相关论文: On Topological Defects

Liquid crystals generally support orientational singularities of the director field known as topological defects. These latter modifiy transport properties in their vicinity as if the geometry was non-Euclidean. We present a state of the…

We revisit the geometric theory of defects. In the differential-geometric models of defects that have been adopted since the 1950s, dislocations have been associated with torsion, disclinations with the full curvature, and point defects…

We develop a language for describing the relationship among observations, mathematical models, and the underlying principles from which they are derived. Using Information Geometry, we consider geometric properties of statistical models for…

Directional media, such as nematic liquid crystals and ferromagnets, are characterized by their topologically stabilized defects in directional order. In nematics, boundary conditions and surface-treated inclusions often create complex…

Topological defects play a key role in the structures and dynamics of liquid crystals (LCs) and other ordered systems. There is a recent interest in studying defects in different biological systems with distinct textures. However, a robust…

We study the topology associated with physical vector and scalar fields. A mathematical object, e.g., a ball, can be continuously deformed, without tearing or gluing, to make other topologically equivalent objects, e.g., a cube or a solid…

Additive manufacturing (AM) enables enormous freedom for design of complex structures. However, the process-dependent limitations that result in discrepancies between as-designed and as-manufactured shapes are not fully understood. The…

The context of this paper is the use of formal methods for topology-based geometric modelling. Topology-based geometric modelling deals with objects of various dimensions and shapes. Usually, objects are defined by a graph-based topological…

This paper is dedicated to studying various aspects of topological defects, appearing in mean-field theory treatments of physical systems such as ultracold atomic gases and gauge field theories. We start by investigating topological charge…

Active matter encompasses different nonequilibrium systems in which individual constituents convert energy into non-conservative forces or motion at the microscale. This review provides an elementary introduction to the role of topology in…

In a previous effort [arXiv:1708.05492] we have created a framework that explains why topological structures naturally arise within a scientific theory; namely, they capture the requirements of experimental verification. This is…

The defect morphology is an essential aspect of the evolution of crystals' microstructure and its response to stress. Existing methods either only report defect concentration or characterize only some of the defect morphologies. The need…

Topological methods can provide a way of proposing new metrics and methods of scrutinising data, that otherwise may be overlooked. In this work, a method of quantifying the shape of data, via a topic called topological data analysis will be…

Combination of topology and general relativity can lead to some profound and farsighted predictions. It is well known that symmetry breaking of the Higgs vacuum field in the early universe possibly induced topological defects in spacetime,…

Topological phases of matter are often understood and predicted with the help of crystal symmetries, although they don't rely on them to exist. In this chapter we review how topological phases have been recently shown to emerge in amorphous…

This is a survey article for the Encyclopedia of Mathematical Physics, 2nd Edition. Topological defects are described in the context of the 2-dimensional Ising model on the lattice, in 2-dimensional quantum field theory, in topological…

Topological materials present unconventional electronic properties that make them attractive for both basic science and next-generation technological applications. The majority of currently known topological materials have been discovered…

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;…

We study the dynamics of topological defects in continuum theories governed by a free energy minimization principle, building on our recently developed framework [Romano J, Mahault B and Golestanian R 2023 J. Stat. Mech.: Theory Exp.…

Structural disorder can improve the optical properties of metasurfaces, whether it is emerging from some large-scale fabrication methods, or explicitly designed and built lithographically. Correlated disorder, induced by a minimum…