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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 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
NASA NTRS1982

Computer program for solving laminar, transitional, or turbulent compressible boundary-layer equations for two-dimensional and axisymmetric flow

A numerical algorithm and computer program are presented for solving the laminar, transitional, or turbulent two dimensional or axisymmetric compressible boundary-layer equations for perfect-gas flows. The governing equations are solved by an iterative three-point implicit finite-difference procedure. The software, program VGBLP, is a modification of the approach presented in NASA TR R-368 and NASA TM X-2458, respectively. The major modifications are: (1) replacement of the fourth-order Runge-Kutta integration technique with a finite-difference procedure for numerically solving the equations required to initiate the parabolic marching procedure; (2) introduction of the Blottner variable-grid scheme; (3) implementation of an iteration scheme allowing the coupled system of equations to be converged to a specified accuracy level; and (4) inclusion of an iteration scheme for variable-entropy calculations. These modifications to the approach presented in NASA TR R-368 and NASA TM X-2458 yield a software package with high computational efficiency and flexibility. Turbulence-closure options include either two-layer eddy-viscosity or mixing-length models. Eddy conductivity is modeled as a function of eddy viscosity through a static turbulent Prandtl number formulation. Several options are provided for specifying the static turbulent Prandtl number. The transitional boundary layer is treated through a streamwise intermittency function which modifies the turbulence-closure model. This model is based on the probability distribution of turbulent spots and ranges from zero to unity for laminar and turbulent flow, respectively. Several test cases are presented as guides for potential users of the software.

Harris, J. E.↗
NASA NTRS1985

The atmospheric effect on the separability of field classes measured from satellites

The atmospheric effect on the upward radiance emerging from the atmosphere above a nonuniform surface results in a reduction of the separability between the surface classes by broadening the radiance probability distribution of each class, while narrowing the total radiance range. The atmospheric modulation transfer function (MTF) is used in Fourier transform analyses to simulate the atmospheric effect on the imagery of a nonuniform surface and to demonstrate the atmospheric effect on separability of field classes.

Kaufman, Y. J.↗
NASA NTRS2022

Analyzing Recharge Dynamics and Storage in a Thick, Karstic Vadose Zone

Karst vadose zone heterogeneity creates complex transmission and storage dynamics that affect the timing and magnitude of aquifer recharge. Young, high-matrix permeability eogenetic karst aquifers may have significantly higher matrix storage than older, lower matrix permeability counterparts. In vulnerable and water-limited karst regions, the timescales of storage may be important for seasonal and sub-seasonal water resource management. We create a framework to quantify storage dynamics in karst aquifers using high-resolution precipitation and groundwater levels from the Northern Guam Lens Aquifer in the US territory of Guam. We estimate recharge using the Water Table Fluctuation method, and then develop transfer functions between precipitation and recharge to quantify storage and release of water from the vadose zone. The transfer functions are partitioned into different flow pathways including conduit, conduit/matrix, and slowly draining matrix. Probability distributions are fit to each pathway to determine the average travel times of infiltrated waters. The results show that aquifer recharge through secondary porosity features typically occurs within a few hours of a rainfall event, but this rapid recharge accounts for only 12%–28% of total recharge. The majority of aquifer recharge (>70%) occurs within a month of a contributing storm event. An additional 10% of recharge, on average, took longer than a month to reach the water table. The framework established can help improve the hydrological modeling and freshwater management for karst aquifers.

Patricia Spellman↗
NASA NTRS2004

Visualizing Time-Varying Distribution Data in EOS Application

In this research, we have developed several novel visualization methods for spatial probability density function data. Our focus has been on 2D spatial datasets, where each pixel is a random variable, and has multiple samples which are the results of experiments on that random variable. We developed novel clustering algorithms as a means to reduce the information contained in these datasets; and investigated different ways of interpreting and clustering the data.

Shen, Han-Wei↗
DOE OSTI2026

Determination of proton PDF uncertainties with Markov chain Monte Carlo

We present an analysis of parton distribution functions (PDFs) of the proton using Markov chain Monte Carlo (MCMC) methods. The MCMC approach naturally implements Bayes’ theorem and, thus, provides a means to directly sample the underlying probability distribution—in this case, the probability distribution of the PDF parameters. This allows for a straightforward propagation of the resulting uncertainties into any PDF-dependent observable, preserving their simple probabilistic interpretation. In our analysis we include a broad set of deep inelastic scattering data from HERA, BCDMS and NMC experiments along with the Drell-Yan, 𝑊 and 𝑍 boson data from LHC and Tevatron experiments, which combined with theoretical calculations at next-to-next-to-leading order in QCD allow for realistic determination of PDFs. The main focus of this analysis is to explore alternative methods for PDF uncertainty estimation that are more firmly grounded in statistical principles. We show that the flexibility of the Bayes framework, allowing one, e.g., to account for non-Gaussianity or inconsistencies of datasets, is crucial to extract realistic uncertainties when such assumptions are not fulfilled. We also demonstrate that MCMC allows one to determine the Δ⁢𝜒 2 value corresponding to a given confidence level in the sample, which can, in turn, be used as a statistically well-founded tolerance criterion used in the Hessian method, thus addressing one of its main long-standing drawbacks.

Risse, Peter Clemens [Universität Münster (Germany↗
NASA NTRS1972

A stochastic bioburden model for spacecraft sterilization.

Development of a stochastic model of the probability distribution for the random variable representing the number of microorganisms on a surface as a function of time. The first basic principle associated with bioburden estimation is that viable particles are removed from surfaces. The second notion important to the analysis is that microorganisms in environments and on surfaces occur in clumps. The last basic principle relating to bioburden modeling is that viable particles are deposited on a surface. The bioburden on a spacecraft is determined by the amount and kind of control exercised on the spacecraft assembly location, the shedding characteristics of the individuals in the vicinity of the spacecraft, its orientation, the geographical location in which the assembly takes place, and the steps in the assembly procedure. The model presented has many of the features which are desirable for its use in the spacecraft sterilization programs currently being planned by NASA.

Roark, A. L.↗
NASA NTRS1971

Stability of uncertain systems

The asymptotic properties of feedback systems are discussed, containing uncertain parameters and subjected to stochastic perturbations. The approach is functional analytic in flavor and thereby avoids the use of Markov techniques and auxiliary Lyapunov functionals characteristic of the existing work in this area. The results are given for the probability distributions of the accessible signals in the system and are proved using the Prohorov theory of the convergence of measures. For general nonlinear systems, a result similar to the small loop-gain theorem of deterministic stability theory is given. Boundedness is a property of the induced distributions of the signals and not the usual notion of boundedness in norm. For the special class of feedback systems formed by the cascade of a white noise, a sector nonlinearity and convolution operator conditions are given to insure the total boundedness of the overall feedback system.

Blankenship, G. L.↗
NASA NTRS1982

Radar scattering laws for the lunar surface

Bistatic radar observations of quasi-specular scatter from the lunar surface at 13 and 116 cm wavelengths have been expressed in terms of probability densities of the underlying surface slope distributions. These show best agreement with a Hagfors scattering function, although other forms having predominantly Gaussian or exponential characteristics also occur. Estimates of root mean square (rms) surface slope derived from these function range from 4 deg rms in maria to at least 8 deg rms in highlands. These are values appropriate to 25 m horizontal scales and represent averages over tens of square kilometers of surface area. The effective scattering roughness varies with wavelength, most strongly in maria, where its behavior is consistent with that expected from an immature, i.e., unsaturated cratered surface. There is very little variation in scattering roughness with wavelength in highlands area.

Simpson, R. A.↗
NASA NTRS1984

Probability of error and radiometric resolution for target discrimination in radar images

A straightforward statistical analysis is presented of the problem of discriminating between two distributed targets in a radar image. The probability of making an error is calculated as a function of the target contrast, the number of samples averaged to form each observation, and the system noise. In the absence of system noise, it is observed that a target contrast of 1 dB could not be detected with less than 10 samples averaged; it is also seen that the error probability is sensitive to the number of samples averaged, as expected. Setting the target contrast at the radiometric resolution, a comparison is made of different definitions for this resolution. The comparison shows that each definition yields a different error probability, ranging from less than 0.05 to 0.35. Attention is also given to the effect of system noise, and it is shown that thermal noise does not have a significant effect on the error probability for a fixed target contrast.

Frost, V. S.↗
NASA NTRS2008

Constraints on Black Hole Spin in a Sample of Broad Iron Line AGN

We present a uniform X-ray spectral analysis of nine type-1 active galactic nuclei (AGN) that have been previously found to harbor relativistically broadened iron emission lines. We show that the need for relativistic effects in the spectrum is robust even when one includes continuum "reflection" from the accretion disk. We then proceed to model these relativistic effects in order to constrain the spin of the supermassive black holes in these AGN. Our principal assumption, supported by recent simulations of geometrically-thin accretion disks, is that no iron line emission (or any associated Xray reflection features) can originate from the disk within the innermost stable circular orbit. Under this assumption, which tends to lead to constraints in the form of lower limits on the spin parameter, we obtain non-trivial spin constraints on five AGN. The spin parameters of these sources range from moderate (a approximates 0.6) to high (a > 0.96). Our results allow, for the first time, an observational constraint on the spin distribution function of local supermassive black holes. Parameterizing this as a power-law in dimensionless spin parameter (f(a) varies as absolute value of (a) exp zeta), we present the probability distribution for zeta implied by our results. Our results suggest 90% and 95% confidence limits of zeta > -0.09 and zeta > -0.3 respectively.

Brenneman, Laura W.↗
NASA NTRS1989

Rain attenuation measurements: Variability and data quality assessment

Year to year variations in the cumulative distributions of rain rate or rain attenuation are evident in any of the published measurements for a single propagation path that span a period of several years of observation. These variations must be described by models for the prediction of rain attenuation statistics. Now that a large measurement data base has been assembled by the International Radio Consultative Committee, the information needed to assess variability is available. On the basis of 252 sample cumulative distribution functions for the occurrence of attenuation by rain, the expected year to year variation in attenuation at a fixed probability level in the 0.1 to 0.001 percent of a year range is estimated to be 27 percent. The expected deviation from an attenuation model prediction for a single year of observations is estimated to exceed 33 percent when any of the available global rain climate model are employed to estimate the rain rate statistics. The probability distribution for the variation in attenuation or rain rate at a fixed fraction of a year is lognormal. The lognormal behavior of the variate was used to compile the statistics for variability.

Crane, Robert K.↗
NASA NTRS1984

Studies of the chemistry of vibrationally and electronically excited species in planetary upper atmospheres

The vibrational distribution of O2(+) in the atmospheres of Venus and Mars was investigated to compare with analogous values in the Earth's atmosphere. The dipole moment of the Z(2) Pi sub u - X(2) Pi sub g transition of O2(+) is calculated as a function of internuclear distance. The band absorption oscillator strengths and band transition probabilities of the second negative system are derived. The vibrational distribution of O2(+) in the ionosphere of Venus is calculated for a model based on data from the Pioneer Venus neutral mass spectrometer.

Fox, J. L.↗
DOE OSTI2025

Statistical evaluation of microscale stress conditions leading to void nucleation in the weak shock regime

Here, we investigate the heterogeneity of the stress state driven by anisotropic deformation response at the single crystal level through five statistical volume element (SVE) calculations of polycrystalline BCC tantalum. This work focuses on grain boundaries as a prominent material defect type prone to void nucleation based upon experimental observations of predominantly intergranular void nucleation in this material. The SVEs are constructed to be statistically representative of larger volumes of material and are meshed such that mean and standard deviation of grain size and orientation information is reconstructed. The computational meshes feature hexahedral (brick) elements and smooth conformal grain boundaries where significant stress concentration is known to occur, a tail effect of interest in the extreme events process of dynamic ductile damage. An existing micromechanical crystallographic plasticity model shown to capture the single crystal behavior of BCC tantalum well is used to perform the polycrystal calculations. The model includes representation of the non-Schmid effect of non-planar screw dislocation kinetics in tantalum. A three-dimensional stress state time profile predicted by damage modeling of a flyer plate impact experiment is applied as boundary conditions to each SVE. Resulting grain boundary stress state statistics are strongly non-Gaussian. Significant structural evolution is observed within the compressive hold before unloading into tension in the stress profile. Strong angular dependence of grain boundary traction magnitude with shock direction is observed. Non-Schmid effects continue to suggest their influence on propensity of microstructural defect types to nucleate voids. A general void nucleation criterion is proposed using probability theory. The general framework is specified to polycrystalline BCC tantalum in the weak shock regime to include the SVE calculations and literature molecular dynamics calculations of grain boundary void nucleation strength. Probability density functions (PDFs) are used to describe the interaction between the local stress state heterogeneity and the distributed grain boundary void nucleation strength state. A causation entropy maximization procedure removes the requirement for ad hoc selection of a PDF functional form and provides a rigorous procedure for data-based PDF determination. The resulting physically informed PDF describes the spatial appearance frequency of nucleated voids as a function of applied macroscale pressure. Lower length scale physics are thus packaged in a precise and computationally efficient way to provide computational plasticity insight to macroscale dynamic ductile damage models.

36 MATERIALS SCIENCE↗
NASA NTRS1985

Are galaxies more strongly correlated than clusters?

Distributions of galaxies and of clusters of galaxies have been investigated using the correlation function, the excess probability over random that there are two objects separated by a distance r. It is shown here that if the amplitudes of the cluster-cluster correlation function are made dimensionless, systematic changes with cluster richness vanish, implying scale invariance in the cluster process. The dimensionless galaxy-galaxy correlation seems stronger, implying gravitational enhancement on smaller scales.

Szalay, A. S.↗
NASA NTRS1991

Gravitational microlensing of high-redshift supernovae by compact objects

An analysis of the effect of microlensing by a cosmologically dominant density of compact objects is performed, using high-redshift Type Ia supernovae (SN Ia's) as probes. The compact objects are modeled as a three-dimensional distribution of point masses, and Monte Carlo simulations are done to calculate the resulting amplification probability distributions for several column densities and cosmologies. By combining these distributions with the intrinsic SN Ia luminosity function and comparing with the results for a perfectly smooth universe, estimates are made of the number of supernovae that would need to be observed to confirm or rule out this lensing scenario. It is found that about 1000 SN Ia's with redshifts of z = 1 would be needed to perform this test, which is beyond what current searches can hope to accomplish. Observations of many fewer high-redshift supernovae, used merely as standard candles, appears a promising way of distinguishing between different cosmological models.

Rauch, Kevin P.↗
NASA NTRS1996

Occurrency frequency of substorm field and plasma signatures observed near-earth by ISEE-1/2

The onset of the majority of substorms occurs when the tail field stops growing more tail-like and begins to become more dipolar. This corresponds to the onset signatures on the ground and in geosynchronous orbit. The AE indices and the IGS Pi 2 data were used to determine the major substorm onsets of 1978 and 1979. The time delay between successive substorms, the distribution of the substorm growth phase duration and the probability of tailward flows were determined as a function of spacecraft location. About a half of the substorms exhibit a plasma signature including earthward or tailward flows or plasma sheet drop out and recovery. Earthward flows are often seen at substorm onset, and almost always during substorm recovery. Tailward flows are occasionally seen at onset as the spacecraft is close enough to the neutral sheet. The experimental results are compared to predictions based on the neutral line and current sheet disruption models.

Hsu, T. S.↗
NASA NTRS2003

Resistance of virus to extinction on bottleneck passages: study of a decaying and fluctuating pattern of fitness loss

RNA viruses display high mutation rates and their populations replicate as dynamic and complex mutant distributions, termed viral quasispecies. Repeated genetic bottlenecks, which experimentally are carried out through serial plaque-to-plaque transfers of the virus, lead to fitness decrease (measured here as diminished capacity to produce infectious progeny). Here we report an analysis of fitness evolution of several low fitness foot-and-mouth disease virus clones subjected to 50 plaque-to-plaque transfers. Unexpectedly, fitness decrease, rather than being continuous and monotonic, displayed a fluctuating pattern, which was influenced by both the virus and the state of the host cell as shown by effects of recent cell passage history. The amplitude of the fluctuations increased as fitness decreased, resulting in a remarkable resistance of virus to extinction. Whereas the frequency distribution of fitness in control (independent) experiments follows a log-normal distribution, the probability of fitness values in the evolving bottlenecked populations fitted a Weibull distribution. We suggest that multiple functions of viral genomic RNA and its encoded proteins, subjected to high mutational pressure, interact with cellular components to produce this nontrivial, fluctuating pattern.

Serial Passage↗