1,203 research outputs found
Skeleton as a probe of the cosmic web: the 2D case
We discuss the skeleton as a probe of the filamentary structures of a 2D
random field. It can be defined for a smooth field as the ensemble of pairs of
field lines departing from saddle points, initially aligned with the major axis
of local curvature and connecting them to local maxima. This definition is thus
non local and makes analytical predictions difficult, so we propose a local
approximation: the local skeleton is given by the set of points where the
gradient is aligned with the local curvature major axis and where the second
component of the local curvature is negative.
We perform a statistical analysis of the length of the total local skeleton,
chosen for simplicity as the set of all points of space where the gradient is
either parallel or orthogonal to the main curvature axis. In all our numerical
experiments, which include Gaussian and various non Gaussian realizations such
as \chi^2 fields and Zel'dovich maps, the differential length is found within a
normalization factor to be very close to the probability distribution function
of the smoothed field. This is in fact explicitly demonstrated in the Gaussian
case.
This result might be discouraging for using the skeleton as a probe of non
Gausiannity, but our analyses assume that the total length of the skeleton is a
free, adjustable parameter. This total length could in fact be used to
constrain cosmological models, in CMB maps but also in 3D galaxy catalogs,
where it estimates the total length of filaments in the Universe. Making the
link with other works, we also show how the skeleton can be used to study the
dynamics of large scale structure.Comment: 15 pages, 11 figures, submitted to MNRA
The three dimensional skeleton: tracing the filamentary structure of the universe
The skeleton formalism aims at extracting and quantifying the filamentary
structure of the universe is generalized to 3D density fields; a numerical
method for computating a local approximation of the skeleton is presented and
validated here on Gaussian random fields. This method manages to trace well the
filamentary structure in 3D fields such as given by numerical simulations of
the dark matter distribution on large scales and is insensitive to monotonic
biasing. Two of its characteristics, namely its length and differential length,
are analyzed for Gaussian random fields. Its differential length per unit
normalized density contrast scales like the PDF of the underlying density
contrast times the total length times a quadratic Edgeworth correction
involving the square of the spectral parameter. The total length scales like
the inverse square smoothing length, with a scaling factor given by 0.21 (5.28+
n) where n is the power index of the underlying field. This dependency implies
that the total length can be used to constrain the shape of the underlying
power spectrum, hence the cosmology. Possible applications of the skeleton to
galaxy formation and cosmology are discussed. As an illustration, the
orientation of the spin of dark halos and the orientation of the flow near the
skeleton is computed for dark matter simulations. The flow is laminar along the
filaments, while spins of dark halos within 500 kpc of the skeleton are
preferentially orthogonal to the direction of the flow at a level of 25%.Comment: 17 pages, 11 figures, submitted to MNRA
Building Merger Trees from Cosmological N-body Simulations
Although a fair amount of work has been devoted to growing Monte-Carlo merger
trees which resemble those built from an N-body simulation, comparatively
little effort has been invested in quantifying the caveats one necessarily
encounters when one extracts trees directly from such a simulation. To somewhat
revert the tide, this paper seeks to provide its reader with a comprehensive
study of the problems one faces when following this route. The first step to
building merger histories of dark matter haloes and their subhaloes is to
identify these structures in each of the time outputs (snapshots) produced by
the simulation. Even though we discuss a particular implementation of such an
algorithm (called AdaptaHOP) in this paper, we believe that our results do not
depend on the exact details of the implementation but extend to most if not all
(sub)structure finders. We then highlight different ways to build merger
histories from AdaptaHOP haloes and subhaloes, contrasting their various
advantages and drawbacks. We find that the best approach to (sub)halo merging
histories is through an analysis that goes back and forth between
identification and tree building rather than one which conducts a
straightforward sequential treatment of these two steps. This is rooted in the
complexity of the merging trees which have to depict an inherently dynamical
process from the partial temporal information contained in the collection of
instantaneous snapshots available from the N-body simulation.Comment: 19 pages, 28 figure
Fluid-loaded metasurfaces
We consider wave propagation along fluid-loaded structures which take the
form of an elastic plate augmented by an array of resonators forming a
metasurface, that is, a surface structured with sub-wavelength resonators. Such
surfaces have had considerable recent success for the control of wave
propagation in electromagnetism and acoustics, by combining the vision of
sub-wavelength wave manipulation, with the design, fabrication and size
advantages associated with surface excitation. We explore one aspect of recent
interest in this field: graded metasurfaces, but within the context of
fluid-loaded structures.
Graded metasurfaces allow for selective spatial frequency separation and are
often referred to as exhibiting rainbow trapping. Experiments, and theory, have
been developed for acoustic, electromagnetic, and even elastic, rainbow devices
but this has not been approached for fluid-loaded structures that support
surface waves coupled with the acoustic field in a bulk fluid. This surface
wave, coupled with the fluid, can be used to create an additional effect by
designing a metasurface to mode convert from surface to bulk waves. We
demonstrate that sub-wavelength control is possible and that one can create
both rainbow trapping and mode conversion phenomena for a fluid-loaded elastic
plate model.Comment: 13 pages, 10 figure
Statistical Tests for CHDM and \LambdaCDM Cosmologies
We apply several statistical estimators to high-resolution N-body simulations
of two currently viable cosmological models: a mixed dark matter model, having
contributed by two massive neutrinos (C+2\nuDM), and a Cold
Dark Matter model with Cosmological Constant (\LambdaCDM) with
and h=0.7. Our aim is to compare simulated galaxy samples with the
Perseus-Pisces redshift survey (PPS). We consider the n-point correlation
functions (n=2-4), the N-count probability functions P_N, including the void
probability function P_0, and the underdensity probability function U_\epsilon
(where \epsilon fixes the underdensity threshold in percentage of the average).
We find that P_0 (for which PPS and CfA2 data agree) and P_1 distinguish
efficiently between the models, while U_\epsilon is only marginally
discriminatory. On the contrary, the reduced skewness and kurtosis are,
respectively, S_3\simeq 2.2 and S_4\simeq 6-7 in all cases, quite independent
of the scale, in agreement with hierarchical scaling predictions and estimates
based on redshift surveys. Among our results, we emphasize the remarkable
agreement between PPS data and C+2\nuDM in all the tests performed. In
contrast, the above \LambdaCDM model has serious difficulties in reproducing
observational data if galaxies and matter overdensities are related in a simple
way.Comment: 12 pages, 10 figures, LaTeX (aaspp4 macro), in press on ApJ, Vol.
479, April 199
Enhanced sensing and conversion of ultrasonic Rayleigh waves by elastic metasurfaces
Recent years have heralded the introduction of metasurfaces that advantageously combine the vision of sub-wavelength wave manipulation, with the design, fabrication and size advantages associated with surface excitation. An important topic within metasurfaces is the tailored rainbow trapping and selective spatial frequency separation of electromagnetic and acoustic waves using graded metasurfaces. This frequency dependent trapping and spatial frequency segregation has implications for energy concentrators and associated energy harvesting, sensing and wave filtering techniques. Different demonstrations of acoustic and electromagnetic rainbow devices have been performed, however not for deep elastic substrates that support both shear and compressional waves, together with surface Rayleigh waves; these allow not only for Rayleigh wave rainbow effects to exist but also for mode conversion from surface into shear waves. Here we demonstrate experimentally not only elastic Rayleigh wave rainbow trapping, by taking advantage of a stop-band for surface waves, but also selective mode conversion of surface Rayleigh waves to shear waves. These experiments performed at ultrasonic frequencies, in the range of 400â600âkHz, are complemented by time domain numerical simulations. The metasurfaces we design are not limited to guided ultrasonic waves and are a general phenomenon in elastic waves that can be translated across scales
Reply to: "Letter to the Editor: Cocaine use and cocaine use disorder - Revisiting epidemiology and clinical impact"
Ray Tracing Simulations of Weak Lensing by Large-Scale Structure
We investigate weak lensing by large-scale structure using ray tracing
through N-body simulations. Photon trajectories are followed through high
resolution simulations of structure formation to make simulated maps of shear
and convergence on the sky. Tests with varying numerical parameters are used to
calibrate the accuracy of computed lensing statistics on angular scales from
about 1 arcminute to a few degrees. Various aspects of the weak lensing
approximation are also tested. For fields a few degrees on a side the shear
power spectrum is almost entirely in the nonlinear regime and agrees well with
nonlinear analytical predictions. Sampling fluctuations in power spectrum
estimates are investigated by comparing several ray tracing realizations of a
given model. For survey areas smaller than a degree on a side the main source
of scatter is nonlinear coupling to modes larger than the survey. We develop a
method which uses this effect to estimate the mass density parameter Omega from
the scatter in power spectrum estimates for subregions of a larger survey. We
show that the power spectrum can be measured accurately from realistically
noisy data on scales corresponding to 1-10 Mpc/h. Non-Gaussian features in the
one point distribution function of the weak lensing convergence (reconstructed
from the shear) are also sensitive to Omega. We suggest several techniques for
estimating Omega in the presence of noise and compare their statistical power,
robustness and simplicity. With realistic noise Omega can be determined to
within 0.1-0.2 from a deep survey of several square degrees.Comment: 59 pages, 22 figures included. Matches version accepted for Ap
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