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Estimating Residual Faults from Code Coverage
Many reliability prediction techniques require an estimate for the number of residual faults. In this paper, a new theory is developed for using test coverage to estimate the number of residual faults. This theory is applied to a specific example with known faults and the results agree well with the theory. The theory is used to justify the use of linear extrapolation to estimate residual faults. It is also shown that it is important to establish the amount of unreachable code in order to make a realistic residual fault estimate
High-frequency data observations from space shuttle main engine low pressure fuel turbopump discharge duct flex joint tripod failure investigation
Observations made by Marshall Space Flight Center (MSFC) engineers during their participation in the Space Shuttle Main Engine (SSME) low pressure fuel turbopump discharge duct flex joint tripod failure investigation are summarized. New signal processing techniques used by the Component Assessment Branch and the Induced Environments Branch during the failure investigation are described in detail. Moreover, nonlinear correlations between frequently encountered anomalous frequencies found in SSME dynamic data are discussed. A recommendation is made to continue low pressure fuel (LPF) duct testing through laboratory flow simulations and MSFC-managed technology test bed SSME testing
Retention of Stellar-Mass Black Holes in Globular Clusters
Globular clusters should be born with significant numbers of stellar-mass
black holes (BHs). It has been thought for two decades that very few of these
BHs could be retained through the cluster lifetime. With masses ~10 MSun, BHs
are ~20 times more massive than an average cluster star. They segregate into
the cluster core, where they may eventually decouple from the remainder of the
cluster. The small-N core then evaporates on a short timescale. This is the
so-called Spitzer instability. Here we present the results of a full dynamical
simulation of a globular cluster containing many stellar-mass BHs with a
realistic mass spectrum. Our Monte Carlo simulation code includes detailed
treatments of all relevant stellar evolution and dynamical processes. Our main
finding is that old globular clusters could still contain many BHs at present.
In our simulation, we find no evidence for the Spitzer instability. Instead,
most of the BHs remain well-mixed with the rest of the cluster, with only the
innermost few tens of BHs segregating significantly. Over the 12 Gyr evolution,
fewer than half of the BHs are dynamically ejected through strong binary
interactions in the cluster core. The presence of BHs leads to long-term
heating of the cluster, ultimately producing a core radius on the high end of
the distribution for Milky Way globular clusters (and those of other galaxies).
A crude extrapolation from our model suggests that the BH--BH merger rate from
globular clusters could be comparable to the rate in the field.Comment: 5 pages, 4 figures, 1 table, published in Astrophysical Journal
Letter
Testing the no-hair theorem with GW150914
We analyze gravitational-wave data from the first LIGO detection of a binary
black-hole merger (GW150914) in search of the ringdown of the remnant black
hole. Using observations beginning at the peak of the signal, we find evidence
of the fundamental quasinormal mode and at least one overtone, both associated
with the dominant angular mode (), with confidence. A
ringdown model including overtones allows us to measure the final mass and spin
magnitude of the remnant exclusively from postinspiral data, obtaining an
estimate in agreement with the values inferred from the full signal. The mass
and spin values we measure from the ringdown agree with those obtained using
solely the fundamental mode at a later time, but have smaller uncertainties.
Agreement between the postinspiral measurements of mass and spin and those
using the full waveform supports the hypothesis that the GW150914 merger
produced a Kerr black hole, as predicted by general relativity, and provides a
test of the no-hair theorem at the level. An independent
measurement of the frequency of the first overtone yields agreement with the
no-hair hypothesis at the level. As the detector sensitivity
improves and the detected population of black hole mergers grows, we can expect
that using overtones will provide even stronger tests.Comment: v2: journal versio
Variational Integrators for Almost-Integrable Systems
We construct several variational integrators--integrators based on a discrete
variational principle--for systems with Lagrangians of the form L = L_A +
epsilon L_B, with epsilon << 1, where L_A describes an integrable system. These
integrators exploit that epsilon << 1 to increase their accuracy by
constructing discrete Lagrangians based on the assumption that the integrator
trajectory is close to that of the integrable system. Several of the
integrators we present are equivalent to well-known symplectic integrators for
the equivalent perturbed Hamiltonian systems, but their construction and error
analysis is significantly simpler in the variational framework. One novel
method we present, involving a weighted time-averaging of the perturbing terms,
removes all errors from the integration at O(epsilon). This last method is
implicit, and involves evaluating a potentially expensive time-integral, but
for some systems and some error tolerances it can significantly outperform
traditional simulation methods.Comment: 14 pages, 4 figures. Version 2: added informative example; as
accepted by Celestial Mechanics and Dynamical Astronom
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