Related papers: Construction of topological defect networks with c…
An interpretation of the gauge anomaly of the two-dimensional multi-phase sigma model is presented in terms of an obstruction to the existence of a topological defect network implementing a local trivialisation of the gauged sigma model.
Topological defects, which are singular points in a director field, play a major role in shaping active systems. Here, we experimentally study topological defects and the flow patterns around them, that are formed during the highly rapid…
Topological defects can arise in symmetry breaking models where the scalar field potential $V(\phi)$ has no minima and is a monotonically decreasing function of $|\phi|$. The properties of such vacuumless defects are quite different from…
We consider the slow and athermal deformations of amorphous solids and show how the ensuing sequence of discrete plastic rearrangements can be mapped onto a directed network. The network topology reveals a set of highly connected regions…
The study of topology in solids is undergoing a renaissance following renewed interest in the properties of ferroic domain walls as well as recent discoveries regarding topological insulators and skyrmionic lattices. Each of these systems…
A family of graphs optimized as the topologies for supercomputer interconnection networks is proposed. The special needs of such network topologies, minimal diameter and mean path length, are met by special constructions of the weight…
We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant…
Multiple scales coexist in complex networks. However, the small world property makes them strongly entangled. This turns the elucidation of length scales and symmetries a defiant challenge. Here, we define a geometric renormalization group…
We deal with the presence of topological defects in models for two real scalar fields. We comment on defects hosting topological defects, and we search for explicit defect solutions using the trial orbit method. As we know, under certain…
Long lived topological features are distinguished from short lived ones (considered as topological noise) in simplicial complexes constructed from complex networks. A new topological invariant, persistent homology, is determined and…
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;…
The ability to reroute and control flow is vital to the function of venation networks across a wide range of organisms. By modifying individual edges in these networks, either by adjusting edge conductances or creating and destroying edges,…
We show that graphs, networks and other related discrete model systems carry a natural supersymmetric structure, which, apart from its conceptual importance as to possible physical applications, allows to derive a series of spectral…
Random walks represent an important tool for probing the structural and dynamical properties of networks and modeling transport and diffusion processes on networks. However, when individuals' movement becomes dictated by more complicated…
The structural analysis of shape boundaries leads to the characterization of objects as well as to the understanding of shape properties. The literature on graphs and networks have contributed to the structural characterization of shapes…
The experiments on verification of the Kibble-Zurek mechanism showed that topological defects are formed most efficiently in the systems of small size or low (quasi-)dimensionality, whereas in the macroscopic two- and three-dimensional…
On the basis of the "molecular-orbital" representation which describes generic flat-band models, we propose a systematic way to construct a class of flat-band models with finite-range hoppings that have topological natures. In these models,…
We derive traffic rule for spectral networks for A_2 theory for Riemann surface with punctures and use it to study in details the moduli space M of flat GL(3,C) connections on P^1 with 3 full punctures. We apply the simplified traffic rule…
Networks are important representations in computer science to communicate structural aspects of a given system of interacting components. The evolution of a network has several topological properties that can provide us information on the…
In this work we introduce new scalar field models and study the defect solutions they may engender. The investigation is based on the deformation procedure, which greatly simplify the calculations, leading us to new models together with the…