Related papers: A Topological Framework for Local Structure Analys…

Many physical systems can be studied as collections of particles embedded in space, evolving through deterministic evolution equations. Natural questions arise concerning how to characterize these arrangements - are they ordered or…

This paper introduces a new approach toward characterizing local structural features of two-dimensional particle systems. The approach can accurately identify and characterize defects in high-temperature crystals, distinguish a wide range…

A theory of structure is formulated for systems of many structureless classical particles with stable local interactions in Euclidean space. Such systems are shown to have their structure in thermodynamic equilibrium determined exactly by a…

Disordered systems like liquids, gels, glasses, or granular materials are not only ubiquitous in daily life and in industrial applications but they are also crucial for the mechanical stability of cells or the transport of chemical and…

We use molecular dynamics to study the ordering of a nematic liquid crystal around a spherical particle or droplet. Homeotropic boundary conditions and strong anchoring create a hedgehog director configuration on the particle surface and in…

Many systems in nature and the synthetic world involve ordered arrangements of units on two-dimensional surfaces. We review here the fundamental role payed by both the topology of the underlying surface and its detailed curvature. Topology…

Machine learning techniques have been used to quantify the relationship between local structural features and variations in local dynamical activity in disordered glass-forming materials. To date these methods have been applied to an array…

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…

Liquid crystals are assemblies of rod-like molecules which self-organize to form mesophases, in-between ordinary liquids and anisotropic crystals. At each point, the molecules collectively orient themselves along a privileged direction,…

The local structure study reveals important aspects of the physical properties, because it is closely related to the electronic structure. Standard crystallographic analysis based on a space group fails to observe disorder in the crystal…

In nonequilibrium statistical physics, quantifying the nearest (and higher-order) neighbors and free volumes of particles in many-body systems is crucial to elucidating the origin of macroscopic collective phenomena, such as glass/granular…

This monograph introduces key concepts and problems in the new research area of Periodic Geometry and Topology for materials applications.Periodic structures such as solid crystalline materials or textiles were previously classified in…

Calculations on atomistic scale are necessary for understanding of physical phenomena occurring during advanced processing of liquids, slurries, and nano-ceramics composite materials. This paper describes some new ideas for using the…

Many standard structural quantities, such as order parameters and correlation functions, exist for common condensed matter systems, such as spherical and rod-like particles. However, these structural quantities are often insufficient for…

The underlying structural order that transcends the liquid, glass and crystalline states is identified using an efficient genetic algorithm (GA). GA identifies the most common energetically favorable packing motif in crystalline structures…

The Voronoi model is a popular tool for studying confluent living tissues. It exhibits an anomalous glassy behavior even at very low temperatures or weak active self-propulsion, and at zero temperature the model exhibits a disordered solid…

The homotopy theory of topological defects is a powerful tool for organizing and unifying many ideas across a broad range of physical systems. Recently, experimental progress has been made in controlling and measuring colloidal inclusions…

In recent years there has been a great interest in topological materials and in their fascinating properties. Topological band theory was initially developed for condensed matter systems, but it can be readily applied to arbitrary wave…

This paper introduces a new open-source software program called VoroTop, which uses Voronoi topology to analyze local structure in atomic systems. Strengths of this approach include its abilities to analyze high-temperature systems and to…

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…