A new dissipation term for finite-difference simulations in Relativity

We present a new numerical dissipation algorithm, which can be efficiently used in combination with centered finite-difference methods. We start from a formulation of centered finite-volume methods for Numerical Relativity, in which third-order space accuracy can be obtained by employing just piecewise-linear reconstruction. We obtain a simplified version of the algorithm, which can be viewed as a centered finite-difference method plus some 'adaptive dissipation'. The performance of this algorithm is confirmed by numerical results obtained from 3D black hole simulations.Comment: Talk presented at the Spanish Relativity Meeting (Tenerife 2007

General-relativistic resistive-magnetohydrodynamic simulations of binary neutron stars

We have studied the dynamics of an equal-mass magnetized neutron-star binary within a resistive magnetohydrodynamic (RMHD) approach in which the highly conducting stellar interior is matched to an electrovacuum exterior. Because our analysis is aimed at assessing the modifications introduced by resistive effects on the dynamics of the binary after the merger and through to collapse, we have carried out a close comparison with an equivalent simulation performed within the traditional ideal magnetohydrodynamic approximation. We have found that there are many similarities between the two evolutions but also one important difference: the survival time of the hyper massive neutron star increases in a RMHD simulation. This difference is due to a less efficient magnetic-braking mechanism in the resistive regime, in which matter can move across magnetic-field lines, thus reducing the outward transport of angular momentum. Both the RMHD and the ideal magnetohydrodynamic simulations carried here have been performed at higher resolutions and with a different grid structure than those in previous work of ours [L. Rezzolla, B. Giacomazzo, L. Baiotti, J. Granot, C. Kouveliotou, and M. A. Aloy, Astrophys. J. Letters 732, L6 (2011)], but confirm the formation of a low-density funnel with an ordered magnetic field produced by the black hole--torus system. In both regimes the magnetic field is predominantly toroidal in the highly conducting torus and predominantly poloidal in the nearly evacuated funnel. Reconnection processes or neutrino annihilation occurring in the funnel, none of which we model, could potentially increase the internal energy in the funnel and launch a relativistic outflow, which, however, is not produced in these simulations.Comment: 26 pages, 17 figures; animations available at http://www.southampton.ac.uk/~kd10g13/movies/index.shtm

General relativistic radiation hydrodynamics of accretion flows: II. Treating stiff source terms and exploring physical limitations

We present the implementation of an implicit-explicit (IMEX) Runge-Kutta numerical scheme for general relativistic hydrodynamics coupled to an optically thick radiation field in two existing GR-hydrodynamics codes. We argue that the necessity of such an improvement arises naturally in astrophysically relevant regimes where the optical thickness is high as the equations become stiff. By performing several 1D tests we verify the codes' new ability to deal with this stiffness and show consistency. Then, still in 1D, we compute a luminosity versus accretion rate diagram for the setup of spherical accretion onto a Schwarzschild black hole and find good agreement with previous work. Lastly, we revisit the supersonic Bondi Hoyle Lyttleton (BHL) accretion in 2D where we can now present simulations of realistic temperatures, down to T~10^6 K. Here we find that radiation pressure plays an important role, but also that these highly dynamical set-ups push our approximate treatment towards the limit of physical applicability. The main features of radiation hydrodynamics BHL flows manifest as (i) an effective adiabatic index approaching gamma_effective ~ 4/3; (ii) accretion rates two orders of magnitude lower than without radiation pressure; (iii) luminosity estimates around the Eddington limit, hence with an overall radiative efficiency as small as eta ~ 10^{-2}; (iv) strong departures from thermal equilibrium in shocked regions; (v) no appearance of the flip-flop instability. We conclude that the current optically thick approximation to the radiation transfer does give physically substantial improvements over the pure hydro also in set-ups departing from equilibrium, and, once accompanied by an optically thin treatment, is likely to provide a fundamental tool for investigating accretion flows in a large variety of astrophysical systems

Using answer set programming to integrate RNA expression with signalling pathway information to infer how mutations affect ageing.

A challenge of systems biology is to integrate incomplete knowledge on pathways with existing experimental data sets and relate these to measured phenotypes. Research on ageing often generates such incomplete data, creating difficulties in integrating RNA expression with information about biological processes and the phenotypes of ageing, including longevity. Here, we develop a logic-based method that employs Answer Set Programming, and use it to infer signalling effects of genetic perturbations, based on a model of the insulin signalling pathway. We apply our method to RNA expression data from Drosophila mutants in the insulin pathway that alter lifespan, in a foxo dependent fashion. We use this information to deduce how the pathway influences lifespan in the mutant animals. We also develop a method for inferring the largest common sub-paths within each of our signalling predictions. Our comparisons reveal consistent homeostatic mechanisms across both long- and short-lived mutants. The transcriptional changes observed in each mutation usually provide negative feedback to signalling predicted for that mutation. We also identify an S6K-mediated feedback in two long-lived mutants that suggests a crosstalk between these pathways in mutants of the insulin pathway, in vivo. By formulating the problem as a logic-based theory in a qualitative fashion, we are able to use the efficient search facilities of Answer Set Programming, allowing us to explore larger pathways, combine molecular changes with pathways and phenotype and infer effects on signalling in in vivo, whole-organism, mutants, where direct signalling stimulation assays are difficult to perform. Our methods are available in the web-service NetEffects: http://www.ebi.ac.uk/thornton-srv/software/NetEffects

Detrimental effects of RNAi: a cautionary note on its use in Drosophila ageing studies

RNA interference (RNAi) provides an important tool for gene function discovery. It has been widely exploited in Caenorhabditis elegans ageing research because it does not appear to have any non-specific effects on ageing-related traits in that model organism. We show here that ubiquitous, adult-onset activation of the RNAi machinery, achieved by expressing a double stranded RNA targeting GFP or lacZ for degradation, or by increasing expression of Dicer substantially reduces lifespan in Drosophila melanogaster. Induction of GFPRNAi construct also alters the response of lifespan to nutrition, exacerbating the lifespan-shortening effects of food containing a high quantity of yeast. Our study indicates that activation of the RNAi machinery may have sequence-independent side-effects on lifespan, and that caution needs to be exercised when employing ubiquitous RNAi in Drosophila ageing studies. However, we also show that RNAi restricted to certain tissues may not be detrimental to lifespan

Implementation of standard testbeds for numerical relativity

We discuss results that have been obtained from the implementation of the initial round of testbeds for numerical relativity which was proposed in the first paper of the Apples with Apples Alliance. We present benchmark results for various codes which provide templates for analyzing the testbeds and to draw conclusions about various features of the codes. This allows us to sharpen the initial test specifications, design a new test and add theoretical insight.Comment: Corrected versio

Three little pieces for computer and relativity

Numerical relativity has made big strides over the last decade. A number of problems that have plagued the field for years have now been mostly solved. This progress has transformed numerical relativity into a powerful tool to explore fundamental problems in physics and astrophysics, and I present here three representative examples. These "three little pieces" reflect a personal choice and describe work that I am particularly familiar with. However, many more examples could be made.Comment: 42 pages, 11 figures. Plenary talk at "Relativity and Gravitation: 100 Years after Einstein in Prague", June 25 - 29, 2012, Prague, Czech Republic. To appear in the Proceedings (Edition Open Access). Collects results appeared in journal articles [72,73, 122-124

From Geometry to Numerics: interdisciplinary aspects in mathematical and numerical relativity

This article reviews some aspects in the current relationship between mathematical and numerical General Relativity. Focus is placed on the description of isolated systems, with a particular emphasis on recent developments in the study of black holes. Ideas concerning asymptotic flatness, the initial value problem, the constraint equations, evolution formalisms, geometric inequalities and quasi-local black hole horizons are discussed on the light of the interaction between numerical and mathematical relativists.Comment: Topical review commissioned by Classical and Quantum Gravity. Discussion inspired by the workshop "From Geometry to Numerics" (Paris, 20-24 November, 2006), part of the "General Relativity Trimester" at the Institut Henri Poincare (Fall 2006). Comments and references added. Typos corrected. Submitted to Classical and Quantum Gravit