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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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Technique is described for adjustment of engineering response information by broadening the application of statistical subjective stimuli theory. The study is specifically concerned with a mathematical evaluation of the expected probability of relative occurrence which can be identified by comparison rating techniques.
The statistical nature of vibroacoustical processes in transmission gears was studied using mathematical models. Special attention was given to high frequency components of vibroacoustical processes generated by spur gearing. Equations are given for describing torsional and tranverse vibrations of pairs of gear wheels when meshing, taking into account the flexibility of their supports.
Four-band multispectral photography obtained from an aerial platform at an altitude of about 10,000 feet has been utilized to measure near-surface turbidity at numerous sampling sites in the Ross Barnett Reservoir, Mississippi. Correlation of the photographs with turbidity measurements has been accomplished via an empirical mathematical model which depends upon visual color recognition when the composited photographs are examined on either an I squared S model 600 or a Spectral Data model 65 color-additive viewer. The mathematical model was developed utilizing least-squares, iterative, and standard statistical methods and includes a time-dependent term related to sun angle. This model is consistent with information obtained from two overflights of the target area - July 30, 1973 and October 30, 1973 - and now is being evaluated with regard to information obtained from a third overflight on November 8, 1974.
Recent research conducted under NASA LaRC's Creativity and Innovation Program has led to the development of an initial approach for a hierarchical fracture mechanics. This methodology unites failure mechanisms occurring at different length scales and provides a framework for a physics-based theory of fracture. At the nanoscale, parametric molecular dynamic simulations are used to compute the energy associated with atomic level failure mechanisms. This information is used in a mesoscale percolation model of defect coalescence to obtain statistics of fracture paths and energies through Monte Carlo simulations. The mathematical structure of predicted crack paths is described using concepts of fractal geometry. The non-integer fractal dimension relates geometric and energy measures between meso- and macroscales. For illustration, a fractal-based continuum strain energy release rate is derived for inter- and transgranular fracture in polycrystalline metals.
Throughout the history of the International Space Station (ISS), crews on board have conducted a variety of scientific research and educational activities. Well into the second year of full utilization of the ISS laboratory, the trend of scientific accomplishments and educational opportunities continues to grow. More than 1500 investigations have been conducted on the ISS since the first module launched in 1998, with over 700 scientific publications. The ISS provides a unique environment for research, international collaboration and educational activities that benefit humankind. This paper will provide an up to date summary of key investigations, facilities, publications, and benefits from ISS research that have developed over the past year. Discoveries in human physiology and nutrition have enabled astronauts to return from ISS with little bone loss, even as scientists seek to better understand the new puzzle of "ocular syndrome" affecting the vision of up to half of astronauts. The geneLAB campaign will unify life sciences investigations to seek genomic, proteomic, and metabolomics of the effect of microgravity on life as a whole. Combustion scientists identified a new "cold flame" phenomenon that has the potential to improve models of efficient combustion back on Earth. A significant number of instruments in Earth remote sensing and astrophysics are providing new access to data or nearing completion for launch, making ISS a significant platform for understanding of the Earth system and the universe. In addition to multidisciplinary research, the ISS partnership conducts a myriad of student led research investigations and educational activities aimed at increasing student interest in science, technology, engineering and mathematics (STEM). Over the past year, the ISS partnership compiled new statistics of the educational impact of the ISS on students around the world. More than 43 million students, from kindergarten to graduate school, with more than 28 million teachers located in 49 countries have participated in some aspect of ISS educational activities. These activities include student-developed investigations, education competitions, and classroom versions of ISS investigations, participating in ISS investigator experiments, ISS hardware development, educational demonstrations, and cultural activities. Through the many inquiry-based educational activities, students and teachers are encouraged to participate in the ISS program thus motivating the next generation of students to pursue careers in STEM.
We develop a statistical framework for the dynamical closure of spatiotemporal dynamics governed by partial differential equations. Employing the mathematical framework of quantum mechanics to embed the original classical dynamics into a quantum mechanical representation, we use the space of quantum density operators to model the unresolved degrees of freedom of the original dynamics in a statistical sense, and the framework of quantum measurement to predict their contributions to the resolved dynamics. The embedded dynamics is discretized by a positivity preserving process, leading to a compressed representation that is invariant under the dynamical symmetries of the resolved dynamics. We present a data based formulation of the closure scheme and apply it to a closure problem for the shallow water equations. The numerical results demonstrate that our closure model can accurately predict the main features of the true dynamics, including for out of sample initial conditions.
Equations of state (EOSs) are a key component in running hydrodynamic simulations as they relate the thermodynamic states for the material. The Davis reactants EOS is commonly used for modeling high explosives (HEs), and the EOS model parameters are calibrated using material specific data. The calibrations are often performed with uncertainty quantification via Bayesian inference to account for uncertainty in the data and generate ensembles of likely parameters. However, there are relatively few HE data sets to use for calibration and many are historical and lack error information. In this work, we simultaneously calibrate the Davis reactants EOS model parameters and unknown data error terms for the high explosive PBX 9501. To quantify the uncertainty in the models and the data, we use a Bayesian framework for the calibration and compute the hierarchical Bayesian posterior distribution with both a posteriori maximization approach and Markov Chain Monte Carlo. In general, we find that, given our assumptions, the two approaches result in similar calibrated parameters, posterior covariance matrices, and insights about the parameters but that the posterior maximization requires far less computational resources.
Report describes application of order statistics to analysis of failure modes in redundant systems. Report provides detailed mathematical discussion of approach, accompanied by graphs and equations. Techniques are relevant to process that demand high reliability, such as manufacture of dangerous chemicals. It also includes discussion of quad-redundant system.
CARES calculates fast-fracture reliability or failure probability of macroscopically isotropic ceramic components. Program uses results from commercial structural-analysis program (MSC/NASTRAN or ANSYS) to evaluate reliability of component in presence of inherent surface- and/or volume-type flaws. Computes measure of reliability by use of finite-element mathematical model applicable to multiple materials in sense model made function of statistical characterizations of many ceramic materials. Reliability analysis uses element stress, temperature, area, and volume outputs, obtained from two-dimensional shell and three-dimensional solid isoparametric or axisymmetric finite elements. Written in FORTRAN 77.
An important part of building high fidelity mathematical models based on measured data is calculating the accuracy associated with statistical estimates of the model parameters. Indeed, without some idea of the accuracy of parameter estimates, the estimates themselves have limited value. In this work, an expression based on theoretical analysis was developed to properly compute parameter accuracy measures for maximum likelihood estimates with colored residuals. This result is important because experience from the analysis of measured data reveals that the residuals from maximum likelihood estimation are almost always colored. The calculations involved can be appended to conventional maximum likelihood estimation algorithms. Simulated data runs were used to show that the parameter accuracy measures computed with this technique accurately reflect the quality of the parameter estimates from maximum likelihood estimation without the need for analysis of the output residuals in the frequency domain or heuristically determined multiplication factors. The result is general, although the application studied here is maximum likelihood estimation of aerodynamic model parameters from flight test data.
The system of two-mode fields interacting with atom by means of multiphotons is addressed, and the non-classical statistic quality of two-mode fields with interaction is discussed. Through mathematical calculation, some new rules of non-classical effects of two-mode fields which evolue with time, are established.
An important part of building mathematical models based on measured data is calculating the accuracy associated with statistical estimates of the model parameters. Indeed, without some idea of this accuracy, the parameter estimates themselves have limited value. In this work, an expression for computing quantitatively correct parameter accuracy measures for maximum likelihood parameter estimates with colored residuals is developed and validated. This result is important because experience in analyzing flight test data reveals that the output residuals from maximum likelihood estimation are almost always colored. The calculations involved can be appended to conventional maximum likelihood estimation algorithms. Monte Carlo simulation runs were used to show that parameter accuracy measures from the new technique accurately reflect the quality of the parameter estimates from maximum likelihood estimation without the need for correction factors or frequency domain analysis of the output residuals. The technique was applied to flight test data from repeated maneuvers flown on the F-18 High Alpha Research Vehicle (HARV). As in the simulated cases, parameter accuracy measures from the new technique were in agreement with the scatter in the parameter estimates from repeated maneuvers, while conventional parameter accuracy measures were optimistic.
An important put of building mathematical models based on measured date is calculating the accuracy associated with statistical estimates of the model parameters. Indeed, without some idea of this accuracy, the parameter estimates themselves have limited value. An expression is developed for computing quantitatively correct parameter accuracy measures for maximum likelihood parameter estimates when the output residuals are colored. This result is important because experience in analyzing flight test data reveals that the output residuals from maximum likelihood estimation are almost always colored. The calculations involved can be appended to conventional maximum likelihood estimation algorithms. Monte Carlo simulation runs were used to show that parameter accuracy measures from the new technique accurately reflect the quality of the parameter estimates from maximum likelihood estimation without the need for correction factors or frequency domain analysis of the output residuals. The technique was applied to flight test data from repeated maneuvers flown on the F-18 High Alpha Research Vehicle. As in the simulated cases, parameter accuracy measures from the new technique were in agreement with the scatter in the parameter estimates from repeated maneuvers, whereas conventional parameter accuracy measures were optimistic.
Exposures in space consist of low-level background components from galactic cosmic rays (GCR), occasional intense-energetic solar-particle events, periodic passes through geomagnetic-trapped radiation, and exposure from possible onboard nuclear-propulsion engines. Risk models for astronaut exposure from such diverse components and modalities must be developed to assure adequate protection in future NASA missions. The low-level background exposures (GCR), including relativistic heavy ions (HZE), will be the ultimate limiting factor for astronaut career exposure. We consider herein a two-mutation, initiation-promotion, radiation-carcinogenesis model in mice in which the initiation stage is represented by a linear kinetics model of cellular repair/misrepair, including the track-structure model for heavy ion action cross-sections. The model is validated by comparison with the harderian gland tumor experiments of Alpen et al. for various ion beams. We apply the initiation-promotion model to exposures from galactic cosmic rays, using models of the cosmic-ray environment and heavy ion transport, and consider the effects of the age of the mice prior to and after the exposure and of the length of time in space on predictions of relative risk. Our results indicate that biophysical models of age-dependent radiation hazard will provide a better understanding of GCR risk than models that rely strictly on estimates of the initial slopes of these radiations.
Abstract Graph theory has a long history in chemistry. Yet as the breadth and variety of chemical data is rapidly changing, so too do graph encoding methods and analyses that yield qualitative and quantitative insights. Using illustrative cases within a basic mathematical framework, we showcase modern chemical graph theory's utility in Chemists' analysis and model development toolkit. The encoding of both experimental and simulation data is discussed at various levels of granularity of information. This is followed by a discussion of the two major classes of graph theoretical analyses: identifying connectivity patterns and partitioning methods. Measures, metrics, descriptors, and topological indices are then introduced with an emphasis upon enhancing interpretability and incorporation into physical models. Challenging data cases are described that include strategies for studying time dependence. Throughout, we incorporate recent advancements in computer science and applied mathematics that are propelling chemical graph theory into new domains of chemical study. This article is categorized under: Molecular and Statistical Mechanics > Molecular Dynamics and Monte‐Carlo Methods Structure and Mechanism > Computational Materials Science Structure and Mechanism > Molecular Structures
Elevated-temperature tensile testing of commercially pure titanium (CP Ti) Grade 2 was conducted for as-received commercially produced sheet and following thermal exposure at 550 and 650 K (531 and 711 F) for times up to 5000 h. The tensile testing revealed some statistical differences between the 11 thermal treatments, but most thermal treatments were statistically equivalent. Previous data from room temperature tensile testing was combined with the new data to allow regression and development of mathematical models relating tensile properties to temperature and thermal exposure. The results indicate that thermal exposure temperature has a very small effect, whereas the thermal exposure duration has no statistically significant effects on the tensile properties. These results indicate that CP Ti Grade 2 will be thermally stable and suitable for long-duration space missions.
Criticism of a statistical approach used by Dasgupta (1972) in analyzing Snyder's (1959) chemical data for minerals from the Duluth Complex in Minnesota. Apart from obvious mathematical objections to citing correlation coefficients to four significant figures from Snyder's relatively inaccurate analytical data, several more fundamental criticisms are leveled at the statistical approach of Dasgupta. These relate to compositional zoning and disequilibrium in the minerals, inhomogeneities of the samples caused by inclusions and exsolved phases, measured site population data for the major cations in olivines and pyroxenes, and the importance of coupled substitutions in the crystal structures. It is concluded that the crystal field predictions of relative enrichments of Ni(2+) and Co(2+) ions in olivine and pyroxene structures have not been disproved by Dasgupta's statistical approach.
The phases of solar cycle minima are compared with an 'ideal' sunspot cycle of the mean period of 11.4 years. The observed departures from the ideal model form a pattern over 16 cycles (approximately 178 years) which appears to be repeated over the next 16 cycles. Both in mathematic sign and amplitude the two 178-year cycles are coherent to a statistically significant level of 98 percent. If true, this furnishes a basis for predicting sunspot cycle minima.