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At least 1,279 records · Page 71

Some Mathematical and Geophysical Considerations in Radioisotope Dating Applications

Some quality considerations for use in isotopic dating are presented to identify and correct heretofore unidentified overestimate scenarios. These include to a lesser degree the statistical interpretation issues with linear-least-squares fitting results but more importantly the isotope effect in the individual components of the isochron coefficient ratios. By taking into consideration the isotope effect (differential mass diffusion rates) when measuring isotopic ratios from very old samples, the distribution dependency in the coefficient ratios will cause a bias if isotopic diffusion rates are not identical throughout a sample. The isotope effect is that isotopes having a smaller atomic mass will diffuse faster throughout a medium than will their heavier counterparts causing concentration gradients of their ratios even when there are no contributions from radioactive decay. The application to Rb/Sr dating is evaluated and shown to result in expected age overestimates when isotopic ratios are employed to linearize the isochron. A suggested method to test for this effect is argued to require rigorous statistical analysis. An associated optimal sampling technique would involve using single-grain etching. It is also shown that the only method to fully eliminate the isotope effect is to not use isotopic ratios at all in radioisotopic dating as the physics do not require the use of isotopic ratios for geochronological dating. However, without the ratios, the data are inherently noisy.

74 ATOMIC AND MOLECULAR PHYSICS↗

Are 100 Ensemble Members Enough to Capture the Remote Atmospheric Response to +2°C Arctic Sea Ice Loss?

This study presents results from the Polar Amplification Multimodel Intercomparison Project (PAMIP) single-year time-slice experiments that aim to isolate the atmospheric response to Arctic sea ice loss at global warming levels of +2°C. Using two general circulation models (GCMs), the ensemble size is increased up to 300 ensemble members, beyond the recommended 100 members. After partitioning the response in groups of 100 ensemble members, the reproducibility of the results is evaluated, with a focus on the response of the midlatitude jet streams in the North Atlantic and North Pacific. Both atmosphere-only and coupled ocean–atmosphere PAMIP experiments are analyzed. Substantial differences in the midlatitude response are found among the different experiment subsets, suggesting that 100-member ensembles are still significantly influenced by internal variability, which can mislead conclusions. Despite an overall stronger response, the coupled ocean–atmosphere runs exhibit greater spread due to additional ENSO-related internal variability when the ocean is interactive. The lack of consistency in the response is true for anomalies that are statistically significant according to Student’s t and false discovery rate tests. This is problematic for the multimodel assessment of the response, as some of the spread may be attributed to different model sensitivities whereas it is due to internal variability. Here, we propose a method to overcome this consistency issue that allows for more robust conclusions when only 100 ensemble members are used.

58 GEOSCIENCES↗

Statistical interpretation of sterile neutrino oscillation searches at reactors

A considerable experimental effort is currently under way to test the persistent hints for oscillations due to an eV-scale sterile neutrino in the data of various reactor neutrino experiments. The assessment of the statistical significance of these hints is usually based on Wilks’ theorem, whereby the assumption is made that the log-likelihood is χ 2 -distributed. However, it is well known that the preconditions for the validity of Wilks’ theorem are not fulfilled for neutrino oscillation experiments. In this work we derive a simple asymptotic form of the actual distribution of the log-likelihood based on reinterpreting the problem as fitting white Gaussian noise. From this formalism we show that, even in the absence of a sterile neutrino, the expectation value for the maximum likelihood estimate of the mixing angle remains non-zero with attendant large values of the log-likelihood. Our analytical results are then confirmed by numerical simulations of a toy reactor experiment. Finally, we apply this framework to the data of the Neutrino-4 experiment and show that the null hypothesis of no-oscillation is rejected at the 2.6 σ level, compared to 3.2 σ obtained under the assumption that Wilks’ theorem applies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Processing Aleatory and Epistemic Uncertainties in Experimental Data From Sparse Replicate Tests of Stochastic Systems for Real-Space Model Validation

This paper presents a practical methodology for propagating and processing uncertainties associated with random measurement and estimation errors (that vary from test-to-test) and systematic measurement and estimation errors (uncertain but similar from test-to-test) in inputs and outputs of replicate tests to characterize response variability of stochastically varying test units. Also treated are test condition control variability from test-to-test and sampling uncertainty due to limited numbers of replicate tests. These aleatory variabilities and epistemic uncertainties result in uncertainty on computed statistics of output response quantities. The methodology was developed in the context of processing experimental data for “real-space” (RS) model validation comparisons against model-predicted statistics and uncertainty thereof. The methodology is flexible and sufficient for many types of experimental and data uncertainty, offering the most extensive data uncertainty quantification (UQ) treatment of any model validation method the authors are aware of. It handles both interval and probabilistic uncertainty descriptions and can be performed with relatively little computational cost through use of simple and effective dimension- and order-adaptive polynomial response surfaces in a Monte Carlo (MC) uncertainty propagation approach. A key feature of the progressively upgraded response surfaces is that they enable estimation of propagation error contributed by the surrogate model. Sensitivity analysis of the relative contributions of the various uncertainty sources to the total uncertainty of statistical estimates is also presented. Finally, the methodologies are demonstrated on real experimental validation data involving all the mentioned sources and types of error and uncertainty in five replicate tests of pressure vessels heated and pressurized to failure. Simple spreadsheet procedures are used for all processing operations.

97 MATHEMATICS AND COMPUTING↗

Comparing Global Spray Combustion Characteristics and Local Shot-to-Shot Variations in a Reacting n -Heptane Spray

In support of efforts to develop improved models of turbulent spray behavior and combustion in diesel engines, experimental data and analysis must be obtained for guidance and validation. For Reynolds-averaged Navier–Stokes (RANS)-based Computational fluid dynamics (CFD) modeling approaches, representative ensemble average experimental results are important. For high-fidelity models such as large eddy simulations (LES)-based CFD, precise individual experimental results are desirable. However, making comparisons between a given experiment and LES is a challenge since local parameters cannot be directly compared. In this work, an optically accessible constant pressure flow rig (CPFR) is utilized to acquire diesel-like fuel injection and reaction behavior simultaneously with three optical diagnostic techniques: rainbow Schlieren deflectometry (RSD), OH* chemiluminescence (OH*), and two-color pyrometry (2CP). The CPFR allows a large number of repeated injection experiments to be performed for statistical analysis and convergence using ensemble-averaging techniques, while maintaining highly repeatable test conditions. Even for stable test conditions, variations in local turbulent fuel–air mixing introduce variability, which manifests as significant differences in OH* and 2CP results. Experimental measurements of characteristic parameters including liquid and vapor jet penetration, liftoff length, soot temperature and concentration, and turbulent flame speed, along with the shot-to-shot variability of each dataset, are presented and discussed. Finally, a statistical method is utilized to analyze the extent of this variability, and to identify superlative injections within the dataset for discussion and analysis of shot-to-shot variations.

42 ENGINEERING↗

Multi-Parent Clustering Algorithms from Stochastic Grammar Data Models

We introduce a statistical data model and an associated optimization-based clustering algorithm which allows data vectors to belong to zero, one or several "parent" clusters. For each data vector the algorithm makes a discrete decision among these alternatives. Thus, a recursive version of this algorithm would place data clusters in a Directed Acyclic Graph rather than a tree. We test the algorithm with synthetic data generated according to the statistical data model. We also illustrate the algorithm using real data from large-scale gene expression assays.

Mjoisness, Eric↗

Metrics of Balance Control for Use in Screening Tests of Vestibular Function

Decrements in balance control have been documented in astronauts after space flight. Reliable measures of balance control are needed for use in postflight field tests at remote landing sites. Diffusion analysis (DA) is a statistical mechanical tool that shows the average difference of the dependent variable on varying time scales. These techniques have been shown to measure differences in open-loop and closed-loop postural control in astronauts and elderly subjects. The goal of this study was to investigate the reliability of these measures of balance control. Eleven subjects were tested using the Clinical Test of Sensory Interaction on Balance: the subject stood with feet together and arms crossed on a stable or compliant surface, with eyes open or closed and with or without head movements in the pitch or yaw plane. Subjects were instrumented with inertial motion sensors attached to their trunk segment. The DA curves for linear acceleration measures were characterized by linear fits measuring open- (Ds) and closed-loop (Dl) control, and their intersection point (X-int, Y-int). Ds and Y-int showed significant differences between the test conditions. Additionally, Ds was correlated with the root mean square (RMS) of the signal, indicating that RMS was dominated by open-loop events (< 0.5 seconds). The Y-int was found to be correlated with the average linear velocity of trunk movements. Thus DA measures could be applied to derive reliable metrics of balance stability during field tests.

Fiedler, Matthew↗

Using LANDSAT digital data for estimating green biomass

The author has identified the following significant results. Relationships between the quantity of mixed prairie rangeland vegetation and LANDSAT MSS response were studied during four growing seasons at test sites throughout the United States Great Plans region. A LANDSAT derived parameter, the normalized difference was developed from theoretical considerations fro statistical estimation of the amount and seasonal condition of rangeland vegetation. This parameter was tested for application to local assessment of green forage biomass and regional monitoring of range feed conditions and drought. Results show that for grasslands in the Great Plains with near continuous vegetative cover and free of heavy brush and forbs, the LANDSAT digital data can provide a useful estimate of the quantity of green forage biomass (within 250 kg/ha), and at least five levels of pasture and range feed conditions can be adequately mapped for extended regions.

Deering, D. W.↗

Implementation and Testing of Turbulence Models for the F18-HARV Simulation

This report presents three methods of implementing the Dryden power spectral density model for atmospheric turbulence. Included are the equations which define the three methods and computer source code written in Advanced Continuous Simulation Language to implement the equations. Time-history plots and sample statistics of simulated turbulence results from executing the code in a test program are also presented. Power spectral densities were computed for sample sequences of turbulence and are plotted for comparison with the Dryden spectra. The three model implementations were installed in a nonlinear six-degree-of-freedom simulation of the High Alpha Research Vehicle airplane. Aircraft simulation responses to turbulence generated with the three implementations are presented as plots.

Yeager, Jessie C.↗

A Method for Calculating the Probability of Successfully Completing a Rocket Propulsion Ground Test

Propulsion ground test facilities face the daily challenge of scheduling multiple customers into limited facility space and successfully completing their propulsion test projects. Over the last decade NASA s propulsion test facilities have performed hundreds of tests, collected thousands of seconds of test data, and exceeded the capabilities of numerous test facility and test article components. A logistic regression mathematical modeling technique has been developed to predict the probability of successfully completing a rocket propulsion test. A logistic regression model is a mathematical modeling approach that can be used to describe the relationship of several independent predictor variables X(sub 1), X(sub 2),.., X(sub k) to a binary or dichotomous dependent variable Y, where Y can only be one of two possible outcomes, in this case Success or Failure of accomplishing a full duration test. The use of logistic regression modeling is not new; however, modeling propulsion ground test facilities using logistic regression is both a new and unique application of the statistical technique. Results from this type of model provide project managers with insight and confidence into the effectiveness of rocket propulsion ground testing.

Messer, Bradley↗

Status of research into lightning effects on aircraft

Developments in aircraft lightning protection since 1938 are reviewed. Potential lightning problems resulting from present trends toward the use of electronic controls and composite structures are discussed, along with presently available lightning test procedures for problem assessment. The validity of some procedures is being questioned because of pessimistic results and design implications. An in-flight measurement program is needed to provide statistics on lightning severity at flight altitudes and to enable more realistic tests, and operators are urged to supply researchers with more details on electronic components damaged by lightning strikes. A need for review of certain aspects of fuel system vulnerability is indicated by several recent accidents, and specific areas for examination are identified. New educational materials and standardization activities are also noted.

Plumer, J. A.↗

Leveraging observed soil heterotrophic respiration fluxes as a novel constraint on global-scale models

Microbially-explicit models may improve understanding and projections of carbon dynamics in response to future climate change, but their fidelity in simulating global-scale soil heterotrophic respiration (RH), a stringent test for soil biogeochemical models, has never been evaluated. We used statistical global RH products, as well as 7,821 daily site-scale RH measurements, to evaluate the spatio-temporal performance of one first-order decay model (CASA-CNP) and two microbially-explicit biogeochemical models (CORPSE and MIMICS) that were forced by two different climate datasets. CORPSE and MIMICS did not provide any measurable performance improvement; instead, the models were highly sensitive to the meteorological input data used to drive them. Spatial RH variability was generally well simulated except in the northern middle latitudes (~50°N) and arid regions; models captured the seasonal variability of RH well, but showed more divergence in tropic and arctic regions. Our results demonstrate that the next generation of biogeochemical models shows promise, but also needs to be improved for realistic spatio-temporal variability of RH. Finally, we emphasize the importance of net primary production, soil moisture, and soil temperature inputs, and that jointly evaluating soil models for their spatial (global scale) and temporal (site scale) performance provides crucial benchmarks for improving biogeochemical models.

Jian, Jinshi↗

Design prediction for long term stress rupture service of composite pressure vessels

Extensive stress rupture studies on glass composites and Kevlar composites were conducted by the Lawrence Radiation Laboratory beginning in the late 1960's and extending to about 8 years in some cases. Some of the data from these studies published over the years were incomplete or were tainted by spurious failures, such as grip slippage. Updated data sets were defined for both fiberglass and Kevlar composite stand test specimens. These updated data are analyzed in this report by a convenient form of the bivariate Weibull distribution, to establish a consistent set of design prediction charts that may be used as a conservative basis for predicting the stress rupture life of composite pressure vessels. The updated glass composite data exhibit an invariant Weibull modulus with lifetime. The data are analyzed in terms of homologous service load (referenced to the observed median strength). The equations relating life, homologous load, and probability are given, and corresponding design prediction charts are presented. A similar approach is taken for Kevlar composites, where the updated stand data do show a turndown tendency at long life accompanied by a corresponding change (increase) of the Weibull modulus. The turndown characteristic is not present in stress rupture test data of Kevlar pressure vessels. A modification of the stress rupture equations is presented to incorporate a latent, but limited, strength drop, and design prediction charts are presented that incorporate such behavior. The methods presented utilize Cartesian plots of the probability distributions (which are a more natural display for the design engineer), based on median normalized data that are independent of statistical parameters and are readily defined for any set of test data.

Robinson, Ernest Y.↗

Dust-polarization Maps and Interstellar Turbulence

Perhaps the most intriguing result of Planck’s dust-polarization measurements is the observation that the power in the E-mode polarization is twice that in the B mode, as opposed to pre-Planck expectations of roughly equal dust powers in the E and B modes. Here we show how the E- and B-mode powers depend on the detailed properties of the fluctuations in the magnetized interstellar medium (ISM). These fluctuations can be decomposed into slow, fast, and Alfvén magnetohydrodynamic (MHD) waves, which comprise a complete basis that can be used to describe linear fluctuations of a magnetized fluid. They can alternatively be decomposed in terms of one longitudinal and two transverse components of a fluid-displacement field. The intensity (T) and E- and B-mode amplitudes induced by each of the three types of waves, in both decompositions, are then calculated. To illustrate how these tools can be applied, we consider a toy model of the ISM in which dust traces a single component of plasma, and obtain the EE/BB ratio and TE correlation for several ansatzes for the power in slow/fast/Alfvén waves and in longitudinal/transverse waves. Although our model may be too simplistic to properly describe the nonlinear structure of interstellar magnetic fields, we find that the observed EE/BB ratio (and its scale invariance) and positive TE correlation—as well as the observed power-law index for the angular spectrum of these fluctuations—are not easily accommodated in terms of simple MHD turbulence prescriptions for the expected powers in slow, fast, and Alfvén waves. We speculate that the ∼0.1–30 pc length scales probed by these dust-polarization measurements are not described by MHD turbulence, but rather probe the large-scale physics that drives ISM turbulence. We find that a slightly anisotropic spectrum of random fluid displacements produces EE/BB≃2 and a positive TE cross-correlation. Furthermore, we find that large EE/BB and positive TE are due primarily to longitudinal, rather than transverse, modes in the random-displacement field, providing, perhaps, some clue to the mechanism that stirs the ISM. Future investigations involving the spatial dependence of the EE/BB ratio, TE correlation, and local departures from statistical isotropy in dust-polarization maps, as well as further tests of some of the assumptions in this analysis, are outlined. This work may also aid in the improvement of foreground-separation techniques for studies of cosmic microwave background polarization.

79 ASTRONOMY AND ASTROPHYSICS↗

Evaluation program for secondary spacecraft cells

A life cycle test of secondary electric batteries for spacecraft applications was conducted. A sample number of nickel cadmium batteries were subjected to general performance tests to determine the limit of their actual capabilities. Weaknesses discovered in cell design are reported and aid in research and development efforts toward improving the reliability of spacecraft batteries. A statistical analysis of the life cycle prediction and cause of failure versus test conditions is provided.

Christy, D. E.↗

Diffusion and mobility of atomic particles in a liquid

The diffusion coefficient of a test atom or molecule in a liquid is determined for the mechanism where the displacement of the test molecule results from the vibrations and motion of liquid molecules surrounding the test molecule and of the test particle itself. This leads to a random change in the coordinate of the test molecule, which eventually results in the diffusion motion of the test particle in space. Two models parameters of interaction of a particle and a liquid are used to find the activation energy of the diffusion process under consideration: the gas-kinetic cross section for scattering of test molecules in the parent gas and the Wigner–Seitz radius for test molecules. In the context of this approach, we have calculated the diffusion coefficient of atoms and molecules in water, where based on experimental data, we have constructed the dependence of the activation energy for the diffusion of test molecules in water on the interaction parameter and the temperature dependence for diffusion coefficient of atoms or molecules in water within the models considered. The statistically averaged difference of the activation energies for the diffusion coefficients of different test molecules in water that we have calculated based on each of the presented models does not exceed 10% of the diffusion coefficient itself. We have considered the diffusion of clusters in water and present the dependence of the diffusion coefficient on the cluster size. The accuracy of the presented formulas for the diffusion coefficient of atomic particles in water is estimated to be 50%.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Detection and removal of B-mode dust foregrounds with signatures of statistical anisotropy

Searches for inflationary gravitational wave signals in the cosmic microwave background (CMB) B-mode polarization are expected to reach unprecedented power over the next decade. A major difficulty in these ongoing searches is that Galactic foregrounds such as dust can easily mimic inflationary signals. Though, typically, foregrounds are separated from primordial signals using the foregrounds’ different frequency dependence, in this paper we investigate instead the extent to which the Galactic dust B-modes’ statistical anisotropy can be used to distinguish them from inflationary B-modes, building on the work of Kamionkowski and Kovetz (2014). In our work, we extend existing anisotropy estimators and apply them to simulations of polarized dust to forecast their performance for future experiments. Considering the application of this method as a null-test for dust contamination to CMB-S4, we find that we can detect residual dust levels corresponding to r ~ 0.001 at 2σ, which implies that statistical anisotropy estimators will be a powerful diagnostic for foreground residuals (though our results show some dependence on the dust simulation used). Finally, considering applications beyond a simple null test, we demonstrate how anisotropy statistics can be used to construct an estimate of the dust B-mode map, which could potentially be used to clean the B-mode sky.

79 ASTRONOMY AND ASTROPHYSICS↗

Advanced Techniques for Assessment of Postural and Locomotor Ataxia, Spatial Orientation, and Gaze Stability

In addition to adapting to microgravity, major neurovestibular problems of space flight include postflight difficulties with standing, walking, turning corners, and other activities that require stable upright posture and gaze stability. These difficulties inhibit astronauts' ability to stand or escape from their vehicle during emergencies. The long-ter7n goal of the NSBRI is the development of countermeasures to ameliorate the effects of long duration space flight. These countermeasures must be tested with valid and reliable tools. This project aims to develop quantitative, parametric approaches for assessing gaze stability and spatial orientation during normal gait and when gait is perturbed. Two of this year's most important findings concern head fixation distance and ideal trajectory analysis. During a normal cycle of walking the head moves up and down linearly. A simultaneous angular pitching motion of the head keeps it aligned toward an imaginary point in space at a distance of about one meter in front of a subject and along the line of march. This distance is called the head fixation distance. Head fixation distance provides the fundamental framework necessary for understanding the functional significance of the vestibular reflexes that couple head motion to eye motion. This framework facilitates the intelligent design of counter-measures for the effects of exposure to microgravity upon the vestibular ocular reflexes. Ideal trajectory analysis is a simple candidate countermeasure based upon quantifying body sway during repeated up and down stair stepping. It provides one number that estimates the body sway deviation from an ideal sinusoidal body sway trajectory normalized on the subject's height. This concept has been developed with NSBRI funding in less than one year. These findings are explained in more detail below. Compared to assessments of the vestibuo-ocular reflex, analysis of vestibular effects on locomotor function is relatively less well developed and quantified. We are improving this situation by applying methodologies such as nonlinear orbital stability to quantify responses and by using multivariate statistical approaches to link together the responses across separate tests. In this way we can exploit the information available and increase the ability to discriminate between normal and pathological responses. Measures of stability and orientation are compared to measures such as dynamic visual acuity and with balance function tests. The responses of normal human subjects and of patients having well documented pathophysiologies are being characterized. When these studies are completed, we should have a clearer idea about normal and abnormal patterns of eye, head, and body movements during locomotion and their stability in a wide range of environments. We plan eventually to use this information to validate the efficacy of candidate neurovestibular and neuromuscular rehabilitative techniques. Some representative studies made during this year are summarized.

Wall, Conrad., III↗