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

Simulation of Binary Black Hole Spacetimes with a Harmonic Evolution Scheme

A numerical solution scheme for the Einstein field equations based on generalized harmonic coordinates is described, focusing on details not provided before in the literature and that are of particular relevance to the binary black hole problem. This includes demonstrations of the effectiveness of constraint damping, and how the time slicing can be controlled through the use of a source function evolution equation. In addition, some results from an ongoing study of binary black hole coalescence, where the black holes are formed via scalar field collapse, are shown. Scalar fields offer a convenient route to exploring certain aspects of black hole interactions, and one interesting, though tentative suggestion from this early study is that behavior reminiscent of "zoom-whirl" orbits in particle trajectories is also present in the merger of equal mass, non-spinning binaries, with appropriately fine-tuned initial conditions.Comment: 16 pages, 14 figures; replaced with published versio

Sudden drawdown and drainage of a horizontal aquifer

Drainage of a saturated horizontal aquifer following a sudden drawdown is reanalyzed using the Boussinesq equation. The effect of the finite length of the aquifer is considered in detail. An analytical approximation based on a superposition principle yields a very good estimate of the outflow when compared to accurate numerical solutions. An illustration of the new analytical approach to analyze basin-scale field data is used to demonstrate possible field applications of the new solution.<br /

Inner tegument protein pUL37 of herpes simplex virus type 1 is involved in directing capsids to the trans-Golgi network for envelopment

Secondary envelopment of herpes simplex virus type 1 has been demonstrated as taking place at the trans-Golgi network (TGN). The inner tegument proteins pUL36 and pUL37 and the envelope glycoproteins gD and gE are known to be important for secondary envelopment. We compared the cellular localizations of capsids from a virus mutant lacking the UL37 gene with those of a virus mutant lacking the genes encoding gD and gE. Although wild-type capsids accumulated at the TGN, capsids of the pUL37− mutant were distributed throughout the cytoplasm and showed no association with TGN-derived vesicles. This was in contrast to capsids from a gD−gE− mutant, which accumulated in the vicinity of TGN vesicles, but did not colocalize with them, suggesting that they were transported to the TGN but were unable to undergo envelopment. We conclude that the inner tegument protein pUL37 is required for directing capsids to the TGN, where secondary envelopment occurs

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&lt;sup&gt;0&lt;/sup&gt;(PMe&lt;sub&gt;3&lt;/sub&gt;)&lt;sub&gt;6&lt;/sub&gt;], [W&lt;sup&gt;II&lt;/sup&gt;Cl&lt;sub&gt;2&lt;/sub&gt;(PMePh&lt;sub&gt;2&lt;/sub&gt;)&lt;sub&gt;4&lt;/sub&gt;], [W&lt;sup&gt;III&lt;/sup&gt;Cl&lt;sub&gt;2&lt;/sub&gt;(dppe)&lt;sub&gt;2&lt;/sub&gt;][PF&lt;sub&gt;6&lt;/sub&gt;] (dppe = 1,2-bis(diphenylphosphino)ethane), [W&lt;sup&gt;IV&lt;/sup&gt;Cl&lt;sub&gt;4&lt;/sub&gt;(PMePh&lt;sub&gt;2&lt;/sub&gt;)&lt;sub&gt;2&lt;/sub&gt;], [W&lt;sup&gt;V&lt;/sup&gt;(NPh)Cl&lt;sub&gt;3&lt;/sub&gt;(PMe&lt;sub&gt;3&lt;/sub&gt;)&lt;sub&gt;2&lt;/sub&gt;], and [W&lt;sup&gt;VI&lt;/sup&gt;Cl&lt;sub&gt;6&lt;/sub&gt;] 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&lt;sub&gt;3,2&lt;/sub&gt;-edges and the L&lt;sub&gt;1&lt;/sub&gt; rising-edge energy with metal Z&lt;sub&gt;eff&lt;/sub&gt;, 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&lt;sup&gt;IV&lt;/sup&gt;(mdt)&lt;sub&gt;2&lt;/sub&gt;(CO)&lt;sub&gt;2&lt;/sub&gt;] and [W&lt;sup&gt;IV&lt;/sup&gt;(mdt)&lt;sub&gt;2&lt;/sub&gt;(CN)&lt;sub&gt;2&lt;/sub&gt;]&lt;sup&gt;2–&lt;/sup&gt; (mdt&lt;sup&gt;2–&lt;/sup&gt; = 1,2-dimethylethene-1,2-dithiolate), which shows that both compounds are effectively W&lt;sup&gt;IV&lt;/sup&gt; 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&lt;sub&gt;eff&lt;/sub&gt; 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&lt;sub&gt;eff&lt;/sub&gt; or, as in the case of [W&lt;sup&gt;IV&lt;/sup&gt;(mdt)&lt;sub&gt;2&lt;/sub&gt;(CO)&lt;sub&gt;2&lt;/sub&gt;], add other subtlety by modulating the redox level of other ligands in the coordination sphere

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

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

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.