842 research outputs found
Higher order corrections for anisotropic bootstrap percolation
We study the critical probability for the metastable phase transition of the
two-dimensional anisotropic bootstrap percolation model with
-neighbourhood and threshold . The first order asymptotics for
the critical probability were recently determined by the first and second
authors. Here we determine the following sharp second and third order
asymptotics:
We note that the second and third order terms are so large that the first order
asymptotics fail to approximate even for lattices of size well beyond
.Comment: 46 page
Initial Hubble Diagram Results from the Nearby Supernova Factory
The use of Type Ia supernovae as distance indicators led to the discovery of
the accelerating expansion of the universe a decade ago. Now that large second
generation surveys have significantly increased the size and quality of the
high-redshift sample, the cosmological constraints are limited by the currently
available sample of ~50 cosmologically useful nearby supernovae. The Nearby
Supernova Factory addresses this problem by discovering nearby supernovae and
observing their spectrophotometric time development. Our data sample includes
over 2400 spectra from spectral timeseries of 185 supernovae. This talk
presents results from a portion of this sample including a Hubble diagram
(relative distance vs. redshift) and a description of some analyses using this
rich dataset.Comment: Short version of proceedings for ICHEP08, Philadelphia PA, July 2008;
see v1 for full-length versio
SAURON Observations of Disks in Early-Type Galaxies
We briefly describe the SAURON project, aimed at determining the intrinsic
shape and internal dynamics of spheroids. We focus here on the ability of
SAURON to identify gaseous and stellar disks and to measure their morphology
and kinematics. We illustrate some of our results with complete maps of
NGC3377, NGC3623, and NGC4365.Comment: 4 pages, 4 figures (newpasp.sty). To appear in ASP Conf. Series
"Galaxy Disks and Disk Galaxies", eds. J.G. Funes S.J. & E.M. Corsini.
Version with full resolution images available at
http://www.strw.leidenuniv.nl/~bureau/pub_list.htm
Dynamical Modeling of SAURON Galaxies
We describe our program for the dynamical modeling of early-type galaxies
observed with the panoramic integral-field spectrograph SAURON. We are using
Schwarzschild's numerical orbit superposition method to reproduce in detail all
kinematical and photometric observables, and recover the intrinsic orbital
structure of the galaxies. Since catastrophes are the most prominent features
in the orbital observables, two-dimensional kinematical coverage is essential
to constrain the dynamical models.Comment: 5 pages, 4 figures, LaTeX. Published in 2003, Carnegie Observatories
Astrophysics Series, Vol. 1: Coevolution of Black Holes and Galaxies, ed. L.
C. Ho (Pasadena: Carnegie Observatories,
http://www.ociw.edu/ociw/symposia/series/symposium1/proceedings.html
Self-avoiding walks and connective constants
The connective constant of a quasi-transitive graph is the
asymptotic growth rate of the number of self-avoiding walks (SAWs) on from
a given starting vertex. We survey several aspects of the relationship between
the connective constant and the underlying graph .
We present upper and lower bounds for in terms of the
vertex-degree and girth of a transitive graph.
We discuss the question of whether for transitive
cubic graphs (where denotes the golden mean), and we introduce the
Fisher transformation for SAWs (that is, the replacement of vertices by
triangles).
We present strict inequalities for the connective constants
of transitive graphs , as varies.
As a consequence of the last, the connective constant of a Cayley
graph of a finitely generated group decreases strictly when a new relator is
added, and increases strictly when a non-trivial group element is declared to
be a further generator.
We describe so-called graph height functions within an account of
"bridges" for quasi-transitive graphs, and indicate that the bridge constant
equals the connective constant when the graph has a unimodular graph height
function.
A partial answer is given to the question of the locality of
connective constants, based around the existence of unimodular graph height
functions.
Examples are presented of Cayley graphs of finitely presented
groups that possess graph height functions (that are, in addition, harmonic and
unimodular), and that do not.
The review closes with a brief account of the "speed" of SAW.Comment: Accepted version. arXiv admin note: substantial text overlap with
arXiv:1304.721
Standardizing Type Ia Supernova Absolute Magnitudes Using Gaussian Process Data Regression
We present a novel class of models for Type Ia supernova time-evolving
spectral energy distributions (SED) and absolute magnitudes: they are each
modeled as stochastic functions described by Gaussian processes. The values of
the SED and absolute magnitudes are defined through well-defined regression
prescriptions, so that data directly inform the models. As a proof of concept,
we implement a model for synthetic photometry built from the spectrophotometric
time series from the Nearby Supernova Factory. Absolute magnitudes at peak
brightness are calibrated to 0.13 mag in the -band and to as low as 0.09 mag
in the blueshifted -band, where the dispersion includes
contributions from measurement uncertainties and peculiar velocities. The
methodology can be applied to spectrophotometric time series of supernovae that
span a range of redshifts to simultaneously standardize supernovae together
with fitting cosmological parameters.Comment: 47 pages, 15 figures, accepted for publication by Astrophysical
Journa
Atmospheric extinction properties above Mauna Kea from the Nearby Supernova Factory spectro-photometric data set
We present a new atmospheric extinction curve for Mauna Kea spanning
3200--9700 \AA. It is the most comprehensive to date, being based on some 4285
standard star spectra obtained on 478 nights spread over a period of 7 years
obtained by the Nearby SuperNova Factory using the SuperNova Integral Field
Spectrograph. This mean curve and its dispersion can be used as an aid in
calibrating spectroscopic or imaging data from Mauna Kea, and in estimating the
calibration uncertainty associated with the use of a mean extinction curve. Our
method for decomposing the extinction curve into physical components, and the
ability to determine the chromatic portion of the extinction even on cloudy
nights, is described and verified over the wide range of conditions sampled by
our large dataset. We demonstrate good agreement with atmospheric science data
obtain at nearby Mauna Loa Observatory, and with previously published
measurements of the extinction above Mauna Kea.Comment: 22 pages, 24 figures, 6 table
Measuring cosmic bulk flows with Type Ia Supernovae from the Nearby Supernova Factory
Context. Our Local Group of galaxies appears to be moving relative to the
cosmic microwave background with the source of the peculiar motion still
uncertain. While in the past this has been studied mostly using galaxies as
distance indicators, the weight of type Ia supernovae (SNe Ia) has increased
recently with the continuously improving statistics of available low-redshift
supernovae.
Aims. We measured the bulk flow in the nearby universe ()
using 117 SNe Ia observed by the Nearby Supernova Factory, as well as the
Union2 compilation of SN Ia data already in the literature.
Methods. The bulk flow velocity was determined from SN data binned in
redshift shells by including a coherent motion (dipole) in a cosmological fit.
Additionally, a method of spatially smoothing the Hubble residuals was used to
verify the results of the dipole fit. To constrain the location and mass of a
potential mass concentration (e.g., the Shapley supercluster) responsible for
the peculiar motion, we fit a Hubble law modified by adding an additional mass
concentration.
Results. The analysis shows a bulk flow that is consistent with the direction
of the CMB dipole up to , thereby doubling the volume over which
conventional distance measures are sensitive to a bulk flow. We see no
significant turnover behind the center of the Shapley supercluster. A simple
attractor model in the proximity of the Shapley supercluster is only marginally
consistent with our data, suggesting the need for another, more distant source.
In the redshift shell , we constrain the bulk flow velocity to
(68% confidence level) for the direction of the CMB
dipole, in contradiction to recent claims of the existence of a large-amplitude
dark flow.Comment: 12 pages, 5 figures, added corrigendum
(http://adsabs.harvard.edu/abs/2015A%26A...578C...1F
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