Black hole evolution by spectral methods

Current methods of evolving a spacetime containing one or more black holes are plagued by instabilities that prohibit long-term evolution. Some of these instabilities may be due to the numerical method used, traditionally finite differencing. In this paper, we explore the use of a pseudospectral collocation (PSC) method for the evolution of a spherically symmetric black hole spacetime in one dimension using a hyperbolic formulation of Einstein's equations. We demonstrate that our PSC method is able to evolve a spherically symmetric black hole spacetime forever without enforcing constraints, even if we add dynamics via a Klein-Gordon scalar field. We find that, in contrast to finite-differencing methods, black hole excision is a trivial operation using PSC applied to a hyperbolic formulation of Einstein's equations. We discuss the extension of this method to three spatial dimensions.Comment: 20 pages, 17 figures, submitted to PR

The SUMO-targeted ubiquitin ligase subunit Slx5 resides in nuclear foci and at sites of DNA breaks

The Slx5/Slx8 protein complex, a heterodimeric SUMO-targeted ubiquitin ligase, plays an important role in genomic integrity. Slx5/Slx8 is believed to interact with sumoylated proteins that reside in the nuclei of budding yeast cells. In this complex, Slx5, owing to at least two SUMO interacting motifs (SIMs), has been proposed to be the targeting subunit of the Slx8 ubiquitin ligase. However, little is known about the exact subnuclear localization and targets of Slx5/Slx8. In this study we show that Slx5, but not Slx8, forms prominent nuclear foci. The formation of these foci depends on SUMO and a SIM in Slx5. Therefore, we investigated the subnuclear localization and potential chromatin association of Slx5. Using co-localization studies in live cells and fixed chromatin, we were able to localize Slx5 to DNA damage induced foci of Rad52 and Rad9, two proteins involved in the cellular response to DNA damage. Subsequent chromatin immunoprecipitation (ChIP) studies revealed that Slx5 is associated with HO endonuclease induced chromosome breaks. Surprisingly, real-time PCR analysis of Slx5 ChIPs revealed that the level of Slx5 at HO breaks in an slx8 deletion background is reduced about 4-fold. These results indicate that the DNA-damage targeting of Slx5/Slx8 depends on formation of the heterodimer and that this occurs at a subset of nuclear foci also containing DNA damage repair and checkpoint factors

Assessment of climate change effects on vegetation and river hydrology in a semi-arid river basin

Climate change plays a key role in changing vegetation productivity dynamics, which ultimately affect the hydrological cycle of a watershed through evapotranspiration (ET). Trends and correlation analysis were conducted to investigate vegetation responses across the whole Upper Jhelum River Basin (UJRB) in the northeast of Pakistan using the normalized difference vegetation index (NDVI), climate variables, and river flow data at inter-annual/monthly scales between 1982 and 2015. The spatial variability in trends calculated with the Mann-Kendall (MK) trend test on NDVI and climate data was assessed considering five dominant land use/cover types. The inter-annual NDVI in four out of five vegetation types showed a consistent increase over the 34-year study period; the exception was for herbaceous vegetation (HV), which increased until the end of the 1990s and then decreased slightly in subsequent years. In spring, significant (p<0.05) increasing trends were found in the NDVI of all vegetation types. Minimum temperature (Tmin) showed a significant increase during spring, while maximum temperature (Tmax) decreased significantly during summer. Average annual increase in Tmin (1.54°C) was much higher than Tmax (0.37°C) over 34 years in the UJRB. Hence, Tmin appears to have an enhancing effect on vegetation productivity over the UJRB. A significant increase in NDVI, Tmin and Tmax during spring may have contributed to reductions in spring river flow by enhancing evapotranspiration observed in the watershed of UJRB. These findings provide valuable information to improve our knowledge and understanding about the interlinkages between vegetation, climate and river flow at a watershed scale

Optimisation of pooled faecal samples for the isolation fo Salmonella from finisher pigs in GB.

Pooled pen floor faecal sampling represents a simple and non-invasive method to measure Salmonella infection in pigs. We extended an existing model of the sensitivity of detection of Salmonella in individual samples to create a mathematical model of the sensitivity of pooled sampling

Rhinal cortex asymmetries in patients with mesial temporal sclerosis

SummaryPurposeThe rhinal cortex, comprising the entorhinal (ErC) and perirhinal (PrC) cortices, is one component of the limbic system that may be affected in patients with epilepsy and other temporal lobe pathologies. This study extended quantitative examination of the limbic system through development and validation of volumetric protocols to measure the ErC and PrC.MethodsVolumes were calculated from MRI studies using ANALYZE 7.5 and based on detailed anatomical definitions developed for the study. Subjects were 61 temporal lobe epilepsy patients with mesial temporal sclerosis (MTS: 33 left, 28 right) and 20 neurologically normal controls. Inter-rater reliabilities for the ErC and PrC volume protocols were found to be high (range 0.86–0.92).ResultsIpsilateral hippocampal volume was reduced in patients with MTS, while contralateral volume did not differ significantly from controls. In the patients, rhinal cortex volumes were reduced as a function of laterality of disease. The pattern of correlations between ErC and PrC differed between disease groups. Hippocampal and rhinal cortex volumes were not significantly correlated. A significant four-way interaction was found between side of MTS, hemisphere, structure and handedness.ConclusionsThis quantitative study demonstrates reliable in vivo evidence of morphometric changes in ErC and PrC in a substantial number of patients with unilateral MTS. The relationship observed between handedness, structure and disease status may suggest a role for cerebral dominance in modulating the expression of MTS

Spatial Scale of Heterogeneity Affects Diet Choice but Not Intake in Beef Cattle

Previous research has shown that sheep (Champion et al., 1998) and dairy cattle (Nuthall et al., 2000) have a partial preference for clover of 70%, and achieve higher daily intakes when offered grass and clover as separate but adjacent monocultures compared with animals grazing mixed swards. This intake benefit could be utilised to increase intake and production on farms by grazing from adjacent strips of the two herbages. This study aimed to establish the minimum strip width required to achieve the benefits of monocultures

Beneficial physiological effects with blackcurrant intake in endurance athletes

Blackcurrant contains anthocyanins, known to influence vasorelaxation and peripheral blood flow. We examined the effects of 7 days intake of Sujon New Zealand blackcurrant powder (6g/day) on the lactate curve, maximum oxygen uptake, and cardiovascular responses at rest and during cycling. Thirteen trained triathletes with >3 yrs experience (8 men, age: 38±8 yrs, body mass: 71±9 kg, BF%: 19±5%, mean±SD) performed two incremental cycling protocols with recording of physiological and cardiovascular responses (Portapres® Model 2). Cardiovascular function was also measured in rest. Experimental design was double-blind, placebo-controlled, randomized and cross-over (wash-out 4 wks). Data was analysed with two-tailed t-tests and 2-way ANOVA and significance accepted at p<0.05. Plasma lactate was lower at 40%, 50%, 60% and 70% of maximum power by 27%, 22%, 17% and 13%. Intensity at 4 mmol∙L-1 OBLA was 6% higher with blackcurrant without effect on heart rate and oxygen uptake. Maximum values of oxygen uptake, heart rate and power were not affected by blackcurrant, but obtained with 14% lower lactate. In rest, blackcurrant increased stroke volume and cardiac output by 25% and 26%, and decreased total peripheral resistance by 16%, with no changes in blood pressure and heart rate. Cardiovascular responses during exercise at 40%, 50%, 60%, 70% and 80% intensity were not affected. Sujon New Zealand blackcurrant powder affects lactate production and/or clearance during exercise. Sujon New Zealand blackcurrant powder affects physiological and cardiovascular responses in rest and during exercise that may have implications for exercise performance

Can a combination of the conformal thin-sandwich and puncture methods yield binary black hole solutions in quasi-equilibrium?

We consider combining two important methods for constructing quasi-equilibrium initial data for binary black holes: the conformal thin-sandwich formalism and the puncture method. The former seeks to enforce stationarity in the conformal three-metric and the latter attempts to avoid internal boundaries, like minimal surfaces or apparent horizons. We show that these two methods make partially conflicting requirements on the boundary conditions that determine the time slices. In particular, it does not seem possible to construct slices that are quasi-stationary and avoid physical singularities and simultaneously are connected by an everywhere positive lapse function, a condition which must obtain if internal boundaries are to be avoided. Some relaxation of these conflicting requirements may yield a soluble system, but some of the advantages that were sought in combining these approaches will be lost.Comment: 8 pages, LaTeX2e, 2 postscript figure

A multidomain spectral method for solving elliptic equations

We present a new solver for coupled nonlinear elliptic partial differential equations (PDEs). The solver is based on pseudo-spectral collocation with domain decomposition and can handle one- to three-dimensional problems. It has three distinct features. First, the combined problem of solving the PDE, satisfying the boundary conditions, and matching between different subdomains is cast into one set of equations readily accessible to standard linear and nonlinear solvers. Second, touching as well as overlapping subdomains are supported; both rectangular blocks with Chebyshev basis functions as well as spherical shells with an expansion in spherical harmonics are implemented. Third, the code is very flexible: The domain decomposition as well as the distribution of collocation points in each domain can be chosen at run time, and the solver is easily adaptable to new PDEs. The code has been used to solve the equations of the initial value problem of general relativity and should be useful in many other problems. We compare the new method to finite difference codes and find it superior in both runtime and accuracy, at least for the smooth problems considered here.Comment: 31 pages, 8 figure

High-accuracy comparison of numerical relativity simulations with post-Newtonian expansions

Numerical simulations of 15 orbits of an equal-mass binary black hole system are presented. Gravitational waveforms from these simulations, covering more than 30 cycles and ending about 1.5 cycles before merger, are compared with those from quasi-circular zero-spin post-Newtonian (PN) formulae. The cumulative phase uncertainty of these comparisons is about 0.05 radians, dominated by effects arising from the small residual spins of the black holes and the small residual orbital eccentricity in the simulations. Matching numerical results to PN waveforms early in the run yields excellent agreement (within 0.05 radians) over the first $\sim 15$ cycles, thus validating the numerical simulation and establishing a regime where PN theory is accurate. In the last 15 cycles to merger, however, {\em generic} time-domain Taylor approximants build up phase differences of several radians. But, apparently by coincidence, one specific post-Newtonian approximant, TaylorT4 at 3.5PN order, agrees much better with the numerical simulations, with accumulated phase differences of less than 0.05 radians over the 30-cycle waveform. Gravitational-wave amplitude comparisons are also done between numerical simulations and post-Newtonian, and the agreement depends on the post-Newtonian order of the amplitude expansion: the amplitude difference is about 6--7% for zeroth order and becomes smaller for increasing order. A newly derived 3.0PN amplitude correction improves agreement significantly ($<1$ amplitude difference throughout most of the run, increasing to 4% near merger) over the previously known 2.5PN amplitude terms.Comment: Updated to agree with published version (various minor clarifications; added description of AH finder in Sec IIB; added discussion of tidal heating in Sec VC