Related papers: A Fast, Parallel Algorithm for Distant-dependent C…
This paper develops a new continuous approach to a similarity between periodic lattices of ideal crystals. Quantifying a similarity between crystal structures is needed to substantially speed up the Crystal Structure Prediction, because the…
Periodic material or crystal property prediction using machine learning has grown popular in recent years as it provides a computationally efficient replacement for classical simulation methods. A crucial first step for any of these…
Accurate models of alkali and halide ions in aqueous solution are necessary for computer simulations of a broad variety of systems. Previous efforts to develop ion force fields have generally focused on reproducing experimental measurements…
This paper introduces some methods to determine the simultaneous approximation constants of a class of well approximable numbers $\zeta_{1},\zeta_{2},...,\zeta_{k}$. The approach relies on results on the connection between the set of all…
A first-principles method is presented to calculate elastic constants up to the fourth order of crystals with the cubic and hexagonal symmetries. The method relies on the numerical differentiation of the second Piola-Kirchhoff stress tensor…
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…
Crystal Structure Prediction (CSP) aims to discover solid crystalline materials by optimizing periodic arrangements of atoms, ions or molecules. CSP takes weeks of supercomputer time because of slow energy minimizations for millions of…
Lattices in three dimensions are oft studied from the ``reciprocal space'' perspective of diffraction. Today, the full lattice of a crystal can often be inferred from direct-space information about three sets of non-parallel lattice planes.…
The increased time- and length-scale of classical molecular dynamics simulations have led to raw data flows surpassing storage capacities, necessitating on-the-fly integration of structural analysis algorithms. As a result, algorithms must…
In this work, we present three linear numerical schemes to model nematic liquid crystals using the Landau-de Gennes $\textbf{Q}$-tensor theory. The first scheme is based on using a truncation procedure of the energy, which allows for an…
This paper presents an efficient parallel direct algorithm with near-optimal complexity for the compact fourth and sixth-order approximation of the three-dimensional Helmholtz equations [1] with the problem coefficient depending on only one…
The paper deals with the developing of the methodological backgrounds for the modeling and simulation of complex dynamical objects. Such backgrounds allow us to perform coordinate transformation and formulate the algorithm of its usage for…
Finding appropriate interatomic potentials which can accurately describe the crystal structure of material is one of important topics in material science. In this paper, several interatomic potentials which comprise of Lennard-Jones (LJ)…
We calculate mean square deviations for crystals in one and two dimensions. For the two dimensional lattices, we consider several distinct geometries (i.e. square, triangular, and honeycomb), and we find the same essential phenomena for…
Many real objects are modeled as discrete sets of points, such as corners or other salient features. For our main applications in chemistry, points represent atomic centers in a molecule or a solid material. We study the problem of…
Atomistic-to-Continuum (AtC) coupling methods are a novel means of computing the properties of a discrete crystal structure, such as those containing defects, that combine the accuracy of an atomistic (fully discrete) model with the…
Lattice constants such as unit cell edge lengths and plane angles are important parameters of the periodic structures of crystal materials. Predicting crystal lattice constants has wide applications in crystal structure prediction and…
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 simulations of crystals, unlike liquids or gases, it may happen that the properties of the studied system depend not only on the volume of the simulation cell but also on its shape. For such cases it is desirable to change the shape of…
The analysis of Coulomb crystallization is extended from one-component to two-component plasmas. Critical parameters for the existence of Coulomb crystals are derived for both classical and quantum crystals. In the latter case, a critical…