Simulating merging binary black holes with nearly extremal spins

Astrophysically realistic black holes may have spins that are nearly extremal (i.e., close to 1 in dimensionless units). Numerical simulations of binary black holes are important tools both for calibrating analytical templates for gravitational-wave detection and for exploring the nonlinear dynamics of curved spacetime. However, all previous simulations of binary-black-hole inspiral, merger, and ringdown have been limited by an apparently insurmountable barrier: the merging holes' spins could not exceed 0.93, which is still a long way from the maximum possible value in terms of the physical effects of the spin. In this paper, we surpass this limit for the first time, opening the way to explore numerically the behavior of merging, nearly extremal black holes. Specifically, using an improved initial-data method suitable for binary black holes with nearly extremal spins, we simulate the inspiral (through 12.5 orbits), merger and ringdown of two equal-mass black holes with equal spins of magnitude 0.95 antialigned with the orbital angular momentum.Comment: 4 pages, 2 figures, updated with version accepted for publication in Phys. Rev. D, removed a plot that was incorrectly included at the end of the article in version v

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

ANWENDUNG DES ZEITOPTIMALEN STEUERUNGSPRINZIPS ZUM ENTWURF EINES DDC REGELUNGSSYSTEMS

There are some similarities between the algorithms of the dead-beat and the time optimal (bang-bang) contro!. The similarities are based on the fact. that in both cases the input signal of the plant is formed by consecutive accelerating and deccelerating portions of constant amplitude. The paper presents a method to approximate the time optimal operation by a dead-beat algorithm. which can be realized in a closed loop

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

Perspective of interstitial hydrides of high-entropy alloys for vehicular hydrogen storage

The transport sector is an important source of CO2 emissions worldwide, and a transition towards hydrogen-fuelled vehicles is a potential remedy. These vehicles require improvements in storage capacities, which can be realised by forming the interstitial hydrides of High-Entropy Alloys (HEAs) by synthesising single-phase hydrides with a randomised atomic distribution of the metal elements within these alloys. Not only is the randomness of elemental distribution in the hydride essential, so too is the affinity of the individual components towards hydride formation, which drastically improves the prospective storage. By evaluating the composition and properties of the best-performing hydride forming alloys, various parameters strongly influencing hydrogen capacities can be inferred. Herein, the state of literature regarding the parameters with the highest importance for hydrogen sorption in HEAs is discussed for the first time with particular focus on how they may be introduced to storage on-board vehicles

A versatile characterization of poly(N-isopropylacrylamideco- N,N'-methylene-bis-acrylamide) hydrogels for composition, mechanical strength, and rheology

Poly(N-isopropylacrylamide-co-N,N"-methylene-bisacrylamide) (P(NIPAAm-co-MBA)) hydrogels were prepared in water using redox initiator. The copolymer composition at high conversion (> 95%) was determined indirectly by HPLC (high performance liquid chromatography) analysis of the leaching water and directly by solid state 13C CP MAS NMR (cross polarization magic angle spinning nuclear magnetic resonance) spectroscopy of the dried gels, and was found to be close to that of the feed. The effect of cross-linker (MBA) content in the copolymer was investigated in the concentration range of 1.1–9.1 mol% (R:90–10; R = mol NIPAAm/mol MBA) on the rheological behaviour and mechanical strength of the hydrogels. Both storage and loss modulus decreased with decreasing cross-linker content as revealed by dynamic rheometry. Gels R70 and R90 with very low cross-linker content (1.2–1.5 mol% MBA) have a very loose network structure, which is significantly different from those with higher cross-linker content manifesting in higher difference in storage modulus. The temperature dependence of the damping factor served the most accurate determination of the volume phase transition temperature, which was not affected by the cross-link density in the investigated range of MBA concentration. Gel R10 with highest cross-linker content (9.1 mol% MBA) behaves anomalously due to heterogeneity and the hindered conformation of the side chains of PNIPAAm

Accuracy and precision of gravitational-wave models of inspiraling neutron star -- black hole binaries with spin: comparison with numerical relativity in the low-frequency regime

Coalescing binaries of neutron stars (NS) and black holes (BH) are one of the most important sources of gravitational waves for the upcoming network of ground based detectors. Detection and extraction of astrophysical information from gravitational-wave signals requires accurate waveform models. The Effective-One-Body and other phenomenological models interpolate between analytic results and $10-30$ orbit numerical relativity (NR) merger simulations. In this paper we study the accuracy of these models using new NR simulations that span $36-88$ orbits, with mass-ratios and black hole spins $(q,\chi_{BH}) = (7, \pm 0.4), (7, \pm 0.6)$, and $(5, -0.9)$. We find that: (i) the recently published SEOBNRv1 and SEOBNRv2 models of the Effective-One-Body family disagree with each other (mismatches of a few percent) for black hole spins $\geq 0.5$ or $\leq -0.3$, with waveform mismatch accumulating during early inspiral; (ii) comparison with numerical waveforms indicate that this disagreement is due to phasing errors of SEOBNRv1, with SEOBNRv2 in good agreement with all of our simulations; (iii) Phenomenological waveforms disagree with SEOBNRv2 over most of the NSBH binary parameter space; (iv) comparison with NR waveforms shows that most of the model's dephasing accumulates near the frequency interval where it switches to a phenomenological phasing prescription; and finally (v) both SEOBNR and post-Newtonian (PN) models are effectual for NSBH systems, but PN waveforms will give a significant bias in parameter recovery. Our results suggest that future gravitational-wave detection searches and parameter estimation efforts targeted at NSBH systems with $q\lesssim 7$ and $\chi_\mathrm{BH} \approx [-0.9, +0.6]$ will benefit from using SEOBNRv2 templates. For larger black hole spins and/or binary mass-ratios, we recommend the models be further investigated as suitable NR simulations become available.Comment: 20 pages, 18 figure

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