Search NASA⌕ Search

SEARCH · Search NASA

Results for “variable order”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 847 records · Page 47
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Software reliability modeling and analysis

A discrete and, as approximation to it, a continuous model for the software reliability growth process are examined. The discrete model is based on independent multinomial trials and concerns itself with the joint distribution of the first occurrence time of its underlying events (bugs). The continuous model is based on the order statistics of N independent nonidentically distributed exponential random variables. It is shown that the spacings between bugs are not necessarily independent or exponentially (geometrically) distributed. However, there is a statistical rationale for viewing them so conditionally. Some identifiability problems are pointed out and resolved. In particular, it appears that the number of bugs in a program is not identifiable. Estimated upper bounds and confidence bounds for the residual program eror content are given based on the spacings of the first k bugs removed.

Scholz, F.-W.↗
NASA NTRS1986

Experiments and modeling of dilution jet flow fields

Experimental and analytical results of the mixing of single, double, and opposed rows of jets with an isothermal or variable-temperature main stream in a straight duct are presented. This study was performed to investigate flow and geometric variations typical of the complex, three-dimensional flow field in the dilution zone of gas-turbine-engine combustion chambers. The principal results, shown experimentally and analytically, were the following: (1) variations in orifice size and spacing can have a significant effect on the temperature profiles; (2) similar distributions can be obtained, independent of orifice diameter, if momentum-flux ratio and orifice spacing are coupled; (3) a first-order approximation of the mixing of jets with a variable-temperature main stream can be obtained by superimposing the main-stream and jets-in-an-isothermal-crossflow profiles; (4) the penetration of jets issuing mixing is slower and is asymmetric with respect to the jet centerplanes, which shift laterally with increasing downstream distance; (5) double rows of jets give temperature distributions similar to those from a single row of equally spaced, equal-area circular holes; (6) for opposed rows of jets, with the orifice centerlines in line, the optimum ratio of orifice spacing to duct height is one-half the optimum value for single-side injection at the same momentum-flux ratiol and (7) for opposed rows of jets, with the orifice centerlines staggered, the optimum ratio of orifice spacing to duct height is twice the optimum value for single-side injection at the same momentum-flux ratio.

Holdeman, James D.↗
NASA NTRS1987

High-energy gamma-ray and hard X-ray observations of Cyg X-3

COS-B viewed the Cyg X-3 region seven times between November, 1975, and February, 1982; a search for steady gamma-ray emission pulsed at the characteristic 4.8-hour period did not reveal its source. Leiden-MIT balloon experiment observations of Cyg X-3 in May, 1979 show the 4.8-hour modulation with sinusoidal light curve and modulation depth of 0.30, for energies of up to about 140 keV. The strong variability of Cyg X-3 over more than one order of magnitude at energies below 20 keV does not emerge in the data collected at hard X-ray energies.

Hermsen, W.↗
NASA NTRS1986

Making statistical inferences about software reliability

Failure times of software undergoing random debugging can be modeled as order statistics of independent but nonidentically distributed exponential random variables. Using this model inferences can be made about current reliability and, if debugging continues, future reliability. This model also shows the difficulty inherent in statistical verification of very highly reliable software such as that used by digital avionics in commercial aircraft.

Miller, Douglas R.↗
NASA NTRS1987

Analysis of eccentric annular incompressible seals. I - A new solution using fast Fourier transforms for determining hydrodynamic force

A new analysis procedure is presented which solves for the flow variables of an incompressible-flow annular pressure seal in which the rotor has a large static displacement from the centered position. The analysis begins with a set of governing equations based on a turbulent bulk-flow model and Moody's friction equation. No simplification of these bulk-flow equations is required for the solution procedure. Perturbation of the flow variables yields a set of zeroth and first-order equations. The zeroth-order equations (which model the large static displacement) are integrated by means of an efficient new method which employs fast Fourier transforms. Further integration of the zeroth-order pressures yields the hydrodynamic reactive force. Predictions for the hydrodynamic forces from this analysis procedure are in excellent agreement with available experimental results.

Nelson, C. C.↗
NASA NTRS1989

Algorithm For Optimal Control Of Large Structures

Cost of computation appears competitive with other methods. Problem to compute optimal control of forced response of structure with n degrees of freedom identified in terms of smaller number, r, of vibrational modes. Article begins with Hamilton-Jacobi formulation of mechanics and use of quadratic cost functional. Complexity reduced by alternative approach in which quadratic cost functional expressed in terms of control variables only. Leads to iterative solution of second-order time-integral matrix Volterra equation of second kind containing optimal control vector. Cost of algorithm, measured in terms of number of computations required, is of order of, or less than, cost of prior algoritms applied to similar problems.

Salama, Moktar A.↗
NASA NTRS1988

Making statistical inferences about software reliability

Failure times of software undergoing random debugging can be modelled as order statistics of independent but nonidentically distributed exponential random variables. Using this model inferences can be made about current reliability and, if debugging continues, future reliability. This model also shows the difficulty inherent in statistical verification of very highly reliable software such as that used by digital avionics in commercial aircraft.

Miller, Douglas R.↗
NASA NTRS1989

Spectral element simulations of laminar and turbulent flows in complex geometries

Spectral element methods are high-order weighted residual techniques based on spectral expansions of variables and geometry for the Navier-Stokes (NS) and transport equations. Here, practical aspects of these methods and their efficient implementation are examined, and several examples of flows in truly complex geometries are presented. The spectral element discretization for NS equations is introduced, and the convergence of the method is addressed. An efficient data management scheme is discussed in the context of parallel processing computations. The method is validated by comparing the spectral element solutions with the exact eigensolutions for the Orr-Sommerfeld equations in two and three dimensions. Computer-aided flow visualizations are presented for an impulsive flow past a sharp edge wedge. Three-dimensional states of channel flow disrupted by an array of cylindrical eddy promoters are studied, and the results of a direct simulation of the turbulent flow in a plane channel are presented.

Karniadakis, George EM↗
NASA NTRS1991

Errors of five-day mean surface wind and temperature conditions due to inadequate sampling

Surface meteorological reports of wind components, wind speed, air temperature, and sea-surface temperature from buoys located in equatorial and midlatitude regions are used in a simulation of random sampling to determine errors of the calculated means due to inadequate sampling. Subsampling the data with several different sample sizes leads to estimates of the accuracy of the subsampled means. The number N of random observations needed to compute mean winds with chosen accuracies of 0.5 (N sub 0.5) and 1.0 (N sub 1,0) m/s and mean air and sea surface temperatures with chosen accuracies of 0.1 (N sub 0.1) and 0.2 (N sub 0.2) C were calculated for each 5-day and 30-day period in the buoy datasets. Mean values of N for the various accuracies and datasets are given. A second-order polynomial relation is established between N and the variability of the data record. This relationship demonstrates that for the same accuracy, N increases as the variability of the data record increases. The relationship is also independent of the data source. Volunteer-observing ship data do not satisfy the recommended minimum number of observations for obtaining 0.5 m/s and 0.2 C accuracy for most locations. The effect of having remotely sensed data is discussed.

Legler, David M.↗
NASA NTRS1991

Fragmentation in stellar collapse

A three dimensional Cartesian code was developed to model molecular cloud collapse and protostellar formation. The basic Eulerian scheme employs spatially second-order accurate, finite difference methods to advance the fluid variables in time. The hydrodynamic equations governing the collapse include the effects of self-gravity, rotation, and radiative transfer. Supplementary equations include Poisson's equation which relates the gravitational potential to the density distribution and a mean intensity equation derived with the Eddington approximation for radiative transfer. The gas pressures and internal energies are determined from equations of state derived for a molecular cloud composed of hydrogen, helium, and heavier elements.

Myhill, E. M.↗
NASA NTRS1992

Nonlinear feedback guidance law for aero-assisted orbit transfer maneuvers

Aero-assisted orbit transfer vehicles have the potential for significantly reducing the fuel requirements in certain classes of orbit transfer operations. Development of a nonlinear feedback guidance law for performing aero-assisted maneuvers that accomplish simultaneous change of all the orbital elements with least vehicle acceleration magnitude is discussed. The analysis is based on a sixth order nonlinear point-mass vehicle model with lift, bank angle, thrust and drag modulation as the control variables. The guidance law uses detailed vehicle aerodynamic and the atmosphere models in the feedback loop. Higher-order gravitational harmonics, planetary atmosphere rotation and ambient winds are included in the formulation. Due to modest computational requirements, the guidance law is implementable on-board an orbit transfer vehicle. The guidance performance is illustrated for three sets of boundary conditions.

Menon, P. K. A.↗
NASA NTRS1991

Empirical models of the latitudinal variations of Te and Ne in the ionosphere at solar maximum

A global spectral model of electron temperature and density is developed in which only the latitudinal variations observed in narrow altitude and local time bands are used. The measurements for this purpose are obtained during intervals that are short as compared to a season. By suppressing all variables except latitude the model can use 17th-order polynomials and generates a latitudinal structure that is similar to that described by the observational data. The treatment is designed to correct for the eccentricity and slow evolution of the data-collection satellite orbit so that small-scale features can be resolved. By comparing the results of a global model and the present latitudinal model to observational measurements of electron temperature and density it is shown that auroral-zone and midlatitude trough structures are not resolved in latitudinal models. The observational data can be used to study the response of electron density and temperature to solar EUV flux variations and geomagnetic activity.

Brace, L. H.↗
NASA NTRS1992

Outbursts by low-mass white dwarfs in symbiotic variables

The high-resolution IUE spectra of the symbiotic variables BF Cygni and EG Andromedae are studied in order to describe the P Cygni-like features of these objects. The 10 high-dispersion IUE spectra are examined for orbital phase-dependent variations in the C IV resonance doublet in terms of velocity and/or structure. One image is found to have a strong He-II absorption feature that coincides in velocity with the C-IV absorption component in P Cygni. The absorbing material for both lines is related to outflow and P Cygni self-absorption near the hot component. The P Cygni profiles do not appear to be related to a red-giant wind nor an expanding circumbinary shell in the in both BF Cyg and EG And. Quasi-static evolutionary model calculations demonstrate an unexpected outburst behavior in response to the assumed accretion. These data are shown to be important for the study of symbiotic systems that contain low-mass white dwarfs.

Sion, Edward M.↗
NASA NTRS1954

Aerodynamics of Slender Bodies at Mach Number of 3.12 and Reynolds Numbers from 2 x 10(exp 6) to 15 x 10(exp 6) IV : Aerodynamic Characteristics of Series of Four Bodies Having Near-parabolic Noses and Cylindrical Afterbodies

Pressure distributions and forces for a series of four bodies of revolution having nose-fineness ratios varying from 4 to 10 have been obtained and compared with theory for a Mach number of 3.12, a Reynolds number range of 2x10(sup)6 to 14x10(sup)6, and angles of attack from zero to 9 degrees. In general, a comparison of the experimental data with a second-order theory showed good agreement for the range of variables investigated.

BODIES - FITNESS RATIO↗
NASA NTRS1994

Oceanographic results from analysis of ERS-1 altimetry

Large scale dynamic ocean topography and its variations were observed using ERS-1 radar altimeter measurements. The altimeter measurements analyzed are primarily from the ESA ocean product (OPR02) and from the Interim Geophysical Data Records (IGDR) generated by NOAA from the fast delivery (FD) data during the ERS-1 35 day repeat orbit phase. The precise orbits used for the dynamic topography solution are computed using dual satellite crossover measurements from ERS-1 and TOPEX (Topology Ocean Experiment)/Poseidon (T/P) as additional tracking data, and using improved models and constants which are consistent with T/P. Analysis of the ERS-1 dynamic topography solution indicates agreement with the T/P solution at the 5 cm root mean square level, with regional differences as large as 15 cm tide gauges at the 8 to 9 cm level. There are differences between the ERS-1 OPR02 and IGDR determined dynamic topography solutions on the order of 5 cm root mean square. Mesoscale oceanic variability time series obtained using collinear analysis of the ERS-1 altimeter data show good qualitative agreement when compared with the T/P results.

Tapley, B. D.↗
NASA NTRS1997

Wing Weight Optimization Under Aeroelastic Loads Subject to Stress Constraints

A minimum weight optimization of the wing under aeroelastic loads subject to stress constraints is carried out. The loads for the optimization are based on aeroelastic trim. The design variables are the thickness of the wing skins and planform variables. The composite plate structural model incorporates first-order shear deformation theory, the wing deflections are expressed using Chebyshev polynomials and a Rayleigh-Ritz procedure is adopted for the structural formulation. The aerodynamic pressures provided by the aerodynamic code at a discrete number of grid points is represented as a bilinear distribution on the composite plate code to solve for the deflections and stresses in the wing. The lifting-surface aerodynamic code FAST is presently being used to generate the pressure distribution over the wing. The envisioned ENSAERO/Plate is an aeroelastic analysis code which combines ENSAERO version 3.0 (for analysis of wing-body configurations) with the composite plate code.

Kapania, Rakesh K.↗
NASA NTRS1996

First-Order Approximation of the Ordered Binary-Symmetric Channel

This paper presents different results related to the ordering of a sequence of N received symbols with respect to their reliability measure, for BPSK transmission over the AWGN channel model. First, a tight approximation of Pe (i; N), the probability that the hard decision associated with the i-th symbol of the ordered sequence is in error, is derived. Then, it is shown that despite the fact that the random variables representing the noise at positions n 1(sub 1), n(sub 2), ..., n(sub j) of the ordering are no longer independent, the events of having a hard decision decoding error at these positions remain almost independent Pe (n(sub i), n2, ..., n(sub j); N), the probability that the hard decisions associated with the symbols at positions n(sub 1), n(sub 2), ..., n(sub j), in the ordered sequence are in error, is thus well approximated from each of the Pe (n(sub i): N), for i is a member of [1, j]. Finally, based on the independence of these events, the fully connected 2(sup N) -state BSC representing the channel after ordering is simplified by N independent time-shared 2-state BSC's. This new model allows one to easily and tightly approximate the capacity of the channel after ordering.

Fossorier, Marc P. C.↗
NASA NTRS1999

The Effect of Temperature and Solution pH on the Nucleation of Tetragonal Lysozyme Crystals

Part of the challenge of macromolecular crystal growth for structure determination is obtaining crystals with a volume suitable for x-ray analysis. In this respect an understanding of the effect of solution conditions on macromolecule nucleation rates is advantageous. This study investigated the effects of supersaturation, temperature, and pH on the nucleation rate of tetragonal lysozyme crystals. Batch crystallization plates were prepared at given solution concentrations and incubated at set temperatures over 1 week. The number of crystals per well with their size and axial ratios were recorded and correlated with solution conditions. Crystal numbers were found to increase with increasing supersaturation and temperature. The most significant variable, however, was pH; crystal numbers changed by two orders of magnitude over the pH range 4.0-5.2. Crystal size also varied with solution conditions, with the largest crystals obtained at pH 5.2. Having optimized the crystallization conditions, we prepared a batch of crystals under the same initial conditions, and 50 of these crystals were analyzed by x-ray diffraction techniques. The results indicate that even under the same crystallization conditions, a marked variation in crystal properties exists.

Judge, Russell A.↗