Related papers: Quantification of local geometry and local symmetr…
The three dimensional structure of large packings of monosized spheres with volume fractions ranging between 0.58 and 0.64 has been studied with X-ray Computed Tomography. We search for signatures of organization, we classify local…
In this paper we propose numerical measures for evaluating the aesthetic interest of simple patterns. The patterns consist of elements (symbols, pixels, etc.) in regular square arrays. The measures depend on two characteristics of the…
Structural heterogeneity of amorphous solids present difficult challenges that stymie the prediction of plastic events, which are intimately connected to their mechanical behavior. Based on a perturbation analysis of the potential energy…
The capacity to devise order metrics for microstructures of multiphase heterogeneous media is a highly challenging task, given the richness of the possible geometries and topologies of the phases that can arise. This investigation initiates…
Computing atomic-scale properties of chemically disordered materials requires an efficient exploration of their vast configuration space. Traditional approaches such as Monte Carlo or Special Quasirandom Structures either entail sampling an…
This work is devoted to the study of the symmetries of (quasi)periodic architectured materials. For this purpose, the weaker symmetry criterion of indistinguishability is used. It relies on a statistical description of the mesostructure and…
We propose a unified framework based on persistent homology (PH) to characterize both local and global structures in disordered systems. It can simultaneously generate local and global descriptors using the same algorithm and data…
Quantum state space is endowed with a metric structure and Riemannian monotone metric is an important geometric entity defined on such a metric space. Riemannian monotone metrics are very useful for information-theoretic and statistical…
Many quantities that characterize network elements are defined in an explicit form and calculated directly from the network structure; examples of include several centrality measures like degree, closeness, or betweenness. However, there…
A comprehensive framework of characterizing complex self-assembled structures with a set of orientational order parameters is presented. It is especially relevant in the context of using anisotropic building blocks with various symmetries.…
In order to characterize molecular structures we introduce configurational fingerprint vectors which are counterparts of quantities used experimentally to identify structures. The Euclidean distance between the configurational fingerprint…
The last decade has seen intense research in materials with reduced dimensionality. The low dimensionality leads to interesting electronic behavior due to electronic confinement and reduced screening. The investigations have to a large…
Many physical systems are well modeled as collections of interacting particles. Nevertheless, a general approach to quantifying the absolute degree of order immediately surrounding a particle has yet to be described. Motivated thus, we…
Symmetry is an important aesthetic criteria in graph drawing and network visualisation. Symmetric graph drawings aim to faithfully represent automorphisms of graphs as geometric symmetries in a drawing. In this paper, we design and…
Coordination geometries describe how the neighbours of a central particle are arranged around it. Such geometries can be thought to lie in an abstract topological space; a model of this space could provide a mathematical basis for…
Spatial symmetries and invariances play an important role in the behaviour of materials and should be respected in the description and modelling of material properties. The focus here is the class of physically symmetric and positive…
This work introduces a complexity measure which addresses some conflicting issues between existing ones by using a new principle - measuring the average amount of symmetry broken by an object. It attributes low (although different)…
Symmetry -- invariance to certain operators -- is a fundamental concept in many branches of physics. We propose ways to measure symmetric properties of vertices, and their surroundings, in networks. To be stable to the randomness inherent…
We present a numerical study of 2D random-bond Potts ferromagnets. The model is studied both below and above the critical value $Q_c=4$ which discriminates between second and first-order transitions in the pure system. Two geometries are…
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…