Very Extended E8E_8 and A8A_8 at low levels, Gravity and Supergravity

We define a level for a large class of Lorentzian Kac-Moody algebras. Using this we find the representation content of very extended $A_{D-3}$ and $E_8$ (i.e. $E_{11}$) at low levels in terms of $A_{D-1}$ and $A_{10}$ representations respectively. The results are consistent with the conjectured very extended $A_8$ and $E_{11}$ symmetries of gravity and maximal supergravity theories given respectively in hep-th/0104081 and hep-th/0107209. We explain how these results provided further evidence for these conjectures.Comment: 16 pages, plain tex (equation 3.3 modified and one reference expanded

Estimation of Sea Ice Thickness Distributions through the Combination of Snow Depth and Satellite Laser Altimetry Data

Combinations of sea ice freeboard and snow depth measurements from satellite data have the potential to provide a means to derive global sea ice thickness values. However, large differences in spatial coverage and resolution between the measurements lead to uncertainties when combining the data. High resolution airborne laser altimeter retrievals of snow-ice freeboard and passive microwave retrievals of snow depth taken in March 2006 provide insight into the spatial variability of these quantities as well as optimal methods for combining high resolution satellite altimeter measurements with low resolution snow depth data. The aircraft measurements show a relationship between freeboard and snow depth for thin ice allowing the development of a method for estimating sea ice thickness from satellite laser altimetry data at their full spatial resolution. This method is used to estimate snow and ice thicknesses for the Arctic basin through the combination of freeboard data from ICESat, snow depth data over first-year ice from AMSR-E, and snow depth over multiyear ice from climatological data. Due to the non-linear dependence of heat flux on ice thickness, the impact on heat flux calculations when maintaining the full resolution of the ICESat data for ice thickness estimates is explored for typical winter conditions. Calculations of the basin-wide mean heat flux and ice growth rate using snow and ice thickness values at the 70 m spatial resolution of ICESat are found to be approximately one-third higher than those calculated from 25 km mean ice thickness values

Application of Discrete Differential Forms to Spherically Symmetric Systems in General Relativity

In this article we describe applications of Discrete Differential Forms in computational GR. In particular we consider the initial value problem in vacuum space-times that are spherically symmetric. The motivation to investigate this method is mainly its manifest coordinate independence. Three numerical schemes are introduced, the results of which are compared with the corresponding analytic solutions. The error of two schemes converges quadratically to zero. For one scheme the errors depend strongly on the initial data.Comment: 22 pages, 6 figures, accepted by Class. Quant. Gra

On certain quasi-local spin-angular momentum expressions for small spheres

The Ludvigsen-Vickers and two recently suggested quasi-local spin-angular momentum expressions, based on holomorphic and anti-holomorphic spinor fields, are calculated for small spheres of radius $r$ about a point $o$. It is shown that, apart from the sign in the case of anti-holomorphic spinors in non-vacuum, the leading terms of all these expressions coincide. In non-vacuum spacetimes this common leading term is of order $r^4$, and it is the product of the contraction of the energy-momentum tensor and an average of the approximate boost-rotation Killing vector that vanishes at $o$ and of the 3-volume of the ball of radius $r$. In vacuum spacetimes the leading term is of order $r^6$, and the factor of proportionality is the contraction of the Bel-Robinson tensor and an other average of the same approximate boost-rotation Killing vector.Comment: 16 pages, Plain Te

Currents and Superpotentials in classical gauge invariant theories I. Local results with applications to Perfect Fluids and General Relativity

E. Noether's general analysis of conservation laws has to be completed in a Lagrangian theory with local gauge invariance. Bulk charges are replaced by fluxes of superpotentials. Gauge invariant bulk charges may subsist when distinguished one-dimensional subgroups are present. As a first illustration we propose a new {\it Affine action} that reduces to General Relativity upon gauge fixing the dilatation (Weyl 1918 like) part of the connection and elimination of auxiliary fields. It allows a comparison of most gravity superpotentials and we discuss their selection by the choice of boundary conditions. A second and independent application is a geometrical reinterpretation of the convection of vorticity in barotropic nonviscous fluids. We identify the one-dimensional subgroups responsible for the bulk charges and thus propose an impulsive forcing for creating or destroying selectively helicity. This is an example of a new and general Forcing Rule.Comment: 64 pages, LaTeX. Version 2 has two more references and one misprint corrected. Accepted in Classical and Quantum Gravit

Covariance properties and regularization of conserved currents in tetrad gravity

We discuss the properties of the gravitational energy-momentum 3-form within the tetrad formulation of general relativity theory. We derive the covariance properties of the quantities describing the energy-momentum content under Lorentz transformations of the tetrad. As an application, we consider the computation of the total energy (mass) of some exact solutions of Einstein's general relativity theory which describe compact sources with asymptotically flat spacetime geometry. As it is known, depending on the choice of tetrad frame, the formal total integral for such configurations may diverge. We propose a natural regularization method which yields finite values for the total energy-momentum of the system and demonstrate how it works on a number of explicit examples.Comment: 36 pages, Revtex, no figures; small changes, published versio

3-dimensional Cauchy-Riemann structures and 2nd order ordinary differential equations

The equivalence problem for second order ODEs given modulo point transformations is solved in full analogy with the equivalence problem of nondegenerate 3-dimensional CR structures. This approach enables an analog of the Feffereman metrics to be defined. The conformal class of these (split signature) metrics is well defined by each point equivalence class of second order ODEs. Its conformal curvature is interpreted in terms of the basic point invariants of the corresponding class of ODEs

Interactive Effects of Climate Change with Nutrients, Mercury, and Freshwater Acidification on Key Taxa in the North Atlantic Landscape Conservation Cooperative Region

The North Atlantic Landscape Conservation Cooperative LCC (NA LCC) is a public-private partnership that provides information to support conservation decisions that may be affected by global climate change (GCC) and other threats. The NA LCC region extends from southeast Virginia to the Canadian Maritime Provinces. Within this region, the US National Climate Assessment documented increases in air temperature, total precipitation, frequency of heavy precipitation events, and rising sea level, and predicted more drastic changes. Here, we synthesize literature on the effects of GCC interacting with selected contaminant, nutrient, and environmental processes to adversely affect natural resources within this region. Using a case study approach, we focused on 3 stressors with sufficient NA LCC region-specific information for an informed discussion. We describe GCC interactions with a contaminant (Hg) and 2 complex environmental phenomena-freshwater acidification and eutrophication. We also prepared taxa case studies on GCC- and GCC-contaminant/nutrient/process effects on amphibians and freshwater mussels. Several avian species of high conservation concern have blood Hg concentrations that have been associated with reduced nesting success. Freshwater acidification has adversely affected terrestrial and aquatic ecosystems in the Adirondacks and other areas of the region that are slowly recovering due to decreased emissions of N and sulfur oxides. Eutrophication in many estuaries within the region is projected to increase from greater storm runoff and less denitrification in riparian wetlands. Estuarine hypoxia may be exacerbated by increased stratification. Elevated water temperature favors algal species that produce harmful algal blooms (HABs). In several of the region\u27s estuaries, HABs have been associated with bird die-offs. In the NA LCC region, amphibian populations appear to be declining. Some species may be adversely affected by GCC through higher temperatures and more frequent droughts. GCC may affect freshwater mussel populations via altered stream temperatures and increased sediment loading during heavy storms. Freshwater mussels are sensitive to un-ionized ammonia that more toxic at higher temperatures. We recommend studying the interactive effects of GCC on generation and bioavailability of methylmercury and how GCC-driven shifts in bird species distributions will affect avian exposure to methylmercury. Research is needed on how decreases in acid deposition concurrent with GCC will alter the structure and function of sensitive watersheds and surface waters. Studies are needed to determine how GCC will affect HABs and avian disease, and how more severe and extensive hypoxia will affect fish and shellfish populations. Regarding amphibians, we suggest research on 1) thermal tolerance and moisture requirements of species of concern, 2) effects of multiple stressors (temperature, desiccation, contaminants, nutrients), and 3) approaches to mitigate impacts of increased temperature and seasonal drought. We recommend studies to assess which mussel species and populations are vulnerable and which are resilient to rising stream temperatures, hydrological shifts, and ionic pollutants, all of which are influenced by GCC

Interactive Effects of Climate Change with Nutrients, Mercury, and Freshwater Acidification on Key Taxa in the North Atlantic Landscape Conservation Cooperative Region

The North Atlantic Landscape Conservation Cooperative LCC (NA LCC) is a public–private partnership that provides information to support conservation decisions that may be affected by global climate change (GCC) and other threats. The NA LCC region extends from southeast Virginia to the Canadian Maritime Provinces. Within this region, the US National Climate Assessment documented increases in air temperature, total precipitation, frequency of heavy precipitation events, and rising sea level, and predicted more drastic changes. Here, we synthesize literature on the effects of GCC interacting with selected contaminant, nutrient, and environmental processes to adversely affect natural resources within this region. Using a case study approach, we focused on 3 stressors with sufficient NA LCC regionspecific information for an informed discussion. We describe GCC interactions with a contaminant (Hg) and 2 complex environmental phenomena—freshwater acidification and eutrophication. We also prepared taxa case studies on GCCand GCC-contaminant/nutrient/process effects on amphibians and freshwater mussels. Several avian species of high conservation concern have blood Hg concentrations that have been associated with reduced nesting success. Freshwater acidification has adversely affected terrestrial and aquatic ecosystems in the Adirondacks and other areas of the region that are slowly recovering due to decreased emissions of N and sulfur oxides. Eutrophication in many estuaries within the region is projected to increase from greater storm runoff and less denitrification in riparian wetlands. Estuarine hypoxia may be exacerbated by increased stratification. Elevated water temperature favors algal species that produce harmful algal blooms (HABs). In several of the region\u27s estuaries, HABs have been associated with bird die-offs. In the NA LCC region, amphibian populations appear to be declining. Some species may be adversely affected by GCC through higher temperatures and more frequent droughts. GCC may affect freshwater mussel populations via altered stream temperatures and increased sediment loading during heavy storms. Freshwater mussels are sensitive to un-ionized ammonia that more toxic at higher temperatures. We recommend studying the interactive effects of GCC on generation and bioavailability of methylmercury and how GCC-driven shifts in bird species distributions will affect avian exposure to methylmercury. Research is needed on how decreases in acid deposition concurrent with GCC will alter the structure and function of sensitive watersheds and surface waters. Studies are needed to determine how GCC will affect HABs and avian disease, and how more severe and extensive hypoxia will affect fish and shellfish populations. Regarding amphibians, we suggest research on 1) thermal tolerance and moisture requirements of species of concern, 2) effects of multiple stressors (temperature, desiccation, contaminants, nutrients), and 3) approaches to mitigate impacts of increased temperature and seasonal drought. We recommend studies to assess which mussel species and populations are vulnerable and which are resilient to rising stream temperatures, hydrological shifts, and ionic pollutants, all of which are influenced by GCC