The Spectrum of Bogomol'nyi Solitons in Gauged Linear Sigma Models

Gauged linear sigma models with C^m-valued scalar fields and gauge group U(1)^d, d \leq m, have soliton solutions of Bogomol'nyi type if a suitably chosen potential for the scalar fields is also included in the Lagrangian. Here such models are studied on (2+1)-dimensional Minkowski space. If the dynamics of the gauge fields is governed by a Maxwell term the appropriate potential is a sum of generalised Higgs potentials known as Fayet-Iliopoulos D-terms. Many interesting topological solitons of Bogomol'nyi type arise in models of this kind, including various types of vortices (e.g. Nielsen-Olesen, semilocal and superconducting vortices) as well as, in certain limits, textures (e.g. CP^(m-1) textures and gauged CP^(m-1) textures). This is explained and general results about the spectrum of topological defects both for broken and partially broken gauge symmetry are proven. When the dynamics of the gauge fields is governed by a Chern-Simons term instead of a Maxwell term a different scalar potential is required for the theory to be of Bogomol'nyi type. The general form of that potential is given and a particular example is discussed.Comment: 32 pages, harvmac, no figure

Assessing texture pattern in slum across scales: an unsupervised approach

According to the Global Report on Human Settlements (United Nations, 2003), almost 1 billion people (32% of the world ’s population) live in squatter settlements or slums. Recently, the perception of these settlements has changed, from harmful tumours which would spread around sickly and unhealthy cities, to a new perspective that interpret them as social expressions of more complex urban dynamics. However, considering a report from UNCHS - United Nations Center for Human Settlements, in relation to illegal and disordered urbanisation issue, some of the main challenges faced by cities are related to mapping and registering geographic information and social data spatial analysis. In this context, we present, in this paper, preliminary results from a study that aims to interpret city from the perspective of urban texture, using for this purpose, high resolution remote sensing images. We have developed analytic experiments of "urban tissue" samples, trying to identify texture patterns which could (or could not) represent distinct levels of urban poverty associated to spatial patterns. Such analysis are based on some complex theory concepts and tools, such as fractal dimension and lacunarity. Preliminary results seems to suggest that the urban tissue is fractal by nature, and from the distinct texture patterns it is possible to relate social pattern to spatial configuration, making possible the development of methodologies and computational tools which could generate, via satellite, alternative and complementary mapping and classifications for urban poverty

"Real Places in Virtual Spaces"

Despite what might seem to be the case, "Virtual" reality can be used to create fully "real" places with their own grammar and norms, where real events take place

A Texture Bestiary

Textures are topologically nontrivial field configurations which can exist in a field theory in which a global symmetry group $G$ is broken to a subgroup $H$, if the third homotopy group \p3 of $G/H$ is nontrivial. We compute this group for a variety of choices of $G$ and $H$, revealing what symmetry breaking patterns can lead to texture. We also comment on the construction of texture configurations in the different models.Comment: 34 pages, plain Tex. (Minor corrections to an old paper.