Related papers: Hedgehog topological defects in 3D amorphous solid…

Simplicial complexes are increasingly used to understand the topology of complex systems as different as brain networks and social interactions. It is therefore of special interest to extend the study of percolation to simplicial complexes.…

The program of understanding Shape Theory layer by layer topologically and geometrically -- proposed in Part I -- is now addressed for 4 points in 1-$d$. Topological shape space graphs are far more complex here, whereas metric shape spaces…

Classical elasticity is concerned with bodies that can be modeled as smooth manifolds endowed with a reference metric that represents local equilibrium distances between neighboring material elements. The elastic energy associated with a…

We study light scattering by a hedgehog-like and linear disclination topological defects in a nematic liquid crystal by a metric approach. Light propagating near such defects feels an effective metric equivalent to the spatial part of the…

Topological defects determine the collective properties of anisotropic materials. How their configurations are controlled is not well understood however, especially in 3D. In living matter moreover, 2D defects have been linked to biological…

Shear bands are narrow zones of intense shear observed during plastic deformations of metals at high strain rates. Because they often precede rupture, their study attracted attention as a mechanism of material failure. Here, we aim to…

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…

In this paper, we propose a method for characterizing 3D shapes from point clouds and we show a direct application on a study of organ temporal deformations. As an example, we characterize the behavior of a bladder during a forced…

The aim of this work is to efficiently and robustly solve the statistical inverse problem related to the identification of the elastic properties at both macroscopic and mesoscopic scales of heterogeneous anisotropic materials with a…

The notion of defects in crystalline phases of matter has been extremely powerful for understanding crystal growth, deformation and melting. Many of these discontinuities in the periodic order of crystals are well described by the Burgers…

Topological holography is a holographic principle that describes the generalized global symmetry of a local quantum system in terms of a topological order in one higher dimension. This framework separates the topological data from the local…

We propose a new topological tool for computer vision - Scalar Function Topology Divergence (SFTD), which measures the dissimilarity of multi-scale topology between sublevel sets of two functions having a common domain. Functions can be…

In the field of holomorphic dynamics in one complex variable, hedgehog is the local invariant set arising about a Cremer point and endowed with a very complicate shape as well as relating to very weak numerical conditions. We give a…

Understanding how topological constraints affect the dynamics of polymers in solution is at the basis of any polymer theory and it is particularly needed for melts of rings. These polymers fold as crumpled and space-filling objects and,…

We study the topology of smectic defects in two and three dimensions. We give a topological classification of smectic point defects and disclination lines in three dimensions. In addition we describe the combination rules for smectic point…

Symmetric second-order tensors are fundamental in various scientific and engineering domains, as they can represent properties such as material stresses or diffusion processes in brain tissue. In recent years, several approaches have been…

Determining the equilibrium configuration and shape of curved two-dimensional films with (generalized) liquid crystalline (LC) order is a difficult infinite dimensional problem of direct relevance to the study of generalized polymersomes,…

Topological invariants have proved useful for analyzing emergent function as they characterize a property of the entire system, and are insensitive to local details, disorder, and noise. They support boundary states, which reduce the system…

This paper describes the systematic application of local topological methods for detecting interfaces and related anomalies in complicated high-dimensional data. By examining the topology of small regions around each point, one can…

Physical systems are frequently modeled as sets of points in space, each representing the position of an atom, molecule, or mesoscale particle. As many properties of such systems depend on the underlying ordering of their constituent…