Related papers: Voronoi-based similarity distances between arbitra…
The Voronoi diagram of a finite set of objects is a fundamental geometric structure that subdivides the embedding space into regions, each region consisting of the points that are closer to a given object than to the others. We may define…
We developed a method for measuring the similarity between materials, focusing on specific physical properties. The obtained information can be utilized to understand the underlying mechanisms and to support the prediction of the physical…
Crystal structure prediction algorithms have become powerful tools for materials discovery in recent years, however, they are usually limited to relatively small systems. The main challenge is that the number of local minima grows…
Predicting phase stabilities of crystal polymorphs is central to computational materials science and chemistry. Such predictions are challenging because they first require searching for potential energy minima and then performing arduous…
Over times shorter than that required for relaxation of enthalpy, a liquid can exhibit striking heterogeneities. The picture of these heterogeneities is complex with transient patches of rigidity, irregular yet persistent, intersected by…
The phase diagram of binary mixtures of particles interacting via a pair potential of parallel dipoles is computed at zero temperature as a function of composition and the ratio of their magnetic susceptibilities. Using lattice sums, a rich…
In this paper the problem of the theory of a quasicrystal structures - the determination of coordinates of each atom of quasicrystal in analytical form - is solved. Within the framework of the proposed model a periodic crystal can be…
This work briefly explores the possibility of approximating spatial distance (alternatively, similarity) between data points using the Isolation Forest method envisioned for outlier detection. The logic is similar to that of isolation: the…
We introduce a computational method to optimize target physical properties in the full configuration space regarding atomic composition, chemical stoichiometry, and crystal structure. The approach combines the universal potential of the…
Polymorphism, the ability of a compound to crystallize in multiple distinct structures, plays a vital role in determining the physical, chemical, and functional properties of materials. Accurate identification and prediction of polymorphic…
In this paper we are concerned with finding the vertices of the Voronoi cell of a Euclidean lattice. Given a basis of a lattice, we prove that computing the number of vertices is a #P-hard problem. On the other hand we describe an algorithm…
Detachment and fracture are central to many tissue-level processes, but they are challenging to simulate with Voronoi-type models that typically assume a confluent tissue. Here we analyze the finite Voronoi model, a nonconfluent extension…
X-ray and Sunyaev-Zeldovich effect observations can be combined to measure the distance to clusters of galaxies. If the intracluster gas distribution is not spherical, but elongated by a factor of Z along the line of sight, the inferred…
The notions of distance and similarity play a key role in many machine learning approaches, and artificial intelligence (AI) in general, since they can serve as an organizing principle by which individuals classify objects, form concepts…
Stable vortex lattices are basic dynamical patterns which have been demonstrated in physical systems including superconductor physics, Bose-Einstein condensates, hydrodynamics and optics. Vortex-antivortex (VAV) ensembles can be produced,…
To extend rational materials design and discovery into the space of metastable polymorphs, rapid and reliable assessment of their lifetimes is essential. Motivated by the early work of Buerger (1951), here we investigate the routes to…
We study random bubble lattices which can be produced by processes such as first order phase transitions, and derive characteristics that are important for understanding the percolation of distinct varieties of bubbles. The results are…
Predicting crystal nucleation is among the most significant long--standing challenges in condensed matter. In the system most studied (hard sphere colloids), the comparison between experiments performed using static light scattering and…
Stable or metastable crystal structures of assembled atoms can be predicted by finding the global or local minima of the energy surface within a broad space of atomic configurations. Generally, this requires repeated first-principles energy…
Three-dimensional Voronoi analysis is used to quantify the clustering of inertial particles in homogeneous isotropic turbulence using data from numerics and experiments. We study the clustering behavior at different density ratios and…