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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 73 records · Page 4

All sources NASA NTRS DOE OSTI

NASA NTRS1990

Concerning the extrapolation of solar nonlinear force-free magnetic fields

This paper contains a review and discussion of the mathematical basis of the extrapolation techniques involved in using photospheric vector magnetograms to obtain the coronal field above the surface. The two basic techniques employing the Cauchy initial value problem and the variational techniques are reviewed in terms of the mathematical and practical applications. A short review is presented of the current research on numerical modeling techniques in the area of extrapolating vector magnetograms; specifically, algorithms to extrapolate nonlinear force-free magnetic fields from the photosphere are considered.

Gary, G. Allen↗

NASA NTRS1993

Things that go bump in the light - On the optical specification of contact severity

Psychologists are intrigued with the idea that optical variables can specify not only the time until an object impacts an observer but also the severity of the impact. However, the mapping between the optical variables and the kinematic variables has been misstated, erroneously implying that there exist critical values of the optical variables used for locomotion and control. In this commentary, the mathematical relationship between the optical and kinematic variables is reexamined and the erroneous assumptions that have led to the proposal of critical values are shown. Also examined are the empirical data on deceleration to approach to assess whether the proposed optical variables are likely candidates for control strategies. Finally, problems associated with numerical approximations to dynamic systems, particularly when analytic solutions exist, are discussed.

Kaiser, Mary K.↗

NASA NTRS1963

A Hypergeometric Mean Value

Generalization of hypergeometric mean value from hypergeometric function without loss of homogeneity - derivation and properties of hypergeometric mean value

HYPERGEOMETRIC FUNCTION↗

NASA NTRS1976

Stability of flow of a thermoviscoelastic fluid between rotating coaxial circular cylinders

The stability problem of thermoviscoelastic fluid flow between rotating coaxial cylinders is investigated using nonlinear thermoviscoelastic constitutive equations due to Eringen and Koh. The velocity field is found to be identical with that of the classical viscous case and the case of the viscoelastic fluid, but the temperature and pressure fields are found to be different. By imposing some physically reasonable mechanical and geometrical restrictions on the flow, and by a suitable mathematical analysis, the problem is reduced to a characteristic value problem. The resulting problem is solved and stability criteria are obtained in terms of critical Taylor numbers. In general, it is found that thermoviscoelastic fluids are more stable than classical viscous fluids and viscoinelastic fluids under similar conditions.

Ghandour, N. N.↗

NASA NTRS1978

Comprehensive thermoelectric properties of n- and p-type 78a/o Si - 22a/o Ge alloy

The time and temperature dependence of the thermoelectric properties on n- and p-type 78 a/o Si - 22 a/o Ge alloy are presented in detail for the range of temperatures of zero to 1000 C and operating times up to twelve years. The mechanisms responsible for the time dependence of the properties are discussed and mathematical models used in the derivation of the property values from experimental data are presented. The thermoelectric properties for each polarity type of the alloy are presented as a function of temperature for various operating times.

Raag, V.↗

NASA NTRS1985

Measures of measurement adequacy

The adequacy of a measurement instrument is often characterized in terms of the precision, accuracy, and confidence that can be assigned to the measurements that it produces. The accuracy of the measurement may be defined as the size of the difference between the true and measured values. The precision of the system over a large number of measurements may be defined in terms of the sample standarad deviation. The confidence in an interval-values measurement may be defined as the probability that this interval contains the true value. These concepts are discussed in terms of their mathematical solutions.

Source record↗

NASA NTRS1988

Dispositional logic

The applicability of conventional mathematical analysis (based on the combination of two-valued logic and probability theory) to problems in which human judgment, perception, or emotions play significant roles is considered theoretically. It is shown that dispositional logic, a branch of fuzzy logic, has particular relevance to the common-sense reasoning typical of human decision-making. The concepts of dispositionality and usuality are defined analytically, and a dispositional conjunctive rule and dispositional modus ponens are derived.

Le Balleur, J. C.↗

NASA NTRS1991

Analysis Of Lock Detection In Costas Loops

Report presents analysis of detection of phase lock in Costas loops, used in coherent binary-phase-shift-keying communication systems to track both subcarrier and suppressed carrier signals. Detection of phase lock important part of operation and monitoring of operation of Costas or other tracking loop, provides insight into behavior of loop in real time. Focuses on effects of phase jitter and correlation between samples of phase error in all-digital Costas loop, in which lock detection implemented via algorithm. Applicable to both sinusoidal and square-law carrier signals, incorporates new mathematical models of square-law and absolute-value detectors.

Mileant, Alexander↗

NASA NTRS1993

The complex structured singular value

A tutorial introduction to the complex structured singular value (mu) is presented, with an emphasis on the mathematical aspects of mu. The mu-based methods discussed here have been useful for analyzing the performance and robustness properties of linear feedback systems. Several tests for robust stability and performance with computable bounds for transfer functions and their state space realizations are compared, and a simple synthesis problem is studied. Uncertain systems are represented using linear fractional transformations which naturally unify the frequency-domain and state space methods.

Packard, A.↗

NASA NTRS1994

Real-time sensor data validation

This report describes the status of an on-going effort to develop software capable of detecting sensor failures on rocket engines in real time. This software could be used in a rocket engine controller to prevent the erroneous shutdown of an engine due to sensor failures which would otherwise be interpreted as engine failures by the control software. The approach taken combines analytical redundancy with Bayesian belief networks to provide a solution which has well defined real-time characteristics and well-defined error rates. Analytical redundancy is a technique in which a sensor's value is predicted by using values from other sensors and known or empirically derived mathematical relations. A set of sensors and a set of relations among them form a network of cross-checks which can be used to periodically validate all of the sensors in the network. Bayesian belief networks provide a method of determining if each of the sensors in the network is valid, given the results of the cross-checks. This approach has been successfully demonstrated on the Technology Test Bed Engine at the NASA Marshall Space Flight Center. Current efforts are focused on extending the system to provide a validation capability for 100 sensors on the Space Shuttle Main Engine.

Bickmore, Timothy W.↗

NASA NTRS2008

A New Bond Albedo for Performing Orbital Debris Brightness to Size Transformations

We have developed a technique for estimating the intrinsic size distribution of orbital debris objects via optical measurements alone. The process is predicated on the empirically observed power-law size distribution of debris (as indicated by radar RCS measurements) and the log-normal probability distribution of optical albedos as ascertained from phase (Lambertian) and range-corrected telescopic brightness measurements. Since the observed distribution of optical brightness is the product integral of the size distribution of the parent [debris] population with the albedo probability distribution, it is a straightforward matter to transform a given distribution of optical brightness back to a size distribution by the appropriate choice of a single albedo value. This is true because the integration of a powerlaw with a log-normal distribution (Fredholm Integral of the First Kind) yields a Gaussian-blurred power-law distribution with identical power-law exponent. Application of a single albedo to this distribution recovers a simple power-law [in size] which is linearly offset from the original distribution by a constant whose value depends on the choice of the albedo. Significantly, there exists a unique Bond albedo which, when applied to an observed brightness distribution, yields zero offset and therefore recovers the original size distribution. For physically realistic powerlaws of negative slope, the proper choice of albedo recovers the parent size distribution by compensating for the observational bias caused by the large number of small objects that appear anomalously large (bright) - and thereby skew the small population upward by rising above the detection threshold - and the lower number of large objects that appear anomalously small (dim). Based on this comprehensive analysis, a value of 0.13 should be applied to all orbital debris albedo-based brightness-to-size transformations regardless of data source. Its prima fascia genesis, derived and constructed from the current RCS to size conversion methodology (SiBAM Size-Based Estimation Model) and optical data reduction standards, assures consistency in application with the prior canonical value of 0.1. Herein we present the empirical and mathematical arguments for this approach and by example apply it to a comprehensive set of photometric data acquired via NASA's Liquid Mirror Telescopes during the 2000-2001 observing season.

Mulrooney, Mark K.↗

NASA NTRS2010

Spatial Standard Observer

The present invention relates to devices and methods for the measurement and/or for the specification of the perceptual intensity of a visual image. or the perceptual distance between a pair of images. Grayscale test and reference images are processed to produce test and reference luminance images. A luminance filter function is convolved with the reference luminance image to produce a local mean luminance reference image . Test and reference contrast images are produced from the local mean luminance reference image and the test and reference luminance images respectively, followed by application of a contrast sensitivity filter. The resulting images are combined according to mathematical prescriptions to produce a Just Noticeable Difference, JND value, indicative of a Spatial Standard Observer. SSO. Some embodiments include masking functions. window functions. special treatment for images lying on or near border and pre-processing of test images.

Watson, Andrw B.↗

NASA NTRS2012

Spatial Standard Observer

The present invention relates to devices and methods for the measurement and/or for the specification of the perceptual intensity of a visual image, or the perceptual distance between a pair of images. Grayscale test and reference images are processed to produce test and reference luminance images. A luminance filter function is convolved with the reference luminance image to produce a local mean luminance reference image. Test and reference contrast images are produced from the local mean luminance reference image and the test and reference luminance images respectively, followed by application of a contrast sensitivity filter. The resulting images are combined according to mathematical prescriptions to produce a Just Noticeable Difference, JND value, indicative of a Spatial Standard Observer, SSO. Some embodiments include masking functions, window functions, special treatment for images lying on or near borders and pre-processing of test images.

Watson, Andrew B.↗

DOE OSTI2024

A flexible class of priors for orthonormal matrices with basis function-specific structure

Statistical modeling of high-dimensional matrix-valued data motivates the use of a low-rank representation that simultaneously summarizes key characteristics of the data and enables dimension reduction. Low-rank representations commonly factor the original data into the product of orthonormal basis functions and weights, where each basis function represents an independent feature of the data. However, the basis functions in these factorizations are typically computed using algorithmic methods that cannot quantify uncertainty or account for basis function correlation structure a priori. While there exist Bayesian methods that allow for a common correlation structure across basis functions, empirical examples motivate the need for basis function-specific dependence structure. We propose a prior distribution for orthonormal matrices that can explicitly model basis function-specific structure. The prior is used within a general probabilistic model for singular value decomposition to conduct posterior inference on the basis functions while accounting for measurement error and fixed effects. We discuss how the prior specification can be used for various scenarios and demonstrate favorable model properties through synthetic data examples. Finally, we apply our method to two-meter air temperature data from the Pacific Northwest, enhancing our understanding of the Earth system’s internal variability.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1983

Multivalued-Velocity-Field Model of Turbulence

Report presents multi-valued-velocity model used in calculations of turbulence formation. Developed as part of continuing study of turbulent fluid motion, model expected to evolve into comprehensive mathematical tool to explain origin and effects of turbulence. Model has great theoretical and practical value in such fields as aerodynamics, meteorology, and combustion.

Zak, M. A.↗

NASA NTRS2003

Analytic Solution to the Problem of Aircraft Electric Field Mill Calibration

It is by no means a simple task to retrieve storm electric fields from an aircraft instrumented with electric field mill sensors. The presence of the aircraft distorts the ambient field in a complicated way. Before retrievals of the storm field can be made, the field mill measurement system must be "calibrated". In other words, a relationship between impressed (i.e., ambient) electric field and mill output must be established. If this relationship can be determined, it is mathematically inverted so that ambient field can be inferred from the mill outputs. Previous studies have primarily focused on linear theories where the relationship between ambient field and mill output is described by a "calibration matrix" M. Each element of the matrix describes how a particular component of the ambient field is enhanced by the aircraft. For example the product M(sub ix), E(sub x), is the contribution of the E(sub x) field to the i(th) mill output. Similarly, net aircraft charge (described by a "charge field component" E(sub q)) contributes an amount M(sub iq)E(sub q) to the output of the i(th) sensor. The central difficulty in obtaining M stems from the fact that the impressed field (E(sub x), E(sub y), E(sub z), E(sub q) is not known but is instead estimated. Typically, the aircraft is flown through a series of roll and pitch maneuvers in fair weather, and the values of the fair weather field and aircraft charge are estimated at each point along the aircraft trajectory. These initial estimates are often highly inadequate, but several investigators have improved the estimates by implementing various (ad hoc) iterative methods. Unfortunately, none of the iterative methods guarantee absolute convergence to correct values (i.e., absolute convergence to correct values has not been rigorously proven). In this work, the mathematical problem is solved directly by analytic means. For m mills installed on an arbitrary aircraft, it is shown that it is possible to solve for a single 2m-vector that provides all other needed variables (i.e., the unknown fair weather field, the unknown aircraft charge, and the unknown matrix M). Numerical tests of the solution, effects of measurement errors, and studies of solution non-uniqueness are ongoing as of this writing.

Koshak, William↗

NASA NTRS1972

An innovative approach to compensator design

The primary goal is to present for a control system a computer-aided-compensator design technique from a frequency domain point of view. The thesis for developing this technique is to describe the open loop frequency response by n discrete frequency points which result in n functions of the compensator coefficients. Several of these functions are chosen so that the system specifications are properly portrayed; then mathematical programming is used to improve all of these functions which have values below minimum standards. In order to do this several definitions in regard to measuring the performance of a system in the frequency domain are given. Next, theorems which govern the number of compensator coefficients necessary to make improvements in a certain number of functions are proved. After this a mathematical programming tool for aiding in the solution of the problem is developed. Then for applying the constraint improvement algorithm generalized gradients for the constraints are derived. Finally, the necessary theory is incorporated in a computer program called CIP (compensator improvement program).

Mitchell, J. R.↗

NASA NTRS1973

An innovative approach to compensator design

The design is considered of a computer-aided-compensator for a control system from a frequency domain point of view. The design technique developed is based on describing the open loop frequency response by n discrete frequency points which result in n functions of the compensator coefficients. Several of these functions are chosen so that the system specifications are properly portrayed; then mathematical programming is used to improve all of these functions which have values below minimum standards. To do this, several definitions in regard to measuring the performance of a system in the frequency domain are given, e.g., relative stability, relative attenuation, proper phasing, etc. Next, theorems which govern the number of compensator coefficients necessary to make improvements in a certain number of functions are proved. After this a mathematical programming tool for aiding in the solution of the problem is developed. This tool is called the constraint improvement algorithm. Then for applying the constraint improvement algorithm generalized, gradients for the constraints are derived. Finally, the necessary theory is incorporated in a Computer program called CIP (compensator Improvement Program). The practical usefulness of CIP is demonstrated by two large system examples.

Mitchell, J. R.↗