Universality of global dynamics for the cubic wave equation

We consider the initial value problem for the spherically symmetric, focusing cubic wave equation in three spatial dimensions. We give numerical and analytical evidence for the existence of a universal attractor which encompasses both global and blowup solutions. As a byproduct we get an explicit description of the critical behavior at the threshold of blowup.Comment: 13 pages, 15 figures. Uses IOP-style. Updated to conform with published versio

Reduced physiological performance in a free-living coralline alga induced by salmon faeces deposition

Maerl beds are formed by the accumulation of free-living coralline algae and have considerable ecological significance due to the high diversity of associated fauna and flora. The rapid expansion of the Atlantic salmon Salmo salar aquaculture industry in Norway may have major impacts on surrounding maerl beds through the release of effluents, including fish faeces. This study is the first to test the effects of salmon faeces and inorganic sediment deposition on the photosynthesis, respiration, calcification and pigment content of the coralline alga Lithothamnion soriferum. In a 6 wk laboratory experiment, inorganic sediment and salmon faeces deposition significantly reduced the amount of light reaching the surface of coralline algae. No impact of inorganic sediment deposition was detected on L. soriferum physiology, while salmon faeces deposition increased respiration rate and reduced net primary production and calcification. The accumulation of salmon faeces stimulates proliferation of bacteria, with adverse consequences on L. soriferum physiology due to the potential release of toxic compounds. Burial by salmon faeces deposition also affects the physiology of coralline algae due to the flocculation of sticky faeces particles, which may limit nutrient and gas exchanges in the vicinity of thalli. Carbon dioxide accumulation in the vicinity of L. soriferum may lead to a decline in pH and alter the calcification process in cell walls. In natural maerl beds, the negative effect of faeces deposition may be exacerbated by longer-term exposure and the presence of other chemicals released by fish farms.publishedVersio

Harmonic Initial-Boundary Evolution in General Relativity

Computational techniques which establish the stability of an evolution-boundary algorithm for a model wave equation with shift are incorporated into a well-posed version of the initial-boundary value problem for gravitational theory in harmonic coordinates. The resulting algorithm is implemented as a 3-dimensional numerical code which we demonstrate to provide stable, convergent Cauchy evolution in gauge wave and shifted gauge wave testbeds. Code performance is compared for Dirichlet, Neumann and Sommerfeld boundary conditions and for boundary conditions which explicitly incorporate constraint preservation. The results are used to assess strategies for obtaining physically realistic boundary data by means of Cauchy-characteristic matching.Comment: 31 pages, 14 figures, submitted to Physical Review

Invasion of the Red Seaweed \u3cem\u3eHeterosiphonia japonica\u3c/em\u3e Spans Biogeographic Provinces in the Western North Atlantic Ocean

The recent invasion of the red alga Heterosiphonia japonica in the western North Atlantic Ocean has provided a unique opportunity to study invasion dynamics across a biogeographical barrier. Native to the western North Pacific Ocean, initial collections in 2007 and 2009 restricted the western North Atlantic range of this invader to Rhode Island, USA. However, through subtidal community surveys, we document the presence of Heterosiphonia in coastal waters from Maine to New York, USA, a distance of more than 700 km. This geographical distribution spans a well-known biogeographical barrier at Cape Cod, Massachusetts. Despite significant differences in subtidal community structure north and south of Cape Cod, Heterosiphonia was found at all but two sites surveyed in both biogeographic provinces, suggesting that this invader is capable of rapid expansion over broad geographic ranges. Across all sites surveyed, Heterosiphonia comprised 14% of the subtidal benthic community. However, average abundances of nearly 80% were found at some locations. As a drifting macrophyte, Heterosiphonia was found as intertidal wrack in abundances of up to 65% of the biomass washed up along beaches surveyed. Our surveys suggest that the high abundance of Heterosiphonia has already led to marked changes in subtidal community structure; we found significantly lower species richness in recipient communities with higher Heterosiphona abundances. Based on temperature and salinity tolerances of the European populations, we believe Heterosiphonia has the potential to invade and alter subtidal communities from Florida to Newfoundland in the western North Atlantic

Gravitational perturbations of Schwarzschild spacetime at null infinity and the hyperboloidal initial value problem

We study gravitational perturbations of Schwarzschild spacetime by solving a hyperboloidal initial value problem for the Bardeen-Press equation. Compactification along hyperboloidal surfaces in a scri-fixing gauge allows us to have access to the gravitational waveform at null infinity in a general setup. We argue that this hyperboloidal approach leads to a more accurate and efficient calculation of the radiation signal than the common approach where a timelike outer boundary is introduced. The method can be generalized to study perturbations of Kerr spacetime using the Teukolsky equation.Comment: 14 pages, 9 figure

A template bank for gravitational waveforms from coalescing binary black holes: non-spinning binaries

Gravitational waveforms from the inspiral and ring-down stages of the binary black hole coalescences can be modelled accurately by approximation/perturbation techniques in general relativity. Recent progress in numerical relativity has enabled us to model also the non-perturbative merger phase of the binary black-hole coalescence problem. This enables us to \emph{coherently} search for all three stages of the coalescence of non-spinning binary black holes using a single template bank. Taking our motivation from these results, we propose a family of template waveforms which can model the inspiral, merger, and ring-down stages of the coalescence of non-spinning binary black holes that follow quasi-circular inspiral. This two-dimensional template family is explicitly parametrized by the physical parameters of the binary. We show that the template family is not only \emph{effectual} in detecting the signals from black hole coalescences, but also \emph{faithful} in estimating the parameters of the binary. We compare the sensitivity of a search (in the context of different ground-based interferometers) using all three stages of the black hole coalescence with other template-based searches which look for individual stages separately. We find that the proposed search is significantly more sensitive than other template-based searches for a substantial mass-range, potentially bringing about remarkable improvement in the event-rate of ground-based interferometers. As part of this work, we also prescribe a general procedure to construct interpolated template banks using non-spinning black hole waveforms produced by numerical relativity.Comment: A typo fixed in Eq.(B11

Aquaculture-derived trophic subsidy boosts populations of an ecosystem engineer

Environmental management of coastal aquaculture is focused on acute impacts of organic and nitrogenous wastes close to farms. However, the energy-rich trophic subsidy that aquaculture provides may create cascades with influences over broader spatial scales. In a fjord region with intensive fish farming, we tested whether an ecosystem engineer, the white urchin Gracilechinus acutus, was more abundant at aquaculture sites than control sites. Further, we tested whether diets influenced by aquaculture waste altered reproductive outputs compared with natural diets. Urchins formed barrens at aquaculture sites where they were 10 times more abundant (38 urchins m-2) than at control sites (4 urchins m-2). Urchins were on average 15 mm larger at control sites. In the laboratory, urchins fed aquafeed diets had 3 times larger gonad indices than urchins fed a natural diet. However, their reproduction was compromised. Eggs from females fed an aquafeed diet had 13% lower fertilisation success and 30% lower larval survival rates at 10 d compared with females fed a natural diet. A reproductive output model showed that enhanced numbers of 10 d old larvae produced by the dense aquaculture-associated aggregations of G. acutus will supersede any detrimental effects on reproduction, with larval outputs from aquaculture sites being on average 5 times greater than control sites. The results show that aquaculture waste can act as a trophic subsidy in fjord ecosystems, stimulating aggregations of urchins and promoting the formation of urchin barrens. Where finfish aquaculture is concentrated, combined effects on the wider environment may produce ecosystem-level consequences

Hyperboloidal foliations and scri-fixing

We discuss a gauge choice which allows us to avoid the introduction of artificial timelike outer boundaries in numerical studies of test fields based on a 3+1 decomposition of asymptotically flat background spacetimes. The main idea is to include null infinity in the computational domain by conformally compactifying the metric on hyperboloidal foliations and fixing the spatial coordinate location of null infinity, i.e. scri-fixing. We construct such coordinates explicitly on Minkowski, Schwarzschild and Kerr spacetimes.Comment: 14 pages, 14 figures. Published versio

Waves in Schwarzschild spacetimes: How strong can imprints of the spacetime curvature be

Misprints corrected, two references added. To appear in the Phys. Rev. D

LISA as a dark energy probe

Recently it was shown that the inclusion of higher signal harmonics in the inspiral signals of binary supermassive black holes (SMBH) leads to dramatic improvements in parameter estimation with the Laser Interferometer Space Antenna (LISA). In particular, the angular resolution becomes good enough to identify the host galaxy or galaxy cluster, in which case the redshift can be determined by electromagnetic means. The gravitational wave signal also provides the luminosity distance with high accuracy, and the relationship between this and the redshift depends sensitively on the cosmological parameters, such as the equation-of-state parameter $w=p_{\rm DE}/\rho_{\rm DE}$ of dark energy. With a single binary SMBH event at $z < 1$ having appropriate masses and orientation, one would be able to constrain $w$ to within a few percent. We show that, if the measured sky location is folded into the error analysis, the uncertainty on $w$ goes down by an additional factor of 2-3, leaving weak lensing as the only limiting factor in using LISA as a dark energy probe.Comment: 11pages, 1 Table, minor changes in text, accepted for publication in Classical and Quantum Gravity (special issue for proceedings of 7th LISA symposium