Página 12 dos resultados de 15310 itens digitais encontrados em 0.005 segundos

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

Shang, Cien; Haiman, Zoltan
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
153.59818%
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...

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

Gaztanaga, E.; Fosalba, P.; Elizalde, E.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
153.59818%
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...

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

Sullivan, Zack; Quackenbush, Seth
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...

Extreme deviations and applications

Frisch, U.; Sornette, D.
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
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...

The Probability Distribution for Non-Gaussianity Estimators

Smith, Tristan L.; Kamionkowski, Marc; Wandelt, Benjamin D.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
153.59818%
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...

Exploring the beta distribution in variable-density turbulent mixing

Bakosi, J.; Ristorcelli, J. R.
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...

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

Taruya, Atsushi; Hamana, Takashi; Kayo, Issha
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...