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

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

Twistor geometry of a pair of second order ODEs

We discuss the twistor correspondence between path geometries in three dimensions with vanishing Wilczynski invariants and anti-self-dual conformal structures of signature $(2, 2)$. We show how to reconstruct a system of ODEs with vanishing invariants for a given conformal structure, highlighting the Ricci-flat case in particular. Using this framework, we give a new derivation of the Wilczynski invariants for a system of ODEs whose solution space is endowed with a conformal structure. We explain how to reconstruct the conformal structure directly from the integral curves, and present new examples of systems of ODEs with point symmetry algebra of dimension four and greater which give rise to anti--self--dual structures with conformal symmetry algebra of the same dimension. Some of these examples are $(2, 2)$ analogues of plane wave space--times in General Relativity. Finally we discuss a variational principle for twistor curves arising from the Finsler structures with scalar flag curvature.Comment: Final version to appear in the Communications in Mathematical Physics. The procedure of recovering a system of torsion-fee ODEs from the heavenly equation has been clarified. The proof of Prop 7.1 has been expanded. Dedicated to Mike Eastwood on the occasion of his 60th birthda

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

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

Acoustic risk balancing by marine mammals : anthropogenic noise can influence the foraging decisions by seals

Funding: Natural Environment Research Council (Grant Number(s): NE/J004251/1, NE/R015007/1)1. Avoidance of anthropogenic sounds has been measured in many species. The results, which are typically based on observations in limited exposure contexts, are frequently used to inform policy and the regulation of industrial activities. However, the occurrence and magnitude of avoidance may be a consequence of complex risk-balancing decisions made by animals. The importance of the factors in decision-making, such as perceived risks associated with the sounds or prey quantity and quality during sound exposure, is unknown. 2. Here we address this knowledge gap by measuring the relative influence of perceived –risk of a sound (silence, pile driving, and a tidal turbine) and prey patch quality on decision-making and foraging success in grey seals Halichoerus grypus. 3. Seals were given access to two underwater ‘prey patches’ in an experimental pool where fish were delivered at controlled rates to simulate a low-density (LD) and a high-density (HD) prey patch. Acoustic playbacks were made using an underwater speaker above one of the prey patches (randomised during the study), and three decision and foraging metrics (foraging duration, foraging effort allocation between the prey patches, and foraging success) were measured. 4. Foraging success was highest during silent controls and was similar regardless of speaker location (LD/HD). Under the tidal turbine and pile-driving treatments, foraging success was similar to the controls when the speaker was located at the HD prey patch but was significantly reduced (~16%–28% lower) when the speaker was located at the LD prey patch. Foraging decisions by the seals were consistent with a risk/profit balancing approach. Avoidance rates depend on the quality of the prey patch as well as the perceived risk. 5. Policy implications. The results suggest that foraging context is important when interpreting avoidance behaviour and should be considered when predicting the effects of anthropogenic activities. For example, sound exposure in different prey patch qualities may result in markedly different avoidance behaviour, potentially leading to contrasting predictions of impact in Environmental Assessments. We recommend future studies explicitly consider foraging context, and other contextual factors such as behavioural state (e.g. foraging or travelling) and habitat quality.Publisher PDFPeer reviewe

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

Photosynthetic adaptation and acclimation to exploit seasonal periods of direct irradiance in three temperate, deciduous-forest herbs

1.  We evaluated the potential for three species of deciduous-forest herbs to exploit seasonal periods of direct irradiance. In particular, we investigated the importance of photosynthetic acclimation as a mechanism for shade-tolerant herbs to utilize direct light reaching the forest floor before canopy expansion in the spring and after canopy leaf drop in the autumn. 2.  We measured the photosynthetic and growth characteristics of three co-occurring herbs of a northern hardwood forest: the spring ephemeral Allium tricoccum Ait., the summer-green Viola pubescens Ait., and the semi-evergreen Tiarella cordifolia L. 3.  Leaf CO 2 exchange, leaf mass per area, and leaf biochemistry differed among species and seasonally within species to match the changing light environment below the forest canopy. From spring to summer, as irradiance dropped with the expansion of the overstorey canopy, Viola leaves exhibited reduction of both photosynthetic capacity and light compensation point. Weaker acclimation of less magnitude occurred in Tiarella leaves over the spring–summer light transition; this was followed by further acclimation to the stronger autumn irradiance. 4.   Viola ’s greater range of photosynthetic acclimation was associated with shifts in allocation between Rubisco and chlorophyll, as well as changes in total leaf nitrogen (N) concentration and leaf mass per area (LMA). In contrast, Tiarella ’s narrow range of acclimation was associated solely with changes in allocation to Rubisco versus chlorophyll, with no changes in total leaf N or LMA. 5.  Seasonal changes in leaf chemistry and structure in Viola suggest a stepwise ontogeny whereby individual leaves are able to function as ‘sun leaves’ for 3–5 weeks in the spring, and then as ‘shade leaves’ for up to 3 months in the summer. 6.  Whole-plant biomass accumulation showed that all three species accumulated most of their annual biomass increment during periods of direct irradiance. These results demonstrate the importance of brief seasonal periods of strong irradiance to the growth of deciduous forest herbs, even shade-tolerant, summer and evergreen species.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75494/1/j.0269-8463.2001.00584.x.pd

Tropospheric Carbon Monoxide Measurements from the Scanning High-Resolution Interferometer Sounder on 7 September 2000 in Southern Africa During SAFARI 2000

[1] Retrieved tropospheric carbon monoxide (CO) column densities are presented for more than 9000 spectra obtained by the University of Wisconsin-Madison (UWis) Scanning High-Resolution Interferometer Sounder (SHIS) during a flight on the NASA ER-2 on 7 September 2000 as part of the Southern African Regional Science Initiative (SAFARI 2000) dry season field campaign. Enhancements in tropospheric column CO were detected in the vicinity of a controlled biomass burn in the Timbavati Game Reserve in northeastern South Africa and over the edge of the river of smoke in south central Mozambique. Relatively clean air was observed over the far southern coast of Mozambique. Quantitative comparisons are presented with in situ measurements from five different instruments flying on two other aircraft: the University of Washington Convair-580 (CV) and the South African Aerocommander JRB in the vicinity of the Timbavati fire. Measured tropospheric CO columns (extrapolated from 337 to 100 mb) of 2.1 × 1018 cm−2 in background air and up to 1.5 × 1019 cm−2 in the smoke plume agree well with SHIS retrieved tropospheric CO columns of (2.3 ± 0.25) × 1018 cm−2 over background air near the fire and (1.5 ± 0.35) × 1019 cm−2 over the smoke plume. Qualitative comparisons are presented with three other in situ CO profiles obtained by the South African JRA aircraft over Mozambique and northern South Africa showing the influence of the river of smoke

Beyond altruism: British football and charity, 1877-1914

Football charity matches and tournaments played a significant part in the development of the sport in Britain, overlapping the era of friendly games and the advent of competitive leagues. The football community prided itself on its contributions to charity, raising more money than any other sport before 1914, and stakeholders within the game – associations, clubs, players and patrons – gained considerable kudos for this perceived altruism. However, this paper will demonstrate that amounts donated, though welcome, were relatively minor sources of revenue for both institutions and individuals, and that the charity match became less important to clubs in a professional, and increasingly commercial, era