Multi-patch methods in general relativistic astrophysics - I. Hydrodynamical flows on fixed backgrounds

Many systems of interest in general relativistic astrophysics, including neutron stars, accreting compact objects in X-ray binaries and active galactic nuclei, core collapse, and collapsars, are assumed to be approximately spherically symmetric or axisymmetric. In Newtonian or fixed-background relativistic approximations it is common practice to use spherical polar coordinates for computational grids; however, these coordinates have singularities and are difficult to use in fully relativistic models. We present, in this series of papers, a numerical technique which is able to use effectively spherical grids by employing multiple patches. We provide detailed instructions on how to implement such a scheme, and present a number of code tests for the fixed background case, including an accretion torus around a black hole.Comment: 26 pages, 20 figures. A high-resolution version is available at http://www.cct.lsu.edu/~bzink/papers/multipatch_1.pd

Hyperboloidal slices for the wave equation of Kerr-Schild metrics and numerical applications

We present new results from two open source codes, using finite differencing and pseudo-spectral methods for the wave equations in (3+1) dimensions. We use a hyperboloidal transformation which allows direct access to null infinity and simplifies the control over characteristic speeds on Kerr-Schild backgrounds. We show that this method is ideal for attaching hyperboloidal slices or for adapting the numerical resolution in certain spacetime regions. As an example application, we study late-time Kerr tails of sub-dominant modes and obtain new insight into the splitting of decay rates. The involved conformal wave equation is freed of formally singular terms whose numerical evaluation might be problematically close to future null infinity.Comment: 15 pages, 12 figure

Numerical relativity with characteristic evolution, using six angular patches

The characteristic approach to numerical relativity is a useful tool in evolving gravitational systems. In the past this has been implemented using two patches of stereographic angular coordinates. In other applications, a six-patch angular coordinate system has proved effective. Here we investigate the use of a six-patch system in characteristic numerical relativity, by comparing an existing two-patch implementation (using second-order finite differencing throughout) with a new six-patch implementation (using either second- or fourth-order finite differencing for the angular derivatives). We compare these different codes by monitoring the Einstein constraint equations, numerically evaluated independently from the evolution. We find that, compared to the (second-order) two-patch code at equivalent resolutions, the errors of the second-order six-patch code are smaller by a factor of about 2, and the errors of the fourth-order six-patch code are smaller by a factor of nearly 50.Comment: 12 pages, 5 figures, submitted to CQG (special NFNR issue

Comparative analysis of homology models of the Ah receptor ligand binding domain: Verification of structure-function predictions by site-directed mutagenesis of a nonfunctional receptor

The aryl hydrocarbon receptor (AHR) is a ligand-dependent transcription factor that mediates the biological and toxic effects of a wide variety of structurally diverse chemicals, including the toxic environmental contaminant 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD). While significant interspecies differences in AHR ligand binding specificity, selectivity, and response have been observed, the structural determinants responsible for those differences have not been determined, and homology models of the AHR ligand-binding domain (LBD) are available for only a few species. Here we describe the development and comparative analysis of homology models of the LBD of 16 AHRs from 12 mammalian and nonmammalian species and identify the specific residues contained within their ligand binding cavities. The ligand-binding cavity of the fish AHR exhibits differences from those of mammalian and avian AHRs, suggesting a slightly different TCDD binding mode. Comparison of the internal cavity in the LBD model of zebrafish (zf) AHR2, which binds TCDD with high affinity, to that of zfAHR1a, which does not bind TCDD, revealed that the latter has a dramatically shortened binding cavity due to the side chains of three residues (Tyr296, Thr386, and His388) that reduce the amount of internal space available to TCDD. Mutagenesis of two of these residues in zfAHR1a to those present in zfAHR2 (Y296H and T386A) restored the ability of zfAHR1a to bind TCDD and to exhibit TCDD-dependent binding to DNA. These results demonstrate the importance of these two amino acids and highlight the predictive potential of comparative analysis of homology models from diverse species. The availability of these AHR LBD homology models will facilitate in-depth comparative studies of AHR ligand binding and ligand-dependent AHR activation and provide a novel avenue for examining species-specific differences in AHR responsiveness. © 2013 American Chemical Society

Evidence for an entropy bound from fundamentally discrete gravity

The various entropy bounds that exist in the literature suggest that spacetime is fundamentally discrete, and hint at an underlying relationship between geometry and "information". The foundation of this relationship is yet to be uncovered, but should manifest itself in a theory of quantum gravity. We present a measure for the maximal entropy of spherically symmetric spacelike regions within the causal set approach to quantum gravity. In terms of the proposal, a bound for the entropy contained in this region can be derived from a counting of potential "degrees of freedom" associated to the Cauchy horizon of its future domain of dependence. For different spherically symmetric spacelike regions in Minkowski spacetime of arbitrary dimension, we show that this proposal leads, in the continuum approximation, to Susskind's well-known spherical entropy bound.Comment: 25 pages, 9 figures. Comment on Bekenstein bound added and smaller corrections. To be published in Class.Quant.Gra

Action Without Awareness: Reaching to an Object You Do Not Remember Seeing

BACKGROUND: Previous work by our group has shown that the scaling of reach trajectories to target size is independent of obligatory awareness of that target property and that "action without awareness" can persist for up to 2000 ms of visual delay. In the present investigation we sought to determine if the ability to scale reaching trajectories to target size following a delay is related to the pre-computing of movement parameters during initial stimulus presentation or the maintenance of a sensory (i.e., visual) representation for on-demand response parameterization. METHODOLOGY/PRINCIPAL FINDINGS: Participants completed immediate or delayed (i.e., 2000 ms) perceptual reports and reaching responses to different sized targets under non-masked and masked target conditions. For the reaching task, the limb associated with a trial (i.e., left or right) was not specified until the time of response cuing: a manipulation that prevented participants from pre-computing the effector-related parameters of their response. In terms of the immediate and delayed perceptual tasks, target size was accurately reported during non-masked trials; however, for masked trials only a chance level of accuracy was observed. For the immediate and delayed reaching tasks, movement time as well as other temporal kinematic measures (e.g., times to peak acceleration, velocity and deceleration) increased in relation to decreasing target size across non-masked and masked trials. CONCLUSIONS/SIGNIFICANCE: Our results demonstrate that speed-accuracy relations were observed regardless of whether participants were aware (i.e., non-masked trials) or unaware (i.e., masked trials) of target size. Moreover, the equivalent scaling of immediate and delayed reaches during masked trials indicates that a persistent sensory-based representation supports the unconscious and metrical scaling of memory-guided reaching

The neuroscience of vision-based grasping: a functional review for computational modeling and bio-inspired robotics

The topic of vision-based grasping is being widely studied using various techniques and with different goals in humans and in other primates. The fundamental related findings are reviewed in this paper, with the aim of providing researchers from different fields, including intelligent robotics and neural computation, a comprehensive but accessible view on the subject. A detailed description of the principal sensorimotor processes and the brain areas involved in them is provided following a functional perspective, in order to make this survey especially useful for computational modeling and bio-inspired robotic application

The Current Status of Binary Black Hole Simulations in Numerical Relativity

Since the breakthroughs in 2005 which have led to long term stable solutions of the binary black hole problem in numerical relativity, much progress has been made. I present here a short summary of the state of the field, including the capabilities of numerical relativity codes, recent physical results obtained from simulations, and improvements to the methods used to evolve and analyse binary black hole spacetimes.Comment: 14 pages; minor changes and corrections in response to referee

Inter-laboratory Variation in the Chemical Analysis of Acidic Forest Soil Reference Samples from Eastern North America

Long-term forest soil monitoring and research often requires a comparison of laboratory data generated at different times and in different laboratories. Quantifying the uncertainty associated with these analyses is necessary to assess temporal changes in soil properties. Forest soil chemical properties, and methods to measure these properties, often differ from agronomic and horticultural soils. Soil proficiency programs do not generally include forest soil samples that are highly acidic, high in extractable Al, low in extractable Ca and often high in carbon. To determine the uncertainty associated with specific analytical methods for forest soils, we collected and distributed samples from two soil horizons (Oa and Bs) to 15 laboratories in the eastern United States and Canada. Soil properties measured included total organic carbon and nitrogen, pH and exchangeable cations. Overall, results were consistent despite some differences in methodology. We calculated the median absolute deviation (MAD) for each measurement and considered the acceptable range to be the median 6 2.5 3 MAD. Variability among laboratories was usually as low as the typical variability within a laboratory. A few areas of concern include a lack of consistency in the measurement and expression of results on a dry weight basis, relatively high variability in the C/N ratio in the Bs horizon, challenges associated with determining exchangeable cations at concentrations near the lower reporting range of some laboratories and the operationally defined nature of aluminum extractability. Recommendations include a continuation of reference forest soil exchange programs to quantify the uncertainty associated with these analyses in conjunction with ongoing efforts to review and standardize laboratory methods

Oriented Matroids -- Combinatorial Structures Underlying Loop Quantum Gravity

We analyze combinatorial structures which play a central role in determining spectral properties of the volume operator in loop quantum gravity (LQG). These structures encode geometrical information of the embedding of arbitrary valence vertices of a graph in 3-dimensional Riemannian space, and can be represented by sign strings containing relative orientations of embedded edges. We demonstrate that these signature factors are a special representation of the general mathematical concept of an oriented matroid. Moreover, we show that oriented matroids can also be used to describe the topology (connectedness) of directed graphs. Hence the mathematical methods developed for oriented matroids can be applied to the difficult combinatorics of embedded graphs underlying the construction of LQG. As a first application we revisit the analysis of [4-5], and find that enumeration of all possible sign configurations used there is equivalent to enumerating all realizable oriented matroids of rank 3, and thus can be greatly simplified. We find that for 7-valent vertices having no coplanar triples of edge tangents, the smallest non-zero eigenvalue of the volume spectrum does not grow as one increases the maximum spin \jmax at the vertex, for any orientation of the edge tangents. This indicates that, in contrast to the area operator, considering large \jmax does not necessarily imply large volume eigenvalues. In addition we give an outlook to possible starting points for rewriting the combinatorics of LQG in terms of oriented matroids.Comment: 43 pages, 26 figures, LaTeX. Version published in CQG. Typos corrected, presentation slightly extende