Effective null Raychaudhuri equation

The effects on Raychaudhuri's equation of an intrinsically-discrete or particle nature of spacetime are investigated. This is done through the consideration of null congruences emerging from, or converging to, a generic point of spacetime, i.e. in geometric circumstances somehow prototypical of singularity issues. We do this from an effective point of view, that is through a (continuous) description of spacetime modified to embody the existence of an intrinsic discreteness on the small scale, this adding to previous results for non-null congruences. Various expressions for the effective rate of change of expansion are derived. They in particular provide finite values for the limiting effective expansion and its rate of variation when approaching the focal point. Further, this results in a non-vanishing of the limiting cross-sectional area itself of the congruence.Comment: 7 pages; v2: some comparisons with other approaches adde

Magnetic fields in supernova remnants and pulsar-wind nebulae

We review the observations of supernova remnants (SNRs) and pulsar-wind nebulae (PWNe) that give information on the strength and orientation of magnetic fields. Radio polarimetry gives the degree of order of magnetic fields, and the orientation of the ordered component. Many young shell supernova remnants show evidence for synchrotron X-ray emission. The spatial analysis of this emission suggests that magnetic fields are amplified by one to two orders of magnitude in strong shocks. Detection of several remnants in TeV gamma rays implies a lower limit on the magnetic-field strength (or a measurement, if the emission process is inverse-Compton upscattering of cosmic microwave background photons). Upper limits to GeV emission similarly provide lower limits on magnetic-field strengths. In the historical shell remnants, lower limits on B range from 25 to 1000 microGauss. Two remnants show variability of synchrotron X-ray emission with a timescale of years. If this timescale is the electron-acceleration or radiative loss timescale, magnetic fields of order 1 mG are also implied. In pulsar-wind nebulae, equipartition arguments and dynamical modeling can be used to infer magnetic-field strengths anywhere from about 5 microGauss to 1 mG. Polarized fractions are considerably higher than in SNRs, ranging to 50 or 60% in some cases; magnetic-field geometries often suggest a toroidal structure around the pulsar, but this is not universal. Viewing-angle effects undoubtedly play a role. MHD models of radio emission in shell SNRs show that different orientations of upstream magnetic field, and different assumptions about electron acceleration, predict different radio morphology. In the remnant of SN 1006, such comparisons imply a magnetic-field orientation connecting the bright limbs, with a non-negligible gradient of its strength across the remnant.Comment: 20 pages, 24 figures; to be published in SpSciRev. Minor wording change in Abstrac

The cost-effectiveness of early goal-directed therapy: an economic evaluation alongside the ARISE trial

Objective: To determine the cost-effectiveness of early goal-directed therapy (EGDT) for patients with early septic shock. Design: Within-trial cost-effectiveness evaluation. Setting: Nineteen hospitals in Australia and New Zealand. Participants and interventions: Patients with early septic shock enrolled in the Australasian Resuscitation in Sepsis Evaluation (ARISE) trial were randomly assigned to EGDT versus usual care. A subgroup of patients participated in a nested economic evaluation study in which detailed resource use data were collected until 12 months after randomisation. Outcome measures: Clinical outcomes included lives saved, lifeyears gained and quality-adjusted life-years (QALYs), with mortality collected until 12 months and health-related quality of life assessed at baseline, 6 and 12 months using the 3-level EuroQol five dimensions questionnaire (EQ-5D-3L). Economic outcomes included health care resource use, costs and cost-effectiveness from the Australian health care payer perspective. Results: A total of 205 patients (100 EGDT, 105 usual care) participated in the nested economic evaluation study, of which 203 had complete resource use data. Unadjusted mean health care costs to 12 months were $67 223 (standard deviation [SD],$72 397) in the EGDT group and $54 179 (SD,$61 980) in the usual care group, with a mean difference of $13 044 (95$5791 to $31 878). There was no difference between groups with regards to lives saved (EGDT, 69.4$50 000 per QALY, the probability of EGDT being cost-effective was only 6.4%. Conclusions: In patients presenting to the emergency department with early septic shock, EGDT compared with usual care was not cost-effective.Alisa M Higgins, Sandra L Peake, Rinaldo Bellomo, D Jamie Cooper, Anthony Delaney, Belinda D Howe, Alistair D Nichol, Steve A Webb, Patricia J Williams and Anthony H Harris, for the ARISE Investigators and the ANZICS Clinical Trials Grou