The Hawking-Penrose singularity theorem for C1,1C^{1,1}-Lorentzian metrics

We show that the Hawking--Penrose singularity theorem, and the generalisation of this theorem due to Galloway and Senovilla, continue to hold for Lorentzian metrics that are of $C^{1, 1}$-regularity. We formulate appropriate weak versions of the strong energy condition and genericity condition for $C^{1,1}$-metrics, and of $C^0$-trapped submanifolds. By regularisation, we show that, under these weak conditions, causal geodesics necessarily become non-maximising. This requires a detailed analysis of the matrix Riccati equation for the approximating metrics, which may be of independent interest.Comment: Minor amendments in v4: Removed non-equivalent condition from Def. 2.2 and adapted Lemma 3.5 and the proof of Lemma 3.

Searching for the missing soldier: identifying casualties from the First World War

In recent years there has been an increase in the numbers of archaeologists and physical anthropologists involved in searching, locating and assisting in the identification of war casualties. These scientists have played an invaluable role within a larger team of professionals, working together to provide a dignified burial to those who fell for their country and remembering them. This paper reviews some of the work undertaken in Europe with regard to WWI casualties and how the war missing are located and ultimately identified when possible, bringing also some closure to their living relatives

The future is not always open

We demonstrate the breakdown of several fundamentals of Lorentzian causality theory in low regularity. Most notably, chronological futures (defined naturally using locally Lipschitz curves) may be non-open, and may differ from the corresponding sets defined via piecewise $C^1$-curves. By refining the notion of a causal bubble from [CG:12],we characterize spacetimes for which such phenomena can occur, and also relate these to the possibility of deforming causal curves of positive length into timelike curves (push-up). The phenomena described here are, in particular, relevant for recent synthetic approaches to low regularity Lorentzian geometry where, in the absence of a differentiable structure, causality has to be based on locally Lipschitz curves.Comment: Minor amendments. Final version. 17 pages, 4 figure

Polarized Radio Sources: A Study of Luminosity, Redshift and Infrared Colors

The Dominion Radio Astrophysical Observatory Deep Field polarization study has been matched with the Spitzer Wide-Area Infrared Extragalactic survey of the European Large Area Infrared Space Observatory Survey North 1 field. We have used VLA observations with a total intensity rms of 87 microJy beam^-1 to match SWIRE counterparts to the radio sources. Infrared color analysis of our radio sample shows that the majority of polarized sources are elliptical galaxies with an embedded active galactic nucleus. Using available redshift catalogs, we found 429 radio sources of which 69 are polarized with redshifts in the range of 0.04 < z <3.2. We find no correlation between redshift and percentage polarization for our sample. However, for polarized radio sources, we find a weak correlation between increasing percentage polarization and decreasing luminosity.Comment: 35 pages, 12 figures, accepted for publication in The Astrophysical Journa

The wave equation on singular space-times

We prove local unique solvability of the wave equation for a large class of weakly singular, locally bounded space-time metrics in a suitable space of generalised functions.Comment: Latex, 19 pages, 1 figure. Discussion of class of metrics covered by our results and some examples added. Conclusion more detailed. Version to appear in Communications in Mathematical Physic

Effect of Alzheimer Caregiving Stress and Age on Frailty Markers Interleukin-6, C-Reactive Protein, and D-Dimer

Background. Elevated plasma levels of interleukin (IL)-6, C-reactive protein (CRP), and D-dimer belong to the biological alterations of the "frailty syndrome,” defining increased vulnerability for diseases and mortality with aging. We hypothesized that, compatible with premature frailty, chronic stress and age are related in predicting inflammation and coagulation activity in Alzheimer caregivers. Methods. Plasma IL-6, CRP, and D-dimer levels were measured in 170 individuals (mean age 73 ± 9 years; 116 caregivers, 54 noncaregiving controls). Demographic factors, diseases, drugs, and lifestyle variables potentially affecting inflammation and coagulation were obtained by history and adjusted for as covariates in statistical analyses. Results. Caregivers had higher mean levels of IL-6 (1.38 ± 1.42 vs 1.00 ± 0.92 pg/mL, p =.032) and of D-dimer (723 ± 530 vs 471 ± 211 ng/mL, p <.001) than controls had. CRP levels were similar between groups (p =.44). The relationship between caregiver status and D-dimer was independent of covariates (p =.037) but affected by role overload. Age accounted for much of the relationship with IL-6. After controlling for covariates, the interaction between caregiver status and age was significant for D-dimer (β =.20, p =.029) and of borderline significance for IL-6 (β =.17, p =.090). Post hoc regression analyses indicated that, among caregivers, age was significantly correlated with both D-dimer (β =.50, p <.001) and IL-6 (β =.38, p =.001). Among controls, however, no significant relationship was observed between age and either D-dimer or IL-6. Conclusions. The interaction between caregiving status and age for D-dimer and IL-6 suggests the possibility that older caregivers could be at risk of a more rapid transition to the frailty syndrome and clinical manifestations of cardiovascular disease

Damage Spreading During Domain Growth

We study damage spreading in models of two-dimensional systems undergoing first order phase transitions. We consider several models from the same non-conserved order parameter universality class, and find unexpected differences between them. An exact solution of the Ohta-Jasnow-Kawasaki model yields the damage growth law $D \sim t^{\phi}$, where $\phi = t^{d/4}$ in $d$ dimensions. In contrast, time-dependent Ginzburg-Landau simulations and Ising simulations in $d= 2$ using heat-bath dynamics show power-law growth, but with an exponent of approximately $0.36$, independent of the system sizes studied. In marked contrast, Metropolis dynamics shows damage growing via $\phi \sim 1$, although the damage difference grows as $t^{0.4}$. PACS: 64.60.-i, 05.50.+qComment: 4 pags of revtex3 + 3 postscript files appended as a compressed and uuencoded file. UIB940320

Scaling in Late Stage Spinodal Decomposition with Quenched Disorder

We study the late stages of spinodal decomposition in a Ginzburg-Landau mean field model with quenched disorder. Random spatial dependence in the coupling constants is introduced to model the quenched disorder. The effect of the disorder on the scaling of the structure factor and on the domain growth is investigated in both the zero temperature limit and at finite temperature. In particular, we find that at zero temperature the domain size, $R(t)$, scales with the amplitude, $A$, of the quenched disorder as $R(t) = A^{-\beta} f(t/A^{-\gamma})$ with $\beta \simeq 1.0$ and $\gamma \simeq 3.0$ in two dimensions. We show that $\beta/\gamma = \alpha$, where $\alpha$ is the Lifshitz-Slyosov exponent. At finite temperature, this simple scaling is not observed and we suggest that the scaling also depends on temperature and $A$. We discuss these results in the context of Monte Carlo and cell dynamical models for phase separation in systems with quenched disorder, and propose that in a Monte Carlo simulation the concentration of impurities, $c$, is related to $A$ by $A \sim c^{1/d}$.Comment: RevTex manuscript 5 pages and 5 figures (obtained upon request via email [email protected]