9,630 research outputs found
Evidence from K2 for rapid rotation in the descendant of an intermediate-mass star
Using patterns in the oscillation frequencies of a white dwarf observed by
K2, we have measured the fastest rotation rate, 1.13(02) hr, of any isolated
pulsating white dwarf known to date. Balmer-line fits to follow-up spectroscopy
from the SOAR telescope show that the star (SDSSJ0837+1856, EPIC 211914185) is
a 13,590(340) K, 0.87(03) solar-mass white dwarf. This is the highest mass
measured for any pulsating white dwarf with known rotation, suggesting a
possible link between high mass and fast rotation. If it is the product of
single-star evolution, its progenitor was a roughly 4.0 solar-mass
main-sequence B star; we know very little about the angular momentum evolution
of such intermediate-mass stars. We explore the possibility that this rapidly
rotating white dwarf is the byproduct of a binary merger, which we conclude is
unlikely given the pulsation periods observed.Comment: 5 pages, 4 figure, 1 table; accepted for publication in The
Astrophysical Journal Letter
Active Sampling-based Binary Verification of Dynamical Systems
Nonlinear, adaptive, or otherwise complex control techniques are increasingly
relied upon to ensure the safety of systems operating in uncertain
environments. However, the nonlinearity of the resulting closed-loop system
complicates verification that the system does in fact satisfy those
requirements at all possible operating conditions. While analytical proof-based
techniques and finite abstractions can be used to provably verify the
closed-loop system's response at different operating conditions, they often
produce conservative approximations due to restrictive assumptions and are
difficult to construct in many applications. In contrast, popular statistical
verification techniques relax the restrictions and instead rely upon
simulations to construct statistical or probabilistic guarantees. This work
presents a data-driven statistical verification procedure that instead
constructs statistical learning models from simulated training data to separate
the set of possible perturbations into "safe" and "unsafe" subsets. Binary
evaluations of closed-loop system requirement satisfaction at various
realizations of the uncertainties are obtained through temporal logic
robustness metrics, which are then used to construct predictive models of
requirement satisfaction over the full set of possible uncertainties. As the
accuracy of these predictive statistical models is inherently coupled to the
quality of the training data, an active learning algorithm selects additional
sample points in order to maximize the expected change in the data-driven model
and thus, indirectly, minimize the prediction error. Various case studies
demonstrate the closed-loop verification procedure and highlight improvements
in prediction error over both existing analytical and statistical verification
techniques.Comment: 23 page
Triangleland. I. Classical dynamics with exchange of relative angular momentum
In Euclidean relational particle mechanics, only relative times, relative
angles and relative separations are meaningful. Barbour--Bertotti (1982) theory
is of this form and can be viewed as a recovery of (a portion of) Newtonian
mechanics from relational premises. This is of interest in the absolute versus
relative motion debate and also shares a number of features with the
geometrodynamical formulation of general relativity, making it suitable for
some modelling of the problem of time in quantum gravity. I also study
similarity relational particle mechanics (`dynamics of pure shape'), in which
only relative times, relative angles and {\sl ratios of} relative separations
are meaningful. This I consider firstly as it is simpler, particularly in 1 and
2 d, for which the configuration space geometry turns out to be well-known,
e.g. S^2 for the `triangleland' (3-particle) case that I consider in detail.
Secondly, the similarity model occurs as a sub-model within the Euclidean
model: that admits a shape--scale split. For harmonic oscillator like
potentials, similarity triangleland model turns out to have the same
mathematics as a family of rigid rotor problems, while the Euclidean case turns
out to have parallels with the Kepler--Coulomb problem in spherical and
parabolic coordinates. Previous work on relational mechanics covered cases
where the constituent subsystems do not exchange relative angular momentum,
which is a simplifying (but in some ways undesirable) feature paralleling
centrality in ordinary mechanics. In this paper I lift this restriction. In
each case I reduce the relational problem to a standard one, thus obtain
various exact, asymptotic and numerical solutions, and then recast these into
the original mechanical variables for physical interpretation.Comment: Journal Reference added, minor updates to References and Figure
Distribution of the Riemann zeros represented by the Fermi gas
The multiparticle density matrices for degenerate, ideal Fermi gas system in
any dimension are calculated. The results are expressed as a determinant form,
in which a correlation kernel plays a vital role. Interestingly, the
correlation structure of one-dimensional Fermi gas system is essentially
equivalent to that observed for the eigenvalue distribution of random unitary
matrices, and thus to that conjectured for the distribution of the non-trivial
zeros of the Riemann zeta function. Implications of the present findings are
discussed briefly.Comment: 7 page
On the spacing distribution of the Riemann zeros: corrections to the asymptotic result
It has been conjectured that the statistical properties of zeros of the
Riemann zeta function near z = 1/2 + \ui E tend, as , to the
distribution of eigenvalues of large random matrices from the Unitary Ensemble.
At finite numerical results show that the nearest-neighbour spacing
distribution presents deviations with respect to the conjectured asymptotic
form. We give here arguments indicating that to leading order these deviations
are the same as those of unitary random matrices of finite dimension , where is a well
defined constant.Comment: 9 pages, 3 figure
Optimal rotations of deformable bodies and orbits in magnetic fields
Deformations can induce rotation with zero angular momentum where dissipation
is a natural ``cost function''. This gives rise to an optimization problem of
finding the most effective rotation with zero angular momentum. For certain
plastic and viscous media in two dimensions the optimal path is the orbit of a
charged particle on a surface of constant negative curvature with magnetic
field whose total flux is half a quantum unit.Comment: 4 pages revtex, 4 figures + animation in multiframe GIF forma
White Dwarf Rotation as a Function of Mass and a Dichotomy of Mode Linewidths: Kepler Observations of 27 Pulsating DA White Dwarfs Through K2 Campaign 8
We present photometry and spectroscopy for 27 pulsating hydrogen-atmosphere
white dwarfs (DAVs, a.k.a. ZZ Ceti stars) observed by the Kepler space
telescope up to K2 Campaign 8, an extensive compilation of observations with
unprecedented duration (>75 days) and duty cycle (>90%). The space-based
photometry reveals pulsation properties previously inaccessible to ground-based
observations. We observe a sharp dichotomy in oscillation mode linewidths at
roughly 800 s, such that white dwarf pulsations with periods exceeding 800 s
have substantially broader mode linewidths, more reminiscent of a damped
harmonic oscillator than a heat-driven pulsator. Extended Kepler coverage also
permits extensive mode identification: We identify the spherical degree of 61
out of 154 unique radial orders, providing direct constraints of the rotation
period for 20 of these 27 DAVs, more than doubling the number of white dwarfs
with rotation periods determined via asteroseismology. We also obtain
spectroscopy from 4m-class telescopes for all DAVs with Kepler photometry.
Using these homogeneously analyzed spectra we estimate the overall mass of all
27 DAVs, which allows us to measure white dwarf rotation as a function of mass,
constraining the endpoints of angular momentum in low- and intermediate-mass
stars. We find that 0.51-to-0.73-solar-mass white dwarfs, which evolved from
1.7-to-3.0-solar-mass ZAMS progenitors, have a mean rotation period of 35 hr
with a standard deviation of 28 hr, with notable exceptions for higher-mass
white dwarfs. Finally, we announce an online repository for our Kepler data and
follow-up spectroscopy, which we collect at http://www.k2wd.org.Comment: 33 pages, 31 figures, 5 tables; accepted for publication in ApJS. All
raw and reduced data are collected at http://www.k2wd.or
Pulsational Mapping of Calcium Across the Surface of a White Dwarf
We constrain the distribution of calcium across the surface of the white
dwarf star G29-38 by combining time series spectroscopy from Gemini-North with
global time series photometry from the Whole Earth Telescope. G29-38 is
actively accreting metals from a known debris disk. Since the metals sink
significantly faster than they mix across the surface, any inhomogeneity in the
accretion process will appear as an inhomogeneity of the metals on the surface
of the star. We measure the flux amplitudes and the calcium equivalent width
amplitudes for two large pulsations excited on G29-38 in 2008. The ratio of
these amplitudes best fits a model for polar accretion of calcium and rules out
equatorial accretion.Comment: Accepted to the Astrophysical Journal. 16 pages, 10 figures
Random matrix theory, the exceptional Lie groups, and L-functions
There has recently been interest in relating properties of matrices drawn at
random from the classical compact groups to statistical characteristics of
number-theoretical L-functions. One example is the relationship conjectured to
hold between the value distributions of the characteristic polynomials of such
matrices and value distributions within families of L-functions. These
connections are here extended to non-classical groups. We focus on an explicit
example: the exceptional Lie group G_2. The value distributions for
characteristic polynomials associated with the 7- and 14-dimensional
representations of G_2, defined with respect to the uniform invariant (Haar)
measure, are calculated using two of the Macdonald constant term identities. A
one parameter family of L-functions over a finite field is described whose
value distribution in the limit as the size of the finite field grows is
related to that of the characteristic polynomials associated with the
7-dimensional representation of G_2. The random matrix calculations extend to
all exceptional Lie groupsComment: 14 page
Hydrology and Sedimentology of Dynamic Rill Networks Volume II: Hydrologic Model for Dynamic Rill Networks
A comprehensive model has been developed for use in modeling the hydrologic response of rill network systems. The model, which is called HYMODRIN, is composed of both a hydrologic runoff component and a hydraulic channel routing component. The hydrologic component of the model uses a Green Ampt infiltration approach linked with a nonlinear reservoir runoff model. The channel routing component of the model is baaed on a finite element solution of the diffusion wave equations. In order to account for backwater effects the model employs a dual level iteration scheme.
The model may be used in either a stand alone mode or as part of a comprehensive integrated rill erosion model. In the latter case, the hydrologic data for the rill network and the associated interrill flow areas is provided by a geographic-hydrologic interface model called GHIM. This model accepts data from a digital elevation model and translates it into a form compatible with the hydrologic model.
This report contains the theoretical development and operating instructions for both GHIM and HYMODRIN. Computer listings for both programs are provided
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