Identification of structure in condensed matter with the topological cluster classification

We describe the topological cluster classification (TCC) algorithm. The TCC detects local structures with bond topologies similar to isolated clusters which minimise the potential energy for a number of monatomic and binary simple liquids with $m\leq13$ particles. We detail a modified Voronoi bond detection method that optimizes the cluster detection. The method to identify each cluster is outlined, and a test example of Lennard-Jones liquid and crystal phases is considered and critically examined.Comment: 28 pages, 28 figure

Recent advances in directional statistics

Mainstream statistical methodology is generally applicable to data observed in Euclidean space. There are, however, numerous contexts of considerable scientific interest in which the natural supports for the data under consideration are Riemannian manifolds like the unit circle, torus, sphere and their extensions. Typically, such data can be represented using one or more directions, and directional statistics is the branch of statistics that deals with their analysis. In this paper we provide a review of the many recent developments in the field since the publication of Mardia and Jupp (1999), still the most comprehensive text on directional statistics. Many of those developments have been stimulated by interesting applications in fields as diverse as astronomy, medicine, genetics, neurology, aeronautics, acoustics, image analysis, text mining, environmetrics, and machine learning. We begin by considering developments for the exploratory analysis of directional data before progressing to distributional models, general approaches to inference, hypothesis testing, regression, nonparametric curve estimation, methods for dimension reduction, classification and clustering, and the modelling of time series, spatial and spatio-temporal data. An overview of currently available software for analysing directional data is also provided, and potential future developments discussed.Comment: 61 page

A transferable machine-learning framework linking interstice distribution and plastic heterogeneity in metallic glasses

When metallic glasses (MGs) are subjected to mechanical loads, the plastic response of atoms is non-uniform. However, the extent and manner in which atomic environment signatures present in the undeformed structure determine this plastic heterogeneity remain elusive. Here, we demonstrate that novel site environment features that characterize interstice distributions around atoms combined with machine learning (ML) can reliably identify plastic sites in several Cu-Zr compositions. Using only quenched structural information as input, the ML-based plastic probability estimates ("quench-in softness" metric) can identify plastic sites that could activate at high strains, losing predictive power only upon the formation of shear bands. Moreover, we reveal that a quench-in softness model trained on a single composition and quenching rate substantially improves upon previous models in generalizing to different compositions and completely different MG systems (Ni62Nb38, Al90Sm10 and Fe80P20). Our work presents a general, data-centric framework that could potentially be used to address the structural origin of any site-specific property in MGs