48,355 research outputs found
Theoretical Predictions for Surface Brightness Fluctuations and Implications for Stellar Populations of Elliptical Galaxies
(Abridged) We present new theoretical predictions for surface brightness
fluctuations (SBFs) using models optimized for this purpose. Our predictions
agree well with SBF data for globular clusters and elliptical galaxies. We
provide refined theoretical calibrations and k-corrections needed to use SBFs
as standard candles. We suggest that SBF distance measurements can be improved
by using a filter around 1 micron and calibrating I-band SBFs with the
integrated V-K galaxy color. We also show that current SBF data provide useful
constraints on population synthesis models, and we suggest SBF-based tests for
future models. The data favor specific choices of evolutionary tracks and
spectra in the models among the several choices allowed by comparisons based on
only integrated light. In addition, the tightness of the empirical I-band SBF
calibration suggests that model uncertainties in post-main sequence lifetimes
are less than +/-50% and that the IMF in ellipticals is not much steeper than
that in the solar neighborhood. Finally, we analyze the potential of SBFs for
probing unresolved stellar populations. We find that optical/near-IR SBFs are
much more sensitive to metallicity than to age. Therefore, SBF magnitudes and
colors are a valuable tool to break the age/metallicity degeneracy. Our initial
results suggest that the most luminous stellar populations of bright cluster
galaxies have roughly solar metallicities and about a factor of three spread in
age.Comment: Astrophysical Journal, in press (uses Apr 20, 2000 version of
emulateapj5.sty). Reposted version has a minor cosmetic change to Table
Apollonian Circle Packings: Geometry and Group Theory III. Higher Dimensions
This paper gives -dimensional analogues of the Apollonian circle packings
in parts I and II. We work in the space \sM_{\dd}^n of all -dimensional
oriented Descartes configurations parametrized in a coordinate system,
ACC-coordinates, as those real matrices \bW with \bW^T
\bQ_{D,n} \bW = \bQ_{W,n} where is the -dimensional Descartes quadratic
form, , and \bQ_{D,n} and
\bQ_{W,n} are their corresponding symmetric matrices. There are natural
actions on the parameter space \sM_{\dd}^n. We introduce -dimensional
analogues of the Apollonian group, the dual Apollonian group and the
super-Apollonian group. These are finitely generated groups with the following
integrality properties: the dual Apollonian group consists of integral matrices
in all dimensions, while the other two consist of rational matrices, with
denominators having prime divisors drawn from a finite set depending on the
dimension. We show that the the Apollonian group and the dual Apollonian group
are finitely presented, and are Coxeter groups. We define an Apollonian cluster
ensemble to be any orbit under the Apollonian group, with similar notions for
the other two groups. We determine in which dimensions one can find rational
Apollonian cluster ensembles (all curvatures rational) and strongly rational
Apollonian sphere ensembles (all ACC-coordinates rational).Comment: 37 pages. The third in a series on Apollonian circle packings
beginning with math.MG/0010298. Revised and extended. Added: Apollonian
groups and Apollonian Cluster Ensembles (Section 4),and Presentation for
n-dimensional Apollonian Group (Section 5). Slight revision on March 10, 200
Apollonian Circle Packings: Geometry and Group Theory I. The Apollonian Group
Apollonian circle packings arise by repeatedly filling the interstices
between four mutually tangent circles with further tangent circles. We observe
that there exist Apollonian packings which have strong integrality properties,
in which all circles in the packing have integer curvatures and rational
centers such that (curvature)(center) is an integer vector. This series
of papers explain such properties. A {\em Descartes configuration} is a set of
four mutually tangent circles with disjoint interiors. We describe the space of
all Descartes configurations using a coordinate system \sM_\DD consisting of
those real matrices \bW with \bW^T \bQ_{D} \bW = \bQ_{W} where
\bQ_D is the matrix of the Descartes quadratic form and \bQ_W of the quadratic form
. There are natural group actions on the
parameter space \sM_\DD. We observe that the Descartes configurations in each
Apollonian packing form an orbit under a certain finitely generated discrete
group, the {\em Apollonian group}. This group consists of integer
matrices, and its integrality properties lead to the integrality properties
observed in some Apollonian circle packings. We introduce two more related
finitely generated groups, the dual Apollonian group and the super-Apollonian
group, which have nice geometrically interpretations. We show these groups are
hyperbolic Coxeter groups.Comment: 42 pages, 11 figures. Extensively revised version on June 14, 2004.
Revised Appendix B and a few changes on July, 2004. Slight revision on March
10, 200
Apollonian Circle Packings: Geometry and Group Theory II. Super-Apollonian Group and Integral Packings
Apollonian circle packings arise by repeatedly filling the interstices
between four mutually tangent circles with further tangent circles. Such
packings can be described in terms of the Descartes configurations they
contain. It observed there exist infinitely many types of integral Apollonian
packings in which all circles had integer curvatures, with the integral
structure being related to the integral nature of the Apollonian group. Here we
consider the action of a larger discrete group, the super-Apollonian group,
also having an integral structure, whose orbits describe the Descartes
quadruples of a geometric object we call a super-packing. The circles in a
super-packing never cross each other but are nested to an arbitrary depth.
Certain Apollonian packings and super-packings are strongly integral in the
sense that the curvatures of all circles are integral and the
curvaturecenters of all circles are integral. We show that (up to
scale) there are exactly 8 different (geometric) strongly integral
super-packings, and that each contains a copy of every integral Apollonian
circle packing (also up to scale). We show that the super-Apollonian group has
finite volume in the group of all automorphisms of the parameter space of
Descartes configurations, which is isomorphic to the Lorentz group .Comment: 37 Pages, 11 figures. The second in a series on Apollonian circle
packings beginning with math.MG/0010298. Extensively revised in June, 2004.
More integral properties are discussed. More revision in July, 2004:
interchange sections 7 and 8, revised sections 1 and 2 to match, and added
matrix formulations for super-Apollonian group and its Lorentz version.
Slight revision in March 10, 200
Film-cooling effectiveness with developing coolant flow through straight and curved tubular passages
The data were obtained with an apparatus designed to determine the influence of tubular coolant passage curvature on film-cooling performance while simulating the developing flow entrance conditions more representative of cooled turbine blade. Data comparisons were made between straight and curved single tubular passages embedded in the wall and discharging at 30 deg angle in line with the tunnel flow. The results showed an influence of curvature on film-cooling effectiveness that was inversely proportional to the blowing rate. At the lowest blowing rate of 0.18, curvature increased the effectiveness of film cooling by 35 percent; but at a blowing rate of 0.76, the improvement was only 10 percent. In addition, the increase in film-cooling area coverage ranged from 100 percent down to 25 percent over the same blowing rates. A data trend reversal at a blowing rate of 1.5 showed the straight tubular passage's film-cooling effectiveness to be 20 percent greater than that of the curved passage with about 80 percent more area coverage. An analysis of turbulence intensity detain the mixing layer in terms of the position of the mixing interface relative to the wall supported the concept that passage curvature tends to reduce the diffusion of the coolant jet into the main stream at blowing rates below about. Explanations for the film-cooling performance of both test sections were made in terms differences in turbulences structure and in secondary flow patterns within the coolant jets as influenced by flow passage geometry
Analysis for predicting adiabatic wall temperatures with single hole coolant injection into a low speed crossflow
Assuming the local adiabatic wall temperature equals the local total temperature in a low speed coolant mixing layer, integral conservation equations with and without the boundary layer effects are formulated for the mixing layer downstream of a single coolant injection hole oriented at a 30 degree angle to the crossflow. These equations are solved numerically to determine the center line local adiabatic wall temperature and the effective coolant coverage area. Comparison of the numerical results with an existing film cooling experiment indicates that the present analysis permits a simplified but reasonably accurate prediction of the centerline effectiveness and coolant coverage area downstream of a single hole crossflow streamwise injection at 30 degree inclination angle
A sub-product construction of Poincare-Einstein metrics
Given any two Einstein (pseudo-)metrics, with scalar curvatures suitably
related, we give an explicit construction of a Poincar\'e-Einstein
(pseudo-)metric with conformal infinity the conformal class of the product of
the initial metrics. We show that these metrics are equivalent to ambient
metrics for the given conformal structure. The ambient metrics have holonomy
that agrees with the conformal holonomy. In the generic case the ambient metric
arises directly as a product of the metric cones over the original Einstein
spaces. In general the conformal infinity of the Poincare metrics we construct
is not Einstein, and so this describes a class of non-conformally Einstein
metrics for which the (Fefferman-Graham) obstruction tensor vanishes.Comment: 23 pages Minor correction to section 5. References update
A simple stochastic model for the evolution of protein lengths
We analyse a simple discrete-time stochastic process for the theoretical
modeling of the evolution of protein lengths. At every step of the process a
new protein is produced as a modification of one of the proteins already
existing and its length is assumed to be random variable which depends only on
the length of the originating protein. Thus a Random Recursive Trees (RRT) is
produced over the natural integers. If (quasi) scale invariance is assumed, the
length distribution in a single history tends to a lognormal form with a
specific signature of the deviations from exact gaussianity. Comparison with
the very large SIMAP protein database shows good agreement.Comment: 12 pages, 4 figure
Universality of the Small-Scale Dynamo Mechanism
We quantify possible differences between turbulent dynamo action in the Sun
and the dynamo action studied in idealized simulations. For this purpose we
compare Fourier-space shell-to-shell energy transfer rates of three
incrementally more complex dynamo simulations: an incompressible, periodic
simulation driven by random flow, a simulation of Boussinesq convection, and a
simulation of fully compressible convection that includes physics relevant to
the near-surface layers of the Sun. For each of the simulations studied, we
find that the dynamo mechanism is universal in the kinematic regime because
energy is transferred from the turbulent flow to the magnetic field from
wavenumbers in the inertial range of the energy spectrum. The addition of
physical effects relevant to the solar near-surface layers, including
stratification, compressibility, partial ionization, and radiative energy
transport, does not appear to affect the nature of the dynamo mechanism. The
role of inertial-range shear stresses in magnetic field amplification is
independent from outer-scale circumstances, including forcing and
stratification. Although the shell-to-shell energy transfer functions have
similar properties to those seen in mean-flow driven dynamos in each simulation
studied, the saturated states of these simulations are not universal because
the flow at the driving wavenumbers is a significant source of energy for the
magnetic field.Comment: 16 pages, 9 figures, accepted for publication in Ap
Removal of acid gases and oxides of nitrogen from space cabin atmospheres
Removal of acid gases and oxides of nitrogen from spacecraft cabin atmospheres at ambient temperature
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