On determining a distribution function known only by its moment and/or moment generating function
Distribution function determination using moment generating function and probability density function
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Distribution function determination using moment generating function and probability density function
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A simulation was conducted to determine whether the sensitivity of secondary task measures of pilot workload could be improved by synchronizing their presentation to the occurrence of specific events or pilot actions. This synchronous method of presentation was compared to the more typical asynchronous method, where secondary task presentations are independent of pilot's flight-related activities. Twelve pilots flew low- and high-difficulty scenarios in a motion-base trainer with and without concurrent secondary tasks (e.g., choice reaction time and time production). The difficulty of each scenario was manipulated by the addition of 21 flight-related tasks superimposed on a standard approach and landing sequence. The insertion of the secondary tasks did not affect primary flight performance. However, secondary task performance did reflect workload differences between scenarios and among flight segments within scenarios, replicating the results of an earlier study in which the secondary tasks were presented asynchronously (Bortolussi et al., 1986).
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Parameterization of cloud microphysics is critical for accurate simulation of weather and climate, in which the characteristics of cloud particle spectrum inevitably further affect climate simulation by changing the cloud evolution and cloud radiation effects. The popular currently used double-moment cloud microphysics schemes in numerical models can predict the intercept (N 0 ) and slope (λ) parameters of cloud particle spectrum but cannot predict the spectral shape parameter (μ), which hinders accurate description of cloud physical processes in climate models. Therefore, in the present study, we built upon the ideas of previously developed triple-moment cloud microphysics scheme, considered radar reflectivity factor as the third predictor in addition to number and mass concentration, and introduced its related prediction equation to the Single Column Atmosphere Model Version 5.3 (SCAM5.3). Moreover, the relevant microphysical process formulas in the model were revised, and a triple-moment ice-cloud microphysics scheme was constructed to predict the μ of ice particle spectrum. Based on this model, a 29-day case of the Atmospheric Radiation Measurement Program in the summer of 1997 (ARM97) was simulated, and the differences in cloud fraction and radiation simulations between the double- and triple-moment schemes were analysed. The μ of ice particle spectrum predicted by the triple-moment scheme mainly ranged from 0 to 4; the peak value was around 2, and at least 85% of the μ values were greater than the default 0. Therefore, the μ=0 setting in the double-moment scheme is unreasonable. Moreover, the developed triple-moment ice-cloud microphysics scheme yielded a narrower ice particle spectrum, which was closer to the observation results of previous studies, than the double-moment cloud microphysics scheme (e.g., height=233 hPa). Furthermore, compared with the double-moment scheme, the triple-moment scheme achieved closer simulations of the cloud fraction observations, particularly for ice clouds in the upper levels. Considering the close association between cloud fraction and radiation, the error with the triple-moment scheme was smaller than that with the double-moment scheme regardless of the shortwave (surface downward shortwave radiation, net downward shortwave radiation at the top of the atmosphere, and net shortwave radiation at the surface) or longwave (surface downward longwave radiation and net longwave radiation at the surface) flux density. Finally, the improvement mechanism of the triple-moment scheme on cloud fraction and radiation simulations was explored. The major reason is that the triple-moment scheme weakens the autoconversion of ice crystal to form snow and enhances the growth process of ice crystal deposition, thereby increasing the mass concentration of ice crystals and ice cloud fraction. Overall, the developed triple-moment ice-cloud microphysics scheme can help improve the simulation ability of models for cloud-climate feedback and other processes.
Abstract Effectively quantifying hot moments of nitrous oxide (N 2 O) emissions from agricultural soils is critical for managing this potent greenhouse gas. However, we are challenged by a lack of standard approaches for identifying hot moments, including (a) determining thresholds above which emissions are considered hot moments, and (b) considering seasonal variation in the magnitude and frequency distribution of net N 2 O fluxes. We used one year of hourly N 2 O flux measurements from 16 autochambers that varied in flux magnitude and frequency distribution in a conventionally tilled maize field in central Illinois, USA, to compare three approaches to identify hot moment thresholds: standard deviations (SD) above the mean, 1.5x the interquartile range (IQR), and isolation forest (IF) identification of anomalous values. We also compared these approaches on seasonally subdivided data (early, late, and non‐growing seasons) versus the whole year. Our analyses revealed that 1.5x IQR method best identified N 2 O hot moments. In contrast, using 2 or 4 SD both yielded hot moment threshold values too high, and IF yielded threshold values too low, leading to missed N 2 O hot moments or low net N 2 O fluxes mischaracterized as hot moments, respectively. Furthermore, seasonally subdividing the data set not only facilitated identification of smaller hot moments in the late‐ and non‐growing seasons when N 2 O hot moments were generally smaller but it also increased hot moment threshold values in the early growing season when N 2 O hot moments were larger. Consequently, of the methods evaluated here, we recommend using the 1.5x IQR method on whole year data sets to identify N 2 O hot moments.
Nuclear fusion science is an example of a scientific field with a rich history of expert involvement and scientific publications, which together, form an expert-knowledge base. One example of a nuclear fusion formalism is the utilization of published reaction rates from a variety of authors. Investigators for Deuterium- Tritium (D-T) ion fusion can choose from using frequently cited methods: the Bosch and Hal reactivity, thermonuclear reaction rates from Caughlan and Fowler, and the reactivity evaluation from Miley, Towner & Ivich which forms the basis of the Naval Research Lab (NRL) formulary. There are other choices available. Each of the reactivity formulations considered here, are based upon the Maxwell-Boltzmann velocity distribution for D-T fusion ion reactants. Numerical methods for computer codes simulating hot, energetic plasmas, include tabulations of the reactivity, and the first moment of energy. This report continues the step toward building understanding of nuclear fusion reactivity formalisms. It is part of a series of reports with the same goal, [5-10] and is the continuation of the Part I paper for defining the mathematical relationship of the first moment of D-T fusion ion kinetic energy, <$E$>, with the fusion cross-section, fusion reactivity and its derivative with ion-temperature. In Part I, three variants of the first moment <$E$> were analytically developed and explored: 1) constant cross-section, 2) a normalized first moment, and 3) a particular function of the first moment from Brysk. In Part II, attention is given to the definition of <$K$>, originally described as a ratio of moments from Brysk, and its relationship to the first moment definitions from Part I. One measure of the progress made in these documents is the identification that Brysk’s ratio of the second moment to the first moment ratio, <$K$>, does not correspond to his provided solution of the first moment of energy. Another measure of (our) progress from this work is the comparison of first moment variants. That comparison includes confirming the importance of cross sections defined in terms of energy. The analytical relationships we have developed among important physics quantities are useful tools in validation and verification (V&V). For example, we can calculate the kinetic energy as a mean or as a first moment, or as a function of the first moment. These analytically-determined values can be compared directly with numerically-determined values, supplied to the authors, representing <$E$>.
Aircraft travel has become a major form of transportation. Several of our major airports are operating near their capacity limit, increasing congestion and delays for travelers. As a result, the National Aeronautics and Space Administration (NASA) has been working in conjunction with the Federal Aviation Administration (FAA), airline operators, and the airline industry to increase airport capacity without sacrificing public safety. One solution to the problem is to increase the number of airports and build new. runways; yet, this solution is becoming increasingly difficult due to limited space. A better solution is to increase the production per runway. This solution increases the possibility that one aircraft will encounter the trailing wake of another aircraft. Hazardous wake vortex encounters occur when an aircraft encounters the wake produced by a heavier aircraft. This heavy-load aircraft produces high-intensity wake turbulence that redistributes the aerodynamic loads of trailing smaller aircraft. This situation is particularly hazardous for smaller aircraft during takeoffs and landings. In order to gain a better understanding of the wake-vortex/aircraft encounter phenomena, NASA Langley Research Center conducted a series of flight tests from 1995 through 1997. These tests were designed to gather data for the development a wake encounter and wake-measurement data set with the accompanying atmospheric state information. This data set is being compiled into a database that can be used by wake vortex researchers to compare with experimental and computational results. The purpose of this research is to derive and implement a procedure for calculating the wake-vortex/aircraft interaction portion of that database by using the data recorded during those flight tests. There were three objectives to this research. Initially, the wake-induced forces and moments from each flight were analyzed based on varying flap deflection angles. The flap setting alternated between 15 and 30 degrees while the separation distance remained constant. This examination was performed to determine if increases in flap deflection would increase or decrease the effects of the wake-induced forces and moments. Next, the wake-induced forces and moments from each flight were analyzed based on separation distances of 1-3 nautical miles. In this comparison, flap deflection was held constant at 30 degrees. The purpose of this study was to determine if increased separation distances reduced the effects of the wake vortex on the aircraft. The last objective compared the wake-induced forces and moments of each flight as it executed a series of maneuvers through the wake-vortex. This analysis was conducted to examine the impact of the wake on the B737 as it traversed the wake horizontally and vertically. Results from the first analysis indicated that there was no difference in wake effect at flap deflections of 15 and 30 degrees. This conclusion is evidenced in the cases of the wake-induced sideforce, rolling moment, and yawing moment. The wake-induced lift, drag, and pitching moment cases yielded less conclusive results. The second analysis compared the wake-induced forces and moments at separation distances of 1-3 nautical miles. Results indicated that there was no significant difference in the wake-induced lift, drag, sideforce, or yawing moment coefficients. The analysis compared the wake-induced forces and moments based on different flight maneuvers. It was found that the wake-induced forces and moments had the greatest impact on out-to-in and in-to-out maneuvers.
Flight tests have been conducted with a single-rotor helicopter to determine the effects of partial-power descents with forward speed, high-speed level turns, pull-outs from autorotation, and high-forward-speed high-rotor-speed autorotation on the flapwise bending and torsional moments of the rotor blade. One blade of the helicopter was equipped at 14 percent and 40 percent of the blade radius with strain gages calibrated to measure moments rather than stresses. The results indicate that the maximum moments encountered in partial-power descents with forward speed tend to be generally reduced from the maximum moments encountered during partid-power descents at zero forward speed. High-speed level turns and pull-outs from auto-rotation caused retreating-blade stall which produced torsional moments (values up to 2,400 inch-pounds). at the 14-percent-radius station that were as large as those encountered during the previous investigations of retreating-blade stall (values up t o 2,500 inch-pounds). High-forward- speed high-rotor-speed autorotation produced flapwise bending moments (values up to 7,200 inch-pounds) at the 40-percent-radius station which were as large as the flapwise bending moments (values up to 7,800 inch-pounds) a t the 14-percent-radius station encountered during partial - power vertical descents. The results of the present investigation (tip-speed ratios up to 0.325 and an unaccelerated level-flight mean lift coefficient of about 0.6), in combination with the related results of at zero forward speed produce the largest rotor-blade vibratory moments. However, inasmuch as these large moments occur only during 1 percent of the cycles and 88 percent of the cycles are at moment values less than 70 percent of these maximum values in partial-power descents, other conditions, such as high-speed flight where the large moments are combined with large percentages of time spent,must not be neglected in any rotor-blade service-life assessment.
Recently, a method to retrieve rain drop size distribution (DSD) moments from X-band dual polarization radar measurements has been developed using copolar reflectivity, differential reflectivity and specific attenuation. Two reference moments are retrieved first, followed by reconstructing the DSDs and calculating other moments using a generalized gamma model to represent the underlying shape, h(x), corresponding to the pair of chosen reference moments. Here we explore a similar approach but the retrieval method in this study uses dual-frequency radar measurements. In the case of GPM-DPR, the two frequencies are 13.8and 35 GHz, and their products include attenuation corrected reflecivities at both frequencies (Z and Z) and the specific attenuation (k, k, if available). Our approach is to use these products to determine two reference moments, namely M3 andM6 representing the third and the sixth moments respectively. Then, as with the polarimetric radar retrievals, we use the most probable h(x) to reconstruct the full DSD spectra, from which other moments are calculated. The best two DPR products for estimating M3 and M6 appear to be A and Z. Figure 1 shows the retrievals versus the ‘true’ moments. 2930 three-minute DSDs were used for the (T-matrix) scattering calculations at Ku and Ka bands but only cases with A > 0.5 dB/km were chosen. For the retrieved moments, the integration was performed only up to 6 mm drop diameter. The [1:1] line is included in Fig. 1. Even with just two DPR products as input the results seem promising, although the lower order moments show somewhat more scatter, especially the zeroth moment, M0. We will quantify the retrieval errors, and additionally examine the stability of h(x). For the latter, data from (i) Greeley, Colorado, (ii) Huntsville, Alabama, and (iii)Wallops, Virginia, will be used. Finally, a GPM overpass case over Huntsville, during a widespread rain event on 11 April 2016, will be considered as an initial test case.
Here, we use the Pasyanos and Chiang (2022) data set to calculate the seismic moment M 0 for each explosion and use the measured explosive yield W to validate the W~M 0 relationship in Denny and Johnson (1991; hereafter, DJ91). The M 0 is corrected by transforming to a potency tensor and applying more appropriate near-source geophysical parameter values in the moment estimate. The mean residual between observed and predicted yield is near zero; however, the standard deviation of the residuals results in an F-value (a 95% confidence factor) of about 5. We re-estimate the coefficients in the DJ91 model and find similar values and only a slight improvement in the F-value. Next, we embark on a similar model selection process as DJ91, allowing for non-cube-root yield scaling and other plausible near-source elastic moduli. As was found by DJ91, the yield dependence is not significantly different from unity, and a cube root assumption is valid. Therefore, we yield scale the seismic moment and test the significance of all plausible explanatory variables. Isotropic moment performs better in the response variable than total moment. The preference for isotropic moment could be due to its relationship to volume change, which would be more directly affected by explosive yield. Surprisingly, we find that the overburden pressure, which is a function of depth, is not a significant parameter in the model. We hypothesize that this is due to the competing depth effects on source asymmetry and the incorporation of depth in the Green’s functions used to calculate the seismic moment tensors. Importantly, this emphasizes that only seismic moment tensor-derived moments should be used in these models. After removing insignificant model parameters, we are left with a simple model to predict explosive yield $\widehat{W}$ in kt from isotropic moment M I in N·m, $\widehat{W}$=κ –1.4132 10 0.035626GP M I , in which κ and GP are the near-source bulk modulus and gas porosity in Pa and %, respectively. The F-value for this model is approximately 3.
The molecule 5,6-diaminobenzene-1,2,3,4-tetracarbonnitrile (MOI) was first synthesized by Müllen and coworkers in 2016 and boasts an ultrastrong dipole moment of $14.1\pm 0.7$ Debye in THF. Gas phase DFT computations do not fully reflect this ultrastrong dipole moment, demonstrating the role of solvent in increasing this dipole moment. Here, we investigate the effect of solvent molecule position on the dipole moment of this species, computationally examining systems with giant dipole moments. These systems are optimized in the gas phase with the B3LYP functional, employing the aug-cc-pVTZ and def2-TZVP basis sets, as well as the B3LYP-D3BJ/aug-cc-pVTZ functional in Orca. Single point DLPNO-CCSD/aug-cc-pVDZ results were obtained from Orca and Psi4, as well as DLPNO-CCSD(T)/CBS information from Psi4. Additionally, these are compared to the dipole moments of di- and tri-hydrated systems, and the SMD models for THF and water at the B3LYP/aug-cc-pVTZ level of theory. The dissociation energies, HOMO-LUMO energy gaps, and dipole moments are presented. These metrics show the nh1nh1′ THF system boasts the largest dissociation energy and dipole moment of the singly solvated systems, due to its strong hydrogen bonding. The importance of solvent placement is highlighted and may guide the synthesis of macromolecules or organic frameworks incorporating the MOI or MOI-like subunits. Remarkably, a single solvent molecule provides a good model for the difference between the gas phase and solvated species. The predicted gas phase dipole moments computed with B3LYP/aug-cc-pVTZ for the MOI, its monohydrated complex, dihydrated complex, and its trihydrated complex are 9.6, 14.2, 16.0, and 16.8 Debye, respectively.
The dipole moment is the molecular property that most directly indicates molecular polarity. The accuracy of computed dipole moments depends strongly on the quality of the calculated electron density, and the breakdown of single-reference methods for strongly correlated systems can lead to poor predictions of the dipole moments in those cases. Here, we derive the analytical expression for obtaining the electric dipole moment by multiconfiguration pair density functional theory (MCPDFT), and we assess the accuracy of MC-PDFT for predicting dipole moments at equilibrium and nonequilibrium geometries. We show that MC-PDFT dipole moment curves have reasonable behavior even for stretched geometries, and they significantly improve upon the CASSCF results by capturing more electron correlation. Herein, the analysis of a dataset consisting of 18 first-row transition metal diatomics and 6 main-group polyatomic molecules with multireference character suggests that MC-PDFT and its hybrid extension (HMC-PDFT) perform comparably to CASPT2 and MRCISD+Q methods and have a mean unsigned deviation of 0.2–0.3 D with respect to the best available dipole moment reference values. We explored the dependence of the predicted dipole moments upon the choice of the on-top density functional and active space, and we recommend the tPBE and hybrid tPBE0 on-top choices for the functionals combined with the moderate correlated participating orbital scheme for selecting the active space. With these choices, the mean unsigned deviations (in debyes) of the calculated equilibrium dipole moments from the best estimates are 0.77 for CASSCF, 0.29 for MC-PDFT, 0.24 for HMCPDFT, 0.28 for CASPT2, and 0.25 for MRCISD+Q. These results are encouraging because the computational cost of MC-PDFT or HMC-PDFT is largely reduced compared to the CASPT2 and MRCISD+Q methods.