An ADM 3+1 formulation for Smooth Lattice General Relativity

A new hybrid scheme for numerical relativity will be presented. The scheme will employ a 3-dimensional spacelike lattice to record the 3-metric while using the standard 3+1 ADM equations to evolve the lattice. Each time step will involve three basic steps. First, the coordinate quantities such as the Riemann and extrinsic curvatures are extracted from the lattice. Second, the 3+1 ADM equations are used to evolve the coordinate data, and finally, the coordinate data is used to update the scalar data on the lattice (such as the leg lengths). The scheme will be presented only for the case of vacuum spacetime though there is no reason why it could not be extended to non-vacuum spacetimes. The scheme allows any choice for the lapse function and shift vectors. An example for the Kasner $T^3$ cosmology will be presented and it will be shown that the method has, for this simple example, zero discretisation error.Comment: 18 pages, plain TeX, 5 epsf figues, gzipped ps file also available at http://newton.maths.monash.edu.au:8000/preprints/3+1-slgr.ps.g

\u3cem\u3eRhizobium leguminosarum\u3c/em\u3e CFN42 Lipopolysaccharide Antigenic Changes Induced by Environmental Conditions

Four monoclonal antibodies were raised against the lipopolysaccharide of Rhizobium leguminosarum bv. phaseoli CFN42 grown in tryptone and yeast extract. Two of these antibodies reacted relatively weakly with the lipopolysaccharide of bacteroids of this strain isolated from bean nodules. Growth ex planta of strain CFN42 at low pH, high temperature, low phosphate, or low oxygen concentration also eliminated binding of one or both of these antibodies. Lipopolysaccharide mobility on gel electrophoresis and reaction with other monoclonal antibodies and polyclonal antiserum indicated that the antigenic changes detected by these two antibodies did not represent major changes in lipopolysaccharide structure. The antigenic changes at low pH were dependent on growth of the bacteria but were independent of nitrogen and carbon sources and the rich or minimal quality of the medium. The Sym plasmid of this strain was not required for the changes induced ex planta. Analysis of bacterial mutants inferred to have truncated O-polysaccharides indicated that part, but not all, of the lipopolysaccharide O-polysaccharide portion was required for binding of these two antibodies. In addition, this analysis suggested that O-polysaccharide structures more distal to lipid A than the epitopes themselves were required for the modifications at low pH that prevented antibody binding. Two mutants were antigenically abnormal, even though they had abundant lipopolysaccharides of apparently normal size. One of these two mutants was constitutively unreactive toward three of the antibodies but indistinguishable from the wild type in symbiotic behavior. The other, whose bacteroids retained an epitope normally greatly diminished in bacteroids, was somewhat impaired in nodulation frequency and nodule development

Fast algorithms for computing defects and their derivatives in the Regge calculus

Any practical attempt to solve the Regge equations, these being a large system of non-linear algebraic equations, will almost certainly employ a Newton-Raphson like scheme. In such cases it is essential that efficient algorithms be used when computing the defect angles and their derivatives with respect to the leg-lengths. The purpose of this paper is to present details of such an algorithm.Comment: 38 pages, 10 figure

Is the Regge Calculus a consistent approximation to General Relativity?

We will ask the question of whether or not the Regge calculus (and two related simplicial formulations) is a consistent approximation to General Relativity. Our criteria will be based on the behaviour of residual errors in the discrete equations when evaluated on solutions of the Einstein equations. We will show that for generic simplicial lattices the residual errors can not be used to distinguish metrics which are solutions of Einstein's equations from those that are not. We will conclude that either the Regge calculus is an inconsistent approximation to General Relativity or that it is incorrect to use residual errors in the discrete equations as a criteria to judge the discrete equations.Comment: 27 pages, plain TeX, very belated update to match journal articl

A simple expression for the ADM mass

We show by an almost elementary calculation that the ADM mass of an asymptotically flat space can be computed as a limit involving a rate of change of area of a closed 2-surface. The result is essentially the same as that given by Brown and York. We will prove this result in two ways, first by direct calculation from the original formula as given by Arnowitt, Deser and Misner and second as a corollary of an earlier result by Brewin for the case of simplicial spaces.Comment: 9 pages, 1 figur

Long term stable integration of a maximally sliced Schwarzschild black hole using a smooth lattice method

We will present results of a numerical integration of a maximally sliced Schwarzschild black hole using a smooth lattice method. The results show no signs of any instability forming during the evolutions to t=1000m. The principle features of our method are i) the use of a lattice to record the geometry, ii) the use of local Riemann normal coordinates to apply the 1+1 ADM equations to the lattice and iii) the use of the Bianchi identities to assist in the computation of the curvatures. No other special techniques are used. The evolution is unconstrained and the ADM equations are used in their standard form.Comment: 47 pages including 26 figures, plain TeX, also available at http://www.maths.monash.edu.au/~leo/preprint

DETECTING PHYTOPLANKTON SIZE CLASS USING SATELLITE EARTH OBSERVATION

A new range of multi-plankton biogeochemical models have recently been developed, designed to advance our understanding of the ocean carbon cycle to improve predictions of its future influence on climate. Synoptic measurements of the different phytoplankton communities are required to validate and ultimately improve such models. Measuring ocean colour from satellite is the only method currently available for synoptically monitoring wide-area properties of ocean ecosystems, such as phytoplankton chlorophyll biomass. Recently, a variety of bio-optical methods have been established that use satellite data to identify and differentiate between either phytoplankton functional types (PFTs) or phytoplankton size classes (PSCs). In this thesis, several of these techniques were evaluated against in situ observations (6504 samples) to determine their ability to detect dominant phytoplankton size classes (micro-, nano- and picoplankton). Results show that spectral-response, ecological and abundance-based approaches can all perform with similar accuracy. However, abundance-based approaches provide better spatial retrieval of PSCs. Based on insights into the abundance-based models, and by utilising a large pigment database, a new three-component model was developed which calculates the fractional contributions of three phytoplankton size classes (micro-, nano- and picoplankton) to the overall chlorophyll-a concentration. Using a globally representative, independent, coupled pigment and satellite dataset the model estimates fractional contributions with a mean accuracy of 9.2 % for microplankton, 17.1 % for nanoplankton and 16.1 % for picoplankton. The effect of optical depth on the model parameters was also investigated and explicitly incorporated into the model. Using the three-component model, the two-component absorption model of Sathyendranath et al. (2001) and Devred et al. (2006) was extended to three-component populations of phytoplankton, namely, pico-, nano- and microplankton. The new model infers total and size-dependent phytoplankton absorption as a function of the total chlorophyll-a concentration. A main characteristic of the model is that all the parameters that describe it have biological or optical interpretation. The three-component model performs better than the two-component model, at retrieving total phytoplankton absorption. Accounting for the contribution of pico- and nanoplankton, rather than the combination of both used in the two-component model, improved significantly the retrieval of phytoplankton absorption at low chlorophyll-a concentrations. The three-component model was applied to a decade of ocean colour observations. In the equatorial region of the Pacific and Indian Oceans, phytoplankton size class anomalies (% total chlorophyll-a) were highly correlated with indices of both the El Niño (La Niña) Southern Oscillation and the Indian Ocean Dipole. Furthermore, in these regions, micro- and nanoplankton size class anomalies were negatively correlated with anomalies of the sea surface temperature, sea surface height and stratification. Whereas, the picoplankton size class anomalies were positively correlated with these physical variables. Results from this thesis indicate that phytoplankton size class can be retrieved from Earth Observation with reasonable accuracy. It is recommended that such information can now be assimilated into multi-plankton biogeochemical models, or alternatively, verify them.NER

Enhancement of primary production in the North Atlantic outside of the spring bloom, identified by remote sensing of ocean colour and temperature

Peer reviewedPublisher PD

Regge Calculus as a Fourth Order Method in Numerical Relativity

The convergence properties of numerical Regge calculus as an approximation to continuum vacuum General Relativity is studied, both analytically and numerically. The Regge equations are evaluated on continuum spacetimes by assigning squared geodesic distances in the continuum manifold to the squared edge lengths in the simplicial manifold. It is found analytically that, individually, the Regge equations converge to zero as the second power of the lattice spacing, but that an average over local Regge equations converges to zero as (at the very least) the third power of the lattice spacing. Numerical studies using analytic solutions to the Einstein equations show that these averages actually converge to zero as the fourth power of the lattice spacing.Comment: 14 pages, LaTeX, 8 figures mailed in separate file or email author directl