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Results for “distribution function moments”

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 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

The large-scale morphology of IRAS galaxies

At present, visual inspection is the only method for comparing the large-scale morphologies in the distribution of galaxies to those in model universes generated by N-body simulations. To remedy the situation, we have developed a set of three structure functions (S1, S2, S3) that quantify the degree of large-scale prolateness, oblateness, and sphericity/uniformity of a 3-D particle distribution and have applied them to a volume-limited (less than = 4000 km/s) sample of 699 IRAS galaxies with f sub 60 greater than 1.2 Jy. To determine the structure functions, we randomly select 500 galaxies as origins of spherical windows of radius R sub w, locate the centroid of the galaxies in the window (assuming all galaxies have equal mass) and then, compute the principal moments of inertia (I sub 1, I sub 2, I sub 3) about the centroid. Each S sub i is a function of (I sub 2)/(I sub 1) and (I sub 3)/I sub 1). S1, S2, and S3 tend to unity for highly prolate, oblate, and uniform distributions, respectively and tend to zero otherwise. The resulting 500 values of S sub i at each scale R sub w are used to construct a histogram.

Babul, Arif↗
NASA NTRS1974

Approach to the origin of turbulence on the basis of two-point kinetic theory

Equations for the fluctuation correlation in an incompressible shear flow are derived on the basis of kinetic theory, utilizing the two-point distribution function which obeys the BBGKY hierarchy equation truncated with the hypothesis of 'ternary' molecular chaos. The step from the molecular to the hydrodynamic description is accomplished by a moment expansion which is a two-point version of the thirteen-moment method, and which leads to a series of correlation equations, viz., the two-point counterparts of the continuity equation, the Navier-Stokes equation, etc. For almost parallel shearing flows the two-point equation is separable and reduces to two Orr-Sommerfeld equations with different physical implications.

Tsuge, S.↗
NASA NTRS1975

Gravitational forces and moments on spacecraft

The solution of problems of attitude dynamics of spacecraft and the influence of gravitational forces and moments is examined. Arguments are presented based on Newton's law of gravitation, and employing the methods of Newtonian (vectorial) mechanics, with minimal recourse to the classical concepts of potential theory. The necessary ideas were developed and relationships were established to permit the representation of gravitational forces and moments exerted on bodies in space by other bodies, both in terms involving the mass distribution properties of the bodies, and in terms of vector operations on those scalar functions classically described as gravitational potential functions.

Kane, T. R.↗
DOE OSTI2020

A Lumped Stochastic Model of Coupled Neutronic Assemblies

The objective of the present work is to apply the Harris ansatz to coupled assemblies in a lumped setting, i.e., ignoring the neutron phase dependence, which hitherto has not been considered. A Master equation for the single-time joint distribution of neutron number in each assembly, accounting for transfer of neutrons from one assembly to another via leakage transition probabilities and intercept or view factors is derived from which equations for the mean and variance in each assembly are developed. Because of the neutronic coupling, it is necessary to additionally compute the correlation function between pairs of assemblies which gives an expanded set of moment equations to solve. The reactivity of each assembly is allowed to vary with time, although a formal mechanism that is responsible for reactivity coupling between assemblies is not considered or proposed. Following Harris, it is then hypothesized that the number distribution in each assembly is a gamma distribution with assembly-specific mean and variance computed exactly from the moment equations. Illustrative numerical results are presented for the moments of a system of four coupled assemblies under various reactivity and neutronic coupling scenarios. The gamma distribution is then used to compute the probability that the neutron population exceeds a threshold value in any assembly. The report concludes with a discussion of recommended further work on this problem.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1980

Second moments of optical degradation due to a thin turbulent layer

The effect of thin turbulent layers, including boundary layers and shear layers, on light propagation is examined from a theoretical point of view. In particular, a mathematical model is developed to describe the interaction between the aerodynamic or, more precisely, the density fluctuations and the electromagnetic field. It is assumed that the turbulence induces a normally distributed phase aberration which is a homogeneous random function in the plane of the aperture. Hypotheses concerning the density fluctuations in the layer sufficient to guarantee such a phase aberration are exhibited. The optical degradation is described in terms of the optical transfer function (OTF) and the Strehl ratio (I/I O ) which are random. Expressions for the first and second moments of these two parameters are developed from the definitions. Asymptotic ("large" aperture) approximations to these expressions are derived and discussed. Finally, the exact and approximate results are compared for several "typical" values of the ratios of aperture diameter to scale of density fluctuations and rms phase aberration to wave length respectively.

W J Steinmetz↗
DOE OSTI2024

Extraction of the neutron F 2 structure function from inclusive proton and deuteron deep-inelastic scattering data

The available world deep-inelastic scattering (DIS) data on proton and deuteron structure functions F 2 p , F 2 d , and their ratios are leveraged to extract the free neutron F 2 n structure function, the F 2 n / F 2 p ratio, and associated uncertainties using the latest nuclear effect calculations in the deuteron. Special attention is devoted to the normalization of the proton and deuteron experimental datasets and to the treatment of correlated systematic errors, as well as the quantification of procedural and theoretical uncertainties. The extracted F 2 n dataset is utilized to evaluate the Q 2 dependence of the Gottfried sum rule and the nonsinglet F 2 p − F 2 n moments. To facilitate replication of our study, as well as for general applications, we provide a comprehensive DIS database including all recent Jefferson Lab 6 GeV measurements, the extracted F n 2 , a modified CTEQ-JLab global parton distribution function fit named CJ15nlo_mod, and grids with calculated proton, neutron, and deuteron DIS structure functions. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Nucleon form factors and parton distributions in nonlocal chiral effective theory

In this work, we present a review of recent applications of nonlocal chiral effective theory to hadron structure studies. Starting from a nonlocal meson-baryon effective chiral Lagrangian, we show how the introduction of a correlation function representing the finite extent of hadrons regularizes the meson loop integrals and introduces momentum dependence in vertex form factors in a gauge invariant manner. We apply the framework to the calculation of nucleon electromagnetic form factors, unpolarized and polarized parton distributions, as well as transverse momentum dependent distributions and generalized parton distributions. Assuming that the nonlocal behavior is a general property of all interactions, we also discuss the application to the lepton anomalous magnetic moment in nonlocal QED.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS2018

Random Variables with Moment-Matching Staircase Density Functions

This paper proposes a family of random variables for uncertainty modeling. The variables of interest have a bounded support set, and prescribed values for the first four moments. We present the feasibility conditions for the existence of any of such variables, and propose a class of variables that conforms to such constraints. This class is called staircase because the density of its members is a piecewise constant function. Convex optimization is used to calculate their distributions according to several optimality criteria, including maximal entropy and maximal log-likelihood. The flexibility and efficiency of staircases enable modeling phenomena having a possibly skewed and/or multimodal response at a low computational cost. Furthermore, we provide a means to account for the uncertainty in the distribution caused by estimating staircases from data. These ideas are illustrated by generating empirical staircase predictor models. We consider the case in which the predictor matches the sample moments exactly (a setting applicable to large datasets), as well as the case in which the predictor accounts for the sampling error in such moments (a setting applicable to sparse datasets). A predictor model for the dynamics of an aeroelastic airfoil subject to flutter instability is used as an example. The resulting predictor not only describes the system's response accurately, but also enables carrying out a risk analysis for safe flight.

Luis G. Crespo↗
DOE OSTI2020

Multi-frequency General Relativistic Radiation-hydrodynamics with M 1 Closure

We report on recent upgrades to our general relativistic radiation-magnetohydrodynamics code, Cosmos++ , which expands the two-moment, M 1 , radiation treatment from gray to multi-frequency transport, including Doppler and gravitational frequency shifts. The solver accommodates either photon (Bose–Einstein) or neutrino (Fermi–Dirac) statistical distribution functions with absorption, emission, and elastic scattering processes. An implicit scheme is implemented to simultaneously solve the primitive inversion problem together with the radiation–matter coupling source terms, providing stability over a broad range of opacities and optical depths where the interaction terms can be stiff. We discuss our formulations and numerical methods, and validate our methods against a wide variety of test problems spanning optically thin to thick regimes in flat, weakly curved, and strongly curved spacetimes.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1973

Description of small-scale fluctuations in the diffuse X-ray background.

An analytical study of the fluctuations on a small angular scale expected in the diffuse X-ray background in the presence of unresolved sources is presented. The source population is described by a function N(S), giving the number of sources per unit solid angle and unit apparent flux S. The distribution of observed flux, s, in each angular resolution element of a complete sky survey is represented by a function Q(s). The analytical relation between the successive, higher-order moments of N(S) and Q(s) is described. The goal of reconstructing the source population from the study of the moments of Q(s) of order higher than the second (i.e., the rms fluctuations) is discussed.

Cavaliere, A.↗
NASA NTRS1974

Two-dimensional Gaussian processes applied to the determination of contact between lubricated rolling surfaces

The effectiveness of a lubricant film preventing metallic contact between two rolling surfaces (such as in ball bearings) as a function of surface roughness parameters was investigated. The parameters considered are the spectral moments of the two-dimensional surface obtained by superposition of the two rolling surfaces. The peak height distribution, estimation of one-dimensional profile spectral moments, and the estimation of two-dimensional surface moments from several profile measurements were considered. Also given is an asymptotic relation between the mean film thickness and contact occurrences.

Sidik, S. M.↗
NASA NTRS1974

Two-dimensional Gaussian processes applied to the determination of contact between lubricated rolling surfaces

Theoretical investigation of how effectively a lubricant film prevents metallic contact between two rolling surfaces (such as in ball bearings) as a function of surface roughness parameters. The parameters considered are the spectral moments of the two-dimensional surface obtained by superposition of the two rolling surfaces. We consider the peak height distribution, estimation of one-dimensional profile spectral moments, and the estimation of two-dimensional surface moments from several profile measurements are taken into account. Also given is an asymptotic relation between the mean film thickness and contact occurrences.

Sidik, S. M.↗
NASA NTRS1996

Chain Dynamics in a Dilute Magnetorheological Fluid

The structure, formation, and dynamics of dilute, mono-dispersive ferrofluid emulsions in an external magnetic field have been investigated using dynamic light scattering techniques. In the absence of the magnetic field, the emulsion particles are randomly distributed and behave like hard spheres in Brownian motion. An applied magnetic field induces a magnetic dipole moment in each particle. Dipolar interactions between particles align them into chains where correlation functions show two decay processes. The short-time decay shows the motion of straight chains as a whole where the apparent chain length increases with the applied magnetic field and the particle volume fraction. Good scaling results are obtained showing that the apparent chain length grows with time following a power law with exponent of 0.6 and depends on the applied field, particle volume fraction, and diffusion constant of the particles. The long-time decay in the correlation function shows oscillation when the chains reach a certain length with time and stiffness with threshold field This result shows that chains not only fluctuate, but move in a periodic motion with a frequency of 364 Hz at lambda = 15. It may suggest the existence of phonons. This work is the first step in the understanding of the structure formation, especially chain coarsening mechanism, of magnetorheological (MR) fluids at higher volume fractions.

Liu, Jing↗
DOE OSTI2025

Evolution of Structure and Magnetism in FeCl 2 and FeCl 3 : From Clusters to Monolayers

In this work, we address one of the most fundamental questions in cluster science─how do the structure and properties evolve from clusters to crystals? Using density functional theory (DFT), we focus our study on the evolution of structure and magnetism in iron-chloride systems, from clusters to monolayers. The choice of this system is motivated by the recent experimental confirmation of one of the author’s earlier theoretical prediction that the FeCl 2 cluster is magnetic with a spin magnetic moment of 4 μ B localized at the Fe site, while its dimer, Fe 2 Cl 4 , is antiferromagnetic. Similarly, FeCl 3 cluster is magnetic with a total spin magnetic moment of 5 μ B , with 4 μ B localized at the Fe site and 1 μ B distributed over the Cl sites. The dimer clusters Fe 2 Cl 4 and Fe 2 Cl 6 have an antiferromagnetic ground state, and upon Li-functionalization, both can be magnetically transformed from antiferromagnetic to ferromagnetic states. In contrast, FeCl 2 and FeCl 3 monolayers exhibit different magnetic ground states in their periodic forms: FeCl 2 is ferromagnetic (FM), but in FeCl 3 , the antiferromagnetic (AFM) and FM states are energetically nearly degenerate. Such a difference arises due to the different chemical coordination of the Fe atoms with the Cl atoms, caused by their different oxidation states, which is +2 in FeCl 2 and +3 in FeCl 3 , respectively. Interestingly, Li-functionalization allows both FeCl 3 and FeCl 2 monolayers to be ferromagnetic. Our study highlights that several, but not all, electronic and magnetic characteristics of isolated clusters are preserved in the extended periodic structures. This systematic investigation of iron-halide clusters is expected to inspire further experimental and theoretical exploration into the magnetism of other transition metal halides.

cluster chemistry↗
NASA NTRS1986

Progress towards a model to describe jet/aerodynamic-surface interference effects

A first generation model is presented which relates the pressure distribution on an aerodynamic surface to properties of the jet plume. The characteristics of a jet in a cross flow are of primary importance in determining the pressure distribution on the aerodynamic surface and are assumed to be (1) a pair of contrasting vortices associated with a jet in a crossflow, (2) entrainment of crossflow fluid into the jet plume, and (3) a wake region near the aerodynamic surface and extending downstream from the jet orifice. The model is applied to the configuration of a round jet exhausting perpendicularly through a flat plate into a uniform crossflow for a range of jet-to-crossflow velocity ratios from three to ten. It is demonstrated that the model is capable of describing the measured pressure distribution on the flat plate with model parameters that are compatable with the incomplete description of the vortex pair that is available. The fore and moments on one plate are presented as functions of jet-to-crossflow velocity ratios.

Fearn, R. L.↗
NASA NTRS2011

A Grobner Basis Solution for Lightning Ground Flash Fraction Retrieval

A Bayesian inversion method was previously introduced for retrieving the fraction of ground flashes in a set of flashes observed from a (low earth orbiting or geostationary) satellite lightning imager. The method employed a constrained mixed exponential distribution model to describe the lightning optical measurements. To obtain the optimum model parameters, a scalar function was minimized by a numerical method. In order to improve this optimization, we introduce a Grobner basis solution to obtain analytic representations of the model parameters that serve as a refined initialization scheme to the numerical optimization. Using the Grobner basis, we show that there are exactly 2 solutions involving the first 3 moments of the (exponentially distributed) data. When the mean of the ground flash optical characteristic (e.g., such as the Maximum Group Area, MGA) is larger than that for cloud flashes, then a unique solution can be obtained.

Solakiewicz, Richard↗
DOE OSTI2025

The Stochastic Gause Predator-Prey model: Noise-induced extinctions and invariance

We consider the Gause predator-prey with general bounded or sub‑linear functional responses, – which includes those of Holling types Ⅰ–Ⅳ. – and multiplicative Gaussian noise. In contrast to previous studies, the prey in our model follows logistic dynamics while the predator's population is solely regulated by consumption of the prey. To ensure well-posedeness, we derive explicit Lyapunov‐type criteria ensuring global positivity and moment boundedness of solutions. We find conditions for noise‑induced extinctions, proving that stochasticity can drive either population to collapse even when the deterministic analogue predicts stable coexistence. In the case when the predator becomes extinct, we establish a limiting distribution for the predator's population. Last, for functional responses of Holling type Ⅰ, we provide sufficient conditions on the intensity of the noise for the existence and uniqueness of a stationary distribution.

Gause model↗