Pseudo-Riemannian VSI spaces

In this paper we consider pseudo-Riemannian spaces of arbitrary signature for which all of their polynomial curvature invariants vanish (VSI spaces). We discuss an algebraic classification of pseudo-Riemannian spaces in terms of the boost weight decomposition and define the ${\bf S}_i$- and ${\bf N}$-properties, and show that if the curvature tensors of the space possess the ${\bf N}$-property then it is a VSI space. We then use this result to construct a set of metrics that are VSI. All of the VSI spaces constructed possess a geodesic, expansion-free, shear-free, and twist-free null-congruence. We also discuss the related Walker metrics.Comment: 14 page

Higher dimensional VSI spacetimes

We present the explicit metric forms for higher dimensional vanishing scalar invariant (VSI) Lorentzian spacetimes. We note that all of the VSI spacetimes belong to the higher dimensional Kundt class. We determine all of the VSI spacetimes which admit a covariantly constant null vector, and we note that in general in higher dimensions these spacetimes are of Ricci type III and Weyl type III. The Ricci type N subclass is related to the chiral null models and includes the relativistic gyratons and the higher dimensional pp-wave spacetimes. The spacetimes under investigation are of particular interest since they are solutions of supergravity or superstring theory.Comment: 14 pages, changes in second paragraph of the discussio

The roots and routes of environmental and sustainability education policy research

Environmental Education Research has developed a Virtual Special Issue (VSI)(http://explore.tandfonline.com/content/ed/ceer-vsi) focusing on studies of environmental and sustainability education (ESE) policy. The VSI draws on key examples of research on this topic published in the Journal from the past two decades, for three reasons. First, to provide readers with a series of snapshots into the genealogy of ESE policy research in this field. Second, to encourage renewed attention to previously published work. And third, to offer commentary on the evolution of research trends, approaches and findings

A Generalized Index for Static Voltage Stability of Unbalanced Polyphase Power Systems including Th\'evenin Equivalents and Polynomial Models

This paper proposes a Voltage Stability Index (VSI) suitable for unbalanced polyphase power systems. To this end, the grid is represented by a polyphase multiport network model (i.e., compound hybrid parameters), and the aggregate behavior of the devices in each node by Th\'evenin Equivalents (TEs) and Polynomial Models (PMs), respectively. The proposed VSI is a generalization of the known L-index, which is achieved through the use of compound electrical parameters, and the incorporation of TEs and PMs into its formal definition. Notably, the proposed VSI can handle unbalanced polyphase power systems, explicitly accounts for voltage-dependent behavior (represented by PMs), and is computationally inexpensive. These features are valuable for the operation of both transmission and distribution systems. Specifically, the ability to handle the unbalanced polyphase case is of particular value for distribution systems. In this context, it is proven that the compound hybrid parameters required for the calculation of the VSI do exist under practical conditions (i.e., for lossy grids). The proposed VSI is validated against state-of-the-art methods for voltage stability assessment using a benchmark system which is based on the IEEE 34-node feeder

VSI: the VLTI spectro-imager

The VLTI Spectro Imager (VSI) was proposed as a second-generation instrument of the Very Large Telescope Interferometer providing the ESO community with spectrally-resolved, near-infrared images at angular resolutions down to 1.1 milliarcsecond and spectral resolutions up to R=12000. Targets as faint as K=13 will be imaged without requiring a brighter nearby reference object. The unique combination of high-dynamic-range imaging at high angular resolution and high spectral resolution enables a scientific program which serves a broad user community and at the same time provides the opportunity for breakthroughs in many areas of astrophysic including: probing the initial conditions for planet formation in the AU-scale environments of young stars; imaging convective cells and other phenomena on the surfaces of stars; mapping the chemical and physical environments of evolved stars, stellar remnants, and stellar winds; and disentangling the central regions of active galactic nuclei and supermassive black holes. VSI will provide these new capabilities using technologies which have been extensively tested in the past and VSI requires little in terms of new infrastructure on the VLTI. At the same time, VSI will be able to make maximum use of new infrastructure as it becomes available; for example, by combining 4, 6 and eventually 8 telescopes, enabling rapid imaging through the measurement of up to 28 visibilities in every wavelength channel within a few minutes. The current studies are focused on a 4-telescope version with an upgrade to a 6-telescope one. The instrument contains its own fringe tracker and tip-tilt control in order to reduce the constraints on the VLTI infrastructure and maximize the scientific return.Comment: 12 pages, to be published in Proc. SPIE conference 7013 "Optical and Infrared Interferometry", Schoeller, Danchi, and Delplancke, F. (eds.). See also http://vsi.obs.ujf-grenoble.f