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A mixed lattice is a lattice-type structure consisting of a set with two partial orderings, and generalizing the notion of a lattice. Mixed lattice theory has previously been studied in various algebraic structures, such as groups and…
The recent synthesis of Goldene, a 2D atomic monolayer of gold, has opened new avenues in exploring novel materials. However, the question of when multilayer Goldene transitions into bulk gold remains unresolved. This study used density…
The edge-to-edge tilings of the sphere by congruent quadrilaterals of Type $a^2bc$ are classified as $3$ classes: a sequence of two-parameter families of $2$-layer earth map tilings with $2n$ $(n\ge3)$ tiles, a one-parameter family of…
3D classification with point cloud input is a fundamental problem in 3D vision. However, due to the discrete nature and the insufficient material description of point cloud representations, there are ambiguities in distinguishing wire-like…
Crystals are the materials which can be described by uniform periodic lattices. Traditionally, only the 1-, 2-, 3-, 4- and 6-fold rotation symmetries are allowed in crystals because other n-fold rotation symmetries are forbidden by the…
Melting in 2D is described by the celebrated Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory. The unbinding of two different types of topological defects destroys translational and orientational order at different temperatures. The…
We study the phase diagram of a system of $2\times2\times2$ hard cubes on a three dimensional cubic lattice. Using Monte Carlo simulations, we show that the system exhibits four different phases as the density of cubes is increased:…
We develop a materials descriptor based on the electronic density of states and investigate the similarity of materials based on it. As an application example, we study the Computational 2D Materials Database that hosts thousands of…
A well known result by Lagarias and Ziegler states that there are finitely many equivalence classes of d-dimensional lattice polytopes having volume at most K, for fixed constants d and K. We describe an algorithm for the complete…
The topology, the symmetry involving the shape of dielectric cylinders, and the lattice structure are among the most important ingredients in the architecture of photonic crystals. In this paper, we present a systematic derivation of the…
Two dimensional (2D) materials have emerged as promising functional materials with many applications such as semiconductors and photovoltaics because of their unique optoelectronic properties. While several thousand 2D materials have been…
In recent years, skeleton-based action recognition has become a popular 3D classification problem. State-of-the-art methods typically first represent each motion sequence as a high-dimensional trajectory on a Lie group with an additional…
It has recently been shown that identical, isotropic particles can form complex crystals and quasicrystals. In order to understand the relation between the particle interaction and the structure, which it stabilizes, the phase behavior of a…
We present a fine-grained approach to identify clusters and perform percolation analysis in a 2D lattice system. In our approach, we develop an algorithm based on the linked-list data structure whereby the members of a cluster are nodes of…
Monodromy in analytic families of smooth complex surfaces yields groups of isotopy classes of orientation preserving diffeomorphisms for each family member X. For all deformation classes of minimal elliptic surfaces with p_g>q=0, we…
The discovery of novel substrate materials has been dominated by trial and error, opening the opportunity for a systematic search. To identify stable crystal surfaces, we generate bonding networks for materials from the Materials Project…
Altermagnetism, recently spotlighted in condensed matter physics, presents captivating physical properties and holds promise for spintronics applications. This study delves into the theoretical description and categorization of…
Current research on three-dimensional metamaterial has largely focused on conventional strut, plate, and shell-based lattice designs. Although these designs offer several advantages, they possess inherent limitations that can restrict their…
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}…
We suggest new modification (we call it a noise reduction procedure) for Steinhardt parameters which are often used for detecting crystalline structures in computer simulation of solids and soft matter systems. We have also developed a new…