Related papers: Computing Defects Associated to Bounded Domain Wal…
We show that the Levin-Wen model of a unitary fusion category $\mathcal{C}$ is a gauge theory with gauge symmetry given by the tube algebra $\operatorname{Tube}(\mathcal{C})$. In particular, we define a model corresponding to a…
The Levin-Wen model of string-net condensation explains how topological phases emerge from the microscopic degrees of freedom of a physical system. However, the original construction is not applicable to all unitary fusion category since…
We give a mathematical definition of a gapped domain wall between topological phases and a gapped boundary of a topological phase. We then provide answers to some recent questions studied by Lan, Wang and Wen in condensed matter physics…
We consider a class of adaptive multilevel domain decomposition-like algorithms, built from a combination of adaptive multilevel finite element, domain decomposition, and partition of unity methods. These algorithms have several interesting…
Vertex algebras (and their modules) can be described as vector spaces together with a linear operator-valued series in one parameter $z$. With the interpretation of $z$ as a coordinate at a point on a curve, one can construct algebraic…
Webs of domain walls are constructed as 1/4 BPS states in d=4, N=2 supersymmetric U(Nc) gauge theories with Nf hypermultiplets in the fundamental representation. Web of walls can contain any numbers of external legs and loops like (p,q)…
Topological domain walls separating 2+1 dimensional topologically ordered phases can be understood in terms of Witt equivalences between the UMTCs describing anyons in the bulk topological orders. However, this picture does not provide a…
The virtual element method (VEM) is a stabilized Galerkin method that is robust and accurate on general polygonal meshes. This feature makes it an appealing candidate for simulations involving meshes with embedded interfaces and evolving…
We present a novel image-based adaptive domain decomposition FEM framework to accelerate the solution of continuum damage mechanics problems. The key idea is to use image-processing techniques in order to identify the moving interface…
We investigate the multifusion generalization of string-net ground states and lattice Hamiltonians, delving into its associated weak Hopf symmetry. For the multifusion string-net, the gauge symmetry manifests as a general weak Hopf algebra,…
There has been recent interest in new types of topological defects arising in models with compact extra dimensions. We discuss in this context the old statement that if only SU(N) gauge fields and adjoint matter live in the bulk, and the…
The BPS spectrum of certain N=2 supersymmetric field theories can be determined algebraically by studying the representation theory of BPS quivers. We introduce methods based on BPS quivers to study line defects. The presence of a line…
Dijkgraaf-Witten theories are extended three-dimensional topological field theories of Turaev-Viro type. They can be constructed geometrically from categories of bundles via linearization. Boundaries and surface defects or interfaces in…
In this work, we propose an extension of the mixed Virtual Element Method (VEM) for bi-dimensional computational grids with curvilinear edge elements. The approximation by means of rectilinear edges of a domain with curvilinear geometrical…
In pursuit of consolidating the face verification systems, prior face anti-spoofing studies excavate the hidden cues in original images to discriminate real persons and diverse attack types with the assistance of auxiliary supervision.…
This is a report on the derivation and application of a generalized version of the Wulff construction in two dimensions. The construction is used to find the shape of a domain containing an XY-like order parameter. In such a domain the…
Implicitly described domains are a well established tool in the simulation of time dependent problems, e.g. using level-set methods. In order to solve partial differential equations on such domains, a range of numerical methods was…
We study a number of domain wall forming models where various types of defect junctions can exist. These illustrate some of the mechanisms that will determine the evolution of defect networks with junctions. Understanding these mechanisms…
In pattern-forming systems, competition between patterns with different wave numbers can lead to domain structures, which consist of regions with differing wave numbers separated by domain walls. For domain structures well above threshold…
We construct a Kitaev model, consisting of a Hamiltonian which is the sum of commuting local projectors, for surfaces with boundaries and defects of dimension 0 and 1. More specifically, we show that one can consider cell decompositions of…