Related papers: Point Group Analysis in Particle Simulation Data

We prove for the first time that, if a linear inverse problem exhibits a group symmetry structure, gradient-based optimizers can be designed to exploit this structure for faster convergence rates. This theoretical finding demonstrates the…

Determining crystal structures from powder X-ray diffraction (PXRD) has been a significant challenge in materials science, particularly when experimental data contain noise or the target structure has a high complexity. While recent AI…

We develop a general stability analysis for objective structures, which constitute a far reaching generalization of crystal lattice systems. We show that these particle systems, although in general neither periodic nor space filling, allow…

Characterizing microstructure-material-property relations calls for software tools which extract point-cloud- and continuum-scale-based representations of microstructural objects. Application examples include atom probe, electron, and…

Convolutional neural networks are increasingly being used to analyze and classify material microstructures, motivated by the possibility that they will be able to identify relevant microstructural features more efficiently and impartially…

A fundamental challenge in materials design is linking building block attributes to crystal structure. Addressing this challenge is particularly difficult for systems that exhibit emergent order, such as entropy-stabilized colloidal…

Machine learning algorithms have been available since the 1990s, but it is much more recently that they have come into use also in the physical sciences. While these algorithms have already proven to be useful in uncovering new properties…

Orienting surface normals correctly and consistently is a fundamental problem in geometry processing. Applications such as visualization, feature detection, and geometry reconstruction often rely on the availability of correctly oriented…

We propose efficient algorithms based on a band-limited version of 2D synchrosqueezed transforms to extract mesoscopic and microscopic information from atomic crystal images. The methods analyze atomic crystal images as an assemblage of…

The ability to reliably predict the structures and stabilities of a molecular crystal and its polymorphs without any prior experimental information would be an invaluable tool for a number of fields, with specific and immediate applications…

Successful scientific applications of large-scale molecular dynamics often rely on automated methods for identifying the local crystalline structure of condensed phases. Many existing methods for structural identification, such as Common…

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…

Given recipe of qualitative, kinetic modelling by geometric methods of three-dimensional dendritic crystals. Characteristic features of the perturbations appearing on the surface of a spherical body, leading to different scenarios of the…

Statistically sound crystallographic symmetry classifications are obtained with information theory based methods in the presence of approximately Gaussian distributed noise. A set of three synthetic images with very strong Fedorov type…

We study numerically the crystallization of a hard-sphere mixture with 8\% polydispersity. Although often used as a model glass former, for small system sizes we observe crystallization in molecular dynamics simulations. This opens the…

Devising a computational tool that assesses the thermodynamic stability of materials is among the most important steps required to build a ``virtual laboratory'', where materials could be designed from first-principles without relying on…

The orientational order of nematic liquid crystals is traditionally studied by means of the second-rank ordering tensor $\mathbb{S}$. When this is calculated through experiments or simulations, the symmetry group of the phase is not known…

Condensed matter compounds typically form crystals, which break the rotational and translational invariance of space but remain invariant under a discrete set of symmetry operations. Understanding the effects allowed by this symmetry…

A novel nonparametric clustering algorithm is proposed using the interpoint distances between the members of the data to reveal the inherent clustering structure existing in the given set of data, where we apply the classical nonparametric…

Data-driven machine learning methods have the potential to dramatically accelerate the rate of materials design over conventional human-guided approaches. These methods would help identify or, in the case of generative models, even create…