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

This article gives the construction and complete classification of all three-dimensional spherical manifolds, and orders them by decreasing volume, in the context of multiconnected universe models with positive spatial curvature. It…

Defects in the multi-dimensional macroscopic quantum field of the He-3 superfluids are localized objects with a topological charge and are topologically stable. They include point-like objects, vortex lines, planar domain-wall-like…

We present a new definition of defects which is based on a Riemannian formulation of incompatible elasticity. Defects are viewed as local deviations of the material's reference metric field, $\bar{\mathfrak{g}}$, from a Euclidian metric.…

Topological disclinations, crystallographic defects that break rotation lattice symmetry, have attracted great interest and exhibited wide applications in cavities, waveguides, and lasers. However, topological disclinations have thus far…

The formulation of a new prism finite element is presented for the nonlinear analysis of solid shells subject to large strains and large displacements. The element is based on hierarchical, heterogeneous, and anisotropic shape functions. As…

We study a notion of strict pseudoconvexity in the context of topologically (often unsmoothably) embedded 3-manifolds in complex surfaces. Topologically pseudoconvex (TPC) 3-manifolds behave similarly to their smooth analogues, cutting out…

We introduce the notion of a topological geodesic in a 3-manifold. Under suitable hypotheses on the fundamental group, for instance word-hyperbolicity, topological geodesics are shown to have the useful properties of, and play the same role…

Topological data analysis (TDA) is a rising branch in modern applied mathematics. It extracts topological structures as features of a given space and uses these features to analyze digital data. Persistent homology, one of the central tools…

Geometry and topology constitute complementary descriptors of three-dimensional shape, yet existing benchmark datasets primarily capture geometric information while neglecting topological structure. This work addresses this limitation by…

Epithelial monolayers are a central building block of complex organisms. Topological defects have emerged as important elements for single cell behavior in flat epithelia. Here we theoretically study such defects in a three-dimensional…

Motivated by Felix Klein's notion that geometry is governed by its group of symmetry transformations, Charles Ehresmann initiated the study of geometric structures on topological spaces locally modeled on a homogeneous space of a Lie group.…

Much recent progress has been made in the study of nematic solids, both glassy and elastomeric, particularly in the realm of stress-free, defect-driven deformation in thin sheets of material. In this paper we consider a subset of texture…

Highly periodic structures are often said to convey the beauty of nature. However, most material properties are strongly influenced by the defects they contain. On the mesoscopic scale, molecular self-assembly exemplifies this interplay;…

In the real world, we often come across soft objects having spatially varying stiffness, such as human palm or a wart on the skin. In this paper, we propose a novel approach to render thin, deformable objects having spatially varying…

Topological defects are found in a variety of systems, and their existence are robust under perturbations due to their topological nature. Here we introduce a new type of topological defects found in electromagnetic waves: topological spin…

This article proposes a topological method that extracts hierarchical structures of various amorphous solids. The method is based on the persistence diagram (PD), a mathematical tool for capturing shapes of multiscale data. The input to the…

Topological defects are distinctive signatures of liquid crystals. They profoundly affect the viscoelastic behavior of the fluid by constraining the orientational structure in a way that inevitably requires global changes not achievable…

In chaotic deterministic systems, seemingly stochastic behavior is generated by relatively simple, though hidden, organizing rules and structures. Prominent among the tools used to characterize this complexity in 1D and 2D systems are…

A path independent measure in order parameter space is introduced such that, when integrated along any closed contour in a three dimensional nematic phase, it yields the topological charge of any line defects encircled by the contour. A…

Topology optimization is a powerful tool utilized in various fields for structural design. However, its application has primarily been restricted to static or passively moving objects, mainly focusing on hard materials with limited…