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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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NASA NTRS1993

Improving the chi-squared approximation for bivariate normal tolerance regions

Let X be a two-dimensional random variable distributed according to N2(mu,Sigma) and let bar-X and S be the respective sample mean and covariance matrix calculated from N observations of X. Given a containment probability beta and a level of confidence gamma, we seek a number c, depending only on N, beta, and gamma such that the ellipsoid R = (x: (x - bar-X)'S(exp -1) (x - bar-X) less than or = c) is a tolerance region of content beta and level gamma; i.e., R has probability gamma of containing at least 100 beta percent of the distribution of X. Various approximations for c exist in the literature, but one of the simplest to compute -- a multiple of the ratio of certain chi-squared percentage points -- is badly biased for small N. For the bivariate normal case, most of the bias can be removed by simple adjustment using a factor A which depends on beta and gamma. This paper provides values of A for various beta and gamma so that the simple approximation for c can be made viable for any reasonable sample size. The methodology provides an illustrative example of how a combination of Monte-Carlo simulation and simple regression modelling can be used to improve an existing approximation.

Feiveson, Alan H.↗
NASA NTRS1993

Faint blue counts from formation of dwarf galaxies at z approximately equals 1

The nature of faint blue objects (FBO's) has been a source of much speculation since their detection in deep CCD images of the sky. Their high surface density argues against them being progenitors of present-day bright galaxies and since they are only weakly clustered on small scales, they cannot be entities that merged together to form present-day galaxies. Babul & Rees (1992) have suggested that the observed faint blue counts may be due to dwarf elliptical galaxies undergoing their initial starburst at z is approximately equal to 1. In generic hierarchical clustering scenarios, however, dwarf galaxy halos (M is approximately 10(exp 9) solar mass) are expected to form at an earlier epoch; for example, typical 10(exp 9) solar mass halos will virialize at z is approximately equal to 2.3 if the power-spectrum for the density fluctuations is that of the standard b = 2 cold dark matter (CDM) model. Under 'ordinary conditions' the gas would rapidly cool, collect in the cores, and undergo star-formation. Conditions at high redshifts are far from 'ordinary'. The intense UV background will prevent the gas in the dwarf halos from cooling, the halos being released from their suspended state only when the UV flux has diminished sufficiently.

Babul, Arif↗
NASA NTRS1992

Approximate reasoning using terminological models

Term Subsumption Systems (TSS) form a knowledge-representation scheme in AI that can express the defining characteristics of concepts through a formal language that has a well-defined semantics and incorporates a reasoning mechanism that can deduce whether one concept subsumes another. However, TSS's have very limited ability to deal with the issue of uncertainty in knowledge bases. The objective of this research is to address issues in combining approximate reasoning with term subsumption systems. To do this, we have extended an existing AI architecture (CLASP) that is built on the top of a term subsumption system (LOOM). First, the assertional component of LOOM has been extended for asserting and representing uncertain propositions. Second, we have extended the pattern matcher of CLASP for plausible rule-based inferences. Third, an approximate reasoning model has been added to facilitate various kinds of approximate reasoning. And finally, the issue of inconsistency in truth values due to inheritance is addressed using justification of those values. This architecture enhances the reasoning capabilities of expert systems by providing support for reasoning under uncertainty using knowledge captured in TSS. Also, as definitional knowledge is explicit and separate from heuristic knowledge for plausible inferences, the maintainability of expert systems could be improved.

Yen, John↗
NASA NTRS1993

Approximation methods for control of structural acoustics models with piezoceramic actuators

The active control of acoustic pressure in a 2-D cavity with a flexible boundary (a beam) is considered. Specifically, this control is implemented via piezoceramic patches on the beam which produces pure bending moments. The incorporation of the feedback control in this manner leads to a system with an unbounded input term. Approximation methods in this manner leads to a system with an unbounded input term. Approximation methods in this manner leads to a system with an unbounded input team. Approximation methods in the context of linear quadratic regulator (LQR) state space control formulation are discussed and numerical results demonstrating the effectiveness of this approach in computing feedback controls for noise reduction are presented.

Banks, H. T.↗
NASA NTRS1991

New approximation of frequency response for structural synthesis and parameter identification

This paper presents two approaches that will improve the accuracy of explicit approximations of frequency responses. They are important components of structural design optimization and system identification. The first is a product form approximation that improves approximated frequency responses near resonant conditions. This approach is applicable to both design optimization and system identification problems. The second is aimed at improving the computed sensitivity coefficients that are used to solve system identification problems.

Miura, Hirokazu↗
NASA NTRS1993

Experiment-specific cosmic microwave background calculations made easier - Approximation formula for smoothed delta T/T windows

Simple and easy to implement elementary function approximations are introduced to the spectral window functions needed in calculations of model predictions of the cosmic microwave backgrond (CMB) anisotropy. These approximations allow the investigator to obtain model delta T/T predictions in terms of single integrals over the power spectrum of cosmological perturbations and to avoid the necessity of performing the additional integrations. The high accuracy of these approximations is demonstrated here for the CDM theory-based calculations of the expected delta T/T signal in several experiments searching for the CMB anisotropy.

Gorski, Krzysztof M.↗
NASA NTRS1993

Function approximations

A development status evaluation is presented for applications of main approximation concepts in nonlinear programming for structural optimization requiring local, midrange, and global approximations. It is noted that there is not yet a sufficient basis for a comprehensive evaluation of relative effectiveness among approximation concepts. Attention is presently given to the careful selection of intermediate-variable and response quantity, and improvements in the traditional Taylor-series expansion by inclusion of either some higher-order terms or information at various points in the design space.

Barthelemy, J.-F. M.↗
NASA NTRS1927

Approximations for column effect in airplane wing spars

The significance attaching to "column effect" in airplane wing spars has been increasingly realized with the passage of time, but exact computations of the corrections to bending moment curves resulting from the existence of end loads are frequently omitted because of the additional labor involved in an analysis by rigorously correct methods. The present report represents an attempt to provide for approximate column effect corrections that can be graphically or otherwise expressed so as to be applied with a minimum of labor. Curves are plotted giving approximate values of the correction factors for single and two bay trusses of varying proportions and with various relationships between axial and lateral loads. It is further shown from an analysis of those curves that rough but useful approximations can be obtained from Perry's formula for corrected bending moment, with the assumed distance between points of inflection arbitrarily modified in accordance with rules given in the report. The discussion of general rules of variation of bending stress with axial load is accompanied by a study of the best distribution of the points of support along a spar for various conditions of loading.

Warner, Edward P↗
NASA NTRS1947

Langley Full-scale-tunnel Investigation of Maximum Lift and Stability Characteristics of an Airplane Having Approximately Triangular Plan Form (DM-1 Glider)

An investigation of the DM-1 Glider, which had approximately triangular plan form, an aspect ratio of 1.8 and a 60 degree sweptback leading edge, has been conducted in the Langley full-scale tunnel. The investigation consisted of the determination of the separate effects of the following modifications made to the glider on its maximum lift and stability characteristics: (a) installation of sharp leading edges over the inboard semispan of the wing, (b) removal of the vertical fin, (c) sealing of the elevon control-balance slots, (d) installation of redesigned thin vertical surfaces, (e) installation of faired sharp leading edges, and (f) installation of canopy. The maximum lift coefficient of the DM-1 glider was increased from 0.61 to 1.01 by the installation of semispan sharp leading edges, and from 1.01 to 1.24 by the removal of the vertical fin and sealing of the elevon control-balance slots. The highest maximum lift coefficient (1.32) was obtained when the faired sharp leading edges and the thin vertical surfaces were attached to the glider. The original DM-1 glider was longitudinally stable. The semispan sharp leading edges shifted the neutral point forward approximately 3 percent of the root chord at moderate lift coefficients, and the glider configuration with these sharp leading edges attached was longitudinally unstable, for the assumed center-of-gravity location, at lift coefficients above 0.73. Sealing the elevon control-balance slots and installing the faired sharp leading edges, the thin vertical surfaces, and the canopy shifted the neutral point forward approximately 8 percent of the root chord.

Lovell, J Calvin↗
NASA NTRS1993

Approximate optimal guidance for the advanced launch system

A real-time guidance scheme for the problem of maximizing the payload into orbit subject to the equations of motion for a rocket over a spherical, non-rotating earth is presented. An approximate optimal launch guidance law is developed based upon an asymptotic expansion of the Hamilton - Jacobi - Bellman or dynamic programming equation. The expansion is performed in terms of a small parameter, which is used to separate the dynamics of the problem into primary and perturbation dynamics. For the zeroth-order problem the small parameter is set to zero and a closed-form solution to the zeroth-order expansion term of Hamilton - Jacobi - Bellman equation is obtained. Higher-order terms of the expansion include the effects of the neglected perturbation dynamics. These higher-order terms are determined from the solution of first-order linear partial differential equations requiring only the evaluation of quadratures. This technique is preferred as a real-time, on-line guidance scheme to alternative numerical iterative optimization schemes because of the unreliable convergence properties of these iterative guidance schemes and because the quadratures needed for the approximate optimal guidance law can be performed rapidly and by parallel processing. Even if the approximate solution is not nearly optimal, when using this technique the zeroth-order solution always provides a path which satisfies the terminal constraints. Results for two-degree-of-freedom simulations are presented for the simplified problem of flight in the equatorial plane and compared to the guidance scheme generated by the shooting method which is an iterative second-order technique.

Feeley, T. S.↗
NASA NTRS1994

Rational positive real approximations for LQG optimal compensators arising in active stabilization of flexible structures

In this paper the approximation problem for a class of optimal compensators for flexible structures is considered. The particular case of a simply supported truss with an offset antenna is dealt with. The nonrational positive real optimal compensator transfer function is determined, and it is proposed that an approximation scheme based on a continued fraction expansion method be used. Comparison with the more popular modal expansion technique is performed in terms of stability margin and parameters sensitivity of the relative approximated closed loop transfer functions.

Desantis, A.↗
NASA NTRS1994

A Planar Approximation for the Least Reliable Bit Log-likelihood Ratio of 8-PSK Modulation

The optimum decoding of component codes in block coded modulation (BCM) schemes requires the use of the log-likelihood ratio (LLR) as the signal metric. An approximation to the LLR for the least reliable bit (LRB) in an 8-PSK modulation based on planar equations with fixed point arithmetic is developed that is both accurate and easily realizable for practical BCM schemes. Through an error power analysis and an example simulation it is shown that the approximation results in 0.06 dB in degradation over the exact expression at an E(sub s)/N(sub o) of 10 dB. It is also shown that the approximation can be realized in combinatorial logic using roughly 7300 transistors. This compares favorably to a look up table approach in typical systems.

Thesling, William H.↗
NASA NTRS1994

The evolution of voids in the adhesion approximation

We apply the adhesion approximation to study the formation and evolution of voids in the universe. Our simulations-carried out using 128(exp 3) particles in a cubical box with side 128 Mpc-indicate that the void spectrum evolves with time and that the mean void size in the standard Cosmic Background Explorer Satellite (COBE)-normalized cold dark matter (CDM) model with H(sub 50) = 1 scals approximately as bar D(z) = bar D(sub zero)/(1+2)(exp 1/2), where bar D(sub zero) approximately = 10.5 Mpc. Interestingly, we find a strong correlation between the sizes of voids and the value of the primordial gravitational potential at void centers. This observation could in principle, pave the way toward reconstructing the form of the primordialpotential from a knowledge of the observed void spectrum. Studying the void spectrum at different cosmological epochs, for spectra with a built in k-space cutoff we find that the number of voids in a representative volume evolves with time. The mean number of voids first increases until a maximum value is reached (indicating that the formation of cellular structure is complete), and then begins to decrease as clumps and filaments erge leading to hierarchical clustering and the subsequent elimination of small voids. The cosmological epoch characterizing the completion of cellular structure occurs when the length scale going nonlinear approaches the mean distance between peaks of the gravitaional potential. A central result of this paper is that voids can be populated by substructure such as mini-sheets and filaments, which run through voids. The number of such mini-pancakes that pass through a given void can be measured by the genus characteristic of an individual void which is an indicator of the topology of a given void in intial (Lagrangian) space. Large voids have on an average a larger measure than smaller voids indicating more substructure within larger voids relative to smaller ones. We find that the topology of individual voids is strongly epoch dependent, with void topologies generally simplifying with time. This means that as voids grow older they become progressively more empty and have less structure within them. We evaluate the genus measure both for individual voids as well as for the entire ensemble of voids predicted by CDM model. As a result we find that the topology of voids when taken together with the void spectrum is a very useful statistical indicator of the evolution of the structure of the universe on large scales.

Sahni, Varun↗
NASA NTRS1994

The emission-line properties of the QSO population at z approximately 2

We compare the ultraviolet emission-line properties of the three subclasses of the QSO population (radio quiet, flat radio spectrum radio loud, steep radio spectrum radio loud) during the 'QSO epoch' at z approximately 2. Our total sample consists of 79 objects that are well matched in luminosity and redshift, which should allow unbiased comparison of their spectral properties. We confirm recent results that radio-loud objects have, on average, narrower and stronger C IV lambda 1549 and C III) lambda 1909 emission lines than radio-quiet objects. This is likely the effect of larger average intermediate-line and/or narrow-line regions in radio loud objects, including a relative excess of emission on very extended (approximately 100 kpc) scales. We additionally find that radio-loud objects show a significantly wider range in the asymmetry of the C IV lambda 1549 profile than radio-quiet objects, with cases of both redward and blueward asymmetry. By contrast, radio-quiet objects almost exclusively show blueward asymmetry in this line, and cases of strong redward asymmetry appear to be limited to steep-spectrum objects. Statistically, there is a closer correspondence between the emission-line properties of radio-quiet and flat-spectrum objects than between either of these subclasses and steep-spectrum objects, whose mean emission-line properties differ strongly from those of the radio-quiet sample. This result is similar to that found for the properties of the optical emission lines in low-redshift objects and is not easily understood under the proposed unified models of the flat- and steep-spectrum sources. We also find that 20%-30% of radio-loud objects show narrow (approximately 1000 km/s) emission in He II lambda 1640. No cases of such emission are found among radio-quiet objects. There is evidence that this spectral feature arises in extended ionized halos, which may thus be associated with the objects' radio ejecta, cluster cooling flows, or a combination of both.

Corbin, Michael R.↗
NASA NTRS1994

A two-fluid approximation for calculating the cosmic microwave background anisotropies

We present a simplified treatment for calculating the cosmic microwave background anisotropy power spectrum in adiabatic models. It consists of solving for the evolution of a two-fluid model until the epoch of recombination and then integrating over the sources to obtain the cosmic microwave background (CMB) anisotropy power spectrum. The approximation is useful both for a physical understanding of CMB anisotropies as well as for a quantitative analysis of cosmological models. Comparison with exact calculations shows that the accuracy is typically 10%-20% over a large range of angles and cosmological models, including those with curvature and cosmological constant. Using this approximation we investigate the dependence of the CMB anisotropy on the cosmological parameters. We identify six dimensionless parameters that uniquely determine the anisotropy power spectrum within our approximation. CMB experiments on different angular scales could in principle provide information on all these parameters. In particular, mapping of the Doppler peaks would allow an independent determination of baryon mass density, matter mass density, and the Hubble constant.

Seljak, Uros↗
NASA NTRS1993

Counterstreaming suprathermal electron events upstream of corotating shocks in the solar wind beyond approximately 2 AU: Ulysses

Enhanced fluxes of suprathermal electrons are commonly observed upstream of corotating forward and reverse shocks in the solar wind at heliocentric distances beyond approximately 2 AU by the Los Alamos plasma experiment on Ulysses. The average duration of these events, which are most intense immediately upstream from the shocks and which fade with increasing distance from them, is approximately 2.4 days near 5 AU. These events are caused by the leakage of shock-heated electrons into the upstream region. The upstream regions of these shocks face back toward the Sun along the interplanetary magnetic field, so these leaked electrons commonly counterstream relative to the normal solar wind electron heat flux. The observations suggest that conservation of magnetic moment and scattering typically limit the sunward propagation of these electrons as beams to field-aligned distances of approximately 15 AU. Although it seems unlikely that these shock-associated events are an important source of counterstreaming events near 1 AU, remnants of the backstreaming beams may contribute importantly to the diffuse solar wind halo electron population there.

Gosling, J. T.↗
NASA NTRS1994

On current sheet approximations in models of eruptive flares

We consider an approximation sometimes used for current sheets in flux-rope models of eruptive flares. This approximation is based on a linear expansion of the background field in the vicinity of the current sheet, and it is valid when the length of the current sheet is small compared to the scale length of the coronal magnetic field. However, we find that flux-rope models which use this approximation predict the occurrence of an eruption due to a loss of ideal-MHD equilibrium even when the corresponding exact solution shows that no such eruption occurs. Determination of whether a loss of equilibrium exists can only be obtained by including higher order terms in the expansion of the field or by using the exact solution.

Bungey, T. N.↗
NASA NTRS1995

Eight-moment approximation solar wind models

Heat conduction from the corona is important in the solar wind energy budget. Until now all hydrodynamic solar wind models have been using the collisionally dominated gas approximation for the heat conductive flux. Observations of the solar wind show particle distribution functions which deviate significantly from a Maxwellian, and it is clear that the solar wind plasma is far from collisionally dominated. We have developed a numerical model for the solar wind which solves the full equation for the heat conductive flux together with the conservation equations for mass, momentum, and energy. The equations are obtained by taking moments of the Boltzmann equation, using an 8-moment approximation for the distribution function. For low-density solar winds the 8-moment approximation models give results which differ significantly from the results obtained in models assuming the gas to be collisionally dominated. The two models give more or less the same results in high density solar winds.

Olsen, Espen Lyngdal↗