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Some results for the bivariate normal distribution analysis are presented. Computer programs for conditional normal probabilities, marginal probabilities, as well as joint probabilities for rectangular regions are given: routines for computing fractile points and distribution functions are also presented. Some examples from a closed circuit television experiment are included.
Dynamic grain growth is demonstrated to be much faster than static grain growth in a body-centered-cubic, interstitial-free steel sheet material at 850°C. Dynamic grain growth occurs during concurrent plastic deformation at elevated temperature, whereas static grain growth occurs during static annealing. Grain growth during steady-state plastic flow in tension at 850°C to a true strain of 0.2 at a true-strain rate of 10 -4 s -1 doubled grain size, while static annealing for the same time produced no increase in grain size. This is described as dynamic normal grain growth (DNGG) because no abnormally large grains were observed. The recrystallized microstructure of the steel demonstrated a log-normal distribution of grain sizes. DNGG produced bimodal grain size distributions that deviate from the theoretical expectation of a simple shift to larger sizes during normal growth. The bimodal distributions contained a remnant of small grains that were not consumed during grain growth. DNGG produced a crystallographic texture that is unique from both the recrystallized material and that produced by lattice rotation alone. DNGG strengthened the {111}⟨110⟩ and {111}⟨112⟩ components of the strong γ-fiber component in the original recrystallization texture. Lattice rotation from tensile deformation, by contrast, strengthened the α-fiber components that intersect the original γ-fiber.
This study characterized and modeled heterogeneous surface wettability in sandstone and investigated the role of spatial heterogeneity and correlation length of surface wettability on relative permeability in a supercritical CO 2 (scCO 2 )-brine-rock system. Understanding the role of wettability heterogeneity on relative permeability is essential to geological CO 2 sequestration, oil and gas recovery, and contaminated groundwater remediation. Although numerous studies have attempted to understand the influences of surface wettability, capillary number (Ca), and viscosity ratio, the role of the spatial variation and correlation length of surface wettability on two-phase flow in three-dimensional (3D) porous media has not been unraveled due to the challenges in the measurement and representation of realistic rock surface wettability. In this work, we conducted in-situ measurements of surface contact angle (CA) in a Bentheimer sandstone after CO 2 flooding using micro-computed tomography (micro-CT), and found that the pore-scale CA distribution on rock surfaces followed a log-normal distribution associated with a spatial correlation length. Based on the statistical information from CT scanning, a Gaussian random field was used to model CA distributions that had desired standard deviations and spatial correlation lengths, which were then adjusted within a certain range of values for sensitivity analyses to study their combined effects on the two-phase flow in the porous medium using the lattice Boltzmann (LB) method. The LB two-phase flow simulation was accelerated using hybrid, multicore parallel computing to overcome the challenges in simulating multiphase flow in a large 3D domain having 800 × 800 × 600 nodes. The simulation results showed that the surface wettability heterogeneity (i.e., standard deviation of CA) had a lesser effect on the relative permeability of the wetting fluid (water) but a more significant impact on the relative permeability of the non-wetting fluid (scCO 2 ). The Corey model was used to fit the LB-simulated relative permeability curves of water and scCO 2 and showed that the variations in the relative permeability curves for both water and scCO 2 increased as the standard deviation and spatial correlation length of CA increased. This study illustrated that the assumption of homogeneous surface wettability may cause errors in multiphase flow simulations. Furthermore, the impacts of both the standard deviation and spatial correlation length of CAs should be accounted for. This is the first study that explored the spatial correlation lengths associated with CA distributions on sandstone surfaces and comprehensively investigated the roles of both spatial variation and correlation length of CA on two-phase flow properties in 3D porous media. The optimized LB multiphase flow model was proved a powerful tool to study the interplays and combined effects of these statistical parameters, which had critical applications in numerous natural and engineering processes that involved multiphase flow in porous media.
TF, Tolerance Factors and Noncentral t Distribution computer program, computes tolerance factor from normal-distribution sample for arbitrarily specified coverage probability, confidence level, and any positive (integer or noninteger) number of degrees of freedom. Used extensively in engineering and quality analyses. Used in place of reference tables. Written in Microsoft QuickBasic v2.0.
The deterministic approach widely adopted in the design of structural components relies on systematically defined design limits using empirically determined safety factors. However, this approach is not always appropriate because structures are subjected to a variety of loads in the practical environment, which may result in excessively conservative design limits. In recent years, a more rigorous probabilistic approach that incorporates material strength distributions has become an important solution. In the probabilistic approach, the probability density functions of material strength properties underpin the design criteria. Here, the objective of this study is to identify the density distribution functions that best describe tensile properties of irradiated F82H to define a reference strength for DEMO design. Due to the limited number of existing data, this study specifically employs a Bayesian prediction method based on Monte Carlo simulations to determine a material reference value with statistical reliability and to investigate its effectiveness. For example, the dependence of tensile properties of 300 °C irradiated materials on irradiation damage and the range predicted by 95% Bayesian estimation was evaluated. As a statistical model for the dose dependence of statistical parameters, the normal distribution exhibited a better fit for 0.2% proof strength and tensile strength, whereas the distribution of total elongation data gave comparable reference values for both the normal and Weibull distribution models. Both models gave comparable criteria for the distribution of total elongation data. The Weibull model also gave better results for uniform elongation. The function best describing the model was a logarithmic law for both 0.2% proof strength and tensile strength, while a power law for both total and uniform elongation, which allowed for more comprehensive data prediction of irradiation data with statistical accuracy for DEMO reactor design.
In this work, we show that the viscosity of carrier liquid affects the dynamic magnetization of thermally blocked multi-core iron oxide nanoparticles. The core size of the nanoparticles was determined from the magnetization curve measured by a specially developed high-T{sub c} SQUID magnetometer and calculated to be 11.7 nm. Using an AC magnetometer developed based on induction coils, the dynamic magnetization of the multi-core iron oxide nanoparticle solution was measured from 3 Hz to 10.48 kHz. Later, we reconstructed of the hydrodynamic size distribution of the particles by assuming a log-normal distribution of particle size in an AC susceptibility model by Shliomis and Stepanov, which accounts for anisotropic directions of the easy axes of magnetic nanoparticles with respect to the excitation field direction. The reconstructed hydrodynamic sizes showed an average diameter of 130 nm and agreed with the size determined by dynamic light scattering method. In the case of increasing viscosity of the carrier liquids from 0.89 to 8.11 mPa s, the dynamic magnetization peaks of the imaginary component have shifted to a lower frequency region. We showed that the harmonics ratio and phase delay upon the magnetic field excitation at 30 Hz could also be used to determine the viscosity of carrier liquid independently.
The maximum fuel pin temperature for nominal operation in an advanced power reactor is 1370 K. Because of possible nitrogen embrittlement of the clad, the fuel temperature was limited to 1622 K. Assuming simultaneous occurrence of the most adverse conditions a deterministic analysis gave a maximum fuel temperature of 1610 K. A statistical analysis, using a synthesized estimate of the standard deviation for the highest fuel pin temperature, showed probabilities of 0.015 of that pin exceeding the temperature limit by the distribution free Chebyshev inequality and virtually nil assuming a normal distribution. The latter assumption gives a 1463 K maximum temperature at 3 standard deviations, the usually assumed cutoff. Further, the distribution and standard deviation of the fuel-clad gap are the most significant contributions to the uncertainty in the fuel temperature.
The radar backscattering model developed by Richards et al. (1987), has been improved and further tested in this research. The trunk term may now be calculated from the exact solution to the electromagnetic wave equations instead of the corner reflector equation. Rough surface models have been introduced into the radar model, so that the forward reflectance and the backscattering from the ground surface are now calculated from the same model and, thus, are consistent. The number of trees in an individual pixel is assumed to be Poisson distributed, with tree height in a stand log-normally distributed. The simulated results show that the match of backscattering coefficients for eight forest stands between SIR-B image data and the simulated results are satisfying, and that the trunk term now seems to be convincingly established as the dominant term in the L-band HH radar return from coniferous forest stands.
Straggling functions for protons in thick silicon radiation detectors are computed by Monte Carlo simulation. Mean energy loss is constrained by the silicon stopping power, providing higher straggling at low energy and probabilities for stopping within the detector volume. By matching the first four moments of simulated energy-loss distributions, straggling functions are approximated by a log-normal distribution that is accurate for Vavilov k is greater than or equal to 0:3. They are verified by comparison to experimental proton data from a charged particle telescope.
Flight crews and air traffic controllers have reported many safety concerns regarding area navigation standard terminal arrival routes (RNAV STARs). Specifically, optimized profile descents (OPDs). However, our information sources to quantify these issues are limited to subjective reporting and time consuming case-by-case investigations. This work is a preliminary study into the objective performance of instrument procedures and provides a framework to track procedural concepts and assess design specifications. We created a tool and analysis methods for gauging aircraft adherence as it relates to RNAV STARs. This information is vital for comprehensive understanding of how our air traffic behaves. In this study, we mined the performance of 24 major US airports over the preceding three years. Overlaying 4D radar track data onto RNAV STAR routes provided a comparison between aircraft flight paths and the waypoint positions and altitude restrictions. NASA Ames Supercomputing resources were utilized to perform the data mining and processing. We assessed STARs by lateral transition path (full-lateral), vertical restrictions (full-lateral/full-vertical), and skipped waypoints (skips). In addition, we graphed frequencies of aircraft altitudes relative to the altitude restrictions. Full-lateral adherence was always greater than Full-lateral/ full- vertical, as it is a subset, but the difference between the rates was not consistent. Full-lateral/full-vertical adherence medians of the 2016 procedures ranged from 0% in KDEN (Denver) to 21% in KMEM (Memphis). Waypoint skips ranged from 0% to nearly 100% for specific waypoints. Altitudes restrictions were sometimes missed by systematic amounts in 1,000 ft. increments from the restriction, creating multi-modal distributions. Other times, altitude misses looked to be more normally distributed around the restriction. This tool may aid in providing acceptability metrics as well as risk assessment information.
In this exploratory archival study we mined the performance of 24 major US airports area navigation standard terminal arrival routes (RNAV STARs) over the preceding three years. Overlaying radar track data on top of RNAV STAR routes provided a comparison between aircraft flight paths and the waypoint positions and altitude restrictions. NASA Ames Supercomputing resources were utilized to perform the data mining and processing. We investigated STARs by lateral transition path (full-lateral), vertical restrictions (full-lateral/full-vertical), and skipped waypoints (skips). In addition, we graphed altitudes and their frequencies of occurrence for altitude restrictions. Full-lateral compliance was generally greater than Full-lateral/full-vertical, but the delta between the rates was not always consistent. Full-lateral/full-vertical usage medians of the 2016 procedures ranged from 0 in KDEN (Denver) to 21 in KMEM (Memphis). Waypoint skips ranged from 0 to nearly 100 for specific waypoints. Altitudes restrictions were sometimes missed by systemic amounts in 1000 ft. increments from the restriction, creating multi-modal distributions. Other times, altitude misses looked to be more normally distributed around the restriction. This work is a preliminary investigation into the objective performance of instrument procedures and provides a framework to track how procedural concepts and design intervention function. In addition, this tool may aid in providing acceptability metrics as well as risk assessment information.
Flight crews and air traffic controllers have reported many safety concerns regarding area navigation standard terminal arrival routes (RNAV STARs). However, our information sources to quantify these issues are limited to subjective reporting and time consuming case-by-case investigations. This work is a preliminary study into the objective performance of instrument procedures and provides a framework to track procedural concepts and assess design functionality. We created a tool and analysis methods for gauging aircraft adherence as it relates to RNAV STARs. This information is vital for comprehensive understanding of how our air traffic behaves. In this exploratory archival study, we mined the performance of 24 major US airports over the preceding three years. Overlaying radar track data on top of RNAV STAR routes provided a comparison between aircraft flight paths and the waypoint positions and altitude restrictions. NASA Ames Supercomputing resources were utilized to perform the data mining and processing. We assessed STARs by lateral transition path (full-lateral), vertical restrictions (full-lateralfull-vertical), and skipped waypoints (skips). In addition, we graphed aircraft altitudes relative to the altitude restrictions and their occurrence rates. Full-lateral adherence was generally greater than Full-lateralfull-vertical, but the difference between the rates was not always consistent. Full-lateralfull-vertical adherence medians of the 2016 procedures ranged from 0 in KDEN (Denver) to 21 in KMEM (Memphis). Waypoint skips ranged from 0 to nearly 100 for specific waypoints. Altitudes restrictions were sometimes missed by systematic amounts in 1000 ft. increments from the restriction, creating multi-modal distributions. Other times, altitude misses looked to be more normally distributed around the restriction. This tool may aid in providing acceptability metrics as well as risk assessment information.
The effects of atmospheric boundary layer turbulence on the loudness variability of a sonic boom N-wave and shaped boom are examined with split-step simulations. The shaped boom is representative of a design iteration of the NASA X-59 aircraft. Inhomogeneous atmospheric boundary layer turbulence is generated in the computational domain by a Fourier synthesis method. The N-wave and shaped boom are propagated through turbulent fields representing eight different convection levels measured at the NASA Kennedy Space Center and the NASA Armstrong Flight Research Center. Probability density functions of the formation of caustic regions along the propagation direction are computed from the N-wave results, and a parameter to collapse the caustic PDFs that accounts for both fluctuation intensities and length scales is proposed. Statistical results concerning loudness metric variability are presented, and the standard deviations of several metrics are shown to collapse across different convection levels of turbulence for small nondimensional propagation distances. The loudness metric distributions are observed to be well approximated by a normal distribution for a given range of propagation distances, and become increasingly skewed as distance increases. A model function for the dose variability is proposed, and the function parameters are found to be related to the convection level of the turbulence. The model for the dose variability distribution is compared to simulation data that were not used to find the regression parameters of the model. At several nondimensional propagation distances, agreement is observed between the model and the simulation data. These results indicate that the model may be suitable for providing quick estimates of noise dose variability in the primary carpet region across a wide range of atmospheric boundary layer conditions.
Although most parameterizations of the drop size distributions (DSD) use the gamma function, there are several advantages to the log-normal form, particularly if we want to characterize the large scale space-time variability of the DSD and rain rate. The advantages of the distribution are twofold: the logarithm of any moment can be expressed as a linear combination of the individual parameters of the distribution; the parameters of the distribution are approximately normally distributed. Since all radar and rainfall-related parameters can be written approximately as a moment of the DSD, the first property allows us to express the logarithm of any radar/rainfall variable as a linear combination of the individual DSD parameters. Another consequence is that any power law relationship between rain rate, reflectivity factor, specific attenuation or water content can be expressed in terms of the covariance matrix of the DSD parameters. The joint-normal property of the DSD parameters has applications to the description of the space-time variation of rainfall in the sense that any radar-rainfall quantity can be specified by the covariance matrix associated with the DSD parameters at two arbitrary space-time points. As such, the parameterization provides a means by which we can use the spaceborne radar-derived DSD parameters to specify in part the covariance matrices globally. However, since satellite observations have coarse temporal sampling, the specification of the temporal covariance must be derived from ancillary measurements and models. Work is presently underway to determine whether the use of instantaneous rain rate data from the TRMM Precipitation Radar can provide good estimates of the spatial correlation in rain rate from data collected in 5(sup 0)x 5(sup 0) x 1 month space-time boxes. To characterize the temporal characteristics of the DSD parameters, disdrometer data are being used from the Wallops Flight Facility site where as many as 4 disdrometers have been used to acquire data over a 2 km path. These data should help quantify the temporal form of the covariance matrix at this site.
The pulse height response of a right angle scattering optical particle counter has been investigated using monodisperse aerosols of polystyrene latex spheres, di-octyl phthalate and methylene blue. The results confirm previous measurements for the variation of mean pulse height as a function of particle diameter and show good agreement with the relative response predicted by Mie scattering theory. Measured cumulative pulse height distributions were found to fit reasonably well to a log normal distribution with a minimum geometric standard deviation of about 1.4 for particle diameters greater than about 2 micrometers. The geometric standard deviation was found to increase significantly with decreasing particle diameter.
Aerosol concentrations and size distributions in the middle and upper troposphere over the remote Pacific Ocean were measured with a forward scattering spectrometer probe (FSSP) on the NASA DC-8 aircraft during NASA's Global Backscatter Experiment (GLOBE) in May-June 1990. The FSSP size channels were recalibrated based on refractive index estimates from flight-level aerosol volatility measurements with a collocated laser optical particle counter (LOPC). The recalibrated FSSP size distributions were averaged over 100-s intervals, fitted with lo-normal distributions and used to calculate aerosol backscatter coefficients at selected wavelengths. The FSSP-derived backscatter estimates were averaged over 300-s intervals to reduce large random fluctuations. The smoothed FSSP aerosol backscatter coefficients were then compared with LOPC-derived backscatter values and with backscatter measured at or near flight level from four lidar systems operating at 0.53, 1.06, 9.11, 9.25, and 10.59 micrometers. Agreement between FSSP-derived and lidar-measured backscatter was generally best at flight level in homogeneous aerosol fields and at high backscatter values. FSSP data often underestimated low backscatter values especially at the longer wavelengths due to poor counting statistics for larger particles (greater than 0.8 micrometers diameter) that usually dominate aerosol backscatter at these wavelengths. FSSP data also underestimated backscatter at shorter wavelengths when particles smaller than the FSSP lower cutoff diameter (0.35 micrometers) made significant contributions to the total backscatter.
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.
In order to demonstrate the advanced CMC technology under development within the Ultra Efficient Engine Technology (UEET) program, it has been planned to fabricate, test and analyze an all CMC turbine vane made of a SiC/SiC composite material. The objective was to utilize a 5-II Satin Weave SiC/CVI SiC/ and MI SiC matrix material that was developed in-house under the Enabling Propulsion Materials (EPM) program, to design and fabricate a stator vane that can endure successfully 1000 hours of engine service conditions operation. The design requirements for the vane are to be able to withstand a maximum of 2400 F within the substrate and the hot surface temperature of 2700 F with the aid of an in-house developed Environmental/Thermal Barrier Coating (EBC/TBC) system. The vane will be tested in a High Pressure Burner Rig at NASA Glenn Research Center facility. This rig is capable of simulating the engine service environment. The present paper focuses on a probabilistic assessment of the vane. The material stress/strain relationship shows a bilinear behavior with a distinct knee corresponding to what is often termed as first matrix cracking strength. This is a critical life limiting consideration for these materials. The vane is therefore designed such that the maximum stresses are within this limit so that the structure is never subjected to loads beyond the first matrix cracking strength. Any violation of this design requirement is considered as failure. Probabilistic analysis is performed in order to determine the probability of failure based on this assumption. In the analysis, material properties, strength, and pressures are considered random variables. The variations in properties and strength are based on the actual experimental data generated in house. The mean values for the pressures on the upper surface and the lower surface are known but their distributions are unknown. In the present analysis the pressures are considered normally distributed with a nominal variation. Temperature profile on the vane is obtained by performing a CFD analysis and is assumed to be deterministic.