372,585 research outputs found
Crawling the Cosmic Network: Identifying and Quantifying Filamentary Structure
We present the Smoothed Hessian Major Axis Filament Finder (SHMAFF), an
algorithm that uses the eigenvectors of the Hessian matrix of the smoothed
galaxy distribution to identify individual filamentary structures. Filaments
are traced along the Hessian eigenvector corresponding to the largest
eigenvalue, and are stopped when the axis orientation changes more rapidly than
a preset threshold. In both N-body simulations and the Sloan Digital Sky Survey
(SDSS) main galaxy redshift survey data, the resulting filament length
distributions are approximately exponential. In the SDSS galaxy distribution,
using smoothing lengths of 10 h^{-1} Mpc and 15 h^{-1} Mpc, we find filament
lengths per unit volume of 1.9x10^{-3} h^2 Mpc^{-2} and 7.6x10^{-4} h^2
Mpc^{-2}, respectively. The filament width distributions, which are much more
sensitive to non-linear growth, are also consistent between the real and mock
galaxy distributions using a standard cosmology. In SDSS, we find mean filament
widths of 5.5 h^{-1} Mpc and 8.4 h^{-1} Mpc on 10 h^{-1} Mpc and 15 h^{-1} Mpc
smoothing scales, with standard deviations of 1.1 h^{-1} Mpc and 1.4 h^{-1}
Mpc, respectively. Finally, the spatial distribution of filamentary structure
in simulations is very similar between z=3 and z=0 on smoothing scales as large
as 15 h^{-1} Mpc, suggesting that the outline of filamentary structure is
already in place at high redshift.Comment: 10 pages, 11 figures, accepted to MNRA
Biased Estimates of Omega from Comparing Smoothed Predicted Velocity Fields to Unsmoothed Peculiar Velocity Measurements
We show that a regression of unsmoothed peculiar velocity measurements
against peculiar velocities predicted from a smoothed galaxy density field
leads to a biased estimate of the cosmological density parameter Omega, even
when galaxies trace the underlying mass distribution and galaxy positions and
velocities are known perfectly. The bias arises because the errors in the
predicted velocities are correlated with the predicted velocities themselves.
We investigate this bias using cosmological N-body simulations and analytic
arguments. In linear perturbation theory, for cold dark matter power spectra
and Gaussian or top hat smoothing filters, the bias in Omega is always
positive, and its magnitude increases with increasing smoothing scale. This
linear calculation reproduces the N-body results for Gaussian smoothing radii
R_s > 10 Mpc/h, while non-linear effects lower the bias on smaller smoothing
scales, and for R_s < 3 Mpc/h Omega is underestimated rather than
overestimated. The net bias in Omega for a given smoothing filter depends on
the underlying cosmological model. The effect on current estimates of Omega
from velocity-velocity comparisons is probably small relative to other
uncertainties, but taking full advantage of the statistical precision of future
peculiar velocity data sets will require either equal smoothing of the
predicted and measured velocity fields or careful accounting for the biases
discussed here.Comment: 11 pages including 2 eps figures. Submitted to Ap
Vey theorem in infinite dimensions and its application to KdV
We consider an integrable infinite-dimensional Hamiltonian system in a
Hilbert space with integrals which can be written as , where ,
for . We assume that the maps define a germ of an
analytic diffeomorphism , such that dF(0)=id(F-id)\kappa\kappa\geq 0FF_jF_j^\primeF_j-F_j^\prime=O(|u|^2)\frac12|F'_j|^2F^\prime: H\to H(F^\prime-id)\kappaI_j(\frac12|F'_j|^2,j\ge1)\kappa=1$ applies to the KdV equation. It implies that in the vicinity of the
origin in a functional space KdV admits the Birkhoff normal form and the
integrating transformation has the form `identity plus a 1-smoothing analytic
map'
Analytical smoothing effect of solution for the boussinesq equations
In this paper, we study the analytical smoothing effect of Cauchy problem for
the incompressible Boussinesq equations. Precisely, we use the Fourier method
to prove that the Sobolev H 1-solution to the incompressible Boussinesq
equations in periodic domain is analytic for any positive time. So the
incompressible Boussinesq equation admet exactly same smoothing effect
properties of incompressible Navier-Stokes equations
The Size and Shape of Local Voids
We study the size and shape of low density regions in the local universe
which we identify in the smoothed density field of the PSCz flux limited IRAS
galaxy catalogue. After quantifying the systematic biases that enter in the
detection of voids using our data set and method, we identify, using a
smoothing length of 5 Mpc, 14 voids within 80 Mpc and using a
smoothing length of 10 Mpc, 8 voids within 130 Mpc. We study
the void size distribution and morphologies and find that there is roughly an
equal number of prolate and oblate-like spheroidal voids. We compare the
measured PSCz void shape and size distributions with those expected in six
different CDM models and find that only the size distribution can discriminate
between models. The models preferred by the PSCz data are those with
intermediate values of , independent of cosmology.Comment: final version, Accepted in MNRA
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