Related papers: Layer group classification of two-dimensional mate…
Due to the subtle balance of intermolecular interactions that govern structure-property relations, predicting the stability of crystal structures formed from molecular building blocks is a highly non-trivial scientific problem. A…
The world of two-dimensional crystals is of great significance for the design and study of structural and functional materials with novel properties. The world of two-dimensional crystals is of great significance for the design and study of…
Common two-dimensional (2D) materials have a layered 3D structure with covalently bonded, atomically thin layers held together by weak van der Waals forces. However, in a recent transmission electron microscopy experiment, atomically thin…
Motivated by lattice mixture identification and grain boundary detection, we present a framework for lattice pattern representation and comparison, and propose an efficient algorithm for lattice separation. We define new scale and shape…
Two-dimensional (2D) materials are among the most promising candidates for beyond-silicon electronic, optoelectronic and quantum computing applications. Recently, their recognized importance sparked a push to discover and characterize novel…
In this study, we investigate the clustering of 5000 droplets, each originating from one of five distinct droplet classes, each representing a unique geometry. The shape coordinates of the droplets are mapped to a 2D latent space through a…
Incorporating known symmetries in data into machine learning models has consistently improved predictive accuracy, robustness, and generalization. However, achieving exact invariance to specific symmetries typically requires designing…
Lattice structure and symmetry of two-dimensional (2D) layered materials are of key importance to their fundamental mechanical, thermal, electronic and optical properties. Raman spectroscopy, as a convenient and nondestructive tool, however…
Entangled structures such as textiles and architected materials are often doubly periodic. Due to this property and their finite transverse thickness, the symmetries of these materials are described by the crystallographic layer groups.…
Property by design is one appealing idea in material synthesis but hard to achieve in practice. A recent successful example is the demonstration of van der Waals (vdW) heterostructures,1-3 in which atomic layers are stacked on each other…
Two-dimensional checkerboard lattice, the simplest line-graph lattice, has been intensively studied as a toy model, while material design and synthesis remain elusive. Here, we report theoretical prediction and experimental realization of…
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…
Using evolutionary algorithm and first-principles calculations, we predict a family group of two-dimensional node-line semimetals MX (M=Pd, Pt; X=S, Se, Te), which has zig-zag type mono-layer structure in Pmm2 layer group. Band structure…
Topological crystalline phases in electronic structures can be generally classified using the spatial symmetry characters of the valence bands and mapping them onto appropriate symmetry indicators. These mappings have been recently applied…
A group theoretical discussion on the hypercubic lattice described by the affine Coxeter-Weyl group Wa(Bn) has been presented. When the lattice is projected onto the Coxeter plane it is noted that the maximal dihedral subgroup Dh of W(Bn)…
Three-dimensional data have become increasingly present in earth observation over the last decades. However, many 3D surveys are still underexploited due to the lack of accessible and explainable automatic classification methods, for…
Liquid crystal textures encode rich structural information, yet mapping these images to mesophase identity remains challenging because visually similar patterns can arise from distinct structures. Here we present a simple, interpretable…
A theoretical model of shape-anisometric particles embedded in a cubic lattice is formulated for binary mixtures combining rod-like, plate-like and spherical particles. The model aims at providing a tool for the prediction and…
In this work, we reconsider the study of 2D materials involving double lattice structures associated with periodic polygons. In tessellated periodic representation, it appears two periodic polygons of $k$ sides of unequal side lengths at…
This paper is devoted to the problem of choosing the most suitable model of a geometrical system for describing the real crystallographic space. It has been shown that all 230 crystallographic groups used to describe the crystalline…