The Merger of Small and Large Black Holes

We present simulations of binary black holes mergers in which, after the common outer horizon has formed, the marginally outer trapped surfaces (MOTSs) corresponding to the individual black holes continue to approach and eventually penetrate each other. This has very interesting consequences according to recent results in the theory of MOTSs. Uniqueness and stability theorems imply that two MOTSs which touch with a common outer normal must be identical. This suggests a possible dramatic consequence of the collision between a small and large black hole. If the penetration were to continue to completion then the two MOTSs would have to coalesce, by some combination of the small one growing and the big one shrinking. Here we explore the relationship between theory and numerical simulations, in which a small black hole has halfway penetrated a large one.Comment: 17 pages, 11 figure

Structural differences between mesophilic, moderately thermophilic and extremely thermophilic protein subunits: results of a comprehensive survey

AbstractBackground: Proteins from thermophilic organisms usually show high intrinsic thermal stability but have structures that are very similar to their mesophilic homologues. From prevous studies it is difficult to draw general conclusions about the structural features underlying the increased thermal stability of thermophilic proteins.Results: In order to reveal the general evolutionary strategy for changing the heat stability of proteins, a non-redundant data set was compiled comprising all high-quality structures of thermophilic proteins and their mesophilic homologues from the Protein Data Bank. The selection (quality) criteria were met by 64 mesophilic and 29 thermophilic protein subunits, representing 25 protein families. From the atomic coordinates, 13 structural parameters were calculated, compared and evaluated using statistical methods. This study is distinguished from earlier ones by the strict quality control of the structures used and the size of the data set.Conclusions: Different protein families adapt to higher temperatures by different sets of structural devices. Regarding the structural parameters, the only generally observed rule is an increase in the number of ion pairs with increasing growth temperature. Other parameters show just a trend, whereas the number of hydrogen bonds and the polarity of buried surfaces exhibit no clear-cut tendency to change with growth temperature. Proteins from extreme thermophiles are stabilized in different ways to moderately thermophilic ones. The preferences of these two groups are different with regards to the number of ion pairs, the number of cavities, the polarity of exposed surface and the secondary structural composition

Comparing Post-Newtonian and Numerical-Relativity Precession Dynamics

Binary black-hole systems are expected to be important sources of gravitational waves for upcoming gravitational-wave detectors. If the spins are not colinear with each other or with the orbital angular momentum, these systems exhibit complicated precession dynamics that are imprinted on the gravitational waveform. We develop a new procedure to match the precession dynamics computed by post-Newtonian (PN) theory to those of numerical binary black-hole simulations in full general relativity. For numerical relativity NR) simulations lasting approximately two precession cycles, we find that the PN and NR predictions for the directions of the orbital angular momentum and the spins agree to better than $\sim 1^{\circ}$ with NR during the inspiral, increasing to $5^{\circ}$ near merger. Nutation of the orbital plane on the orbital time-scale agrees well between NR and PN, whereas nutation of the spin direction shows qualitatively different behavior in PN and NR. We also examine how the PN equations for precession and orbital-phase evolution converge with PN order, and we quantify the impact of various choices for handling partially known PN terms

Well-Posed Initial-Boundary Evolution in General Relativity

Maximally dissipative boundary conditions are applied to the initial-boundary value problem for Einstein's equations in harmonic coordinates to show that it is well-posed for homogeneous boundary data and for boundary data that is small in a linearized sense. The method is implemented as a nonlinear evolution code which satisfies convergence tests in the nonlinear regime and is robustly stable in the weak field regime. A linearized version has been stably matched to a characteristic code to compute the gravitational waveform radiated to infinity.Comment: 5 pages, 6 figures; added another convergence plot to Fig. 2 + minor change

An Improved Gauge Driver for the Generalized Harmonic Einstein System

A new gauge driver is introduced for the generalized harmonic (GH) representation of Einstein's equation. This new driver allows a rather general class of gauge conditions to be implemented in a way that maintains the hyperbolicity of the combined evolution system. This driver is more stable and effective, and unlike previous drivers, allows stable evolutions using the dual-frame evolution technique. Appropriate boundary conditions for this new gauge driver are constructed, and a new boundary condition for the ``gauge'' components of the spacetime metric in the GH Einstein system is introduced. The stability and effectiveness of this new gauge driver are demonstrated through numerical tests, which impose a new damped-wave gauge condition on the evolutions of single black-hole spacetimes.Comment: v2: final version to be published in PRD; 15 pages, 5 figure

Sensor Drift Compensation Using Fuzzy Interference System and Sparse-Grid Quadrature Filter in Blood Glucose Control

Diabetes mellitus is a serious chronic condition of the human metabolism. The development of an automated treatment has reached clinical phase in the last few years. The goal is to keep the blood glucose concentration within a certain region with minimal interaction required by the patient or medical personnel. However, there are still several prac- tical problems to solve. One of these would be that the available sensors have significant noise and drift. The latter is rather difficult to manage, because the deviating signal can cause the controller to drive the glu- cose concentration out of the safe region even in the case of frequent calibration. In this study a linear-quadratic-Gaussian (LQG) controller is employed on a widely used diabetes model and enhanced with an ad- vanced Sparse-grid quadratic filter and a fuzzy interference system-based calibration supervisor

Stigmatising the Poor Without Negative Images: Images of Extreme Poverty and the Formation of Welfare Attitudes.

In the past two decades, many studies have warned of the role the popular media might play in the stigmatisation of the poor. Media reports about poverty often include references to antisocial behaviour, which make the principle of deservingness particularly conspicuous and could also strengthen the effects of ethnic stereotypes. We argue, however, that it could be misleading to place all the blame for stigmatisation on direct references to 'undeserving' behaviour. Media images of extreme distress themselves could have a selective stigmatising effect. Thus, even benevolent portrayal of the poor could erode sympathy. This paper presents the results of a video-vignette experiment on a sample of Hungarian students. The subjects watched one of four versions of a video interview with a poor person (none of them contained any references to antisocial behaviour) and then expressed their attitudes towards welfare payments. We found that support for welfare was higher where a version highlighted signs of extreme distress. But this was only the case if there were no mention of ethnic minorities. If the video report emphasized that Roma (Gypsies), the largest disadvantaged minority group in Hungary, lived in the neighbourhood, signs of their extreme hardship lowered the support for welfare payments

Three-Coordinate Copper(I) Amido and Aminyl Radical Complexes

Electron transfer (ET) through proteins often utilizes copper-containing active sites as efficient one-electron relays. The type-1 active sites of the blue copper proteins are prominent examples. It is generally thought that high ET rates through type-1 redox sites occur because the protein environments enforce unusual trigonally distorted coordination spheres to allow for minimal structural reorganization during ET. Though large Cu^II/Cu^I self-exchange ET rate constants (kS) in the range observed for type-1 sites have been achieved in certain synthetic monocopper systems using geometries distinct from trigonal environments, ET studies have yet to be conducted in a synthetic system featuring isolated, trigonally disposed copper centers. The simplest such systems would contain a trigonal planar geometry. Here we report the structural characterization of a trigonal planar system featuring formally Cu^II and Cu^I amido complexes related by a reversible one-electron redox event. We find in this system that ET is extremely rapid and is accompanied by a small degree of structural reorganization during redox. We propose that this structural rigidity in the absence of secondary coordination sphere effects results from significant covalency of the copper-amide linkages. In fact, a CuI-aminyl radical description of the formally Cu^II-amide complex may be most appropriate

Algebraic stability analysis of constraint propagation

The divergence of the constraint quantities is a major problem in computational gravity today. Apparently, there are two sources for constraint violations. The use of boundary conditions which are not compatible with the constraint equations inadvertently leads to 'constraint violating modes' propagating into the computational domain from the boundary. The other source for constraint violation is intrinsic. It is already present in the initial value problem, i.e. even when no boundary conditions have to be specified. Its origin is due to the instability of the constraint surface in the phase space of initial conditions for the time evolution equations. In this paper, we present a technique to study in detail how this instability depends on gauge parameters. We demonstrate this for the influence of the choice of the time foliation in context of the Weyl system. This system is the essential hyperbolic part in various formulations of the Einstein equations.Comment: 25 pages, 5 figures; v2: small additions, new reference, publication number, classification and keywords added, address fixed; v3: update to match journal versio

A Numerical Relativity Waveform Surrogate Model for Generically Precessing Binary Black Hole Mergers

A generic, non-eccentric binary black hole (BBH) system emits gravitational waves (GWs) that are completely described by 7 intrinsic parameters: the black hole spin vectors and the ratio of their masses. Simulating a BBH coalescence by solving Einstein's equations numerically is computationally expensive, requiring days to months of computing resources for a single set of parameter values. Since theoretical predictions of the GWs are often needed for many different source parameters, a fast and accurate model is essential. We present the first surrogate model for GWs from the coalescence of BBHs including all $7$ dimensions of the intrinsic non-eccentric parameter space. The surrogate model, which we call NRSur7dq2, is built from the results of $744$ numerical relativity simulations. NRSur7dq2 covers spin magnitudes up to $0.8$ and mass ratios up to $2$, includes all $\ell \leq 4$ modes, begins about $20$ orbits before merger, and can be evaluated in $\sim~50\,\mathrm{ms}$. We find the largest NRSur7dq2 errors to be comparable to the largest errors in the numerical relativity simulations, and more than an order of magnitude smaller than the errors of other waveform models. Our model, and more broadly the methods developed here, will enable studies that would otherwise require millions of numerical relativity waveforms, such as parameter inference and tests of general relativity with GW observations.Comment: 10 pages, 5 figures; Added report numbe