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We propose a systematic method to construct crystal-based molecular structures often needed as input for computational chemistry studies. These structures include crystal ``slabs" with periodic boundary conditions (PBCs) and non-periodic…
We realize Lobachevsky geometry in a simulation lab, by producing a carbon-based mechanically stable molecular structure, arranged in the shape of a Beltrami pseudosphere. We find that this structure: i) corresponds to a non-Euclidean…
We present a method of creation of photonic structures whose optical spectrum of the reflection coefficient has an arbitrary shape and has predetermined features. We develop an algorithm for the construction of a photonic crystal structure,…
We examine nanoparticles (NPs) forming polyhedral sections of the ideal cubic lattice, simple (sc), body centered (bcc), and face centered (fcc) cubic, which are confined by facets characterized by densest and second densest {h k l}…
Crystal structures can be viewed as assemblies of space-filling polyhedra, which play a critical role in determining material properties such as ionic conductivity and dielectric constant. However, most conventional crystal structure…
We use ab initio density functional calculations to study the stability, elastic properties and electronic structure of sp2 carbon minimal surfaces with negative Gaussian curvature, called schwarzites. We focus on two systems with cubic…
We consider the action of the group $\mathrm{PGL}_4(K)$ on the smooth cubic surfaces of $\mathbb{P}^3_K$ ($K$ an algebraically closed field of characteristic zero). We classify, in an explicit way, all the smooth cubic surfaces with non…
Crystal structure design is important for the discovery of new highly functional materials because crystal structure strongly influences material properties. Crystal structures are composed of space-filling polyhedra, which affect material…
A new method to construct quasicrystalline lattices is proposed. It is based on Landau crystallization theory. Like well-known cut and projection methods our approach deals with N dimensional crystallography, but we don't need any…
We study structurable algebras of skew-dimension one. We present two different equivalent constructions for such algebras: one in terms of non-linear isotopies of cubic norm structures, and one in terms of hermitian cubic norm structures.…
We develop a general stability analysis for objective structures, which constitute a far reaching generalization of crystal lattice systems. We show that these particle systems, although in general neither periodic nor space filling, allow…
Nowadays sp carbon chains terminated by graphene or graphitic-like carbon are synthesized routinely in several nanotech labs. We propose an ab-initio study of such carbon-only materials, by computing their structure and stability, as well…
We examine the structure of compact metal nanoparticles (NPs) forming polyhedral sections of face centered (fcc) and body centered (bcc) cubic lattices, which are confined by facets characterized by highly dense {100}, {110}, and {111}…
A generalized complex structure is called stable if its defining anticanonical section vanishes transversally, on a codimension-two submanifold. Alternatively, it is a zero elliptic residue symplectic structure in the elliptic tangent…
We report on our project to construct non-singular cubic surfaces over $\bbQ$ with a rational line. Our method is to start with degree 4 Del Pezzo surfaces in diagonal form. For these, we develop an explicit version of Galois descent.
Systematic enumeration of crystalline networks with some special topological characters is of considerable interest in both mathematics and crystallography. Based on the restriction of lattice in cubic and inequivalent nodes not exceeding…
We construct a minimal complex surface of general type with $p_g=0$, $K^2 =4$, and $\pi_1=\mathbb{Z}/2\mathbb{Z}$ using a rational blow-down surgery and a $\mathbb{Q}$-Gorenstein smoothing theory. In a similar fashion, we also construct a…
When flat or on a firm mechanical substrate, the atomic composition and atomistic structure of two-dimensional crystals dictate their chemical, electronic, optical, and mechanical properties. These properties change when the two-dimensional…
We propose and compare various techiques available to produce smooth cubic hypersurfaces over a non-algebraically-closed field which have rational points but which are not stably rational over their ground field.
During past years, a number of reports have been published on synthesis of tetragonal allotrope of boron, t-B52 phase. However, no unambiguous characterization of the crystal structure has been performed to the present time, while…