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Resultados filtrados por Publicador: Universidade Cornell

## Cosmology with Standard Sirens: the Importance of the Shape of the Lensing Magnification Distribution

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 20/04/2010
Português

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The gravitational waves (GWs) emitted by inspiraling binary black holes,
expected to be detected by the Laser Interferometer Space Antenna (LISA), could
be used to determine the luminosity distance to these sources with the
unprecedented precision of <~ 1%. We study cosmological parameter constraints
from such standard sirens, in the presence of gravitational lensing by
large-scale structure. Lensing introduces magnification with a probability
distribution function (PDF) whose shape is highly skewed and depends on
cosmological parameters. We use Monte-Carlo simulations to generate mock
samples of standard sirens, including a small intrinsic scatter, as well as the
additional, larger scatter from lensing, in their inferred distances. We derive
constraints on cosmological parameters, by simultaneously fitting the mean and
the distribution of the residuals on the distance vs redshift (d_L - z) Hubble
diagram. We find that for standard sirens at redshift z ~ 1, the sensitivity to
a single cosmological parameter, such as the matter density Omega_m, or the
dark energy equation of state w, is ~ 50%-80% tighter when the skewed lensing
PDF is used, compared to the sensitivity derived from a Gaussian PDF with the
same variance. When these two parameters are constrained simultaneously...

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## Gravitational Evolution of the Large-Scale Probability Density Distribution: The Edgeworth & Gamma Expansions

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 17/06/1999
Português

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The gravitational evolution of the cosmic one-point probability distribution
function (PDF) has been estimated using an analytic approximation that combines
gravitational perturbation theory with the Edgeworth expansion around a
Gaussian PDF. Despite the remarkable success of the Edgeworth expansion in
modeling the weakly non-linear growth of fluctuations around the peak of the
cosmic PDF, it fails to reproduce the expected behaviour in the tails of the
distribution. Besides, this expansion is ill-defined as it predicts negative
densities and negative probabilities for the cosmic fields. This is a natural
consequence of using an expansion around the Gaussian distribution, which is
not rigorously well-defined when describing a positive variate, such as the
density field. Here we present an alternative to the Edgeworth series based on
an expansion around the Gamma PDF. The Gamma expansion is designed to converge
when the PDF exhibits exponential tails. The proposed expansion is better
suited for describing a real PDF as it always yields positive densities and the
PDF is effectively positive-definite. We compare the performance of the
Edgeworth and the Gamma expansions for a wide dynamical range making use of
cosmological N-body simulations and assess their range of validity. In general...

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## Improving parton distribution uncertainties in a W mass measurement at the LHC

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

153.59818%

We reexamine the dominant contribution of parton distribution function (PDF)
uncertainties to the W mass measurement, and determine their contribution is
+-39(30) MeV when running the Large Hadron Collider at 7(13) TeV. We find that
spurious correlations in older PDF sets led to over-optimistic assumptions
regarding normalization to Z observables. In order to understand the origin of
the large uncertainties we break down the contribution of the PDF errors into
effects at the hard matrix element level, in showering, and in sensitivity to
finite detector resolutions.
Using CT10, CT10W, and charm enhanced PDF sets in comparison to older PDF
sets, we develop a robust analysis that examines correlations between
transverse mass reconstructions of W and Z decays (scaled by cos $\theta_W$) to
leptons. We find that central leptons (|$\eta_l$| < 1.3) from W and Z bosons
carry the most weight in reducing the PDF uncertainty, and estimate a PDF error
of +10/-12 MeV is achievable in a W mass measurement at the LHC. Further
reductions of the W mass uncertainty will require improved fits to the parton
distribution functions.; Comment: 6 pages, Presentation at the DPF 2015 Meeting of the American
Physical Society Division of Particles and Fields...

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## Extreme deviations and applications

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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153.59818%

Stretched exponential probability density functions (pdf), having the form of
the exponential of minus a fractional power of the argument, are commonly found
in turbulence and other areas. They can arise because of an underlying random
multiplicative process. For this, a theory of extreme deviations is developed,
devoted to the far tail of the pdf of the sum $X$ of a finite number $n$ of
independent random variables with a common pdf $e^{-f(x)}$. The function $f(x)$
is chosen (i) such that the pdf is normalized and (ii) with a strong convexity
condition that $f''(x)>0$ and that $x^2f''(x)\to +\infty$ for $|x|\to\infty$.
Additional technical conditions ensure the control of the variations of
$f''(x)$. The tail behavior of the sum comes then mostly from individual
variables in the sum all close to $X/n$ and the tail of the pdf is $\sim
e^{-nf(X/n)}$. This theory is then applied to products of independent random
variables, such that their logarithms are in the above class, yielding usually
stretched exponential tails. An application to fragmentation is developed and
compared to data from fault gouges. The pdf by mass is obtained as a weighted
superposition of stretched exponentials, reflecting the coexistence of
different fragmentation generations. For sizes near and above the peak size...

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## The Probability Distribution for Non-Gaussianity Estimators

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 05/04/2011
Português

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One of the principle efforts in cosmic microwave background (CMB) research is
measurement of the parameter fnl that quantifies the departure from Gaussianity
in a large class of non-minimal inflationary (and other) models. Estimators for
fnl are composed of a sum of products of the temperatures in three different
pixels in the CMB map. Since the number ~Npix^2 of terms in this sum exceeds
the number Npix of measurements, these ~Npix^2 terms cannot be statistically
independent. Therefore, the central-limit theorem does not necessarily apply,
and the probability distribution function (PDF) for the fnl estimator does not
necessarily approach a Gaussian distribution for N_pix >> 1. Although the
variance of the estimators is known, the significance of a measurement of fnl
depends on knowledge of the full shape of its PDF. Here we use Monte Carlo
realizations of CMB maps to determine the PDF for two minimum-variance
estimators: the standard estimator, constructed under the null hypothesis
(fnl=0), and an improved estimator with a smaller variance for |fnl| > 0. While
the PDF for the null-hypothesis estimator is very nearly Gaussian when the true
value of fnl is zero, the PDF becomes significantly non-Gaussian when |fnl| >
0. In this case we find that the PDF for the null-hypothesis estimator fnl_hat
is skewed...

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## Exploring the beta distribution in variable-density turbulent mixing

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

153.59818%

In assumed probability density function (pdf) methods of turbulent
combustion, the shape of the scalar pdf is assumed a priori and the pdf is
parametrized by its moments for which model equations are solved. In
non-premixed flows the beta distribution has been a convenient choice to
represent the mixture fraction in binary mixtures or a progress variable in
combustion. Here the beta-pdf approach is extended to variable-density mixing:
mixing between materials that have very large density differences and thus the
scalar fields are active. As a consequence, new mixing phenomena arise due to
1) cubic non-linearities in the Navier-Stokes equation, 2) additional
non-linearities in the molecular diffusion terms and 3) the appearance of the
specific volume as a dynamical variable. The assumed beta-pdf approach is
extended to transported pdf methods by giving the associated stochastic
differential equation (SDE). The beta distribution is shown to be a realizable,
consistent and sufficiently general representation of the marginal pdf of the
fluid density, an active scalar, in non-premixed variable-density turbulent
mixing. The moment equations derived from mass conservation are compared to the
moment equations derived from the governing SDE. This yields a series of
relations between the non-stationary coefficients of the SDE and the mixing
physics. Our treatment of this problem is general: the mixing is mathematically
represented by the divergence of the velocity field which can only be specified
once the problem is defined. In this paper we seek to describe a theoretical
framework to subsequent applications. We report and document several rigorous
mathematical results...

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## Non-Gaussian Tails of Cosmological Density Distribution Function from Dark Halo Approach

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 23/10/2002
Português

Relevância na Pesquisa

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We present a simple model based on the dark halo approach which provides a
useful way to understand key points determining the shape of the non-Gaussian
tails of the dark matter one-point probability distribution function(PDF). In
particular, using the scale-free models with power-law profile of dark halos,
we derive a simple analytic expression for the one-point PDF. It is found that
the shape of the PDF changes at the characteristic value of $\delta_*$ which is
defined by the smoothed density of a halo with the characteristic mass $M_*$ at
the epoch. In cold dark matter models with top-hat smoothing filters, the
characteristic smoothed density at present time typically takes the value
$\delta_*\gg 1$ for a small smoothing scale $\rth\sim 1$Mpc$/h$ and conversely
$\delta_*\ll 1$ for a large smoothing scale $\rth > 10$Mpc$/h$. On the range
$\delta/\delta_*<1$, the shape of the PDF is almost solely determined by the
outer slope of halos and scales as a power-law. The resultant non-Gaussian
tails of PDF then resemble the log-normal PDFs in that range and show a good
agreement with N-body simulations, which can be ascribed to the universality of
the outer slope of the halo profile. In contrast, tails of one-point PDF in the
range $\delta/\delta_*>1$ basically follow the steep exponential tails of the
halo mass function...

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