Stability of Relative Equilibria in the Planar N-Vortex Problem

We study the linear and nonlinear stability of relative equilibria in the planar N-vortex problem, adapting the approach of Moeckel from the corresponding problem in celestial mechanics. After establishing some general theory, a topological approach is taken to show that for the case of positive circulations, a relative equilibrium is linearly stable if and only if it is a nondegenerate minimum of the Hamiltonian restricted to a level surface of the angular impulse (moment of inertia). Using a criterion of Dirichlet's, this implies that any linearly stable relative equilibrium with positive vorticities is also nonlinearly stable. Two symmetric families, the rhombus and the isosceles trapezoid, are analyzed in detail, with stable solutions found in each case.Comment: 23 pages, 3 figure

On the Anisotropic Nature of MRI-Driven Turbulence in Astrophysical Disks

The magnetorotational instability is thought to play an important role in enabling accretion in sufficiently ionized astrophysical disks. The rate at which MRI-driven turbulence transports angular momentum is related to both the strength of the amplitudes of the fluctuations on various scales and the degree of anisotropy of the underlying turbulence. This has motivated several studies of the distribution of turbulent power in spectral space. In this paper, we investigate the anisotropic nature of MRI-driven turbulence using a pseudo-spectral code and introduce novel ways to robustly characterize the underlying turbulence. We show that the general flow properties vary in a quasi-periodic way on timescales comparable to 10 inverse angular frequencies motivating the temporal analysis of its anisotropy. We introduce a 3D tensor invariant analysis to quantify and classify the evolution of the anisotropic turbulent flow. This analysis shows a continuous high level of anisotropy, with brief sporadic transitions towards two- and three-component isotropic turbulent flow. This temporal-dependent anisotropy renders standard shell-average, especially when used simultaneously with long temporal averages, inadequate for characterizing MRI-driven turbulence. We propose an alternative way to extract spectral information from the turbulent magnetized flow, whose anisotropic character depends strongly on time. This consists of stacking 1D Fourier spectra along three orthogonal directions that exhibit maximum anisotropy in Fourier space. The resulting averaged spectra show that the power along each of the three independent directions differs by several orders of magnitude over most scales, except the largest ones. Our results suggest that a first-principles theory to describe fully developed MRI-driven turbulence will likely have to consider the anisotropic nature of the flow at a fundamental level.Comment: 13 pages, 13 figures, submitted to Ap

An investigation to establish whether property maintenance can diminish the number of empty commercial buildings in Sheffield and Leeds

Property maintenance has long been considered an undesirable and overlooked area amongst the construction and property industries; however, a large proportion of construction output comes from such maintenance works. Empty commercial property is an emotive and challenging area, which has been made more topical due to the implementation of the Rating (Empty Property) Act 2007 placing further financial liability on owners with the aim of „incentivising‟ them either to develop, re-let or sell their vacant buildings. As such, the level of property maintenance is important to allow the building to be at a lettable or saleable standard, which in turn should allow the number of unused commercial buildings in the United Kingdom (UK) to reduce. A mixture of primary and secondary sources were utilised to fulfil this research to determine whether incentives exist or can exist to increase the level of property maintenance to diminish the number of vacant commercial buildings in Leeds and Sheffield. The primary data was based on six case studies, four example cases in point and two interviews. Ratings were assigned according to factors and incentives to analyse the data to assist in the findings of this research. This change in Government policy is causing outrage amongst UK businesses and professional bodies of the property industry, in extreme cases leading to the demolition of the building to avoid liability and other detrimental consequences, such as staff reductions to make up for the liability. It has come also alongside the worst recession of recent times

Local quantum critical point in the pseudogap Anderson model: finite-T dynamics and omega/T scaling

The pseudogap Anderson impurity model is a paradigm for locally critical quantum phase transitions. Within the framework of the local moment approach we study its finite-T dynamics, as embodied in the single-particle spectrum, in the vicinity of the symmetric quantum critical point (QCP) separating generalized Fermi-liquid (Kondo screened) and local moment phases. The scaling spectra in both phases, and at the QCP itself, are obtained analytically. A key result is that pure omega/T-scaling obtains at the QCP, where the Kondo resonance has just collapsed. The connection between the scaling spectra in either phase and that at the QCP is explored in detail.Comment: 12 pages, 7 figure

A study into annotation ranking metrics in geo-tagged image corpora

Community contributed datasets are becoming increasingly common in automated image annotation systems. One important issue with community image data is that there is no guarantee that the associated metadata is relevant. A method is required that can accurately rank the semantic relevance of community annotations. This should enable the extracting of relevant subsets from potentially noisy collections of these annotations. Having relevant, non heterogeneous tags assigned to images should improve community image retrieval systems, such as Flickr, which are based on text retrieval methods. In the literature, the current state of the art approach to ranking the semantic relevance of Flickr tags is based on the widely used tf-idf metric. In the case of datasets containing landmark images, however, this metric is inefficient due to the high frequency of common landmark tags within the data set and can be improved upon. In this paper, we present a landmark recognition framework, that provides end-to-end automated recognition and annotation. In our study into automated annotation, we evaluate 5 alternate approaches to tf-idf to rank tag relevance in community contributed landmark image corpora. We carry out a thorough evaluation of each of these ranking metrics and results of this evaluation demonstrate that four of these proposed techniques outperform the current commonly-used tf-idf approach for this task

DCU linking runs at MediaEval 2012: search and hyperlinking task

We describe Dublin City University (DCU)'s participation in the Hyperlinking sub-task of the MediaEval 2012 Search and Hyperlinking Task. Our strategy involves combining textual metadata, automatic speech recognition (ASR) transcripts, and visual content analysis to create anchor summaries for each video segment available for linking. Two categories of fusion strategy, score-based and rank-based methods, were used to combine scores from different modalities to produce potential inter-item links