Variational description of multi-fluid hydrodynamics: Uncharged fluids

We present a formalism for Newtonian multi-fluid hydrodynamics derived from an unconstrained variational principle. This approach provides a natural way of obtaining the general equations of motion for a wide range of hydrodynamic systems containing an arbitrary number of interacting fluids and superfluids. In addition to spatial variations we use ``time shifts'' in the variational principle, which allows us to describe dissipative processes with entropy creation, such as chemical reactions, friction or the effects of external non-conservative forces. The resulting framework incorporates the generalization of the entrainment effect originally discussed in the case of the mixture of two superfluids by Andreev and Bashkin. In addition to the conservation of energy and momentum, we derive the generalized conservation laws of vorticity and helicity, and the special case of Ertel's theorem for the single perfect fluid. We explicitly discuss the application of this framework to thermally conducting fluids, superfluids, and superfluid neutron star matter. The equations governing thermally conducting fluids are found to be more general than the standard description, as the effect of entrainment usually seems to be overlooked in this context. In the case of superfluid He4 we recover the Landau--Khalatnikov equations of the two-fluid model via a translation to the ``orthodox'' framework of superfluidity, which is based on a rather awkward choice of variables. Our two-fluid model for superfluid neutron star matter allows for dissipation via mutual friction and also ``transfusion'' via beta-reactions between the neutron fluid and the proton-electron fluid.Comment: uses RevTeX 4; 20 pages. To appear in PRD. v2: removed discussion of charged fluids and coupling to electromagnetic fields, which are submitted as a separate paper for a clearer presentation v3: fixed typo in Eq.(9), updated some reference

Betamethasone phosphate reduces the efficacy of antenatal steroid therapy and is associated with lower birth weights when administered to pregnant sheep in combination with betamethasone acetate

Background Antenatal corticosteroid (ACS) therapy is standard of care for women at imminent risk of preterm labour. Despite this, much remains to be understood regarding an optimal (maximum benefit, minimal risk of side effects) ACS dosing strategy. Although conveying overall benefit when given to the right patient at the right time, ACS treatment efficacy is highly variable, and is not risk-free. Building on earlier findings, we hypothesized that when administered in combination with slow-release betamethasone acetate, betamethasone phosphate and the high materno-fetal betamethasone concentrations it generates are redundant for fetal lung maturation. Objective Using an established sheep model of prematurity and post-natal ventilation of the preterm lamb, we aimed to compare the pharmacodynamic effects of a low-dose treatment with betamethasone acetate only against a standard dose of betamethasone phosphate and betamethasone acetate as recommended by the American College of Obstetricians and Gynaecologists for women at risk of imminent preterm delivery between 24 and 35+6 weeks’ gestation. Methods Ewes carrying a single fetus at 122±1 d gestational age (term=150d) were randomized to receive either: i) maternal intramuscular injections of sterile saline (the Saline Negative Control Group, n=12), ii) two maternal intramuscular injections of 0.25 mg/kg betamethasone phosphate + acetate spaced by 24h (the Beta-P+Ac Group, n=12); or iii) two maternal intramuscular injections of 0.125 mg/kg betamethasone acetate spaced by 24h (the Beta-Ac Group, n=11). Fetuses were surgically delivered 48h after treatment initiation and ventilated for 30 minutes to determine functional lung maturation. Fetuses were euthanized after ventilation and lung were collected for analysis using quantitative polymerase chain reaction and western blot assays. Fetal plasma ACTH levels were measured in the cord blood samples taken at delivery. Results Preterm lambs were defined as either ACS treatment responders or non-responders using an arbitrary cut-off, being a PaCO2 level at 30 minutes of ventilation being more extreme than two standard deviations from the mean value of the normally-distributed Saline Control Group values. Relative to Saline Control Group animals, both ACS treatment group animals showed significantly improved lung physiological responses (blood gas and ventilation data) and had a biochemical signature (mRNA and surfactant protein assays) consistent with functional maturation. However, the Beta-Ac Group had a significantly higher treatment response rate than the Beta-P+Ac Group. These physiological results were strongly correlated to the amount of surfactant protein A. Birth weight was lower in Beta-P+Ac Group and the fetal HPA axis was supressed to a greater extent in the Beta-P+Ac Group. Conclusion Low dose ACS therapy solely employing Beta-Ac was sufficient for fetal lung maturation. The elevated materno-fetal betamethasone concentrations associated with the co-administration of betamethasone phosphate did not additionally improve lung maturation, but were associated with greater HPA axis suppression, a lower ACS treatment response rate, and lower birth weight – outcomes not desirable in a clinical setting. These data warrant a clinical investigation of sustained, low-dose ACS treatments that avoid high materno-fetal betamethasone exposures

Empty singularities in higher-dimensional Gravity

We study the exact solution of Einstein's field equations consisting of a ($n+2$)-dimensional static and hyperplane symmetric thick slice of matter, with constant and positive energy density $\rho$ and thickness $d$, surrounded by two different vacua. We explicitly write down the pressure and the external gravitational fields in terms of $\rho$ and $d$, the pressure is positive and bounded, presenting a maximum at an asymmetrical position. And if $\sqrt{\rho}\,d$ is small enough, the dominant energy condition is satisfied all over the spacetime. We find that this solution presents many interesting features. In particular, it has an empty singular boundary in one of the vacua.Comment: 13 page

Back reaction in the formation of a straight cosmic string

A simple model for the formation of a straight cosmic string, wiggly or unperturbed is considered. The gravitational field of such string is computed in the linear approximation. The vacuum expectation value of the stress tensor of a massless scalar quantum field coupled to the string gravitational field is computed to the one loop order. Finally, the back-reaction effect on the gravitational field of the string is obtained by solving perturbatively the semiclassical Einstein's equations.Comment: 29 pages, LaTeX, no figures. A postcript version can be obtained from anonymous ftp at ftp://ftp.ifae.es/preprint.f

Gravitational Collapse of Phantom Fluid in (2+1)-Dimensions

This investigation is devoted to the solutions of Einstein's field equations for a circularly symmetric anisotropic fluid, with kinematic self-similarity of the first kind, in $(2+1)$-dimensional spacetimes. In the case where the radial pressure vanishes, we show that there exists a solution of the equations that represents the gravitational collapse of an anisotropic fluid, and this collapse will eventually form a black hole, even when it is constituted by the phantom energy.Comment: 10 page

Relativistic superfluid models for rotating neutron stars

This article starts by providing an introductory overview of the theoretical mechanics of rotating neutron stars as developped to account for the frequency variations, and particularly the discontinuous glitches, observed in pulsars. The theory suggests, and the observations seem to confirm, that an essential role is played by the interaction between the solid crust and inner layers whose superfluid nature allows them to rotate independently. However many significant details remain to be clarified, even in much studied cases such as the Crab and Vela. The second part of this article is more technical, concentrating on just one of the many physical aspects that needs further development, namely the provision of a satisfactorily relativistic (local but not microscopic) treatment of the effects of the neutron superfluidity that is involved.Comment: 42 pages LateX. Contribution to Physics of Neutron Star Interiors, ed. D. Blasche, N.K. Glendenning, A. Sedrakian (ECT workshop, Trento, June 2000

Rotating metrics admitting non-perfect fluids in General Relativity

In this paper, by applying Newman-Janis algorithm in spherical symmetric metrics, a class of embedded rotating solutions of field equations is presented. These solutions admit non-perfect fluidsComment: LaTex, 39 page

Variability in the efficacy of a standardized antenatal steroid treatment is not due to maternal or fetal plasma drug levels. Evidence from a sheep model of pregnancy.

Background Antenatal steroids (ANS) are standard of care for women judged to be at imminent risk of preterm delivery. Worldwide, there is significant variation in ANS dosing strategy, selection for treatment criteria, and agent choice. This, combined with very limited optimization of ANS use per se means that treatment efficacy is highly variable and the rate of respiratory distress syndrome is decreased perhaps as little as 40%. In some cases, ANS use is associated with limited benefit and potential harm. Objective We hypothesized that individual differences in maternal and fetal steroid exposure would contribute to observed variability in ANS treatment efficacy. Using a chronically catheterized sheep model of pregnancy, we aimed to explore the relationship between materno-fetal steroid exposure and ANS treatment efficacy as determined by functional lung maturation in preterm lambs undergoing ventilation. Methods Ewes carrying a single fetus had surgery to catheterize a fetal and maternal jugular vein at 119 days’ gestation. Animals recovered for 24h before being randomized to either: i) a single maternal intramuscular injection (IM) of 2ml saline (Negative Control Group, n=10); or ii) a single maternal IM of 0.25mg/kg betamethasone phosphate + acetate (ANS Group, n=20). Serial maternal and fetal plasma samples were collected from each animal over 48h before fetuses were delivered and ventilated for 30 minutes. Total and free plasma betamethasone concentration was measured by mass spectrometry. Fetal lung tissue was collected for analysis using quantitative polymerase chain reaction. Results One animal of the Control Group and one animal from the ANS Group had did not complete their treatment protocol and were removed from analyses. Animals in the ANS Group were divided into a Responder (n=12/19) Sub-Group and a Non-Responder Sub-Group (n=7/19) using a cut-off of a PaCO2 at 30 minutes ventilation within 2SD of the mean value from saline-treated Negative Control Group animals. While ANS improved fetal lung maturation in the undivided ANS group, and in the Responder Sub-Group both physiologically (blood gas and ventilation related data) and biochemically (mRNA expression related to fetal lung maturation), these values were not improved relative to saline-treated Control Group animals in the ANS Non-Responder Sub-Group. Interestingly, no differences in betamethasone distribution, clearance, or protein binding were identified between the ANS Responder and Non-Responder Sub-Groups. Conclusion This study correlated individual materno-fetal steroid exposures with preterm lung maturation as determined by pulmonary ventilation. Herein, approximately 40% of preterm lambs exposed to antenatal steroids had lung maturation not significantly different to saline-treated Control Group animals. These non-responsive animals received maternal and fetal betamethasone exposures identical to animals that had a significant improvement in functional lung maturation. These data suggest that the efficacy of ANS therapy is not solely determined by materno-fetal drug levels, and that individual fetal or maternal factors may play a role in determining treatment outcomes in response to glucocorticoid-driven signaling

Direct administration of the non-competitive interleukin-1 receptor antagonist rytvela transiently reduced intrauterine inflammation in an extremely preterm sheep model of chorioamnionitis

Background Intraamniotic inflammation is associated with up to 40% of preterm births, most notably in deliveries occurring prior to 32 weeks’ gestation. Despite this, there are few treatment options allowing the prevention of preterm birth and associated fetal injury. Recent studies have shown that the small, non-competitive allosteric interleukin (IL)-1 receptor inhibitor, rytvela, may be of use in resolving inflammation associated with preterm birth (PTB) and fetal injury. We aimed to use an extremely preterm sheep model of chorioamnionitis to investigate the anti-inflammatory efficacy of rytvela in response to established intra-amniotic (IA) lipopolysaccharide (LPS) exposure. We hypothesized that rytvela would reduce LPS-induced IA inflammation in amniotic fluid (AF) and fetal tissues. Methods Sheep with a single fetus at 95 days gestation (estimated fetal weight 1.0 kg) had surgery to place fetal jugular and IA catheters. Animals were recovered for 48 hours before being randomized to either: i) IA administration of 2 ml saline 24 hours before 2 ml IA and 2 ml fetal intravenous (IV) administration of saline (Saline Group, n = 7); ii) IA administration of 10 mg LPS in 2 ml saline 24 hours before 2 ml IA and 2 ml fetal IV saline (LPS Group, n = 10); 3) IA administration of 10 mg LPS in 2 ml saline 24 hours before 0.3 mg/fetal kg IA and 1 mg/fetal kg fetal IV rytvela in 2 ml saline, respectively (LPS + rytvela Group, n = 7). Serial AF samples were collected for 120 h. Inflammatory responses were characterized by quantitative polymerase chain reaction (qPCR), histology, fluorescent immunohistochemistry, enzyme-linked inmmunosorbent assay (ELISA), fluorescent western blotting and blood chemistry analysis. Results LPS-treated animals had endotoxin and AF monocyte chemoattractant protein (MCP)-1 concentrations that were significantly higher at 24 hours (immediately prior to rytvela administration) relative to values from Saline Group animals. Following rytvela administration, the average MCP-1 concentrations in the AF were significantly lower in the LPS + rytvela Group relative to in the LPS Group. In delivery samples, the expression of IL-1β in fetal skin was significantly lower in the LPS + rytvela Group compared to the LPS Group. Conclusion A single dose of rytvela was associated with partial, modest inhibition in the expression of a panel of cytokines/chemokines in fetal tissues undergoing an active inflammatory response

Agnesi Weighting for the Measure Problem of Cosmology

The measure problem of cosmology is how to assign normalized probabilities to observations in a universe so large that it may have many observations occurring at many different spacetime locations. I have previously shown how the Boltzmann brain problem (that observations arising from thermal or quantum fluctuations may dominate over ordinary observations if the universe expands sufficiently and/or lasts long enough) may be ameliorated by volume averaging, but that still leaves problems if the universe lasts too long. Here a solution is proposed for that residual problem by a simple weighting factor 1/(1+t^2) to make the time integral convergent. The resulting Agnesi measure appears to avoid problems other measures may have with vacua of zero or negative cosmological constant.Comment: 26 pages, LaTeX; discussion is added of how Agnesi weighting appears better than other recent measure