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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 OSTI2015

Understanding the distinctively skewed and heavy tailed character of atmospheric and oceanic probability distributions

The probability distributions of large-scale atmospheric and oceanic variables are generally skewed and heavy-tailed. We argue that their distinctive departures from Gaussianity arise fundamentally from the fact that in a quadratically nonlinear system with a quadratic invariant, the coupling coefficients between system components are not constant but depend linearly on the system state in a distinctive way. In particular, the skewness arises from a tendency of the system trajectory to linger near states of weak coupling. We show that the salient features of the observed non-Gaussianity can be captured in the simplest such nonlinear 2-component system. If the system is stochastically forced and linearly damped, with one component damped much more strongly than the other, then the strongly damped fast component becomes effectively decoupled from the weakly damped slow component, and its impact on the slow component can be approximated as a stochastic noise forcing plus an augmented nonlinear damping. In the limit of large time-scale separation, the nonlinear augmentation of the damping becomes small, and the noise forcing can be approximated as an additive noise plus a correlated additive and multiplicative noise (CAM noise) forcing. Much of the diversity of observed large-scale atmospheric and oceanic probability distributions can be interpreted in this minimal framework.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
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 OSTI2019

On the role of joint probability distributions of incompatible observables in Bell and Kochen–Specker Theorems

Highlights: •Bell and Kochen–Specker theorems rule out local or noncontextual realist models. •Still, they assume a joint probability distribution for incompatible observables. •Those joint probability distributions do not exist in quantum mechanics. •Realist models without joint distributions for incompatible observables are given. •A reformulation of Bell and Kochen–Specker arguments is provided to rule them out. -- Abstract: We analyze the validity of Bell and Kochen–Specker theorems under local (or noncontextual) realism but avoiding an assumption of the existence of a joint probability distribution for incompatible observables. We formulate a realist model which complies with this requirement. This is obtained by employing divergent sequences that nevertheless have marginals which are convergent. We find that under standard reasonable assumptions this possibility does not lead to a loophole of those theorems, by deriving a short of CHSH inequality valid for any finite size ensemble. Moreover, we analyze a Hardy’s paradox setting where noncontextual realism imposes the existence of joint probabilities for incompatible observables.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Oscillations in probability distributions for stochastic gene expression

The phenomenon of oscillations in probability distribution functions of number of components is found for a model of stochastic gene expression. It takes place in cases of low levels of molecules or strong intracellular noise. The oscillations distinguish between more probable even and less probable odd number of particles. The even-odd symmetry restores as the number of molecules increases with the probability distribution function tending to Poisson distribution. We discuss the possibility of observation of the phenomenon in gene, protein, and mRNA expression experiments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
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 OSTI2019

Thermodynamic and Dynamic Mechanisms for Hydrological Cycle Intensification over the Full Probability Distribution of Precipitation Events

Abstract Precipitation changes in a warming climate have been examined with a focus on either mean precipitation or precipitation extremes, but changes in the full probability distribution of precipitation have not been well studied. This paper develops a methodology for the quantile-conditional column moisture budget of the atmosphere for the full probability distribution of precipitation. Analysis is performed on idealized aquaplanet model simulations under 3-K uniform SST warming across different horizontal resolutions. Because the covariance of specific humidity and horizontal mass convergence is much reduced when conditioned onto a given precipitation percentile range, their conditional averages yield a clear separation between the moisture (thermodynamic) and circulation (dynamic) effects of vertical moisture transport on precipitation. The thermodynamic response to idealized climate warming can be understood as a generalized “wet get wetter” mechanism, in which the heaviest precipitation of the probability distribution is enhanced most from increased gross moisture stratification, at a rate controlled by the change in lower-tropospheric moisture rather than column moisture. The dynamic effect, in contrast, can be interpreted by shifts in large-scale atmospheric circulations such as the Hadley cell circulation or midlatitude storm tracks. Furthermore, horizontal moisture advection, albeit of secondary role, is important for regional precipitation change. Although similar mechanisms are at play for changes in both mean precipitation and precipitation extremes, the thermodynamic contributions of moisture transport to increases in high percentiles of precipitation tend to be more widespread across a wide range of latitudes than increases in the mean, especially in the subtropics.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2014

Multiobjective fuzzy stochastic linear programming problems with inexact probability distribution

This study deals with multiobjective fuzzy stochastic linear programming problems with uncertainty probability distribution which are defined as fuzzy assertions by ambiguous experts. The problem formulation has been presented and the two solutions strategies are; the fuzzy transformation via ranking function and the stochastic transformation when α{sup –}. cut technique and linguistic hedges are used in the uncertainty probability distribution. The development of Sen’s method is employed to find a compromise solution, supported by illustrative numerical example.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Measurement of probability distributions for internal stresses in dislocated crystals

Here, we analyse residual stress distributions obtained from various crystal systems using high resolution electron backscatter diffraction (EBSD) measurements. Histograms showing stress probability distributions exhibit tails extending to very high stress levels. We demonstrate that these extreme stress values are consistent with the functional form that should be expected for dislocated crystals. Analysis initially developed by Groma and co-workers for X-ray line profile analysis and based on the so-called “restricted second moment of the probability distribution” can be used to estimate the total dislocation density. The generality of the results are illustrated by application to three quite different systems, namely, face centred cubic Cu deformed in uniaxial tension, a body centred cubic steel deformed to larger strain by cold rolling, and hexagonal InAlN layers grown on misfitting sapphire and silicon carbide substrates.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Exact solutions and symmetry analysis for the limiting probability distribution of quantum walks

In the literature, there are numerous studies of one-dimensional discrete-time quantum walks (DTQWs) using a moving shift operator. However, there is no exact solution for the limiting probability distributions of DTQWs on cycles using a general coin or swapping shift operator. In this paper, we derive exact solutions for the limiting probability distribution of quantum walks using a general coin and swapping shift operator on cycles for the first time. Based on the exact solutions, we show how to generate symmetric quantum walks and determine the condition under which a symmetric quantum walk appears. Our results suggest that choosing various coin and initial state parameters can achieve a symmetric quantum walk. By defining a quantity to measure the variation of symmetry, deviation and mixing time of symmetric quantum walks are also investigated.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

The neutron number probability distribution in coupled lumped assemblies

Here, the validity of the gamma distribution in describing the neutron number probability distribution function for both isolated and coupled multiplying assemblies when constrained to reproduce the true mean and variance is investigated in lumped geometry by numerical comparison with kinetic Monte Carlo simulations. The mean and variance are obtained from numerical solution of moment equations constructed from the relevant forward Master equation with assembly coupling coefficients obtained from a view factor method. Numerical results for a two-group, two coupled assemblies model, with static and dynamic reactivity insertion, show that except for subcritical assemblies, the gamma distribution well-approximates the number distribution. Differences in the fast and thermal neutron population shapes are explained in terms of effective source strengths due to downscatter and coupling.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
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↗
DOE OSTI2014

Using L/E Oscillation Probability Distributions

This paper explores the use of L /E oscillation probability distributions to compare experimental measurements and to evaluate oscillation models. In this case, L is the distance of neutrino travel and E is a measure of the interacting neutrino’s energy. While comparisons using allowed and excluded regions for oscillation model parameters are likely the only rigorous method for these comparisons, the L /E distributions are shown to give qualitative information on the agreement of an experiment’s data with a simple two-neutrino oscillation model. In more detail, this paper also outlines how the L /E distributions can be best calculated and used for model comparisons. Specifically, the paper presents the L /E data points for the final MiniBooNE data samples and, in the Appendix, explains and corrects the mistaken analysis published by the ICARUS collaboration.

Aguilar-Arevalo, A. A.↗
DOE OSTI2024

The reproduction number and its probability distribution for stochastic viral dynamics

We consider stochastic models of individual infected cells. The reproduction number, R, is understood as a random variable representing the number of new cells infected by one initial infected cell in an otherwise susceptible (target cell) population. Variability in R results partly from heterogeneity in the viral burst size (the number of viral progeny generated from an infected cell during its lifetime), which depends on the distribution of cellular lifetimes and on the mechanism of virion release. We analyse viral dynamics models with an eclipse phase: the period of time after a cell is infected but before it is capable of releasing virions. The duration of the eclipse, or the subsequent infectious, phase is non-exponential, but composed of stages. We derive the probability distribution of the reproduction number for these viral dynamics models, and show it is a negative binomial distribution in the case of constant viral release from infectious cells, and under the assumption of an excess of target cells. In a deterministic model, the ultimate in-host establishment or extinction of the viral infection depends entirely on whether the mean reproduction number is greater than, or less than, one, respectively. Here, the probability of extinction is determined by the probability distribution of R, not simply its mean value. In particular, we show that in some cases the probability of infection is not an increasing function of the mean reproduction number.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2016

Neutron Number Probability Distributions in a Subcritical System Using the Forward Master Equation

The subject of this paper is the determination of the equilibrium probability distribution function (PDF) of the neutron population within a subcritical multiplying system in the presence of an intrinsic random source as a result of spontaneous fission (SF). Such systems are strongly stochastic and low order moments such as the mean and variance of the neutron number are not sufficient to characterize the true state of the neutron population. We base our work on the forward Master equation in a lumped model formulation for P{sub n} (t), n = 0, 1, 2,..., the probability of there existing η neutrons at time t and obtain solutions for the steady state distributions. The key parameters in this model, neutron lifetime and fission probability, are rigorously obtained by numerically solving the k-eigenvalue problem in a one-dimensional spherical system and using standard definitions of lumped parameters in terms of production and loss rates in finite systems. Previous work has examined single-chain PDFs (a single fission and the resulting progeny) for neutrons, uncoupled neutron-photon single-chain PDFs, both using a lumped backward Master equation formulation, as well as neutron PDFs in supercritical systems. In this paper, we analyze strictly subcritical systems, for which we compare analytically derived solutions with numerical computations for different multiplicity distribution models. For subcritical systems where the neutron population remains finite at steady state, we show that the forward Master equation can be very efficiently solved numerically to obtain the equilibrium distributions. Finally, this work is motivated by potential application to passive interrogation for detection of diverted nuclear materials as well to criticality safety. The equilibrium neutron number probability distribution in subcritical systems has been numerically investigated for several models of the induced and spontaneous fission multiplicity distribution. A well known approximate but closed form solution, namely the quadratic model, was shown to be unacceptably accurate for subcritical media. The matrix inversion and the recursion methods agree well and were benchmarked with the binary fission model, but the recursion formulation proves far more computationally efficient. A qualitative change in the shape of the neutron PDF is observed for increasing source strength, as expected, and a transition from a stochastic to a deterministic system is expected for a sufficiently strong source. We are currently extending this approach to obtain the equilibrium joint distribution of neutrons within the system and those that have leaked, to explicitly represent the neutron PDF as observed by an external detector. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗