Initial data transients in binary black hole evolutions

We describe a method for initializing characteristic evolutions of the Einstein equations using a linearized solution corresponding to purely outgoing radiation. This allows for a more consistent application of the characteristic (null cone) techniques for invariantly determining the gravitational radiation content of numerical simulations. In addition, we are able to identify the {\em ingoing} radiation contained in the characteristic initial data, as well as in the initial data of the 3+1 simulation. We find that each component leads to a small but long lasting (several hundred mass scales) transient in the measured outgoing gravitational waves.Comment: 18 pages, 4 figure

Black Hole Mergers and Unstable Circular Orbits

We describe recent numerical simulations of the merger of a class of equal mass, non-spinning, eccentric binary black hole systems in general relativity. We show that with appropriate fine-tuning of the initial conditions to a region of parameter space we denote the threshold of immediate merger, the binary enters a phase of close interaction in a near-circular orbit, stays there for an amount of time proportional to logarithmic distance from the threshold in parameter space, then either separates or merges to form a single Kerr black hole. To gain a better understanding of this phenomena we study an analogous problem in the evolution of equatorial geodesics about a central Kerr black hole. A similar threshold of capture exists for appropriate classes of initial conditions, and tuning to threshold the geodesics approach one of the unstable circular geodesics of the Kerr spacetime. Remarkably, with a natural mapping of the parameters of the geodesic to that of the equal mass system, the scaling exponent describing the whirl phase of each system turns out to be quite similar. Armed with this lone piece of evidence that an approximate correspondence might exist between near-threshold evolution of geodesics and generic binary mergers, we illustrate how this information can be used to estimate the cross section and energy emitted in the ultra relativistic black hole scattering problem. This could eventually be of use in providing estimates for the related problem of parton collisions at the Large Hadron Collider in extra dimension scenarios where black holes are produced.Comment: 16 pages, 12 figures; updated to coincide with journal versio

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

Parameter Estimation Method that Directly Compares Gravitational Wave Observations to Numerical Relativity

We present and assess a Bayesian method to interpret gravitational wave signals from binary black holes. Our method directly compares gravitational wave data to numerical relativity simulations. This procedure bypasses approximations used in semi-analytical models for compact binary coalescence. In this work, we use only the full posterior parameter distribution for generic nonprecessing binaries, drawing inferences away from the set of NR simulations used, via interpolation of a single scalar quantity (the marginalized log-likelihood, $\ln {\cal L}$) evaluated by comparing data to nonprecessing binary black hole simulations. We also compare the data to generic simulations, and discuss the effectiveness of this procedure for generic sources. We specifically assess the impact of higher order modes, repeating our interpretation with both $l\le2$ as well as $l\le3$ harmonic modes. Using the $l\le3$ higher modes, we gain more information from the signal and can better constrain the parameters of the gravitational wave signal. We assess and quantify several sources of systematic error that our procedure could introduce, including simulation resolution and duration; most are negligible. We show through examples that our method can recover the parameters for equal mass, zero spin; GW150914-like; and unequal mass, precessing spin sources. Our study of this new parameter estimation method demonstrates we can quantify and understand the systematic and statistical error. This method allows us to use higher order modes from numerical relativity simulations to better constrain the black hole binary parameters

Numerical Relativity Using a Generalized Harmonic Decomposition

A new numerical scheme to solve the Einstein field equations based upon the generalized harmonic decomposition of the Ricci tensor is introduced. The source functions driving the wave equations that define generalized harmonic coordinates are treated as independent functions, and encode the coordinate freedom of solutions. Techniques are discussed to impose particular gauge conditions through a specification of the source functions. A 3D, free evolution, finite difference code implementing this system of equations with a scalar field matter source is described. The second-order-in-space-and-time partial differential equations are discretized directly without the use first order auxiliary terms, limiting the number of independent functions to fifteen--ten metric quantities, four source functions and the scalar field. This also limits the number of constraint equations, which can only be enforced to within truncation error in a numerical free evolution, to four. The coordinate system is compactified to spatial infinity in order to impose physically motivated, constraint-preserving outer boundary conditions. A variant of the Cartoon method for efficiently simulating axisymmetric spacetimes with a Cartesian code is described that does not use interpolation, and is easier to incorporate into existing adaptive mesh refinement packages. Preliminary test simulations of vacuum black hole evolution and black hole formation via scalar field collapse are described, suggesting that this method may be useful for studying many spacetimes of interest.Comment: 18 pages, 6 figures; updated to coincide with journal version, which includes some expanded discussions and a new appendix with a stability analysis of a simplified problem using the same discretization scheme described in the pape

X-ray absorption spectroscopy systematics at the tungsten L-edge

A series of mononuclear six-coordinate tungsten compounds spanning formal oxidation states from 0 to +VI, largely in a ligand environment of inert chloride and/or phosphine, has been interrogated by tungsten L-edge X-ray absorption spectroscopy. The L-edge spectra of this compound set, comprised of [W<sup>0</sup>(PMe<sub>3</sub>)<sub>6</sub>], [W<sup>II</sup>Cl<sub>2</sub>(PMePh<sub>2</sub>)<sub>4</sub>], [W<sup>III</sup>Cl<sub>2</sub>(dppe)<sub>2</sub>][PF<sub>6</sub>] (dppe = 1,2-bis(diphenylphosphino)ethane), [W<sup>IV</sup>Cl<sub>4</sub>(PMePh<sub>2</sub>)<sub>2</sub>], [W<sup>V</sup>(NPh)Cl<sub>3</sub>(PMe<sub>3</sub>)<sub>2</sub>], and [W<sup>VI</sup>Cl<sub>6</sub>] correlate with formal oxidation state and have usefulness as references for the interpretation of the L-edge spectra of tungsten compounds with redox-active ligands and ambiguous electronic structure descriptions. The utility of these spectra arises from the combined correlation of the estimated branching ratio (EBR) of the L<sub>3,2</sub>-edges and the L<sub>1</sub> rising-edge energy with metal Z<sub>eff</sub>, thereby permitting an assessment of effective metal oxidation state. An application of these reference spectra is illustrated by their use as backdrop for the L-edge X-ray absorption spectra of [W<sup>IV</sup>(mdt)<sub>2</sub>(CO)<sub>2</sub>] and [W<sup>IV</sup>(mdt)<sub>2</sub>(CN)<sub>2</sub>]<sup>2–</sup> (mdt<sup>2–</sup> = 1,2-dimethylethene-1,2-dithiolate), which shows that both compounds are effectively W<sup>IV</sup> species. Use of metal L-edge XAS to assess a compound of uncertain formulation requires: 1) Placement of that data within the context of spectra offered by unambiguous calibrant compounds, preferably with the same coordination number and similar metal ligand distances. Such spectra assist in defining upper and/or lower limits for metal Z<sub>eff</sub> in the species of interest; 2) Evaluation of that data in conjunction with information from other physical methods, especially ligand K-edge XAS; 3) Increased care in interpretation if strong π-acceptor ligands, particularly CO, or π-donor ligands are present. The electron-withdrawing/donating nature of these ligand types, combined with relatively short metal-ligand distances, exaggerate the difference between formal oxidation state and metal Z<sub>eff</sub> or, as in the case of [W<sup>IV</sup>(mdt)<sub>2</sub>(CO)<sub>2</sub>], add other subtlety by modulating the redox level of other ligands in the coordination sphere

Versatile Coordination of Cyclopentadienyl-Arene Ligands and Its Role in Titanium-Catalyzed Ethylene Trimerization

Cationic titanium(IV) complexes with ansa-(η5-cyclopentadienyl,η6-arene) ligands were synthesized and characterized by X-ray crystallography. The strength of the metal-arene interaction in these systems was studied by variable-temperature NMR spectroscopy. Complexes with a C1 bridge between the cyclopentadienyl and arene moieties feature hemilabile coordination behavior of the ligand and consequently are active ethylene trimerization catalysts. Reaction of the titanium(IV) dimethyl cations with CO results in conversion to the analogous cationic titanium(II) dicarbonyl species. Metal-to-ligand backdonation in these formally low-valent complexes gives rise to a strongly bonded, partially reduced arene moiety. In contrast to the η6-arene coordination mode observed for titanium, the more electron-rich vanadium(V) cations [cyclopentadienyl-arene]V(NiPr2)(NC6H4-4-Me)+ feature η1-arene binding, as determined by a crystallographic study. The three different metal-arene coordination modes that we experimentally observed model intermediates in the cycle for titanium-catalyzed ethylene trimerization. The nature of the metal-arene interaction in these systems was studied by DFT calculations.

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

Vaccination coverage and reasons for non-vaccination in a district of Istanbul

BACKGROUND: In order to control and eliminate the vaccine preventable diseases it is important to know the vaccination coverage and reasons for non-vaccination. The primary objective of this study was to determine the complete vaccination rate; the reasons for non-vaccination and the predictors that influence vaccination of children. The other objective was to determine coverage of measles vaccination of the Measles Immunization Days (MID) 2005 for children aged 9 month to 6 years in a region of Umraniye, Istanbul, Turkey. METHODS: A '30 × 7' cluster sampling design was used as the sampling method. Thirty streets were selected at random from study area. Survey data were collected by a questionnaire which was applied face to face to parents of 221 children. A Chi-square test and logistic regression was used for the statistical analyses. Content analysis method was used to evaluate the open-ended questions. RESULTS: The complete vaccination rate for study population was 84.5% and 3.2% of all children were totally non-vaccinated. The siblings of non-vaccinated children were also non-vaccinated. Reasons for non-vaccination were as follows: being in the village and couldn't reach to health care services; having no knowledge about vaccination; the father of child didn't allow vaccination; intercurrent illness of child during vaccination time; missed opportunities like not to shave off a vial for only one child. In logistic regression analysis, paternal and maternal levels of education and immigration time of both parents to Istanbul were found to influence whether children were completely vaccinated or non-vaccinated. Measles vaccination coverage during MID was 79.3%. CONCLUSION: Efforts to increase vaccination coverage should take reasons for non-vaccination into account