Here, a method for absolute spectral metrology is presented. A photon energy…
Analyzing large X-ray diffraction (XRD) datasets is a key step in high-throughput mapping of the compositional phase diagrams of combinatorial materials libraries. Optimizing and automating this task can help accelerate the process of…
Infinitely rising one-dimensional potentials constitute impenetrable barriers which reflect totally any incident wave. However, the scattering by such kind of potentials is not structureless: resonances may occur for certain values of the…
Accurately determining the crystallographic structure of a material, organic or inorganic, is a critical primary step in material development and analysis. The most common practices involve analysis of diffraction patterns produced in…
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…
Following Kashiwara's algebraic approach in one-parameter case, we construct crystal bases for two-parameter quantum algebras and for their integrable modules. We also show that the global crystal basis coincides with the canonical basis…
A peculiar feature of quantum states is that they may embody so-called projective representations of symmetries rather than ordinary representations. Projective representations of space groups-the defining symmetry of crystals-remain…
Geometric information such as the space groups and crystal systems plays an important role in the properties of crystal materials. Prediction of crystal system and space group thus has wide applications in crystal material property…
Recently the algebraic structure of gauge-invariant operators in multi-matrix quantum mechanics has been clarified: this space forms a module over a freely generated ring. The ring is generated by a set of primary invariants, while the…
Accurate structural analysis is essential to gain physical knowledge and understanding of atomic-scale processes in materials from atomistic simulations. However, traditional analysis methods often reach their limits when applied to…
The advent of accelerator-driven free-electron lasers (FEL) has opened new avenues for high-resolution structure determination via diffraction methods that go far beyond conventional x-ray crystallography methods. These techniques rely on…
The phase field crystal (PFC) method has emerged as a promising technique for modeling materials with atomistic resolution on mesoscopic time scales. The approach is numerically much more efficient than classical density functional theory…
This paper introduces a SAT-based technique that calculates a compact and complete symmetry-break for finite model finding, with the focus on structures with a single binary operation (magmas). Classes of algebraic structures are typically…
Matrix spectral factorization is traditionally described as finding spectral factors having a fixed analytic pole configuration. The classification of spectral factors then involves studying the solutions of a certain algebraic Riccati…
Efficient heuristics have predicted many functional materials such as high-temperature superconducting hydrides, while inorganic structural chemistry explains why and how the crystal structures are stabilized. Here we develop the paired…
In this work, phase diagrams of a modified two-mode phase-field crystal (PFC) that show two-dimensional (2D) and three-dimensional (3D) crystallographic structures were determined by utilizing a free energy minimization method. In this…
The structure of graphite-like BCx phases (x = 1, 1.5, 3, 4, 32) has been studied using conventional X-ray diffraction. The results have been obtained, which unambiguously point to turbostratic (one- dimensionally disordered) structure of…
The morphologies of phase separating systems have formal distinctions such as symmetry groups, but the analysis protocol for labeling a particular phase field with a morphology requires manual expertise, arbitrary thresholds, or established…