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We classify all integrable complex structures on 6-dimensional Lie algebras of the form $\mathfrak{g}\times\mathfrak{g}$.
Methods to constrain the surface mineralogy of asteroids have seen considerable development during the last decade with advancement in laboratory spectral calibrations and validation of our interpretive methodologies by spacecraft…
The work function is a fundamental electronic property of a solid that varies with the facets of a crystalline surface. It is a crucial parameter in spectroscopy as well as materials design, especially for technologies such as thermionic…
We present n-1 different embeddings of string polytopes of type A. We characterize their compatibility with the crystal structure on the string polytopes, and formulate a conjecture describing how to obtain n-1 different atomic…
Despite the simplicity of the original perovskite crystal structure, this family of compounds shows an enormous variety of structural modifications and variants. In the following, we will describe several examples of perovskites, their…
We introduce the notion of integrable connections for a sheaf of differential graded algebras on a topological space. We then describe them in the finite locally projective setting, when the sheaf is either the de Rham complex of a formal…
The recent discovery of topological insulators has revived interest in the topological properties of insulating band structures. In this work, we extend the topological classification of insulating band structures to include certain point…
We have theoretically investigated the elastic properties of three topologically identical zeolitic imidazolate frameworks: ZIF-4, ZIF-62 and TIF-4, by means of ab initio calculations. The ZIFs are a subset of metal organic frameworks…
Structural studies on the icosahedral quasicrystals in Zn-Mg-Sc, Cu-Ga-Mg-Sc, and Zn-Mg-Ti alloys as well as their corresponding 1/1 cubic approximants, have revealed that these quasicrystals belong to a new structural group similar to…
Renewable energy sources are of great interest to combat global warming, yet promising sources like photovoltaic (PV) cells are not efficient and cheap enough to act as an alternative to traditional energy sources. Perovskite has high…
Elpasolite is the predominant quaternary crystal structure (AlNaK$_2$F$_6$ prototype) reported in the Inorganic Crystal Structure Database. We have developed a machine learning model to calculate density functional theory quality formation…
A new categorical crystal structure for the quantum affine algebras is presented. We introduce the extended crystal $\widehat{B}_{\mathfrak{g}}(\infty)$ for an arbitrary quantum group, which is the product of infinite copies of the crystal…
High-pressure research is a productive route to new structures and emergent properties. However, crucial high-pressure structural information remains highly fragmented across individual publications and heterogeneous computational…
Computational methods that automatically extract knowledge from data are critical for enabling data-driven materials science. A reliable identification of lattice symmetry is a crucial first step for materials characterization and…
We outline the necessary background to understand the interaction of colloids in liquid crystals through boundary conditions and topology.
Developing new metal hydrides is a critical step toward efficient hydrogen storage in carbon-neutral energy systems. However, existing materials databases, such as the Materials Project, contain a limited number of well-characterized…
Based on static and dynamical density functional theory, a phase-field-crystal model is derived which involves both the translational density and the orientational degree of ordering as well as a local director field. The model exhibits…
The potential to utilize metal-organic frameworks as a replacement for rare earth materials as well as in technological applications has prompted increased interested in this material class. The simulation of organic materials, including…
To each discrete translationally periodic bar-joint framework $\C$ in $\bR^d$ we associate a matrix-valued function $\Phi_\C(z)$ defined on the d-torus. The rigid unit mode spectrum $\Omega(\C)$ of $\C$ is defined in terms of the…
We present reflected light spectral observations from 0.4 to 2.5 micron of 24 asteroids chosen from the population of asteroids initially classified as Tholen X-type objects (Tholen, 1984). The X complex in the Tholen taxonomy comprises the…