The Lazarus project: A pragmatic approach to binary black hole evolutions

We present a detailed description of techniques developed to combine 3D numerical simulations and, subsequently, a single black hole close-limit approximation. This method has made it possible to compute the first complete waveforms covering the post-orbital dynamics of a binary black hole system with the numerical simulation covering the essential non-linear interaction before the close limit becomes applicable for the late time dynamics. To determine when close-limit perturbation theory is applicable we apply a combination of invariant a priori estimates and a posteriori consistency checks of the robustness of our results against exchange of linear and non-linear treatments near the interface. Once the numerically modeled binary system reaches a regime that can be treated as perturbations of the Kerr spacetime, we must approximately relate the numerical coordinates to the perturbative background coordinates. We also perform a rotation of a numerically defined tetrad to asymptotically reproduce the tetrad required in the perturbative treatment. We can then produce numerical Cauchy data for the close-limit evolution in the form of the Weyl scalar $\psi_4$ and its time derivative $\partial_t\psi_4$ with both objects being first order coordinate and tetrad invariant. The Teukolsky equation in Boyer-Lindquist coordinates is adopted to further continue the evolution. To illustrate the application of these techniques we evolve a single Kerr hole and compute the spurious radiation as a measure of the error of the whole procedure. We also briefly discuss the extension of the project to make use of improved full numerical evolutions and outline the approach to a full understanding of astrophysical black hole binary systems which we can now pursue.Comment: New typos found in the version appeared in PRD. (Mostly found and collected by Bernard Kelly

Magnetic force microscopy of single-domain cobalt dots patterned using interference lithography

We have fabricated arrays of Co dots of diameters 100 and 70 nm using interference lithography. Density of these arrays is 7.2x10{sup 9}/in{sup 2}. Magnetic force microscopy indicate that the Co dots are single domain with moments that can be controlled to point either in-plane or out-of-plane. Interference lithography is a process that is easily scaled to large areas and is potentially capable of high throughput. Large, uniform arrays of single-domain structures are potentially useful for high-density, low-noise data storage

Modeling gravitational radiation from coalescing binary black holes

With the goal of bringing theory, particularly numerical relativity, to bear on an astrophysical problem of critical interest to gravitational wave observers we introduce a model for coalescence radiation from binary black hole systems. We build our model using the "Lazarus approach", a technique that bridges far and close limit approaches with full numerical relativity to solve Einstein equations applied in the truly nonlinear dynamical regime. We specifically study the post-orbital radiation from a system of equal-mass non-spinning black holes, deriving waveforms which indicate strongly circularly polarized radiation of roughly 3% of the system's total energy and 12% of its total angular momentum in just a few cycles. Supporting this result we first establish the reliability of the late-time part of our model, including the numerical relativity and close-limit components, with a thorough study of waveforms from a sequence of black hole configurations varying from previously treated head-on collisions to representative target for ``ISCO'' data corresponding to the end of the inspiral period. We then complete our model with a simple treatment for the early part of the spacetime based on a standard family of initial data for binary black holes in circular orbit. A detailed analysis shows strong robustness in the results as the initial separation of the black holes is increased from 5.0 to 7.8M supporting our waveforms as a suitable basic description of the astrophysical radiation from this system. Finally, a simple fitting of the plunge waveforms is introduced as a first attempt to facilitate the task of analyzing data from gravitational wave detectors.Comment: 23 pages, 36 figures, RevTeX

Preparation of facilities for fundamental research with ultracold neutrons at PNPI

The WWR-M reactor of PNPI offers a unique opportunity to prepare a source for ultracold neutrons (UCN) in an environment of high neutron flux (about 3*10^12 n/cm^2/s) at still acceptable radiation heat release (about 4*10^-3 W/g). It can be realized within the reactor thermal column situated close to the reactor core. With its large diameter of 1 m, this channel allows to install a 15 cm thick bismuth shielding, a graphite premoderator (300 dm^3 at 20 K), and a superfluid helium converter (35 dm^3). At a temperature of 1.2 K it is possible to remove the heat release power of about 20 W. Using the 4pi flux of cold neutrons within the reactor column can bring more than a factor 100 of cold neutron flux incident on the superfluid helium with respect to the present cold neutron beam conditions at the ILL reactor. The storage lifetime for UCN in superfluid He at 1.2 K is about 30 s, which is sufficient when feeding experiments requiring a similar filling time. The calculated density of UCN with energy between 50 neV and 250 neV in an experimental volume of 40 liters is about 10^4 n/cm^3. Technical solutions for realization of the project are discussed.Comment: 10 pages, more detail

Weak convergence of finite element approximations of linear stochastic evolution equations with additive noise II. Fully discrete schemes

We present an abstract framework for analyzing the weak error of fully discrete approximation schemes for linear evolution equations driven by additive Gaussian noise. First, an abstract representation formula is derived for sufficiently smooth test functions. The formula is then applied to the wave equation, where the spatial approximation is done via the standard continuous finite element method and the time discretization via an I-stable rational approximation to the exponential function. It is found that the rate of weak convergence is twice that of strong convergence. Furthermore, in contrast to the parabolic case, higher order schemes in time, such as the Crank-Nicolson scheme, are worthwhile to use if the solution is not very regular. Finally we apply the theory to parabolic equations and detail a weak error estimate for the linearized Cahn-Hilliard-Cook equation as well as comment on the stochastic heat equation

Effects of small surface tension in Hele-Shaw multifinger dynamics: an analytical and numerical study

We study the singular effects of vanishingly small surface tension on the dynamics of finger competition in the Saffman-Taylor problem, using the asymptotic techniques described in [S. Tanveer, Phil. Trans. R. Soc. Lond. A 343, 155 (1993)]and [M. Siegel, and S. Tanveer, Phys. Rev. Lett. 76, 419 (1996)] as well as direct numerical computation, following the numerical scheme of [T. Hou, J. Lowengrub, and M. Shelley,J. Comp. Phys. 114, 312 (1994)]. We demonstrate the dramatic effects of small surface tension on the late time evolution of two-finger configurations with respect to exact (non-singular) zero surface tension solutions. The effect is present even when the relevant zero surface tension solution has asymptotic behavior consistent with selection theory.Such singular effects therefore cannot be traced back to steady state selection theory, and imply a drastic global change in the structure of phase-space flow. They can be interpreted in the framework of a recently introduced dynamical solvability scenario according to which surface tension unfolds the structually unstable flow, restoring the hyperbolicity of multifinger fixed points.Comment: 16 pages, 15 figures, submitted to Phys. Rev

Dynamical Systems approach to Saffman-Taylor fingering. A Dynamical Solvability Scenario

A dynamical systems approach to competition of Saffman-Taylor fingers in a channel is developed. This is based on the global study of the phase space structure of the low-dimensional ODE's defined by the classes of exact solutions of the problem without surface tension. Some simple examples are studied in detail, and general proofs concerning properties of fixed points and existence of finite-time singularities for broad classes of solutions are given. The existence of a continuum of multifinger fixed points and its dynamical implications are discussed. The main conclusion is that exact zero-surface tension solutions taken in a global sense as families of trajectories in phase space spanning a sufficiently large set of initial conditions, are unphysical because the multifinger fixed points are nonhyperbolic, and an unfolding of them does not exist within the same class of solutions. Hyperbolicity (saddle-point structure) of the multifinger fixed points is argued to be essential to the physically correct qualitative description of finger competition. The restoring of hyperbolicity by surface tension is discussed as the key point for a generic Dynamical Solvability Scenario which is proposed for a general context of interfacial pattern selection.Comment: 3 figures added, major rewriting of some sections, submitted to Phys. Rev.

Large internal waves in Massachusetts Bay transport sediments offshore

This paper is not subject to U.S. copyright. The definitive version was published in Continental Shelf Research 26 (2006): 2029-2049, doi:10.1016/j.csr.2006.07.022.A field experiment was carried out in Massachusetts Bay in August 1998 to assess the role of large-amplitude internal waves (LIWs) in resuspending bottom sediments. The field experiment consisted of a four-element moored array extending from just west of Stellwagen Bank (90-m water depth) across Stellwagen Basin (85- and 50-m water depth) to the coast (24-m water depth). The LIWs were observed in packets of 5–10 waves, had periods of 5–10 min and wavelengths of 200–400 m, and caused downward excursions of the thermocline of as much as 30 m. At the 85-m site, the current measured 1 m above bottom (mab) typically increased from near 0 to 0.2 m/s offshore in a few minutes upon arrival of the LIWs. At the 50-m site, the near-bottom offshore flow measured 6 mab increased from about 0.1 to 0.4–0.6 m/s upon arrival of the LIWs and remained offshore in the bottom layer for 1–2 h. The near-bottom currents associated with the LIWs, in concert with the tidal currents, were directed offshore and sufficient to resuspend the bottom sediments at both the 50- and 85-m sites. When LIWs are present, they may resuspend sediments for as long as 5 hours each tidal cycle as they travel westward across Stellwagen Basin. At 85-m water depth, resuspension associated with LIWs is estimated to occur for about 0.4 days each summer, about the same amount of time as caused by surface waves.MBIWE98 was supported by the USGS and the Office of Naval Research (ONR). The long-term observations at LT-A and LT-B were conducted under a Joint Funding Agreement between the USGS and the Massachusetts Water Resources Authority and an Inter-Service Agreement with the US Coast Guard. A. Scotti received support from the WHOI Postdoctoral Scholar program, the Johnson Foundation, the USGS, and ONR through grant N00014-01-1-0172; R. Beardsley through ONR grants N00014-98-1-0059, N00014-00-1-0210 and the WHOI Smith Chair in Coastal Physical Oceanography; and S. Anderson through ONR grant N000140-97-1-0158

Life path analysis: scaling indicates priming effects of social and habitat factors on dispersal distances

1. Movements of many animals along a life-path can be separated into repetitive ones within home ranges and transitions between home ranges. We sought relationships of social and environmental factors with initiation and distance of transition movements in 114 buzzards Buteo buteo that were marked as nestlings with long-life radio tags. 2. Ex-natal dispersal movements of 51 buzzards in autumn were longer than for 30 later in their first year and than 35 extra-natal movements between home ranges after leaving nest areas. In the second and third springs, distances moved from winter focal points by birds that paired were the same or less than for unpaired birds. No post-nuptial movement exceeded 2 km. 3. Initiation of early ex-natal dispersal was enhanced by presence of many sibs, but also by lack of worm-rich loam soils. Distances travelled were greatest for birds from small broods and with relatively little short grass-feeding habitat near the nest. Later movements were generally enhanced by the absence of loam soils and short grassland, especially with abundance of other buzzards and probable poor feeding habitats (heathland, long grass). 4. Buzzards tended to persist in their first autumn where arable land was abundant, but subsequently showed a strong tendency to move from this habitat. 5. Factors that acted most strongly in ½-km buffers round nests, or round subsequent focal points, usually promoted movement compared with factors acting at a larger scale. Strong relationships between movement distances and environmental characteristics in ½-km buffers, especially during early ex-natal dispersal, suggested that buzzards became primed by these factors to travel far. 6. Movements were also farthest for buzzards that had already moved far from their natal nests, perhaps reflecting genetic predisposition, long-term priming or poor habitat beyond the study area

Influence of storm surge on tidal range energy

The regular and predictable nature of the tide makes the generation of electricity with a tidal lagoon or barrage an attractive form of renewable energy, yet storm surges affect the total water-level. Here, we present the first assessment of the potential impact of storm surges on tidal-range power. Water-level data (2000–2012) at nine UK tide gauges, where tidal-range energy is suitable for development (e.g. Bristol Channel), was used to predict power. Storm surge affected annual resource estimates −5% to +3%, due to inter-annual variability, which is lower than other sources of uncertainty (e.g. lagoon design); therefore, annual resource estimation from astronomical tides alone appears sufficient. However, instantaneous power output was often significantly affected (Normalised Root Mean Squared Error: 3%–8%, Scatter Index: 15%–41%) and so a storm surge prediction system may be required for any future electricity generation scenario that includes large amounts of tidal-range generation. The storm surge influence to tidal-range power varied with the electricity generation strategy considered (flooding tide only, ebb-only or dual; both flood and ebb), but with some spatial and temporal variability. The flood-only strategy was most affected by storm surge, mostly likely because tide-surge interaction increases the chance of higher water-levels on the flooding tide