The state space and physical interpretation of self-similar spherically symmetric perfect-fluid models

The purpose of this paper is to further investigate the solution space of self-similar spherically symmetric perfect-fluid models and gain deeper understanding of the physical aspects of these solutions. We achieve this by combining the state space description of the homothetic approach with the use of the physically interesting quantities arising in the comoving approach. We focus on three types of models. First, we consider models that are natural inhomogeneous generalizations of the Friedmann Universe; such models are asymptotically Friedmann in their past and evolve fluctuations in the energy density at later times. Second, we consider so-called quasi-static models. This class includes models that undergo self-similar gravitational collapse and is important for studying the formation of naked singularities. If naked singularities do form, they have profound implications for the predictability of general relativity as a theory. Third, we consider a new class of asymptotically Minkowski self-similar spacetimes, emphasizing that some of them are associated with the self-similar solutions associated with the critical behaviour observed in recent gravitational collapse calculations.Comment: 24 pages, 12 figure

Self-similar spherically symmetric cosmological models with a perfect fluid and a scalar field

Self-similar, spherically symmetric cosmological models with a perfect fluid and a scalar field with an exponential potential are investigated. New variables are defined which lead to a compact state space, and dynamical systems methods are utilised to analyse the models. Due to the existence of monotone functions global dynamical results can be deduced. In particular, all of the future and past attractors for these models are obtained and the global results are discussed. The essential physical results are that initially expanding models always evolve away from a massless scalar field model with an initial singularity and, depending on the parameters of the models, either recollapse to a second singularity or expand forever towards a flat power-law inflationary model. The special cases in which there is no barotropic fluid and in which the scalar field is massless are considered in more detail in order to illustrate the asymptotic results. Some phase portraits are presented and the intermediate dynamics and hence the physical properties of the models are discussed.Comment: 31 pages, 4 figure

Timelike self-similar spherically symmetric perfect-fluid models

Einstein's field equations for timelike self-similar spherically symmetric perfect-fluid models are investigated. The field equations are rewritten as a first-order system of autonomous differential equations. Dimensionless variables are chosen in such a way that the number of equations in the coupled system is reduced as far as possible and so that the reduced phase space becomes compact and regular. The system is subsequently analysed qualitatively using the theory of dynamical systems.Comment: 23 pages, 6 eps-figure

Closed cosmologies with a perfect fluid and a scalar field

Closed, spatially homogeneous cosmological models with a perfect fluid and a scalar field with exponential potential are investigated, using dynamical systems methods. First, we consider the closed Friedmann-Robertson-Walker models, discussing the global dynamics in detail. Next, we investigate Kantowski-Sachs models, for which the future and past attractors are determined. The global asymptotic behaviour of both the Friedmann-Robertson-Walker and the Kantowski-Sachs models is that they either expand from an initial singularity, reach a maximum expansion and thereafter recollapse to a final singularity (for all values of the potential parameter kappa), or else they expand forever towards a flat power-law inflationary solution (when kappa^2<2). As an illustration of the intermediate dynamical behaviour of the Kantowski-Sachs models, we examine the cases of no barotropic fluid, and of a massless scalar field in detail. We also briefly discuss Bianchi type IX models.Comment: 15 pages, 10 figure

A unified treatment of cubic invariants at fixed and arbitrary energy

Cubic invariants for two-dimensional Hamiltonian systems are investigated using the Jacobi geometrization procedure. This approach allows for a unified treatment of invariants at both fixed and arbitrary energy. In the geometric picture the invariant generally corresponds to a third rank Killing tensor, whose existence at a fixed energy value forces the metric to satisfy a nonlinear integrability condition expressed in terms of a Kahler potential. Further conditions, leading to a system of equations which is overdetermined except for singular cases, are added when the energy is arbitrary. As solutions to these equations we obtain several new superintegrable cases in addition to the previously known cases. We also discover a superintegrable case where the cubic invariant is of a new type which can be represented by an energy dependent linear invariant. A complete list of all known systems which admit a cubic invariant at arbitrary energy is given.Comment: 16 pages, LaTeX2e, slightly revised version. To appear in J. Math. Phys. vol 41, pp 370-384 (2000

Spatially self-similar spherically symmetric perfect-fluid models

Einstein's field equations for spatially self-similar spherically symmetric perfect-fluid models are investigated. The field equations are rewritten as a first-order system of autonomous differential equations. Dimensionless variables are chosen in such a way that the number of equations in the coupled system is reduced as far as possible and so that the reduced phase space becomes compact and regular. The system is subsequently analysed qualitatively with the theory of dynamical systems.Comment: 21 pages, 6 eps-figure

Observatory/data centre partnerships and the VO-centric archive: The JCMT Science Archive experience

We present, as a case study, a description of the partnership between an observatory (JCMT) and a data centre (CADC) that led to the development of the JCMT Science Archive (JSA). The JSA is a successful example of a service designed to use Virtual Observatory (VO) technologies from the start. We describe the motivation, process and lessons learned from this approach.Comment: Accepted for publication in the second Astronomy & Computing Special Issue on the Virtual Observatory; 10 pages, 5 figure

Venous bicarbonate and creatine kinase as diagnostic and prognostic tools in the setting of acute traumatic rhabdomyolysis

Background. Myorenal or crush syndrome often develops following soft-tissue traumatic injury. It is a spectrum of disease that may result in severe renal dysfunction and kidney injury requiring renal replacement therapy.Objectives. To review a large cohort of patients with so-called myorenal or crush syndrome and assess the biochemical markers of venous bicarbonate and creatine kinase as predictors for the development of acute kidney injury (AKI).Methods. All patients with myorenal syndrome who presented to Khayelitsha District Hospital, Cape Town, South Africa (SA), and Ngwelezana Hospital, Empangeni, KwaZulu-Natal, SA, between January and December 2017 were identified and reviewed.Results. A total of 212 patients were included in the study. At both hospitals, 94% of the patients were male. Using the Pearson correlation coefficient, we compared creatinine kinase (CK) against serum creatinine. The mean CK level was 5 311.8 U/L and the mean creatinine level 133.457 μmol/L. The r-value was 0.2533. Although this is a technically positive correlation, the relationship between the variables is weak. Using the Pearson R Calculator, we inserted the r-value to calculate the p-value. The p-value was 0.000208. When comparing venous bicarbonate (HCO3) against creatinine, the mean HCO3 level was 22.296 mmol/L and the mean creatinine level 162.053 μmol/L. The r-value was –0.3468. Although this is a technically negative correlation, the relationship between the variables is weak. Using the Pearson R Calculator, we inserted the r-value to calculate the p-value. The p-value was 0.000013. The inverse ratio shown with HCO3 v. creatinine, although still a weak correlation, is significantly better in predicting an increase in creatinine compared with the weak positive correlation of CK v. creatinine.Conclusions. Although both venous HCO3 and CK showed a weak correlation with creatinine, the former performed significantly better in predicting AKI. In a resource-constrained system, we recommend that HCO3 be measured to assess patients with crush injury and that CK be regarded as a complementary modality