1,208 research outputs found
Greedy kernel methods for accelerating implicit integrators for parametric ODEs
We present a novel acceleration method for the solution of parametric ODEs by
single-step implicit solvers by means of greedy kernel-based surrogate models.
In an offline phase, a set of trajectories is precomputed with a high-accuracy
ODE solver for a selected set of parameter samples, and used to train a kernel
model which predicts the next point in the trajectory as a function of the last
one. This model is cheap to evaluate, and it is used in an online phase for new
parameter samples to provide a good initialization point for the nonlinear
solver of the implicit integrator. The accuracy of the surrogate reflects into
a reduction of the number of iterations until convergence of the solver, thus
providing an overall speedup of the full simulation. Interestingly, in addition
to providing an acceleration, the accuracy of the solution is maintained, since
the ODE solver is still used to guarantee the required precision. Although the
method can be applied to a large variety of solvers and different ODEs, we will
present in details its use with the Implicit Euler method for the solution of
the Burgers equation, which results to be a meaningful test case to demonstrate
the method's features
New Techniques for Relating Dynamically Close Galaxy Pairs to Merger and Accretion Rates : Application to the SSRS2 Redshift Survey
We introduce two new pair statistics, which relate close galaxy pairs to the
merger and accretion rates. We demonstrate the importance of correcting these
(and other) pair statistics for selection effects related to sample depth and
completeness. In particular, we highlight the severe bias that can result from
the use of a flux-limited survey. The first statistic, denoted N_c, gives the
number of companions per galaxy, within a specified range in absolute
magnitude. N_c is directly related to the galaxy merger rate. The second
statistic, called L_c, gives the total luminosity in companions, per galaxy.
This quantity can be used to investigate the mass accretion rate. Both N_c and
L_c are related to the galaxy correlation function and luminosity function in a
straightforward manner. We outline techniques which account for various
selection effects, and demonstrate the success of this approach using Monte
Carlo simulations. If one assumes that clustering is independent of luminosity
(which is appropriate for reasonable ranges in luminosity), then these
statistics may be applied to flux-limited surveys.
These techniques are applied to a sample of 5426 galaxies in the SSRS2
redshift survey. Using close dynamical pairs, we find N_c(-21<M_B<-18) =
0.0226+/-0.0052 and L_c(-21<M_B<-18) = 0.0216+/-0.0055 10^{10} h^2 L_sun at
z=0.015. These are the first secure estimates of low-z close pair statistics.
If N_c remains fixed with redshift, simple assumptions imply that ~ 6.6% of
present day galaxies with -21<M_B<-18 have undergone mergers since z=1. When
applied to redshift surveys of more distant galaxies, these techniques will
yield the first robust estimates of evolution in the galaxy merger and
accretion rates. [Abridged]Comment: 26 pages (including 10 postscript figures) plus 3 gif figures.
Accepted for publication in ApJ. Paper (including full resolution images)
also available at http://www.astro.utoronto.ca/~patton/ssrs2, along with
associated pair classification experiment (clickable version of Figure 5
Is there Evidence for a Hubble bubble? The Nature of Type Ia Supernova Colors and Dust in External Galaxies
We examine recent evidence from the luminosity-redshift relation of Type Ia
Supernovae (SNe Ia) for the detection of a ``Hubble bubble'' --
a departure of the local value of the Hubble constant from its globally
averaged value \citep{Jha:07}. By comparing the MLCS2k2 fits used in that study
to the results from other light-curve fitters applied to the same data, we
demonstrate that this is related to the interpretation of SN color excesses
(after correction for a light-curve shape-color relation) and the presence of a
color gradient across the local sample. If the slope of the linear relation
() between SN color excess and luminosity is fit empirically, then the
bubble disappears. If, on the other hand, the color excess arises purely from
Milky Way-like dust, then SN data clearly favors a Hubble bubble. We
demonstrate that SN data give , instead of the
one would expect from purely Milky-Way-like dust. This suggests that either SN
intrinsic colors are more complicated than can be described with a single
light-curve shape parameter, or that dust around SN is unusual. Disentangling
these possibilities is both a challenge and an opportunity for large-survey SN
Ia cosmology.Comment: Further information and data at
http://qold.astro.utoronto.ca/conley/bubble/ Accepted for publication in ApJ
Galaxy Clustering and Large-Scale Structure from z = 0.2 to z = 0.5 in Two Norris Redshift Surveys
(abridged) We present a study of the nature and evolution of large-scale
structure based on two independent redshift surveys of faint field galaxies
conducted with the 176-fiber Norris Spectrograph on the Palomar 200-inch
telescope. The two surveys together sparsely cover ~20 sq. degrees and contain
835 r < 21 mag galaxies with redshifts 0.2 < z < 0.5. Both surveys have a
median redshift of z = 0.30. In order to obtain a rough estimate of the cosmic
variance, we analyze the two surveys independently. We measure the comoving
correlation length to be 3.70 +/- 0.13 h^-1 Mpc at z = 0.30 with a power-law
slope gamma = 1.77 +/- 0.05. Dividing the sample into low (0.2 < z < 0.3) and
high (0.32 < z < 0.5) redshift intervals, we see no evidence for a change in
the comoving correlation length over the redshift range 0.2 < z < 0.5. Similar
to the well-established results in the local universe, we find that
intrinsically bright galaxies are more strongly clustered than intrinsically
faint galaxies and that galaxies with little ongoing star formation, as judged
from the rest-frame equivalent width of the [OII]3727, are more strongly
clustered than galaxies with significant ongoing star formation. The rest-frame
pairwise velocity dispersion of the sample is 326^+67_-52 km s^-1, ~25% lower
than typical values measured locally. The appearance of the galaxy
distribution, particularly in the more densely sampled Abell 104 field, is
quite striking. The pattern of sheets and voids which has been observed locally
continues at least to z ~ 0.5. A friends-of-friends analysis of the galaxy
distribution supports the visual impression that > 90% of all galaxies at z <
0.5 are part of larger structures with overdensities of > 5.Comment: 40 pages including 26 Postscript figures; revised version to match
version accepted by Ap
The Luminosity Function of Field Galaxies in the CNOC1 Redshift Survey
We have computed the luminosity function for 389 field galaxies from the
Canadian Network for Observational Cosmology cluster redshift survey (CNOC1),
over redshifts z = 0.2-0.6. We find Schechter parameters M^* - 5 log h = -19.6
\pm 0.3 and \alpha = -0.9 \pm 0.2 in rest-frame B_{AB}. We have also split our
sample at the color of a redshifted but nonevolving Sbc galaxy, and find
distinctly different luminosity functions for red and blue galaxies. Red
galaxies have a shallow slope \alpha \approx -0.4 and dominate the bright end
of the luminosity function, while blue galaxies have a steep \alpha \approx
-1.4 and prevail at the faint end. Comparisons of the CNOC1 results to those
from the Canada-France (CFRS) and Autofib redshift surveys show broad agreement
among these independent samples, but there are also significant differences
which will require larger samples to resolve. Also, in CNOC1 the red galaxy
luminosity density stays about the same over the range z = 0.2-0.6, while the
blue galaxy luminosity density increases steadily with redshift. These results
are consistent with the trend of the luminosity density vs. redshift relations
seen in the CFRS, though the normalizations of the luminosity densities appear
to differ for blue galaxies. Comparison to the local luminosity function from
the Las Campanas redshift survey (LCRS) shows that the luminosity density at z
\approx 0.1 is only about half that seen at z \approx 0.4. A change in the
luminosity function shape, particularly at the faint end, appears to be
required to match the CNOC1 and LCRS luminosity functions, if galaxy evolution
is the sole cause of the differences seen. However, it should be noted that the
specific details of the construction of different surveys may complicate the
comparison of results and so may need to be considered carefully.Comment: 22 pages, including 6 postscript figures, uses AASTEX v4.0 style
files. Corrected minor typos and updated references. Results and conclusions
unchanged. Final version to appear in the Astrophysical Journa
Virial mass in DGP brane cosmology
We study the virial mass discrepancy in the context of a DPG brane-world
scenario and show that such a framework can offer viable explanations to
account for the mass discrepancy problem. This is done by defining a
geometrical mass that we prove to be proportional to the virial
mass. Estimating using observational data, we show that it
behaves linearly with and has a value of the order of , pointing
to a possible resolution of the virial mass discrepancy. We also obtain the
radial velocity dispersion of galaxy clusters and show that it is compatible
with the radial velocity dispersion profile of such clusters. This velocity
dispersion profile can be used to differentiate various models predicting the
virial mass.Comment: 12 pages, 1 figure, to appear in CQ
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