1,175 research outputs found
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 and its time derivative
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
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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
'Education, education, education' : legal, moral and clinical
This article brings together Professor Donald Nicolson's intellectual interest in professional legal ethics and his long-standing involvement with law clinics both as an advisor at the University of Cape Town and Director of the University of Bristol Law Clinic and the University of Strathclyde Law Clinic. In this article he looks at how legal education may help start this process of character development, arguing that the best means is through student involvement in voluntary law clinics. And here he builds upon his recent article which argues for voluntary, community service oriented law clinics over those which emphasise the education of students
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