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Results for “Probability Distribution Function”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Characterizing the Lyα forest flux probability distribution function using Legendre polynomials

The Lyman-α forest is a highly non-linear field with considerable information available in the data beyond the power spectrum. The flux probability distribution function (PDF) has been used as a successful probe of small-scale physics. In this paper we argue that measuring coefficients of the Legendre polynomial expansion of the PDF offers several advantages over measuring the binned values as is commonly done. In particular, the n -th Legendre coefficient can be expressed as a linear combination of the first n moments, allowing these coefficients to be measured in the presence of noise and allowing a clear route for marginalisation over mean flux. Moreover, in the presence of noise, our numerical work shows that a finite number of coefficients are well measured with a very sharp transition into noise dominance. This compresses the available information into a small number of well-measured quantities. In conclusion, we find that the amount of recoverable information is a very non-linear function of spectral noise that strongly favors fewer quasars measured at better signal to noise.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Vectorization techniques for probability distribution functions using VecCore

Probability distribution functions (PDFs) are very used in modeling random processes and physics simulations. Improving the performance of algorithms that generate many random numbers under complex PDFs is often a very challenging task when methods as direct functions are not available. In this work we present general strategies on how to vectorize some PDFs using VecCore library. We show the results for the Exponential, Gaussian, discrete Poisson and Gamma probability distributions.

Chaparro Amaro, Oscar R.↗
DOE OSTI2015

IGM CONSTRAINTS FROM THE SDSS-III/BOSS DR9 Lyα FOREST TRANSMISSION PROBABILITY DISTRIBUTION FUNCTION

The Lyα forest transmission probability distribution function (PDF) is an established probe of the intergalactic medium (IGM) astrophysics, especially the temperature-density relationship of the IGM. We measure the transmission PDF from 3393 Baryon Oscillations Spectroscopic Survey (BOSS) quasars from Sloan Digital Sky Survey Data Release 9, and compare with mock spectra that include careful modeling of the noise, continuum, and astrophysical uncertainties. The BOSS transmission PDFs, measured at (z) = [2.3, 2.6, 3.0], are compared with PDFs created from mock spectra drawn from a suite of hydrodynamical simulations that sample the IGM temperature-density relationship, γ, and temperature at mean density, T {sub 0}, where T(Δ) = T {sub 0}Δ{sup γ} {sup –} {sup 1}. We find that a significant population of partial Lyman-limit systems (LLSs) with a column-density distribution slope of β{sub pLLS} ∼ – 2 are required to explain the data at the low-transmission end of transmission PDF, while uncertainties in the mean Lyα forest transmission affect the high-transmission end. After modeling the LLSs and marginalizing over mean transmission uncertainties, we find that γ = 1.6 best describes the data over our entire redshift range, although constraints on T {sub 0} are affected by systematic uncertainties. Within our model framework, isothermal or inverted temperature-density relationships (γ ≤ 1) are disfavored at a significance of over 4σ, although this could be somewhat weakened by cosmological and astrophysical uncertainties that we did not model.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Cosmological constraints from the Subaru Hyper Suprime-Cam year 1 shear catalogue lensing convergence probability distribution function

Here we utilize the probability distribution function (PDF) of normalized convergence maps reconstructed from the Subaru Hyper Suprime-Cam (HSC) year 1 shear catalogue, in combination with the power spectrum, to measure the matter clustering amplitude S 8 = σ 8 $\sqrt {Ω_{m}/0.3}$. The large-scale structure’s statistical properties are incompletely described by the traditional two-point statistics, motivating our investigation of the PDF—a complementary higher-order statistic. By defining the PDF over the standard-deviation-normalized convergence map, we are able to isolate the non-Gaussian information. We use tailored simulations to compress the data vector and construct a likelihood approximation. We mitigate the impact of survey and astrophysical systematics with cuts on smoothing scales, redshift bins, and data vectors. We find S 8 = $0.860^{+0.066}_{–0.109}$ from the PDF alone and S 8 = 0.798$^{+0.029}_{–0.042}$ from the combination of the PDF and power spectrum (68% confidential level (CL)). The PDF improves the power-spectrum-only constraint by about 10%.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

An Improved Double-Gaussian Closure for the Subgrid Vertical Velocity Probability Distribution Function

Abstract The vertical velocity probability distribution function (PDF) is analyzed throughout the depth of the lower atmosphere, including the subcloud and cloud layers, in four large-eddy simulation (LES) cases of shallow cumulus and stratocumulus. Double-Gaussian PDF closures are examined to test their ability to represent a wide range of turbulence statistics, from stratocumulus cloud layers characterized by Gaussian turbulence to shallow cumulus cloud layers displaying strongly non-Gaussian turbulence statistics. While the majority of the model closures are found to perform well in the former case, the latter presents a considerable challenge. A new model closure is suggested that accounts for high skewness and kurtosis seen in shallow cumulus cloud layers. The well-established parabolic relationship between skewness and kurtosis is examined, with results in agreement with previous studies for the subcloud layer. In cumulus cloud layers, however, a modified relationship is necessary to improve performance. The new closure significantly improves the estimation of the vertical velocity PDF for shallow cumulus cloud layers, in addition to performing well for stratocumulus. In particular, the long updraft tail representing the bulk of cloudy points is much better represented and higher-order moments diagnosed from the PDF are also greatly improved. However, some deficiencies remain owing to fundamental limitations of representing highly non-Gaussian turbulence statistics with a double-Gaussian PDF.

Fitch, A. C.↗
DOE OSTI2020

Position-dependent matter density probability distribution function

Here, we introduce the position-dependent probability distribution function (PDF) of the smoothed matter field as a cosmological observable. In comparison to the PDF itself, the spatial variation of the position-dependent PDF is simpler to model and has distinct dependence on cosmological parameters. We demonstrate that the position-dependent PDF is characterized by variations in the local mean density, and we compute the linear response of the PDF to the local density using separate universe N-body simulations. The linear response of the PDF to the local density field can be thought of as the linear bias of regions of the matter field selected based on density. We provide a model for the linear response, which accurately predicts our simulation measurements. We also validate our results and test the separate universe consistency relation for the local PDF using global universe simulations. We find excellent agreement between the two, and we demonstrate that the separate universe method gives a lower variance determination of the linear response.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1991

Probability distribution functions in turbulent convection

Results of an extensive investigation of probability distribution functions (pdfs) for Rayleigh-Benard convection, in hard turbulence regime, are presented. It is shown that the pdfs exhibit a high degree of internal universality. In certain cases this universality is established within two Kolmogorov scales of a boundary. A discussion of the factors leading to the universality is presented.

Balachandar, S.↗
NASA NTRS1991

Probability distribution functions in turbulent convection

Results of an extensive investigation of probability distribution functions (pdf's) for Rayleigh-Benard convection, in the hard turbulence regime, are presented. It is seen that the pdf's exhibit a high degree of internal universality. In certain cases this universality is established within two Kolmogorov scales of a boundary. A discussion of the factors leading to universality is presented.

Balachandar, S.↗
NASA NTRS1999

Seasonal Variability of Middle Latitude Ozone in the Lowermost Stratosphere Derived from Probability Distribution Functions

We present a study of the distribution of ozone in the lowermost stratosphere with the goal of characterizing the observed variability. The air in the lowermost stratosphere is divided into two population groups based on Ertel's potential vorticity at 300 hPa. High (low) potential vorticity at 300 hPa indicates that the tropopause is low (high), and the identification of these two groups is made to account for the dynamic variability. Conditional probability distribution functions are used to define the statistics of the ozone distribution from both observations and a three-dimensional model simulation using winds from the Goddard Earth Observing System Data Assimilation System for transport. Ozone data sets include ozonesonde observations from northern midlatitude stations (1991-96) and midlatitude observations made by the Halogen Occultation Experiment (HALOE) on the Upper Atmosphere Research Satellite (UARS) (1994- 1998). The conditional probability distribution functions are calculated at a series of potential temperature surfaces spanning the domain from the midlatitude tropopause to surfaces higher than the mean tropical tropopause (approximately 380K). The probability distribution functions are similar for the two data sources, despite differences in horizontal and vertical resolution and spatial and temporal sampling. Comparisons with the model demonstrate that the model maintains a mix of air in the lowermost stratosphere similar to the observations. The model also simulates a realistic annual cycle. Results show that during summer, much of the observed variability is explained by the height of the tropopause. During the winter and spring, when the tropopause fluctuations are larger, less of the variability is explained by tropopause height. This suggests that more mixing occurs during these seasons. During all seasons, there is a transition zone near the tropopause that contains air characteristic of both the troposphere and the stratosphere. The relevance of the results to the assessment of the environmental impact of aircraft effluence is also discussed.

Rood, Richard B.↗
DOE OSTI2021

Position-dependent Voronoi probability distribution functions for matter and halos

Here, we measure the Voronoi density probability distribution function (PDF) for both dark matter and halos in N-body simulations. For the dark matter, Voronoi densities represent the matter density field smoothed on a uniform mass scale, which approximates the Lagrangian density field. For halos, the Voronoi densities contain information about the local environment of each halo. We measure the halo virial masses, the total amount of dark matter within each halo Voronoi cell, and the halo Voronoi cell volumes, and we show how halo abundances depend on these three quantities. We then study the position-dependent Voronoi density PDF, measured within finite subregions of the Universe, using separate universe simulations. We demonstrate that the spatial variation of the position-dependent PDF is due to large-scale density fluctuations, indicating that the position-dependent PDF is a biased tracer of large-scale structure. We measure this bias for the dark matter, and interpret it as the bias of regions of the Lagrangian density field that are selected based on density. For the halos, this bias can be interpreted as a form of assembly bias. We present the mapping from late-time to early-time Voronoi density for each simulation dark matter particle, which is highly stochastic. We compare the median of this stochastic map with spherical collapse calculations and discuss challenges involved in modeling the evolution of the density field on these scales.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1999

Seasonal Variability of Middle Latitude Ozone in the Lowermost Stratosphere Derived from Probability Distribution Functions

We present a study of the distribution of ozone in the lowermost stratosphere with the goal of understanding the relative contribution to the observations of air of either distinctly tropospheric or stratospheric origin. The air in the lowermost stratosphere is divided into two population groups based on Ertel's potential vorticity at 300 hPa. High [low] potential vorticity at 300 hPa suggests that the tropopause is low [high], and the identification of the two groups helps to account for dynamic variability. Conditional probability distribution functions are used to define the statistics of the mix from both observations and model simulations. Two data sources are chosen. First, several years of ozonesonde observations are used to exploit the high vertical resolution. Second, observations made by the Halogen Occultation Experiment [HALOE] on the Upper Atmosphere Research Satellite [UARS] are used to understand the impact on the results of the spatial limitations of the ozonesonde network. The conditional probability distribution functions are calculated at a series of potential temperature surfaces spanning the domain from the midlatitude tropopause to surfaces higher than the mean tropical tropopause [about 380K]. Despite the differences in spatial and temporal sampling, the probability distribution functions are similar for the two data sources. Comparisons with the model demonstrate that the model maintains a mix of air in the lowermost stratosphere similar to the observations. The model also simulates a realistic annual cycle. By using the model, possible mechanisms for the maintenance of mix of air in the lowermost stratosphere are revealed. The relevance of the results to the assessment of the environmental impact of aircraft effluence is discussed.

Cerniglia, M. C.↗
NASA NTRS1999

Seasonal Variability of Middle Latitude Ozone in the Lowermost Stratosphere Derived from Probability Distribution Functions

We present a study of the distribution of ozone in the lowermost stratosphere with the goal of understanding the relative contribution to the observations of air of either distinctly tropospheric or stratospheric origin. The air in the lowermost stratosphere is divided into two population groups based on Ertel's potential vorticity at 300 hPa. High [low] potential vorticity at 300 hPa suggests that the tropopause is low [high], and the identification of the two groups helps to account for dynamic variability. Conditional probability distribution functions are used to define the statistics of the mix from both observations and model simulations. Two data sources are chosen. First, several years of ozonesonde observations are used to exploit the high vertical resolution. Second, observations made by the Halogen Occultation Experiment [HALOE) on the Upper Atmosphere Research Satellite [UARS] are used to understand the impact on the results of the spatial limitations of the ozonesonde network. The conditional probability distribution functions are calculated at a series of potential temperature surfaces spanning the domain from the midlatitude tropopause to surfaces higher than the mean tropical tropopause [approximately 380K]. Despite the differences in spatial and temporal sampling, the probability distribution functions are similar for the two data sources. Comparisons with the model demonstrate that the model maintains a mix of air in the lowermost stratosphere similar to the observations. The model also simulates a realistic annual cycle. By using the model, possible mechanisms for the maintenance of mix of air in the lowermost stratosphere are revealed. The relevance of the results to the assessment of the environmental impact of aircraft effluence is discussed.

Cerniglia, M. C.↗
DOE OSTI2013

THE EFFECTS OF RADIATIVE TRANSFER ON THE PROBABILITY DISTRIBUTION FUNCTIONS OF MOLECULAR MAGNETOHYDRODYNAMIC TURBULENCE

We study the effects of radiative transfer on the probability distribution functions (PDFs) of simulations of magnetohydrodynamic turbulence in the widely studied {sup 13}CO 2-1 transition. We find that the integrated intensity maps generally follow a log-normal distribution, with the cases that have {tau} Almost-Equal-To 1 best matching the PDF of the column density. We fit a two-dimensional variance-sonic Mach number relationship to our logarithmic PDFs of the form {sigma}{sub ln}{sup 2}{sub ({Sigma}/{Sigma}0}) = A x ln(1+b{sup 2}M{sub s}{sup 2}) and find that, for parameter b = 1/3, parameter A depends on the radiative transfer environment. We also explore the variance, skewness, and kurtosis of the linear PDFs finding that higher moments reflect both higher sonic Mach number and lower optical depth. Finally, we apply the Tsallis incremental PDF function and find that the fit parameters depend on both Mach numbers, but also are sensitive to the radiative transfer parameter space, with the {tau} Almost-Equal-To 1 case best fitting the incremental PDF of the true column density. We conclude that, for PDFs of low optical depth cases, part of the gas is always subthermally excited so that the spread of the line intensities exceeds the spread of the underlying column densities and hence the PDFs do not reflect the true column density. Similarly, PDFs of optically thick cases are dominated by the velocity dispersion and therefore do not represent the true column density PDF. Thus, in the case of molecules like carbon monoxide, the dynamic range of intensities, structures observed, and, consequently, the observable PDFs are less determined by turbulence and more often determined by radiative transfer effects.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

PROBABILITY DISTRIBUTION FUNCTIONS OF COSMOLOGICAL LENSING: CONVERGENCE, SHEAR, AND MAGNIFICATION

We perform high-resolution ray-tracing simulations to investigate probability distribution functions (PDFs) of lensing convergence, shear, and magnification on distant sources up to the redshift of z{sub s} = 20. We pay particular attention to the shot noise effect in N-body simulations by explicitly showing how it affects the variance of the convergence. We show that the convergence and magnification PDFs are closely related to each other via the approximate relation {mu} = (1 - {kappa}){sup -2}, which can reproduce the behavior of PDFs surprisingly well up to the high magnification tail. The mean convergence measured in the source plane is found to be systematically negative, rather than zero as often assumed, and is correlated with the convergence variance. We provide simple analytical formulae for the PDFs, which reproduce simulated PDFs reasonably well for a wide range of redshifts and smoothing sizes. As explicit applications of our ray-tracing simulations, we examine the strong-lensing probability and the magnification effects on the luminosity functions of distant galaxies and quasars.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2012

Reproducibility of Tumor Motion Probability Distribution Function in Stereotactic Body Radiation Therapy of Lung Cancer

Purpose: To evaluate the reproducibility of tumor motion probability distribution function (PDF) in stereotactic body radiation therapy (SBRT) of lung cancer using cine megavoltage (MV) images. Methods and Materials: Cine MV images of 20 patients acquired during three-dimensional conformal (6-11 beams) SBRT treatments were retrospectively analyzed to extract tumor motion trajectories. For each patient, tumor motion PDFs were generated per fraction (PDF{sub n}) using three selected 'usable' beams. Patients without at least three usable beams were excluded from the study. Fractional PDF reproducibility (R{sub n}) was calculated as the Dice similarity coefficient between PDF{sub n} to a 'ground-truth' PDF (PDF{sub g}), which was generated using the selected beams of all fractions. The mean of R{sub n}, labeled as R{sub m}, was calculated for each patient and correlated to the patient's mean tumor motion rang (A{sub m}). Change of R{sub m} during the course of SBRT treatments was also evaluated. Intra- and intersubject coefficient of variation (CV) of R{sub m} and A{sub m} were determined. Results: Thirteen patients had at least three usable beams and were analyzed. The mean of R{sub m} was 0.87 (range, 0.84-0.95). The mean of A{sub m} was 3.18 mm (range, 0.46-7.80 mm). R{sub m} was found to decrease as A{sub m} increases following an equation of R{sub m} = 0.17e{sup -0.9Am} + 0.84. R{sub m} also decreased slightly throughout the course of treatments. Intersubject CV of R{sub m} (0.05) was comparable to intrasubject CV of R{sub m} (range, 0.02-0.09); intersubject CV of A{sub m} (0.73) was significantly greater than intrasubject CV of A{sub m} (range, 0.09-0.24). Conclusions: Tumor motion PDF can be determined using cine MV images acquired during the treatments. The reproducibility of lung tumor motion PDF decreased exponentially as the tumor motion range increased and decreased slightly throughout the course of the treatments.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2016

The H I probability distribution function and the atomic-to-molecular transition in molecular clouds

We characterize the column-density probability distribution functions (PDFs) of the atomic hydrogen gas, H i, associated with seven Galactic molecular clouds (MCs). We use 21 cm observations from the Leiden/Argentine/Bonn Galactic H i Survey to derive column-density maps and PDFs. We find that the peaks of the H i PDFs occur at column densities in the range ∼1–2 × 10{sup 21} cm{sup −2} (equivalently, ∼0.5–1 mag). The PDFs are uniformly narrow, with a mean dispersion of σ{sub HI}≈10{sup 20} cm{sup −2} (∼0.1 mag). We also investigate the H i-to-H{sub 2} transition toward the cloud complexes and estimate H i surface densities ranging from 7 to 16 M{sub ⊙} pc{sup −2} at the transition. We propose that the H i PDF is a fitting tool for identifying the H i-to-H{sub 2} transition column in Galactic MCs.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Approximating Density Probability Distribution Functions Across Cosmologies

Using a suite of self-similar cosmological simulations, we measure the probability distribution functions (PDFs) of real-space density, redshift-space density, and their geometric mean. We find that the real-space density PDF is well-described by a function of two parameters: ns, the spectral slope, and σL, the linear rms density fluctuation. For redshift-space density and the geometric mean of real- and redshift-space densities, we introduce a third parameter, ${s}_{L}=\sqrt{\langle {\left({{dv}}_{\mathrm{pec}}^{L}/{dr}\right)}^{2}\rangle }/H$. We find that density PDFs for the LCDM cosmology is also well-parameterized by these three parameters. As a result, we are able to use a suite of self-similar cosmological simulations to approximate density PDFs for a range of cosmologies. We make the density PDFs publicly available and provide an analytical fitting formula for them.

79 ASTRONOMY AND ASTROPHYSICS↗