Type O pure radiation metrics with a cosmological constant

In this paper we complete the integration of the conformally flat pure radiation spacetimes with a non-zero cosmological constant $\Lambda$, and $\tau \ne 0$, by considering the case $\Lambda +\tau\bar\tau \ne 0$. This is a further demonstration of the power and suitability of the generalised invariant formalism (GIF) for spacetimes where only one null direction is picked out by the Riemann tensor. For these spacetimes, the GIF picks out a second null direction, (from the second derivative of the Riemann tensor) and once this spinor has been identified the calculations are transferred to the simpler GHP formalism, where the tetrad and metric are determined. The whole class of conformally flat pure radiation spacetimes with a non-zero cosmological constant (those found in this paper, together with those found earlier for the case $\Lambda +\tau\bar\tau = 0$) have a rich variety of subclasses with zero, one, two, three, four or five Killing vectors

Obtaining a class of Type N pure radiation metrics using invariant operators

We develop further the integration procedure in the generalised invariant formalism, and demonstrate its efficiency by obtaining a class of Petrov type N pure radiation metrics without any explicit integration, and with comparatively little detailed calculations. The method is similar to the one exploited by Edgar and Vickers when deriving the general conformally flat pure radiation metric. A major addition to the technique is the introduction of non-intrinsic elements in generalised invariant formalism, which can be exploited to keep calculations manageable.Comment: This work was presented in July 2004, in the Gr17 meeting held in Dublin-Irelan

Invariant classification and the generalised invariant formalism: conformally flat pure radiation metrics, with zero cosmological constant

Metrics obtained by integrating within the generalised invariant formalism are structured around their intrinsic coordinates, and this considerably simplifies their invariant classification and symmetry analysis. We illustrate this by presenting a simple and transparent complete invariant classification of the conformally flat pure radiation metrics (except plane waves) in such intrinsic coordinates; in particular we confirm that the three apparently non-redundant functions of one variable are genuinely non-redundant, and easily identify the subclasses which admit a Killing and/or a homothetic Killing vector. Most of our results agree with the earlier classification carried out by Skea in the different Koutras-McIntosh coordinates, which required much more involved calculations; but there are some subtle differences. Therefore, we also rework the classification in the Koutras-McIntosh coordinates, and by paying attention to some of the subtleties involving arbitrary functions, we are able to obtain complete agreement with the results obtained in intrinsic coordinates. In particular, we have corrected and completed statements and results by Edgar and Vickers, and by Skea, about the orders of Cartan invariants at which particular information becomes available.Comment: Extended version of GRG publication, with some typos etc correcte

Well-Centered Triangulation

Meshes composed of well-centered simplices have nice orthogonal dual meshes (the dual Voronoi diagram). This is useful for certain numerical algorithms that prefer such primal-dual mesh pairs. We prove that well-centered meshes also have optimality properties and relationships to Delaunay and minmax angle triangulations. We present an iterative algorithm that seeks to transform a given triangulation in two or three dimensions into a well-centered one by minimizing a cost function and moving the interior vertices while keeping the mesh connectivity and boundary vertices fixed. The cost function is a direct result of a new characterization of well-centeredness in arbitrary dimensions that we present. Ours is the first optimization-based heuristic for well-centeredness, and the first one that applies in both two and three dimensions. We show the results of applying our algorithm to small and large two-dimensional meshes, some with a complex boundary, and obtain a well-centered tetrahedralization of the cube. We also show numerical evidence that our algorithm preserves gradation and that it improves the maximum and minimum angles of acute triangulations created by the best known previous method.Comment: Content has been added to experimental results section. Significant edits in introduction and in summary of current and previous results. Minor edits elsewher

Obtaining a class of Type O pure radiation metrics with a cosmological constant, using invariant operators

Using the generalised invariant formalism we derive a class of conformally flat spacetimes whose Ricci tensor has a pure radiation and a Ricci scalar component. The method used is a development of the methods used earlier for pure radiation spacetimes of Petrov types O and N respectively. In this paper we demonstrate how to handle, in the generalised invariant formalism, spacetimes with isotropy freedom and rich Killing vector structure. Once the spacetimes have been constructed, it is straightforward to deduce their Karlhede classification: the Karlhede algorithm terminates at the fourth derivative order, and the spacetimes all have one degree of null isotropy and three, four or five Killing vectors.Comment: 29 page

Optimal control algorithm design for a prototype of active noise control system

High-level noise can represent a serious risk for the health, industrial operations often represent continuous exposure to noise, thus an important trouble to handle. An alternative of solution can be the use of passive mechanisms of noise reductions, nonetheless its application cannot diminish low-frequency noise. Active Noise Control (ANC) is the solution used for low-frequency noise, ANC systems work according to the superposition principle generating a secondary anti-noise signal to reduce both. Nevertheless, the generation of an anti-noise signal with same oppose characteristics of the original noise signal presupposes the utilization of special techniques such as adaptive algorithms. These algorithms involve computational costs. The present research present the optimization of a specific ANC algorithm in the step-size criteria. Delayed Filtered-x LMS (FxLMS) algorithm using an optimal step-size is evaluated in a prototype of ANC system.Tesi

What do people do at work when they are not working?

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Management from the NOVA – School of Business and EconomicsThe objective of this work is to understand what kind of activities people develop at the workplace when they are not working and which are their work-related effects. The study of this subject was conducted through twenty interviews with people from different areas - tourism, banking, consulting, telecommunications, informatics, ambient, pharmaceutical, psychological, financial, and advocacy – that were not occupying leading positions inside their companies. The observed outcomes of these research show that people engage in a lot of different non-work related practices everyday that have diverse causes and consequences in their work life. The results reveal that in most of the cases, interruptions and breaks have a very positive impact on the work process and progress, increasing productivity and efficiency, improving the work rhythm and the most important thing – contributing for the solutions for wok-related problems and issues that cannot be resolved without a pause in the work. This means that the solution for some problems related to working issues, comes from the break that was done, this is, the revenue obtained is higher when there has been a pause than when there was not any interruption, as it is going to be explained further in this work