Generalisation of the Einstein-Straus model to anisotropic settings

We study the possibility of generalising the Einstein--Straus model to anisotropic settings, by considering the matching of locally cylindrically symmetric static regions to the set of $G_4$ on $S_3$ locally rotationally symmetric (LRS) spacetimes. We show that such matchings preserving the symmetry are only possible for a restricted subset of the LRS models in which there is no evolution in one spacelike direction. These results are applied to spatially homogeneous (Bianchi) exteriors where the static part represents a finite bounded interior region without holes. We find that it is impossible to embed finite static strings or other locally cylindrically symmetric static objects (such as bottle or coin-shaped objects) in reasonable Bianchi cosmological models, irrespective of the matter content. Furthermore, we find that if the exterior spacetime is assumed to have a perfect fluid source satisfying the dominant energy condition, then only a very particular family of LRS stiff fluid solutions are compatible with this model. Finally, given the interior/exterior duality in the matching procedure, our results have the interesting consequence that the Oppenheimer-Snyder model of collapse cannot be generalised to such anisotropic cases.Comment: LaTeX, 24 pages. Text unchanged. Labels removed from the equations. Submitted for publicatio

The Hunt

The youth descended briskly the steep side of the gully. His two dogs, already at the bottom, trotted through the light snow. Their high noses and quickening steps were read by the young trapper as definite signs that a catch was to be expected. The trap he had set a day ago at a den on the side of the small tributary gully ahead probably held a victim. In any event, the set had looked good -- several fresh skunk tracks

Degradation of Toluene and Trichloroethylene by Burkholderia cepacia G4 in Growth-Limited Fed-Batch Culture

Burkholderia (Pseudomonas) cepacia G4 was cultivated in a fed-batch bioreactor on either toluene or toluene plus trichloroethylene (TCE). The culture was allowed to reach a constant cell density under conditions in which the amount of toluene supplied equals the maintenance energy demand of the culture. Compared with toluene only, the presence of TCE at a toluene/TCE ratio of 2.3 caused a fourfold increase in the specific maintenance requirement for toluene from 22 to 94 nmol mg of cells (dry weight)-1 h-1. During a period of 3 weeks, approximately 65% of the incoming TCE was stably converted to unidentified products from which all three chlorine atoms were liberated. When toluene was subsequently omitted from the culture feed while TCE addition continued, mutants which were no longer able to grow on toluene or to degrade TCE appeared. These mutants were also unable to grow on phenol or m- or o-cresol but were still able to grow on catechol and benzoate. Plasmid analysis showed that the mutants had lost the plasmid involved in toluene monooxygenase formation (pTOM). Thus, although strain G4 is much less sensitive to TCE toxicity than methanotrophs, deleterious effects may still occur, namely, an increased maintenance energy demand in the presence of toluene and plasmid loss when no toluene is added.

Singularity-Free Cylindrical Cosmological Model

A cylindrically symmetric perfect fluid spacetime with no curvature singularity is shown. The equation of state for the perfect fluid is that of a stiff fluid. The metric is diagonal and non-separable in comoving coordinates for the fluid. It is proven that the spacetime is geodesically complete and globally hyperbolic.Comment: LaTeX 2e, 8 page

A classification (uniqueness) theorem for rotating black holes in 4D Einstein-Maxwell-dilaton theory

In the present paper we prove a classification (uniqueness) theorem for stationary, asymptotically flat black hole spacetimes with connected and non-degenerate horizon in 4D Einstein-Maxwell-dilaton theory with an arbitrary dilaton coupling parameter $\alpha$. We show that such black holes are uniquely specified by the length of the horizon interval, angular momentum, electric and magnetic charge and the value of the dilaton field at infinity when the dilaton coupling parameter satisfies $0\le \alpha^2\le3$. The proof is based on the nonpositivity of the Riemann curvature operator on the space of the potentials. A generalization of the classification theorem for spacetimes with disconnected horizons is also given.Comment: 15 pages, v2 typos correcte

Influence of general convective motions on the exterior of isolated rotating bodies in equilibrium

The problem of describing isolated rotating bodies in equilibrium in General Relativity has so far been treated under the assumption of the circularity condition in the interior of the body. For a fluid without energy flux, this condition implies that the fluid flow moves only along the angular direction, i.e. there is no convection. Using this simplification, some recent studies have provided us with uniqueness and existence results for asymptotically flat vacuum exterior fields given the interior sources. Here, the generalisation of the problem to include general sources is studied. It is proven that the convective motions have no direct influence on the exterior field, and hence, that the aforementioned results on uniqueness and existence of exterior fields apply equally in the general case.Comment: 8 pages, LaTex, uses iopart style files. To appear in Class. Quatum Gra

Symmetry-preserving matchings

In the literature, the matchings between spacetimes have been most of the times implicitly assumed to preserve some of the symmetries of the problem involved. But no definition for this kind of matching was given until recently. Loosely speaking, the matching hypersurface is restricted to be tangent to the orbits of a desired local group of symmetries admitted at both sides of the matching and thus admitted by the whole matched spacetime. This general definition is shown to lead to conditions on the properties of the preserved groups. First, the algebraic type of the preserved group must be kept at both sides of the matching hypersurface. Secondly, the orthogonal transivity of two-dimensional conformal (in particular isometry) groups is shown to be preserved (in a way made precise below) on the matching hypersurface. This result has in particular direct implications on the studies of axially symmetric isolated bodies in equilibrium in General Relativity, by making up the first condition that determines the suitability of convective interiors to be matched to vacuum exteriors. The definition and most of the results presented in this paper do not depend on the dimension of the manifolds involved nor the signature of the metric, and their applicability to other situations and other higher dimensional theories is manifest.Comment: LaTeX, 19 page

The Wahlquist-Newman solution

Based on a geometrical property which holds both for the Kerr metric and for the Wahlquist metric we argue that the Kerr metric is a vacuum subcase of the Wahlquist perfect-fluid solution. The Kerr-Newman metric is a physically preferred charged generalization of the Kerr metric. We discuss which geometric property makes this metric so special and claim that a charged generalization of the Wahlquist metric satisfying a similar property should exist. This is the Wahlquist-Newman metric, which we present explicitly in this paper. This family of metrics has eight essential parameters and contains the Kerr-Newman-de Sitter and the Wahlquist metrics, as well as the whole Pleba\'nski limit of the rotating C-metric, as particular cases. We describe the basic geometric properties of the Wahlquist-Newman metric, including the electromagnetic field and its sources, the static limit of the family and the extension of the spacetime across the horizon.Comment: LaTeX, 18 pages, no figures. Accepted for publication in Phys. Rev.

Discrimination of Semi-Quantitative Models by Experiment Selection: Method and Application in Population Biology

Modeling an experimental system often results in a number of alternative models that are justified equally well by the experimental data. In order to discriminate between these models, additional experiments are needed. We present a method for the discrimination of models in the form of semiquantitative differential equations. The method is a generalization of previous work in model discrimination. It is based on an entropy criterion for the selection of the most informative experiment which can handle cases where the models predict multiple qualitative behaviors. The applicability of the method is demonstrated on a real-life example, the discrimination of a set of competing models of the growth of phytoplankton in a bioreactor

The effect of icepack cooling on skin and muscle temperature at rest and after exercise

Objective. To compare cooling of skin, subcutaneous fat and muscle, produced by an icepack, at rest and after short-duration exhaustive exercise. Methods. Eight male subjects were studied. With the subject supine, hypodermic needle-tip thermistors were inserted into the subcutaneous fat and the mid-portion of the left rectus femoris, to a depth of 1 cm plus the adipose thickness at the site, and a temperature probe was placed on the skin overlying the needle tips. A pack of crushed ice was applied for 15 minutes and temperatures were recorded before, during, and for 45 minutes after icepack application. Thereafter, subjects underwent a ramped, treadmill, VO2max test, an icepack was applied after temperature probes were inserted into the right leg and measurements were made as before. Results. After the treadmill run, skin (Sk), subcutaneous (SC) and muscle (Ms) temperatures (mean ± standard deviation (SD)) were 0.9 ± 1.3, 1.0 ± 0.7 and 1.3 ± 0.8°C higher than at rest. After 15 minutes of icepack cooling, temperatures fell in the exercised limb by 22.7 ± 1.5°C (Sk), 13.5 ± 4.2°C (SC) and 9.3 ± 5.5°C (Ms) and in the control limb by 20.7 ± 2.9°C (Sk), 11.4 ± 2.0°C (SC) and 8.7 ± 2.6°C (Ms). The reductions in temperature were significant in both the control and exercised limbs. Forty-five minutes after icepack cooling, muscle temperature was still approximately 5°C lower in both the rested and exercised muscle (p < 0.001). Individual variations in response to cooling were noted. Conclusions. Cooling of superficial muscle occurs after high-intensity exercise. The degree of cooling is not uniform. This may be due to differences in the sympathetic response to cooling, influencing haemodynamic and thermoregulatory changes after exercise. This needs further investigation. South African Journal of Sports Medicine Vol. 18 (3) 2006: pp. 60-6