Related papers: Crystal Representation in the Reciprocal Space
Two dimensional (2D) photonic crystals are well known for its ability to manipulate the propagation of electromagnetic wave inside the crystal. 1D and 2D photonic crystals are relatively easier to fabricate than 3D because the former work…
Time crystals are an enigmatic phase of matter in which a quantum mechanical system displays repetitive, observable motion - they spontaneously break the time translation symmetry. On the other hand optomechanical systems, where mechanical…
It is known that quaternions represent rotations in 3D Euclidean and Minkowski spaces. However, product by a quaternion gives rotation in two independent planes at once and to obtain single-plane rotations one has to apply by half-angle…
Refraction and diffraction of waves in natural crystals and artificial crystals formed by anisotropically scattering centers are considered. A detailed study of the electromagnetic wave refraction in a two-dimensional photonic crystal…
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…
How are the symmetries encoded in quasicrystals? As a compensation for the lack of translational symmetry, quasicrystals admit non-crystallographic symmetries such as 5- and 8-fold rotations in two-dimensional space. It is originated from…
We have developed an efficient and reliable methodology for crystal structure prediction, merging ab initio total-energy calculations and a specifically devised evolutionary algorithm. This method allows one to predict the most stable…
Atomic-level modeling performed at large scales enables the investigation of mesoscale materials properties with atom-by-atom resolution. The spatial complexity of such cross-scale simulations renders them unsuitable for simple human visual…
Machine Learning models have emerged as a powerful tool for fast and accurate prediction of different crystalline properties. Exiting state-of-the-art models rely on a single modality of crystal data i.e. crystal graph structure, where they…
In this study, we present a novel approach along with the needed computational strategies for efficient and scalable feature engineering of the crystal structure in compounds of different chemical compositions. This approach utilizes a…
The discovery of new crystalline materials calls for generative models that handle periodic boundary conditions, crystallographic symmetries, and physical constraints, while scaling to large and structurally diverse unit cells. We propose a…
The formation of a phase of matter can be associated with the spontaneous breaking of a symmetry. For crystallization, this broken symmetry is the spatial translation symmetry, as the atoms spontaneously localize in a periodic fashion. In…
The study of granular crystals, metamaterials that consist of closely packed arrays of particles that interact elastically, is a vibrant area of research that combines ideas from disciplines such as materials science, nonlinear dynamics,…
We explain how following the representation of 3D crystallographic space groups in geometric algebra it is further possible to similarly represent the 162 socalled subperiodic groups of crystallography in geometric algebra. We construct a…
Structural response of crystals to an applied external perturbation is important as a key for understanding microscopic origin of physical properties. Experimental investigation of structural response is a great challenge for modern…
Generative AI models, such as score-based diffusion models, have recently advanced the field of computational materials science by enabling the generation of new materials with desired properties. In addition, these models could also be…
Two-dimensional (2D) photonic crystals offer strong control over the propagation of light through their bands. Theoretical methods for computing the band structure in 2D are well-established and fast because 2D photonic crystals are…
Standard procedures for local crystal-structure optimisation involve numerous energy and force calculations. It is common to calculate an energy-volume curve, fitting an equation of state around the equilibrium cell volume. This is a…
An inverse Doppler shift occurs in a photonic crystal (PC) bounded by a moving wall. The interpretation of this result has stirred some controversy. In this paper, we address the problem using a diagrammatic approach. This visual…
Rotational symmetry plays a central role in physics, providing an elegant framework to describe how the properties of 3D objects -- from atoms to the macroscopic scale -- transform under the action of rigid rotations. Equivariant models of…