3,296 research outputs found
Nonlinear Evolution of the Genus Statistics with Zel'dovich Approximation
Evolution of genus density is calculated from Gaussian initial conditions
using Zel'dovich approximation. A new approach is introduced which formulates
the desired quantity in a rotationally invariant manner. It is shown that
normalized genus density does not depend on the initial spectral shape but is a
function of the fluctuation amplitude only.Comment: 21 pages, 6 Postscript figures, LaTe
Phase diagram of a dilute ferromagnet model with antiferromagnetic next-nearest-neighbor interactions
We have studied the spin ordering of a dilute classical Heisenberg model with
spin concentration , and with ferromagnetic nearest-neighbor interaction
and antiferromagnetic next-nearest-neighbor interaction . Magnetic
phases at absolute zero temperature are determined examining the
stiffness of the ground state, and those at finite temperatures are
determined calculating the Binder parameter and the spin correlation
length . Three ordered phases appear in the phase diagram: (i) the
ferromagnetic (FM) phase; (ii) the spin glass (SG) phase; and (iii) the mixed
(M) phase of the FM and the SG. Near below the ferromagnetic threshold , a reentrant SG transition occurs. That is, as the temperature is decreased
from a high temperature, the FM phase, the M phase and the SG phase appear
successively. The magnetization which grows in the FM phase disappears in the
SG phase. The SG phase is suggested to be characterized by ferromagnetic
clusters. We conclude, hence, that this model could reproduce experimental
phase diagrams of dilute ferromagnets FeAu and EuSrS.Comment: 9 pages, 23 figure
A Test of the Particle Paradigm in N-Body Simulations
We present results of tests of the evolution of small ``fluid elements'' in
cosmological N--body simulations, to examine the validity of their treatment as
particles. We find that even very small elements typically collapse along one
axis while expanding along another, often to twice or more their initial
comoving diameter. This represents a possible problem for high--resolution uses
of such simulations.Comment: Uses aasms4.sty; accepted for publication in ApJ Letters. Files
available also at ftp://kusmos.phsx.ukans.edu/preprints/ates
Identifying short motifs by means of extreme value analysis
The problem of detecting a binding site -- a substring of DNA where
transcription factors attach -- on a long DNA sequence requires the recognition
of a small pattern in a large background. For short binding sites, the matching
probability can display large fluctuations from one putative binding site to
another. Here we use a self-consistent statistical procedure that accounts
correctly for the large deviations of the matching probability to predict the
location of short binding sites. We apply it in two distinct situations: (a)
the detection of the binding sites for three specific transcription factors on
a set of 134 estrogen-regulated genes; (b) the identification, in a set of 138
possible transcription factors, of the ones binding a specific set of nine
genes. In both instances, experimental findings are reproduced (when available)
and the number of false positives is significantly reduced with respect to the
other methods commonly employed.Comment: 6 pages, 5 figure
The intermittent behavior and hierarchical clustering of the cosmic mass field
The hierarchical clustering model of the cosmic mass field is examined in the
context of intermittency. We show that the mass field satisfying the
correlation hierarchy is intermittent if , where is the dimension of the field, and is the power-law
index of the non-linear power spectrum in the discrete wavelet transform (DWT)
representation. We also find that a field with singular clustering can be
described by hierarchical clustering models with scale-dependent coefficients
and that this scale-dependence is completely determined by the
intermittent exponent and . Moreover, the singular exponents of a field
can be calculated by the asymptotic behavior of when is large.
Applying this result to the transmitted flux of HS1700 Ly forests, we
find that the underlying mass field of the Ly forests is significantly
intermittent. On physical scales less than about 2.0 h Mpc, the observed
intermittent behavior is qualitatively different from the prediction of the
hierarchical clustering with constant . The observations, however, do show
the existence of an asymptotic value for the singular exponents. Therefore, the
mass field can be described by the hierarchical clustering model with
scale-dependent . The singular exponent indicates that the cosmic mass
field at redshift is weakly singular at least on physical scales as
small as 10 h kpc.Comment: AAS Latex file, 33 pages,5 figures included, accepted for publication
in Ap
Beyond Zel'dovich-Type Approximations in Gravitational Instability Theory --- Pad\'e Prescription in Spheroidal Collapse ---
Among several analytic approximations for the growth of density fluctuations
in the expanding Universe, Zel'dovich approximation in Lagrangian coordinate
scheme is known to be unusually accurate even in mildly non-linear regime. This
approximation is very similar to the Pad\'e approximation in appearance. We
first establish, however, that these two are actually different and independent
approximations with each other by using a model of spheroidal mass collapse.
Then we propose Pad\'e-prescribed Zel'dovich-type approximations and
demonstrate, within this model, that they are much accurate than any other
known nonlinear approximations.Comment: 4 pages, latex, 3 figures include
Perturbative Analysis of Adaptive Smoothing Methods in Quantifying Large-Scale Structure
Smoothing operation to make continuous density field from observed point-like
distribution of galaxies is crucially important for topological or
morphological analysis of the large-scale structure, such as, the genus
statistics or the area statistics (equivalently the level crossing statistics).
It has been pointed out that the adaptive smoothing filters are more efficient
tools to resolve cosmic structures than the traditional spatially fixed
filters. We study weakly nonlinear effects caused by two representative
adaptive methods often used in smoothed hydrodynamical particle (SPH)
simulations. Using framework of second-order perturbation theory, we calculate
the generalized skewness parameters for the adaptive methods in the case of
initially power-law fluctuations.
Then we apply the multidimensional Edgeworth expansion method and investigate
weakly nonlinear evolution of the genus statistics and the area statistics.
Isodensity contour surfaces are often parameterized by the volume fraction of
the regions above a given density threshold. We also discuss this
parameterization method in perturbative manner.Comment: 42 pages including 9 figure, ApJ 537 in pres
The Topology of Large Scale Structure in the 1.2 Jy IRAS Redshift Survey
We measure the topology (genus) of isodensity contour surfaces in volume
limited subsets of the 1.2 Jy IRAS redshift survey, for smoothing scales
\lambda=4\hmpc, 7\hmpc, and 12\hmpc. At 12\hmpc, the observed genus
curve has a symmetric form similar to that predicted for a Gaussian random
field. At the shorter smoothing lengths, the observed genus curve shows a
modest shift in the direction of an isolated cluster or ``meatball'' topology.
We use mock catalogs drawn from cosmological N-body simulations to investigate
the systematic biases that affect topology measurements in samples of this size
and to determine the full covariance matrix of the expected random errors. We
incorporate the error correlations into our evaluations of theoretical models,
obtaining both frequentist assessments of absolute goodness-of-fit and Bayesian
assessments of models' relative likelihoods. We compare the observed topology
of the 1.2 Jy survey to the predictions of dynamically evolved, unbiased,
gravitational instability models that have Gaussian initial conditions. The
model with an , power-law initial power spectrum achieves the best
overall agreement with the data, though models with a low-density cold dark
matter power spectrum and an power-law spectrum are also consistent. The
observed topology is inconsistent with an initially Gaussian model that has
, and it is strongly inconsistent with a Voronoi foam model, which has a
non-Gaussian, bubble topology.Comment: ApJ submitted, 39 pages, LaTeX(aasms4), 12 figures, 1 Tabl
Fundamental Discreteness Limitations of Cosmological N-Body Clustering Simulations
We explore some of the effects that discreteness and two-body scattering may
have on N-body simulations with ``realistic'' cosmological initial conditions.
We use an identical subset of particles from the initial conditions for a
Particle-Mesh (PM) calculation as the initial conditions for a variety
PM and Tree code runs. We investigate the effect of mass resolution (the
mean interparticle separation) since most ``high resolution'' codes only have
high resolution in gravitational force. The phase-insensitive two--point
statistics, such as the power spectrum (autocorrelation) are somewhat affected
by these variations, but phase-sensitive statistics show greater differences.
Results converge at the mean interparticle separation scale of the lowest
mass-resolution code. As more particles are added, but the force resolution is
held constant, the PM and the Tree runs agree more and more strongly with
each other and with the PM run which had the same initial conditions. This
shows high particle density is necessary for correct time evolution, since many
different results cannot all be correct. However, they do not so converge to a
PM run which continued the fluctuations to small scales. Our results show that
ignoring them is a major source of error on comoving scales of the missing
wavelengths. This can be resolved by putting in a high particle density. Since
the codes never agree well on scales below the mean comoving interparticle
separation, we find little justification for quantitative predictions on this
scale. Some measures vary by 50%, but others can be off by a factor of three or
more. Our results suggest possible problems with the density of galaxy halos,
formation of early generation objects such as QSO absorber clouds, etc.Comment: Revised version to be published in Astrophysical Journal. One figure
changed; expanded discussion, more information on code parameters. Latex, 44
pages, including 19 figures. Higher resolution versions of Figures 10-15
available at: ftp://kusmos.phsx.ukans.edu/preprints/nbod
- âŠ