Related papers: Topics on mathematical crystallography
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…
Crystal structures are characterized by atomic bases within a primitive unit cell that repeats along a regular lattice throughout 3D space. The periodic and infinite nature of crystals poses unique challenges for geometric graph…
The prediction of material structure from chemical composition has been a long-standing challenge in natural science. Although there have been various methodological developments and successes with computer simulations, the prediction of…
Optical properties of materials related to light absorption and scattering are explained by the excitation of electrons. The Bethe-Salpeter equation is the state-of-the-art approach to describe these processes from first principles (ab…
We perceive the world through images formed by scattering. The ability to interpret scattering data mathematically has opened to our scrutiny the constituents of matter, the building blocks of life, and the remotest corners of the universe.…
Colloids are abundant in nature, science and technology, with examples ranging from milk to quantum dots and the "colloidal atom" paradigm. Similarly, liquid crystal ordering is important in contexts ranging from biological membranes to…
Atomic structure analysis of crystalline materials is a paramount endeavor in both chemical and material sciences. This sophisticated technique necessitates not only a solid foundation in crystallography but also a profound comprehension of…
Phyllotaxis, the search for the most homogeneous and dense organizations of small disks inside a large circular domain, was first developed to analyze arrangements of leaves or florets in plants. Then it has become an object of study not…
Traditional general circulation models, or GCMs -- i.e. 3D dynamical models with unresolved terms represented in equations with tunable parameters -- have been a mainstay of climate research for several decades, and some of the pioneering…
We apply methods of nonstandard mathematics in order to regard analytic geometry in a very different way. For example, complex spaces are seen to be the "standard part" of certain algebraic nonstandard schemes. We construct a category of…
Prediction of stable crystal structures at given pressure-temperature conditions, based only on the knowledge of the chemical composition, is a central problem of condensed matter physics. This extremely challenging problem is often termed…
Asteroseismology has the capability of delivering stellar properties which would otherwise be inaccessible, such as radii, masses and thus ages of stars. When coupling this information with classical determinations of stellar parameters,…
The radial distribution function is a characteristic geometric quantity of a point set in Euclidean space that reflects itself in the corresponding diffraction spectrum and related objects of physical interest. The underlying combinatorial…
Optical microscopy is one of the oldest scientific instruments that is still used in forefront research. Ernst Abbe's nineteenth century formulation of the resolution limit in microscopy let generations of scientists believe that optical…
This work develops new numerical methods for the solution of the tomography problem in domains with reflecting obstacles. We compare the solution's performance for Lambertian reflection, for classical tomography with ubroken rays and for…
This article introduces a new efficient particle method for the numerical simulation of crystallization and precipitation at the pore scale of real rock geometries extracted by X-Ray tomography. It is based on the coupling between…
The recently developed information-theoretic approach to crystallographic symmetry classifications and quantifications in two dimensions (2D) from digital transmission electron and scanning probe microscope images is adapted for the…
Metric graphs are important models for capturing the structure of complex data across various domains. While much effort has been devoted to extracting geometric and topological features from graph data, computational aspects of metric…
We demonstrate that higher-order electric susceptibilities in crystals can be enhanced and understood through nontrivial topological invariants and quantum geometry, using one-dimensional $\pi$-conjugated chains as representative model…
This is a write-up of the author's invited talk at the Eighth International Congress of Chinese Mathematicians (ICCM) held at Beijing in June 2019. We give a survey on joint works with Naichung Conan Leung and Ziming Nikolas Ma where we…