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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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At least 451 records · Page 25
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

A multidimensional model of the effect of gravity on the spatial orientation of the monkey

A "sensory conflict" model of spatial orientation was developed. This mathematical model was based on concepts derived from observer theory, optimal observer theory, and the mathematical properties of coordinate rotations. The primary hypothesis is that the central nervous system of the squirrel monkey incorporates information about body dynamics and sensory dynamics to develop an internal model. The output of this central model (expected sensory afference) is compared to the actual sensory afference, with the difference defined as "sensory conflict." The sensory conflict information is, in turn, used to drive central estimates of angular velocity ("velocity storage"), gravity ("gravity storage"), and linear acceleration ("acceleration storage") toward more accurate values. The model successfully predicts "velocity storage" during rotation about an earth-vertical axis. The model also successfully predicts that the time constant of the horizontal vestibulo-ocular reflex is reduced and that the axis of eye rotation shifts toward alignment with gravity following postrotatory tilt. Finally, the model predicts the bias, modulation, and decay components that have been observed during off-vertical axis rotations (OVAR).

NASA Discipline Neuroscience↗
DOE OSTI2025

A consensus mathematical model of vaccine-induced antibody dynamics for multiple vaccine platforms and pathogens

Introduction: Vaccine platforms used in successful, licensed vaccines have varied among pathogens. However, antibody level is still the main clinical correlate of protection in most approved vaccines. Decisions as to the best vaccine platform to pursue for a given pathogen may be informed through improved understanding of the process of antibody generation and its temporal dynamics, as well as the relationship between these processes and the type of vaccine. Methods: We have analyzed the dynamics of antibody generation for different vaccine platforms against diverse pathogens, and developed a consensus mathematical model that captures antibody dynamics across these diverse systems. Initially, the model was fitted to a rich dataset of antibody and immune cell concentrations in a SARS-CoV-2 vaccine experiment. We then used concepts from machine learning, such as transfer learning, to apply the same model to a variety of systems, involving different pathogens, vaccine platforms, and booster dose use/timing, fixing most parameter values relating to the dynamics of the immune system. Results: The model includes B cell proliferation and differentiation, as well as the generation of plasma cells, which secrete large amounts of antibody, and memory B cells. Overall, the model describes antibody generation in all systems tested well and shows that the main differences across platforms are related to the dynamics of antigen presentation. Discussion: This model can be used to predict antibody generation in pairs of vaccine platform/pathogen, allowing for the use of in silico results to narrow down experimental burden in vaccine development.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1993

Alveolar ventilation to perfusion heterogeneity and diffusion impairment in a mathematical model of gas exchange

This study describes a two-compartment model of pulmonary gas exchange in which alveolar ventilation to perfusion (VA/Q) heterogeneity and impairment of pulmonary diffusing capacity (D) are simultaneously taken into account. The mathematical model uses as input data measurements usually obtained in the lung function laboratory. It consists of two compartments and an anatomical shunt. Each compartment receives fractions of alveolar ventilation and blood flow. Mass balance equations and integration of Fick's law of diffusion are used to compute alveolar and blood O2 and CO2 values compatible with input O2 uptake and CO2 elimination. Two applications are presented. The first is a method to partition O2 and CO2 alveolar-arterial gradients into VA/Q and D components. The technique is evaluated in data of patients with chronic obstructive pulmonary disease (COPD). The second is a theoretical analysis of the effects of blood flow variation in alveolar and blood O2 partial pressures. The results show the importance of simultaneous consideration of D to estimate VA/Q heterogeneity in patients with diffusion impairment. This factor plays an increasing role in gas alveolar-arterial gradients as severity of COPD increases. Association of VA/Q heterogeneity and D may produce an increase of O2 arterial pressure with decreasing QT which would not be observed if only D were considered. We conclude that the presented computer model is a useful tool for description and interpretation of data from COPD patients and for performing theoretical analysis of variables involved in the gas exchange process.

NASA Discipline Environmental Health↗
NASA NTRS2005

Fitting Nonlinear Curves by use of Optimization Techniques

MULTIVAR is a FORTRAN 77 computer program that fits one of the members of a set of six multivariable mathematical models (five of which are nonlinear) to a multivariable set of data. The inputs to MULTIVAR include the data for the independent and dependent variables plus the user s choice of one of the models, one of the three optimization engines, and convergence criteria. By use of the chosen optimization engine, MULTIVAR finds values for the parameters of the chosen model so as to minimize the sum of squares of the residuals. One of the optimization engines implements a routine, developed in 1982, that utilizes the Broydon-Fletcher-Goldfarb-Shanno (BFGS) variable-metric method for unconstrained minimization in conjunction with a one-dimensional search technique that finds the minimum of an unconstrained function by polynomial interpolation and extrapolation without first finding bounds on the solution. The second optimization engine is a faster and more robust commercially available code, denoted Design Optimization Tool, that also uses the BFGS method. The third optimization engine is a robust and relatively fast routine that implements the Levenberg-Marquardt algorithm.

Hill, Scott A.↗
NASA NTRS1977

A life cycle cost economics model for projects with uniformly varying operating costs

A mathematical model is developed for calculating the life cycle costs for a project where the operating costs increase or decrease in a linear manner with time. The life cycle cost is shown to be a function of the investment costs, initial operating costs, operating cost gradient, project life time, interest rate for capital and salvage value. The results show that the life cycle cost for a project can be grossly underestimated (or overestimated) if the operating costs increase (or decrease) uniformly over time rather than being constant as is often assumed in project economic evaluations. The following range of variables is examined: (1) project life from 2 to 30 years; (2) interest rate from 0 to 15 percent per year; and (3) operating cost gradient from 5 to 90 percent of the initial operating costs. A numerical example plus tables and graphs is given to help calculate project life cycle costs over a wide range of variables.

Remer, D. S.↗
NASA NTRS1984

A mathematical model of the UH-60 helicopter

This report documents the revisions made to a ten-degree-of-freedom, full-flight envelope, generic helicopter mathematical model to represent the UH-60 helicopter accurately. The major modifications to the model include fuselage aerodynamic force and moment equations specific to the UH-60, a canted tail rotor, a horizontal stabilator with variable incidence, and a pitch bias actuator (PBA). In addition, this report presents a full set of parameters and numerical values which describe the helicopter configuration and physical characteristics. Model validation was accomplished by comparison of trim and stability derivative data generated from the UH-60 math model with data generated from a similar total force and moment math model.

Hilbert, K. B.↗
NASA NTRS1990

Dynamic test input generation for multiple-fault isolation

Recent work is Causal Reasoning has provided practical techniques for multiple fault diagnosis. These techniques provide a hypothesis/measurement diagnosis cycle. Using probabilistic methods, they choose the best measurements to make, then update fault hypotheses in response. For many applications such as computers and spacecraft, few measurement points may be accessible, or values may change quickly as the system under diagnosis operates. In these cases, a hypothesis/measurement cycle is insufficient. A technique is presented for a hypothesis/test-input/measurement diagnosis cycle. In contrast to generating tests a priori for determining device functionality, it dynamically generates tests in response to current knowledge about fault probabilities. It is shown how the mathematics previously used for measurement specification can be applied to the test input generation process. An example from an efficient implementation called Multi-Purpose Causal (MPC) is presented.

Schaefer, Phil↗
NASA NTRS1994

AutoClass: A Bayesian Approach to Classification

We describe a Bayesian approach to the untutored discovery of classes in a set of cases, sometimes called finite mixture separation or clustering. The main difference between clustering and our approach is that we search for the "best" set of class descriptions rather than grouping the cases themselves. We describe our classes in terms of a probability distribution or density function, and the locally maximal posterior probability valued function parameters. We rate our classifications with an approximate joint probability of the data and functional form, marginalizing over the parameters. Approximation is necessitated by the computational complexity of the joint probability. Thus, we marginalize w.r.t. local maxima in the parameter space. We discuss the rationale behind our approach to classification. We give the mathematical development for the basic mixture model and describe the approximations needed for computational tractability. We instantiate the basic model with the discrete Dirichlet distribution and multivariant Gaussian density likelihoods. Then we show some results for both constructed and actual data.

Stutz, John↗
DOE OSTI2025

Determining the Axes of a Range-Doppler Image

Synthetic aperture radar (SAR) images formed with dechirp-on-receive data collection and rectangular format processing algorithm are the result of a two-dimensional discrete Fourier transform (DFT) applied to sampled data. There are several steps required to compute the range and Doppler values associated with each pixel in a SAR range-Doppler image. This memo walks readers through the process.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

Get Non-Real: Randomized Sketching for High-Dimensional Non-Real Valued Data (Final Report)

In our final report for DE-C0022186, we describe the work we did on this grant towards the goals we proposed. Our first goal was characterizing fundamental limits for sketching of discrete high-dimensional matrices with low-dimensional structures. Our second main goal was designing algorithms for data reconstruction from sketches. We focus on approaches that are either specifically designed for non-real-valued data (binary, finite field) or that will translate more readily to that setting.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1972

Comparison of satellite theories

The accuracy of five mathematical models in computing a nominal orbit for the Vanguard 2 satellite by using a position velocity vector is considered. Either numerical integration or analytical theories are used in all models as well as the same force model that corresponds to a potential with the zonal harmonics to order four. The amounts of spread in the values of the total energy and the z-component of the angular momentum for a set of times are considered as measures of accuracy.

Hertz, H. G.↗
NASA NTRS1976

Analytical and experimental studies of an optimum multisegment phased liner noise suppression concept

Results are presented from detailed analytical studies made to define methods for obtaining improved multisegment lining performance by taking advantage of relative placement of each lining segment. Properly phased liner segments reflect and spatially redistribute the incident acoustic energy and thus provide additional attenuation. A mathematical model was developed for rectangular ducts with uniform mean flow. Segmented acoustic fields were represented by duct eigenfunction expansions, and mode-matching was used to ensure continuity of the total field. Parametric studies were performed to identify attenuation mechanisms and define preliminary liner configurations. An optimization procedure was used to determine optimum liner impedance values for a given total lining length, Mach number, and incident modal distribution. Optimal segmented liners are presented and it is shown that, provided the sound source is well-defined and flow environment is known, conventional infinite duct optimum attenuation rates can be improved. To confirm these results, an experimental program was conducted in a laboratory test facility. The measured data are presented in the form of analytical-experimental correlations. Excellent agreement between theory and experiment verifies and substantiates the analytical prediction techniques. The results indicate that phased liners may be of immediate benefit in the development of improved aircraft exhaust duct noise suppressors.

Sawdy, D. T.↗
DOE OSTI2025

A Class of Sparse Johnson–Lindenstrauss Transforms and Analysis of their Extreme Singular Values

The Johnson–Lindenstrauss (JL) lemma is a powerful tool for dimensionality reduction in modern algorithm design. The lemma states that any set of high-dimensional points in a Euclidean space can be projected into lower dimensions while approximately preserving pairwise Euclidean distances. Random matrices satisfying this lemma are called JL transforms (JLTs). Inspired by existing $s$-hashing JLTs with exactly $s$ nonzero elements on each column, the present work introduces an ensemble of sparse matrices encompassing so-called $s$-hashing-like matrices whose expected number of nonzero elements on each column is $s$. The independence of the sub-Gaussian entries of these matrices and the knowledge of their exact distribution play an important role in their analyses. Using properties of independent sub-Gaussian random variables, these matrices are demonstrated to be JLTs, and their smallest nontrivial singular values and largest singular values are estimated nonasymptotically using a technique from geometric functional analysis. As the dimensions of the matrix grow to infinity, these singular values are proved to converge almost surely to fixed quantities (by using the universal Bai–Yin law) and in distribution to the Gaussian orthogonal ensemble Tracy–Widom law after proper rescalings. Understanding the behaviors of extreme singular values is important in general because they are often used to define a measure of stability of matrix algorithms. For example, JLTs were recently used in derivative-free optimization algorithmic frameworks to select random subspaces in which are constructed random models or poll directions to achieve scalability, and hence estimating their smallest singular value in particular helps determine the dimension of these subspaces.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

On the practical usefulness of the Hardware Efficient Ansatz

Variational Quantum Algorithms (VQAs) and Quantum Machine Learning (QML) models train a parametrized quantum circuit to solve a given learning task. The success of these algorithms greatly hinges on appropriately choosing an ansatz for the quantum circuit. Perhaps one of the most famous ansatzes is the one-dimensional layered Hardware Efficient Ansatz (HEA), which seeks to minimize the effect of hardware noise by using native gates and connectives. The use of this HEA has generated a certain ambivalence arising from the fact that while it suffers from barren plateaus at long depths, it can also avoid them at shallow ones. In this work, we attempt to determine whether one should, or should not, use a HEA. We rigorously identify scenarios where shallow HEAs should likely be avoided (e.g., VQA or QML tasks with data satisfying a volume law of entanglement). More importantly, we identify a Goldilocks scenario where shallow HEAs could achieve a quantum speedup: QML tasks with data satisfying an area law of entanglement. We provide examples for such scenario (such as Gaussian diagonal ensemble random Hamiltonian discrimination), and we show that in these cases a shallow HEA is always trainable and that there exists an anti-concentration of loss function values. Our work highlights the crucial role that input states play in the trainability of a parametrized quantum circuit, a phenomenon that is verified in our numerics.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1976

On the applicability of integrated circuit technology to general aviation orientation estimation

The criteria of the significant value of the panel instruments used in general aviation were examined and kinematic equations were added for comparison. An instrument survey was performed to establish the present state of the art in linear and angular accelerometers, pressure transducers, and magnetometers. A very preliminary evaluation was done of the computers available for data evaluation and estimator mechanization. The mathematical model of a light twin aircraft employed in the evaluation was documented, the results of the sensor survey and the results of the design studies were presented.

Debra, D. B.↗
NASA NTRS1980

Determination of the complex refractive index and size distribution of atmospheric particulates from bistatic-monostatic lidar and solar radiometer measurements

A method is presented for inferring both the size distribution and the complex refractive index of atmospheric particulates from combined bistatic-monostatic lidar and solar radiometer observations. The basic input measurements are spectral optical depths at several visible and near-infrared wavelengths as obtained with a solar radiometer and backscatter and angular scatter coefficients as obtained from a biostatic-monostatic lidar. The spectral optical depth measurements obtained from the radiometer are mathematically inverted to infer a columnar particulate size distribution. Advantage is taken of the fact that the shape of the size distribution obtained by inverting the particulate optical depth is relatively insensitive to the particle refractive index assumed in the inversion. Bistatic-monostatic angular scatter and backscatter lidar data are then processed to extract an optimum value for the particle refractive index subject to the constraint that the shape of the particulate size distribution be the same as that inferred from the solar radiometer data. Specifically, the scattering parameters obtained from the bistatic-monostatic lidar data are compared with corresponding theoretical computations made for various assumed refractive index values. That value which yields best agreement, in a weighted least squares sense, is selected as the optimal refractive index estimate. The results of this procedure applied to a set of simulated measurements as well as to measurements collected on two separate days are presented and discussed.

Reagan, J. A.↗
NASA NTRS1992

Experimental validation of clock synchronization algorithms

The objective of this work is to validate mathematically derived clock synchronization theories and their associated algorithms through experiment. Two theories are considered, the Interactive Convergence Clock Synchronization Algorithm and the Midpoint Algorithm. Special clock circuitry was designed and built so that several operating conditions and failure modes (including malicious failures) could be tested. Both theories are shown to predict conservative upper bounds (i.e., measured values of clock skew were always less than the theory prediction). Insight gained during experimentation led to alternative derivations of the theories. These new theories accurately predict the behavior of the clock system. It is found that a 100 percent penalty is paid to tolerate worst-case failures. It is also shown that under optimal conditions (with minimum error and no failures) the clock skew can be as much as three clock ticks. Clock skew grows to six clock ticks when failures are present. Finally, it is concluded that one cannot rely solely on test procedures or theoretical analysis to predict worst-case conditions.

Palumbo, Daniel L.↗
NASA NTRS1996

X-29A Lateral-Directional Stability and Control Derivatives Extracted From High-Angle-of-Attack Flight Data

The lateral-directional stability and control derivatives of the X-29A number 2 are extracted from flight data over an angle-of-attack range of 4 degrees to 53 degrees using a parameter identification algorithm. The algorithm uses the linearized aircraft equations of motion and a maximum likelihood estimator in the presence of state and measurement noise. State noise is used to model the uncommanded forcing function caused by unsteady aerodynamics over the aircraft at angles of attack above 15 degrees. The results supported the flight-envelope-expansion phase of the X-29A number 2 by helping to update the aerodynamic mathematical model, to improve the real-time simulator, and to revise flight control system laws. Effects of the aircraft high gain flight control system on maneuver quality and the estimated derivatives are also discussed. The derivatives are plotted as functions of angle of attack and compared with the predicted aerodynamic database. Agreement between predicted and flight values is quite good for some derivatives such as the lateral force due to sideslip, the lateral force due to rudder deflection, and the rolling moment due to roll rate. The results also show significant differences in several important derivatives such as the rolling moment due to sideslip, the yawing moment due to sideslip, the yawing moment due to aileron deflection, and the yawing moment due to rudder deflection.

Iliff, Kenneth W.↗