456 research outputs found
Surface Impedance Determination via Numerical Resolution of the Inverse Helmholtz Problem
Assigning boundary conditions, such as acoustic impedance, to the frequency
domain thermoviscous wave equations (TWE), derived from the linearized
Navier-Stokes equations (LNSE) poses a Helmholtz problem, solution to which
yields a discrete set of complex eigenfunctions and eigenvalue pairs. The
proposed method -- the inverse Helmholtz solver (iHS) -- reverses such
procedure by returning the value of acoustic impedance at one or more unknown
impedance boundaries (IBs) of a given domain, via spatial integration of the
TWE for a given real-valued frequency with assigned conditions on other
boundaries. The iHS procedure is applied to a second-order spatial
discretization of the TWEs on an unstructured staggered grid arrangement. Only
the momentum equation is extended to the center of each IB face where pressure
and velocity components are co-located and treated as unknowns. The iHS is
finally closed via assignment of the surface gradient of pressure phase over
the IBs, corresponding to assigning the shape of the acoustic waveform at the
IB. The iHS procedure can be carried out independently for different
frequencies, making it embarrassingly parallel, and able to return the complete
broadband complex impedance distribution at the IBs in any desired frequency
range to arbitrary numerical precision. The iHS approach is first validated
against Rott's theory for viscous rectangular and circular ducts. The impedance
of a toy porous cavity with a complex geometry is then reconstructed and
validated with companion fully compressible unstructured Navier-Stokes
simulations resolving the cavity geometry. Verification against one-dimensional
impedance test tube calculations based on time-domain impedance boundary
conditions (TDIBC) is also carried out. Finally, results from a preliminary
analysis of a thermoacoustically unstable cavity are presented.Comment: As submitted to AIAA Aviation 201
Numerical Solver for Multiphase Flows
The technological development of micro-scale electronic devices is bounded by the challenge of dissipating their heat output. Latent heat absorbed by a fluid during phase transition offers exceptional cooling capabilities while allowing for the design of compact heat exchangers. The understanding of heat transport dynamics in the context of multiphase flow physics is hampered by the limited access to detailed flow features offered by experimental measurements. Computational Fluid Dynamics (CFD) can overcome such difficulties by providing a complete description of the three-dimensional instantaneous flow field. Unfortunately, the majority of the numerical investigations in this field at Purdue are carried out with closed-source commercial CFD software which is computationally inefficient, (financially) expensive, and allows for extremely limited algorithmic development. The goal of this project is to initiate the development of an in-house code at Purdue that can simulate multiphase-flow physics that can exploit state-of-the-art supercomputing architectures, performing very large-size computations in a cost-efficient way. A first step has been the development of a simple 2D Python toy code relying on the volume of fluid (VOF) method coupled with a continuum surface force model (CSF), which treats surface tension effects as a localized body force. Results are compared with companion simulations carried out with the commercial software Fluent, revealing a noticeable improvement in the quality of the solution and a reduced computational cost. Future works involves the implementation of interface tracking methods and the extension of an existing highly-parallelized 3D incompressible Navier-Stokes code to include multi-phase problem capabilities
Self-Regulated Growth of Supermassive Black Holes in Galaxies as the Origin of the Optical and X-ray Luminosity Functions of Quasars
We postulate that supermassive black-holes grow in the centers of galaxies
until they unbind the galactic gas that feeds them. We show that the
corresponding self-regulation condition yields a correlation between black-hole
mass (Mbh) and galaxy velocity dispersion (sigma) as inferred in the local
universe, and recovers the observed optical and X-ray luminosity functions of
quasars at redshifts up to z~6 based on the hierarchical evolution of galaxy
halos in a Lambda-CDM cosmology. With only one free parameter and a simple
algorithm, our model yields the observed evolution in the number density of
optically bright or X-ray faint quasars between 2<z<6 across 3 orders of
magnitude in bolometric luminosity and 3 orders of magnitude in comoving
density per logarithm of luminosity. The self-regulation condition identifies
the dynamical time of galactic disks during the epoch of peak quasar activity
(z~2.5) as the origin of the inferred characteristic quasar lifetime of ~10
million years. Since the lifetime becomes comparable to the Salpeter e-folding
time at this epoch, the model also implies that the Mbh-sigma relation is a
product of feedback regulated accretion during the peak of quasar activity. The
mass-density in black-holes accreted by that time is consistent with the local
black-hole mass density of ~(0.8-6.3) times 10^5 solar masses per cubic Mpc,
which we have computed by combining the Mbh-sigma relation with the measured
velocity dispersion function of SDSS galaxies (Sheth et al.~2003). Applying a
similar self-regulation principle to supernova-driven winds from starbursts, we
find that the ratio between the black hole mass and the stellar mass of
galactic spheroids increases with redshift as (1+z)^1.5 although the Mbh-sigma
relation is redshift-independent.Comment: 10 pages, 5 figures, submitted to Ap
Looking for Distributed Star Formation in L1630: A Near-infrared (J, H, K) Survey
We have carried out a simultaneous, multi-band (J, H, K) survey over an area
of 1320 arcmin^2 in the L1630 region, concentrating on the region away from the
dense molecular cores and with modest visual extinctions (\leq 10 mag).
Previous studies found that star formation in L1630 occurs mainly in four
localized clusters, which in turn are associated with the four most massive
molecular cores (Lada et al. 1991; Lada 1992). The goal of this study is to
look for a distributed population of pre-main-sequence stars in the outlying
areas outside the known star-forming cores. More than 60% of the
pre-main-sequence stars in the active star forming regions of NGC 2024 and NGC
2023 show a near-infrared excess in the color-color diagram. In the outlying
areas of L1630, excluding the known star forming regions, we found that among
510 infrared sources with the near-infrared colors ((J-H) and (H-K)) determined
and photometric uncertainty at K better than 0.10 mag, the fraction of the
sources with a near-infrared excess is 3%--8%; the surface density of the
sources with a near-infrared excess is less than half of that found in the
distributed population in L1641, and 1/20 of that in the young cluster NGC
2023. This extremely low fraction and low surface density of sources with a
near-infrared excess strongly indicates that recent star formation activity has
been very low in the outlying region of L1630. The sources without a
near-infrared excess could be either background/foreground field stars, or
associated with the cloud, but formed a long time ago (more than 2 Myrs). Our
results are consistent with McKee's model of photoionization-regulated star
formation.Comment: 30 pages, 10 figures To appear in ApJ Oct 1997, Vol 48
The Variation of Integrated Star IMFs among Galaxies
The integrated galaxial initial mass function (IGIMF) is the relevant
distribution function containing the information on the distribution of stellar
remnants, the number of supernovae and the chemical enrichment history of a
galaxy. Since most stars form in embedded star clusters with different masses
the IGIMF becomes an integral of the assumed (universal or invariant) stellar
IMF over the embedded star-cluster mass function (ECMF). For a range of
reasonable assumptions about the IMF and the ECMF we find the IGIMF to be
steeper (containing fewer massive stars per star) than the stellar IMF, but
below a few Msol it is invariant and identical to the stellar IMF for all
galaxies. However, the steepening sensitively depends on the form of the ECMF
in the low-mass regime. Furthermore, observations indicate a relation between
the star formation rate of a galaxy and the most massive young stellar cluster
in it. The assumption that this cluster mass marks the upper end of a
young-cluster mass function leads to a connection of the star formation rate
and the slope of the IGIMF above a few Msol. The IGIMF varies with the star
formation history of a galaxy. Notably, large variations of the IGIMF are
evident for dE, dIrr and LSB galaxies with a small to modest stellar mass. We
find that for any galaxy the number of supernovae per star (NSNS) is suppressed
relative to that expected for a Salpeter IMF. Dwarf galaxies have a smaller
NSNS compared to massive galaxies. For dwarf galaxies the NSNS varies
substantially depending on the galaxy assembly history and the assumptions made
about the low-mass end of the ECMF. The findings presented here may be of some
consequence for the cosmological evolution of the number of supernovae per
low-mass star and the chemical enrichment of galaxies of different mass.Comment: 27 pages, accepted for publication by Ap
The Stellar Populations and Evolution of Lyman Break Galaxies
Using deep near-IR and optical observations of the HDF-N from the HST NICMOS
and WFPC2 and from the ground, we examine the spectral energy distributions
(SEDs) of Lyman break galaxies (LBGs) at 2.0 < z < 3.5. The UV-to-optical
rest-frame SEDs of the galaxies are much bluer than those of present-day spiral
and elliptical galaxies, and are generally similar to those of local starburst
galaxies with modest amounts of reddening. We use stellar population synthesis
models to study the properties of the stars that dominate the light from LBGs.
Under the assumption that the star-formation rate is continuous or decreasing
with time, the best-fitting models provide a lower bound on the LBG mass
estimates. LBGs with ``L*'' UV luminosities are estimated to have minimum
stellar masses ~ 10^10 solar masses, or roughly 1/10th that of a present-day L*
galaxy. By considering the effects of a second component of maximally-old
stars, we set an upper bound on the stellar masses that is ~ 3-8 times the
minimum estimate. We find only loose constraints on the individual galaxy ages,
extinction, metallicities, initial mass functions, and prior star-formation
histories. We find no galaxies whose SEDs are consistent with young (< 10^8
yr), dust-free objects, which suggests that LBGs are not dominated by ``first
generation'' stars, and that such objects are rare at these redshifts. We also
find that the typical ages for the observed star-formation events are
significantly younger than the time interval covered by this redshift range (~
1.5 Gyr). From this, and from the relative absence of candidates for quiescent,
non-star-forming galaxies at these redshifts in the NICMOS data, we suggest
that star formation in LBGs may be recurrent, with short duty cycles and a
timescale between star-formation events of < 1 Gyr. [Abridged]Comment: LaTeX, 37 pages, 21 figures. Accepted for publication in the
Astrophysical Journa
Large Area Mapping at 850 Microns. V. Analysis of the Clump Distribution in the Orion A South Molecular Cloud
We present results from a 2300 arcmin^2 survey of the Orion A molecular cloud
at 450 and 850 micron using the Submillimetre Common-User Bolometer Array
(SCUBA) on the James Clerk Maxwell Telescope. The region mapped lies directly
south of the OMC1 cloud core and includes OMC4, OMC5, HH1/2, HH34, and L1641N.
We identify 71 independent clumps in the 850 micron map and compute size, flux,
and degree of central concentration in each. Comparison with isothermal,
pressure-confined, self-gravitating Bonnor-Ebert spheres implies that the
clumps have internal temperatures T_d ~ 22 +/- K and surface pressures log
(k^-1 P cm^-3 K) = 6.0 +/- 0.2. The clump masses span the range 0.3 - 22 Msun
assuming a dust temperature T_d ~ 20 K and a dust emissivity kappa_850 = 0.02
cm^2 g^-1. The distribution of clump masses is well characterized by a
power-law N(M) propto M^-alpha with alpha = 2.0 +/- 0.5 for M > 3.0 Msun,
indicating a clump mass function steeper than the stellar Initial Mass
Function. Significant incompleteness makes determination of the slope at lower
masses difficult. A comparison of the submillimeter emission map with an H_2
2.122 micron survey of the same region is performed. Several new Class 0
sources are revealed and a correlation is found between both the column density
and degree of concentration of the submillimeter sources and the likelihood of
coincident H_2 shock emission.Comment: 44 pages, 17 figures, accepted by Ap
On the Similarity between Cluster and Galactic Stellar Initial Mass Functions
The stellar initial mass functions (IMFs) for the Galactic bulge, the Milky
Way, other galaxies, clusters of galaxies, and the integrated stars in the
Universe are composites from countless individual IMFs in star clusters and
associations where stars form. These galaxy-scale IMFs, reviewed in detail
here, are not steeper than the cluster IMFs except in rare cases. This is true
even though low mass clusters generally outnumber high mass clusters and the
average maximum stellar mass in a cluster scales with the cluster mass. The
implication is that the mass distribution function for clusters and
associations is a power law with a slope of -2 or shallower. Steeper slopes,
even by a few tenths, upset the observed equality between large and small scale
IMFs. Such a cluster function is expected from the hierarchical nature of star
formation, which also provides independent evidence for the IMF equality when
it is applied on sub-cluster scales. We explain these results with analytical
expressions and Monte Carlo simulations. Star clusters appear to be the relaxed
inner parts of a widespread hierarchy of star formation and cloud structure.
They are defined by their own dynamics rather than pre-existing cloud
boundaries.Comment: 22 pages, 2 figures, ApJ, 648, in press, September 1, 200
How many young star clusters exist in the Galactic center?
We study the evolution and observability of young compact star clusters
within about 200pc of the Galactic center. Calculations are performed using
direct N-body integration on the GRAPE-4, including the effects of both stellar
and binary evolution and the external influence of the Galaxy. The results of
these detailed calculations are used to calibrate a simplified model applicable
over a wider range of cluster initial conditions. We find that clusters within
200 pc from the Galactic center dissolve within about 70 Myr. However, their
projected densities drop below the background density in the direction of the
Galactic center within 20 Myr, effectively making these clusters undetectable
after that time. Clusters farther from the Galactic center but at the same
projected distance are more strongly affected by this selection effect, and may
go undetected for their entire lifetimes. Based on these findings, we conclude
that the region within 200 pc of the Galactic center could easily harbor some
50 clusters with properties similar to those of the Arches or the Quintuplet
systems.Comment: ApJ Letters in pres
The M/L ratio of massive young clusters
We point out a strong time-evolution of the mass-to-light conversion factor
\eta commonly used to estimate masses of dense star clusters from observed
cluster radii and stellar velocity dispersions. We use a gas-dynamical model
coupled with the Cambridge stellar evolution tracks to compute line-of-sight
velocity dispersions and half-light radii weighted by the luminosity. Stars at
birth are assumed to follow the Salpeter mass function in the range [0.15--17
M_\sun]. We find that , and hence the estimated cluster mass, increases
by factors as large as 3 over time-scales of 20 million years. Increasing the
upper mass limit to 50 M_\sun leads to a sharp rise of similar amplitude but
in as little as 10 million years.
Fitting truncated isothermal (Michie-King) models to the projected light
profile leads to over-estimates of the concentration par ameter c of compared to the same functional fit applied to the proj ected
mass density.Comment: Draft version of an ApJ lette
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