5,479 research outputs found
It takes a village to raise a tide: nonlinear multiple-mode coupling and mode identification in KOI-54
We explore the tidal excitation of stellar modes in binary systems using
Kepler observations of the remarkable eccentric binary KOI-54 (HD 187091; KIC
8112039), which displays strong ellipsoidal variation as well as a variety of
linear and nonlinear pulsations. We report the amplitude and phase of over 120
harmonic and anharmonic pulsations in the system. We use pulsation phases to
determine that the two largest-amplitude pulsations, the 90th and 91st
harmonics, most likely correspond to axisymmetric m=0 modes in both stars, and
thus cannot be responsible for resonance locks as had been recently proposed.
We find evidence that the amplitude of at least one of these two pulsations is
decreasing with a characteristic timescale of ~100 yr. We also use the
pulsations' phases to confirm the onset of the traveling wave regime for
harmonic pulsations with frequencies <~50 Omega_orbit, in agreement with
theoretical expectations. We present evidence that many pulsations that are not
harmonics of the orbital frequency correspond to modes undergoing simultaneous
nonlinear coupling to multiple linearly driven parent modes. Since coupling
among multiple modes can lower the threshold for nonlinear interactions,
nonlinear phenomena may be easier to observe in highly eccentric systems, where
broader arrays of driving frequencies are available. This may help to explain
why the observed amplitudes of the linear pulsations are much smaller than the
theoretical threshold for decay via three-mode coupling.Comment: Accepted for publication in MNRAS. Only minor corrections. 16 Pages;
8 Figures; 3 Table
Production of Hypervelocity Stars through Encounters with Stellar-Mass Black Holes in the Galactic Centre
Stars within 0.1 pc of the supermassive black hole Sgr A* at the Galactic
centre are expected to encounter a cluster of stellar-mass black holes (BHs)
that have segregated to that region. Some of these stars will scatter off an
orbiting BH and be kicked out of the Galactic centre with velocities up to
~2000 km/s. We calculate the resulting ejection rate of hypervelocity stars
(HVSs) by this process under a variety of assumptions, and find it to be
comparable to the tidal disruption rate of binary stars by Sgr A*, first
discussed by Hills (1988). Under some conditions, this novel process is
sufficient to account for all of the hypervelocity B-stars observed in the
halo, and may dominate the production rate of all HVSs with lifetimes much less
than the relaxation time-scale at a distance ~2 pc from Sgr A* (>~ 2 Gyr).
Since HVSs are produced by at least two unavoidable processes, the statistics
of HVSs could reveal bimodal velocity and mass distributions, and can constrain
the distribution of BHs and stars in the innermost 0.1 pc around Sgr A*.Comment: 8 pages, 3 figures. Accepted for publication in MNRAS. Some major
changes to text, however conclusions remain the sam
Modeling Algorithms in SystemC and ACL2
We describe the formal language MASC, based on a subset of SystemC and
intended for modeling algorithms to be implemented in hardware. By means of a
special-purpose parser, an algorithm coded in SystemC is converted to a MASC
model for the purpose of documentation, which in turn is translated to ACL2 for
formal verification. The parser also generates a SystemC variant that is
suitable as input to a high-level synthesis tool. As an illustration of this
methodology, we describe a proof of correctness of a simple 32-bit radix-4
multiplier.Comment: In Proceedings ACL2 2014, arXiv:1406.123
Two paths of cluster evolution: global expansion versus core collapse
All gravitationally bound clusters expand, due to both gas loss from their
most massive members and binary heating. All are eventually disrupted tidally,
either by passing molecular clouds or the gravitational potential of their host
galaxies. However, their interior evolution can follow two very different
paths. Only clusters of sufficiently large initial population and size undergo
the combined interior contraction and exterior expansion that leads eventually
to core collapse. In all other systems, core collapse is frustrated by binary
heating. These clusters globally expand for their entire lives, up to the point
of tidal disruption.
Using a suite of direct N-body calculations, we trace the "collapse line" in
r_v-N space that separates these two paths. Here, r_v and N are the cluster's
initial virial radius and population, respectively. For realistic starting
radii, the dividing N-value is from 10^4 to over 10^5. We also show that there
exists a minimum population, N_min, for core collapse. Clusters with N < N_min
tidally disrupt before core collapse occurs. At the Sun's Galactocentric
radius, R_G = 8.5 kpc, we find N_min >~ 300. The minimum population scales with
Galactocentric radius as R_G^{-9/8}.
The position of an observed cluster relative to the collapse line can be used
to predict its future evolution. Using a small sample of open clusters, we find
that most lie below the collapse line, and thus will never undergo core
collapse. Most globular clusters, on the other hand, lie well above the line.
In such a case, the cluster may or may not go through core collapse, depending
on its initial size. We show how an accurate age determination can help settle
this issue.Comment: Accepted for publication in MNRAS. 14 Pages, 9 Figures, 2 Table
Analysis of ultrasonic transducers with fractal architecture
Ultrasonic transducers composed of a periodic piezoelectric composite are generally accepted as the design of choice in many applications. Their architecture is normally very regular and this is due to manufacturing constraints rather than performance optimisation. Many of these manufacturing restrictions no longer hold due to new production methods such as computer controlled, laser cutting, and so there is now freedom to investigate new types of geometry. In this paper, the plane wave expansion model is utilised to investigate the behaviour of a transducer with a self-similar architecture. The Cantor set is utilised to design a 2-2 conguration, and a 1-3 conguration is investigated with a Sierpinski Carpet geometry
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