1,414 research outputs found
Zener diode function generator requires no external reference voltage
Function generator utilizing parallel impedance networks with zener diodes produces functions which are discontinuous in slope. The function generated appears at the output of the parallel network in the form of a voltage varying in time
The spin contribution to the form factor of quantum graphs
Following the quantisation of a graph with the Dirac operator (spin-1/2) we
explain how additional weights in the spectral form factor K(\tau) due to spin
propagation around orbits produce higher order terms in the small-\tau
asymptotics in agreement with symplectic random matrix ensembles. We determine
conditions on the group of spin rotations sufficient to generate CSE
statistics.Comment: 9 page
Spectral Statistics for the Dirac Operator on Graphs
We determine conditions for the quantisation of graphs using the Dirac
operator for both two and four component spinors. According to the
Bohigas-Giannoni-Schmit conjecture for such systems with time-reversal symmetry
the energy level statistics are expected, in the semiclassical limit, to
correspond to those of random matrices from the Gaussian symplectic ensemble.
This is confirmed by numerical investigation. The scattering matrix used to
formulate the quantisation condition is found to be independent of the type of
spinor. We derive an exact trace formula for the spectrum and use this to
investigate the form factor in the diagonal approximation
Intermediate statistics for a system with symplectic symmetry: the Dirac rose graph
We study the spectral statistics of the Dirac operator on a rose-shaped
graph---a graph with a single vertex and all bonds connected at both ends to
the vertex. We formulate a secular equation that generically determines the
eigenvalues of the Dirac rose graph, which is seen to generalise the secular
equation for a star graph with Neumann boundary conditions. We derive
approximations to the spectral pair correlation function at large and small
values of spectral spacings, in the limit as the number of bonds approaches
infinity, and compare these predictions with results of numerical calculations.
Our results represent the first example of intermediate statistics from the
symplectic symmetry class.Comment: 26 pages, references adde
Carbon and Strontium Abundances of Metal-Poor Stars
We present carbon and strontium abundances for 100 metal-poor stars measured
from R7000 spectra obtained with the Echellette Spectrograph and Imager
at the Keck Observatory. Using spectral synthesis of the G-band region, we have
derived carbon abundances for stars ranging from [Fe/H] to
[Fe/H]. The formal errors are dex in [C/Fe]. The strontium
abundance in these stars was measured using spectral synthesis of the resonance
line at 4215 {\AA}. Using these two abundance measurments along with the barium
abundances from our previous study of these stars, we show it is possible to
identify neutron-capture-rich stars with our spectra. We find, as in other
studies, a large scatter in [C/Fe] below [Fe/H]. Of the stars with
[Fe/H], 94% can be classified as carbon-rich metal-poor stars. The Sr
and Ba abundances show that three of the carbon-rich stars are
neutron-capture-rich, while two have normal Ba and Sr. This fraction of carbon
enhanced stars is consistent with other studies that include this metallicity
range.Comment: ApJ, Accepte
From error bounds to the complexity of first-order descent methods for convex functions
This paper shows that error bounds can be used as effective tools for
deriving complexity results for first-order descent methods in convex
minimization. In a first stage, this objective led us to revisit the interplay
between error bounds and the Kurdyka-\L ojasiewicz (KL) inequality. One can
show the equivalence between the two concepts for convex functions having a
moderately flat profile near the set of minimizers (as those of functions with
H\"olderian growth). A counterexample shows that the equivalence is no longer
true for extremely flat functions. This fact reveals the relevance of an
approach based on KL inequality. In a second stage, we show how KL inequalities
can in turn be employed to compute new complexity bounds for a wealth of
descent methods for convex problems. Our approach is completely original and
makes use of a one-dimensional worst-case proximal sequence in the spirit of
the famous majorant method of Kantorovich. Our result applies to a very simple
abstract scheme that covers a wide class of descent methods. As a byproduct of
our study, we also provide new results for the globalization of KL inequalities
in the convex framework.
Our main results inaugurate a simple methodology: derive an error bound,
compute the desingularizing function whenever possible, identify essential
constants in the descent method and finally compute the complexity using the
one-dimensional worst case proximal sequence. Our method is illustrated through
projection methods for feasibility problems, and through the famous iterative
shrinkage thresholding algorithm (ISTA), for which we show that the complexity
bound is of the form where the constituents of the bound only depend
on error bound constants obtained for an arbitrary least squares objective with
regularization
NGC 2419, M92, and the Age Gradient in the Galactic Halo
The WFPC2 camera on HST has been used to obtain deep main sequence photometry
of the low-metallicity ([Fe/H]=-2.14), outer-halo globular cluster NGC 2419. A
differential fit of the NGC 2419 CMD to that of the similarly metal-poor \
standard cluster M92 shows that they have virtually identical principal
sequences and thus the same age to well within 1 Gyr. Since other
low-metallicity clusters throughout the Milky Way halo have this same age to
within the 1-Gyr precision of the differential age technique, we conclude that
the earliest star (or globular cluster) formation began at essentially the same
time everywhere in the Galactic halo throughout a region now almost 200 kpc in
diameter. Thus for the metal-poorest clusters in the halo there is no
detectable age gradient with Galactocentric distance. To estimate the absolute
age of NGC 2419 and M92, we fit newly computed isochrones transformed through
model-atmosphere calculations to the (M_V,V-I) plane, with assumed distance
scales that represent the range currently debated in the literature.
Unconstrained isochrone fits give M_V(RR) = 0.55 \pm 0.06 and a resulting age
of 14 to 15 Gyr. Incorporating the full effects of helium diffusion would
further reduce this estimate by about 1 Gyr. A distance scale as bright as
M_V(RR) = 0.15 for [Fe/H] = -2, as has recently been reported, would leave
several serious problems which have no obvious solution in the context of
current stellar models.Comment: 32 pages, aastex, 9 postscript figures; accepted for publication in
AJ, September 1997. Also available by e-mail from [email protected]
Photometry of the Globular Cluster NGC 5466: Red Giants and Blue Stragglers
We present wide-field BVI photometry for about 11,500 stars in the
low-metallicity cluster NGC 5466. We have detected the red giant branch bump
for the first time, although it is at least 0.2 mag fainter than expected
relative to the turnoff. The number of red giants (relative to main sequence
turnoff stars) is in excellent agreement with stellar models from the
Yonsei-Yale and Teramo groups, and slightly high compared to Victoria-Regina
models. This adds to evidence that an abnormally large ratio of red giant to
main-sequence stars is not correlated with cluster metallicity. We discuss
theoretical predictions from different research groups and find that the
inclusion or exclusion of helium diffusion and strong limit Coulomb
interactions may be partly responsible.
We also examine indicators of dynamical history: the mass function exponent
and the blue straggler frequency. NGC 5466 has a very shallow mass function,
consistent with large mass loss and recently-discovered tidal tails. The blue
straggler sample is significantly more centrally concentrated than the HB or
RGB stars. We see no evidence of an upturn in the blue straggler frequency at
large distances from the center. Dynamical friction timescales indicate that
the stragglers should be more concentrated if the cluster's present density
structure has existed for most of its history. NGC 5466 also has an unusually
low central density compared to clusters of similar luminosity. In spite of
this, the specific frequency of blue stragglers that puts it right on the
frequency -- cluster M_V relation observed for other clusters.Comment: 51 pages, 21 figures, 1 electronic table, accepted to Ap
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