Related papers: Quantification of local geometry and local symmetr…
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…
We describe a framework for random pairwise comparisons matrices, inspired by selected constructions releted to the so called inconsistency reduction of pairwise comparisons (PC) matrices. In to build up structures on random pairwise…
The ability to control forces between sub-micron-scale building blocks offers considerable potential for designing new materials through self-assembly. A typical paradigm is to first identify a particular (crystal) structure that has some…
In this work, we present an atomistic first-principles framework for modeling the low-temperature electronic and transport properties of disordered two-dimensional (2D) materials with randomly distributed point defects (impurities). The…
Order parameters based on spherical harmonics and Fourier coefficients already play a significant role in condensed matter research in the context of systems of spherical or point particles. Here, we extend these types of order parameter to…
We introduce and discuss (local) symmetries of geometric structures. These symmetries generalize the classical (locally) symmetric spaces to various other geometries. Our main tools are homogeneous Cartan geometries and their explicit…
Accurate structural analysis is essential to gain physical knowledge and understanding of atomic-scale processes in materials from atomistic simulations. However, traditional analysis methods often reach their limits when applied to…
Mott physics - the interplay between itinerancy and localization of electrons - is undergoing a paradigm shift from the binary "bandwidth - filling" tuning framework to an intertwining of geometric, topological, and fractionalized degrees…
We explore the use of first and second order same-time atomic spatial correlation functions as a diagnostic for probing the small scale spatial structure of atomic samples trapped in optical lattices. Assuming an ensemble of equivalent…
Atom probe tomography is often introduced as providing "atomic-scale" mapping of the composition of materials and as such is often exploited to analyse atomic neighbourhoods within a material. Yet quantifying the actual spatial performance…
Identifying local structural motifs and packing patterns of molecular solids is a challenging task for both simulation and experiment. We demonstrate two novel approaches to characterize local environments in different polymorphs of…
Symmetry in biological and physical systems is a product of self organization driven by evolutionary processes, or mechanical systems under constraints. Symmetry based feature extrac-tion or representation by neural networks may unravel the…
Grain boundaries, the two-dimensional (2D) defects between differently oriented crystals, control mechanical and transport properties of materials. Our fundamental understanding of grain boundaries is still incomplete even after nearly a…
Symmetry is one of the most central concepts in physics, and it is no surprise that it has also been widely adopted as an inductive bias for machine-learning models applied to the physical sciences. This is especially true for models…
The advent of high-resolution electron and scanning probe microscopy imaging has opened the floodgates for acquiring atomically resolved images of bulk materials, 2D materials, and surfaces. This plethora of data contains an immense volume…
Methods for the design of physical parameterization schemes that possess certain invariance properties are discussed. These methods are based on different techniques of group classification and provide means to determine expressions for…
Symmetries are a key concept to connect mathematical elegance with physical insight. We consider measurement assemblages in quantum mechanics and show how their symmetry can be described by means of the so-called discrete bundles. It turns…
Parametric projections let analysts embed new points in real time, but input variations from measurement noise or data drift can produce unpredictable shifts in the 2D layout. Whether and where a projection is locally stable remains largely…
We measure and compare three correlation lengths proposed to describe the extent of structural order in amorphous systems. In particular, the recently proposed "patch correlation length" is measured as a function of temperature and…
Exploiting the notion of measurement-induced nonlocality [Phys.Rev. Lett. 106, 120401 (2011)], we introduce a new measure to quantify the nonbilocal correlation. We establish a simple relation between the nonlocal and nonbilocal measures…