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All sourcesNASA NTRSDOE OSTI
NASA NTRS1999

Improving the Accuracy of Quadrature Method Solutions of Fredholm Integral Equations that Arise from Nonlinear Two-Point Boundary Value Problems

In this paper we are concerned with high-accuracy quadrature method solutions of nonlinear Fredholm integral equations of the form y(x) = r(x) + integral(0 to 1) g(x,t) F(t, y(t)) dt, 0 less than or equal to x less than or equal to 1, where the kernel function g(x,t) is continuous, but its partial derivatives have finite jump discontinuities across x = t. Such integrals equations arise, e.g., when one applies Green's function techniques to nonlinear two-point boundary value problems of the form U''(x) = f(x,y(x)), 0 less than or equal to x less than or equal to 1, with y(0) = y(sub 0) and g(l) = y(sub 1), or other linear boundary conditions. A quadrature method that is especially suitable and that has been employed for such equations is one based on the trapezoidal rule that has a low accuracy. By analyzing the corresponding Euler-Maclaurin expansion, we derive suitable correction terms that we add to the trapezoidal thus obtaining new numerical quadrature formulas of arbitrarily high accuracy that we also use in defining quadrature methods for the integral equations above. We prove an existence and uniqueness theorem for the quadrature method solutions, and show that their accuracy is the same as that of the underlying quadrature formula. The solution of the nonlinear systems resulting from the quadrature methods is achieved through successive approximations whose convergence is also proved. The results are demonstrated with numerical examples.

Sidi, Avram↗
NASA NTRS1999

Generalized Functions for the Fractional Calculus

Previous papers have used two important functions for the solution of fractional order differential equations, the Mittag-Leffler functionE(sub q)[at(exp q)](1903a, 1903b, 1905), and the F-function F(sub q)[a,t] of Hartley & Lorenzo (1998). These functions provided direct solution and important understanding for the fundamental linear fractional order differential equation and for the related initial value problem (Hartley and Lorenzo, 1999). This paper examines related functions and their Laplace transforms. Presented for consideration are two generalized functions, the R-function and the G-function, useful in analysis and as a basis for computation in the fractional calculus. The R-function is unique in that it contains all of the derivatives and integrals of the F-function. The R-function also returns itself on qth order differ-integration. An example application of the R-function is provided. A further generalization of the R-function, called the G-function brings in the effects of repeated and partially repeated fractional poles.

Lorenzo, Carl F.↗
NASA NTRS1997

Interactions between integrin receptors and fibronectin are required for calvarial osteoblast differentiation in vitro

We previously showed that anti-fibronectin antibodies or soluble fibronectin fragments containing the central cell-binding domain inhibit formation of mineralized nodules by fetal calvarial osteoblasts in vitro. These findings suggest a critical role for fibronectin in osteoblast differentiation and morphogenesis. In this study we tested the hypothesis that fibronectin's effects on osteogenesis are mediated via direct interactions with integrin receptors for fibronectin on osteoblasts. Immunocytochemical analysis identified the integrin fibronectin receptor alpha5ss1 in fetal rat calvarial tissue and in cultured osteoblasts at all stages of differentiation. Three other integrins, alpha3ss1, alpha8ss1 and alphavss3, which can bind fibronectin, as well as other matrix components, were also identified in tissue and at all stages of cell culture. Immunoprecipitation data showed that alpha5ss1 levels are constant throughout osteoblast differentiation whereas levels of alpha3ss1 and alpha8ss1 decline in mature mineralized cultures. To determine whether integrin fibronectin receptors are required for osteoblast formation of mineralized nodules, we examined the extent of nodule formation in the presence and absence of function-perturbing anti-integrin antibodies. The antibodies were present continuously in cultures beginning at confluence (day 3), and nodule formation was measured at days 10 and 20. An anti-alpha5 integrin subunit antibody reduced nodule formation to less than 5% of control values at both time points. Inhibition of nodule formation was reversible and did not affect cell attachment and viability. Function-perturbing antibodies against alpha3ss1 and alpha8ss1 also reduced nodule formation, to less than 20% of control values. In contrast, function-perturbing antibodies to alphavss3 and alphavss5 did not affect nodule formation, indicating that the inhibitions noted were indeed specific. To determine the effect of antibody treatment on gene expression, steady-state mRNA expression was examined and found to be suppressed for osteoblast markers alkaline phosphatase and osteocalcin. Together, these results indicate that direct osteoblast interactions with the extracellular matrix are mediated by a select group of integrin receptors that includes alpha5ss1, alpha3ss1 and alpha8ss1. We further conclude that the specific alpha5ss1 fibronectin receptor mediates critical interactions between osteoblasts and fibronectin required for both bone morphogenesis and osteoblast differentiation.

NASA Center ARC↗
NASA NTRS1999

Improving the Accuracy of Quadrature Method Solutions of Fredholm Integral Equations That Arise from Nonlinear Two-Point Boundary Value Problems

In this paper we are concerned with high-accuracy quadrature method solutions of nonlinear Fredholm integral equations of the form y(x) = r(x) + definite integral of g(x, t)F(t,y(t))dt with limits between 0 and 1,0 less than or equal to x les than or equal to 1, where the kernel function g(x,t) is continuous, but its partial derivatives have finite jump discontinuities across x = t. Such integral equations arise, e.g., when one applied Green's function techniques to nonlinear two-point boundary value problems of the form y "(x) =f(x,y(x)), 0 less than or equal to x less than or equal to 1, with y(0) = y(sub 0) and y(l) = y(sub l), or other linear boundary conditions. A quadrature method that is especially suitable and that has been employed for such equations is one based on the trepezoidal rule that has a low accuracy. By analyzing the corresponding Euler-Maclaurin expansion, we derive suitable correction terms that we add to the trapezoidal rule, thus obtaining new numerical quadrature formulas of arbitrarily high accuracy that we also use in defining quadrature methods for the integral equations above. We prove an existence and uniqueness theorem for the quadrature method solutions, and show that their accuracy is the same as that of the underlying quadrature formula. The solution of the nonlinear systems resulting from the quadrature methods is achieved through successive approximations whose convergence is also proved. The results are demonstrated with numerical examples.

Sidi, Avram↗
NASA NTRS1972

On optimizing the treatment of exchange perturbations.

Most theories of exchange perturbations would give the exact energy and wave function if carried out to an infinite order. However, the different methods give different values for the second-order energy, and different values for E(1), the expectation value of the Hamiltonian corresponding to the zeroth- plus first-order wave function. In the presented paper, it is shown that the zeroth- plus first-order wave function obtained by optimizing the basic equation which is used in most exchange perturbation treatments is the exact wave function for the perturbation system and E(1) is the exact energy.

Hirschfelder, J. O.↗
NASA NTRS1995

Uncertainties for two-dimensional models of solar rotation from helioseismic eigenfrequency splitting

Observed solar p-mode frequency splittings can be used to estimate angular velocity as a function of position in the solar interior. Formal uncertainties of such estimates depend on the method of estimation (e.g., least-squares), the distribution of errors in the observations, and the parameterization imposed on the angular velocity. We obtain lower bounds on the uncertainties that do not depend on the method of estimation; the bounds depend on an assumed parameterization, but the fact that they are lower bounds for the 'true' uncertainty does not. Ninety-five percent confidence intervals for estimates of the angular velocity from 1986 Big Bear Solar Observatory (BBSO) data, based on a 3659 element tensor-product cubic-spline parameterization, are everywhere wider than 120 nHz, and exceed 60,000 nHz near the core. When compared with estimates of the solar rotation, these bounds reveal that useful inferences based on pointwise estimates of the angular velocity using 1986 BBSO splitting data are not feasible over most of the Sun's volume. The discouraging size of the uncertainties is due principally to the fact that helioseismic measurements are insensitive to changes in the angular velocity at individual points, so estimates of point values based on splittings are extremely uncertain. Functionals that measure distributed 'smooth' properties are, in general, better constrained than estimates of the rotation at a point. For example, the uncertainties in estimated differences of average rotation between adjacent blocks of about 0.001 solar volumes across the base of the convective zone are much smaller, and one of several estimated differences we compute appears significant at the 95% level.

Genovese, Christopher R.↗
NASA NTRS1993

FNAS computational modeling

Numerical calculations of the electronic properties of liquid II-VI semiconductors, particularly CdTe and ZnTe were performed. The measured conductivity of these liquid alloys were modeled by assuming that the dominant temperature effect is the increase in the number of dangling bonds with increasing temperature. For low to moderate values of electron correlation, the calculated conductivity as a function of dangling bond concentration closely follows the measured conductivity as a function of temperature. Both the temperature dependence of the chemical potential and the thermal smearing in region of the Fermi surface have a large effect on calculated values of conductivity.

Franz, J. R.↗
NASA NTRS2015

Development and Characterization of a Rate-Dependent Three-Dimensional Macroscopic Plasticity Model Suitable for Use in Composite Impact Problems

Several key capabilities have been identified by the aerospace community as lacking in the material/models for composite materials currently available within commercial transient dynamic finite element codes such as LS-DYNA. Some of the specific desired features that have been identified include the incorporation of both plasticity and damage within the material model, the capability of using the material model to analyze the response of both three-dimensional solid elements and two dimensional shell elements, and the ability to simulate the response of composites composed with a variety of composite architectures, including laminates, weaves and braids. In addition, a need has been expressed to have a material model that utilizes tabulated experimentally based input to define the evolution of plasticity and damage as opposed to utilizing discrete input parameters (such as modulus and strength) and analytical functions based on curve fitting. To begin to address these needs, an orthotropic macroscopic plasticity based model suitable for implementation within LS-DYNA has been developed. Specifically, the Tsai-Wu composite failure model has been generalized and extended to a strain-hardening based orthotropic plasticity model with a non-associative flow rule. The coefficients in the yield function are determined based on tabulated stress-strain curves in the various normal and shear directions, along with selected off-axis curves. Incorporating rate dependence into the yield function is achieved by using a series of tabluated input curves, each at a different constant strain rate. The non-associative flow-rule is used to compute the evolution of the effective plastic strain. Systematic procedures have been developed to determine the values of the various coefficients in the yield function and the flow rule based on the tabulated input data. An algorithm based on the radial return method has been developed to facilitate the numerical implementation of the material model. The presented paper will present in detail the development of the orthotropic plasticity model and the procedures used to obtain the required material parameters. Methods in which a combination of actual testing and selective numerical testing can be combined to yield the appropriate input data for the model will be described. A specific laminated polymer matrix composite will be examined to demonstrate the application of the model.

Impact↗
NASA NTRS2003

Theory of Collective Intelligence

In this chapter an analysis of the behavior of an arbitrary (perhaps massive) collective of computational processes in terms of an associated "world" utility function is presented We concentrate on the situation where each process in the collective can be viewed as though it were striving to maximize its own private utility function. For such situations the central design issue is how to initialize/update the collective's structure, and in particular the private utility functions, so as to induce the overall collective to behave in a way that has large values of the world utility. Traditional "team game" approaches to this problem simply set each private utility function equal to the world utility function. The "Collective Intelligence" (COIN) framework is a semi-formal set of heuristics that recently have been used to construct private utility. functions that in many experiments have resulted in world utility values up to orders of magnitude superior to that ensuing from use of the team game utility. In this paper we introduce a formal mathematics for analyzing and designing collectives. We also use this mathematics to suggest new private utilities that should outperform the COIN heuristics in certain kinds of domains. In accompanying work we use that mathematics to explain previous experimental results concerning the superiority of COIN heuristics. In that accompanying work we also use the mathematics to make numerical predictions, some of which we then test. In this way these two papers establish the study of collectives as a proper science, involving theory, explanation of old experiments, prediction concerning new experiments, and engineering insights.

Nash equilibrium↗
NASA NTRS1978

TNT equivalency of M10 propellant

Peak, side-on blast overpressure and scaled, positive impulse have been measured for M10 single-perforated propellant, web size 0.018 inches, using configurations that simulate the handling of bulk material during processing and shipment. Quantities of 11.34, 22.7, 45.4, and 65.8 kg were tested in orthorhombic shipping containers and fiberboard boxes. High explosive equivalency values for each test series were obtained as a function of scaled distance by comparison to known pressure, arrival time and impulse characteristics for hemispherical TNT surface bursts. The equivalencies were found to depend significantly on scaled distance, with higher values of 150-100 percent (pressure) and 350-125 percent (positive impulse) for the extremes within the range from 1.19 to 3.57 m/cube root of kg. Equivalencies as low as 60-140 percent (pressure) and 30-75 percent (positive impulse) were obtained in the range of 7.14 to 15.8 m/cube root of kg. Within experimental error, both peak pressure and positive impulse scaled as a function of charge weight for all quantities tested in the orthorhombic configuration.

Mcintyre, F. L.↗
NASA NTRS2019

Updating the Space Communications and Navigation (SCaN) Link Tool Executable Software to Version 5

NASA’s Space Communications and Navigation (SCaN) program is responsible for providing space communication channels in low Earth orbit, geosynchronous orbit, and deep space for a variety of space missions. The SCaN Link Tool is a standalone, executable, and personal computer (PC)-based software operated via a user interface, which provides NASA civil servants and contractors, as well as the public by way of the tool’s inclusion in the NASA Software Catalog, with in-depth satellite communications link analysis capability. Version 4 of the tool was built using PythonTM (Python Software Foundation) with the help of libraries such as NumPy and SciPy for numerical calculations, Matplotlib for graphical visualizations, and PyQt5 for the graphical user interface. It utilizes radiofrequency (RF) and optical communications link analysis calculations to give users the ability to input known link parameters and calculate select link performance outputs. With the development of the next-generation architecture for space satellite communications in the coming decade, NASA will benefit by having more in-depth communications link analysis tools at its disposal. The tool’s update from version 4 to version 5 aims to provide higher output value accuracy, the ability to solve for a more diverse set of output variables, as well as analog and digital repeater capabilities. Options included in the tool’s functionality, such as the ability to save configuration parameter values, graphs, and results, as well as the provision of default parameter values, increase the tool’s versatility. Users will have access to in-depth, accurate communications link analysis as more advanced satellite constellations are designed and deployed by NASA and the growing commercial aerospace community.

Green, Jack L.↗
NASA NTRS1983

Supplemental basis functions for the second transition row elements

It is noted that for molecular calculations, the basis sets presented by Huzinaga (1977) need to be augmented by (1) 5p functions to describe the 5s - 5p near degeneracy; (2) a diffuse 4d function to provide for a balanced description of the 5s2 4dn, 5s1 4d(n+1), and 4d(n+2) states of the atom; and (3) a set of 4f functions to correlate the 4d functions. Here, the diffuse 4d function is similar in function to the diffuse 3d function for the first transition row elements recommended by Hay (1977). A table is included giving the optimized values for the diffuse 4d, the 5p, and 4f (STO exponent) functions. The diffuse 4d function and the 5p functions are optimized at the SCF level on the basis of the 5s1 4d(n+1) state (except for Pd, which is optimized for the 4d10 state) and the 5s1 5p1 4dn state, respectively. The table also gives the energies and the atomic symmetries for each of the SCF calculations.

Walch, S. P.↗
NASA NTRS1981

Computation of averaged monthly zonal albedo utilizing the solar zenith angle, properties of clear and cloudy atmospheres

The zonal temporal averages of albedos at the top of the atmosphere were considered as a function of the length of the day. The length of the day were used to determine the average daily values of mu sub 0(=Cos of the solar zenith angle, theta sub 0). Polynominal fits of the slope and intercept functions of A sub s (cloud-free albedo) and A sub c(cloud albedo) as function of Cos theta sub 0 were obtained by using the sample values of albedo corresponding to solar zenith angles from 0 to 90 deg with interval of 5 deg. The daily zonal values of mu sub 0 and the surface albedos were used to compute the daily zonal values of albedos at the top of the clear and cloudy atmosphere. The monthly zonal cloud fractions were used to compute planetary albedo A at the top of the atmosphere. The global values of monthly albedos A sub s, A sub c and A were computed by using the weighting function defined as the difference of the sins of zonal values of latitudes. The computer program implementation is also described.

Dhuria, H.↗
NASA NTRS1978

Atmospheric turbulence chamber for optical transmission experiment Characterization by thermal method

Consideration is given to an atmospheric turbulence chamber designed for optical wave propagation experiments. The chamber consists of ten small electric heater/blowers with an aluminum foil screen and three screens of 2-mm aluminum wire meshes. Calculations are made of the temperature structure constant squared on the basis of temperature structure function measurements derived from a differential microthermocouple system. Values are presented for the refractive-index structure constant squared. The average wind velocity and temperature are found to be, respectively, 0.41 m/sec and 53 C. The inner and outer scales of turbulence are 5.0 mm and 6.5 cm. It is shown that the measured temperature structure function and the power spectrum of temperature fluctuations satisfy, respectively, the 2/3 and -5/3 power similarity laws in the inertial subrange. Possible chamber improvements are discussed.

Gamo, H.↗
NASA NTRS1981

The Lyman-alpha/H-alpha ratio in solar flares and quasars

Constant temperature and density solar flare models are constructed with temperature and hydrogen density values that reflect reasonable nonlinear averages of those parameters in the depth dependent solar flare chromosphere models of Lites and Cook (1979). Acceptable values of the intensity ratios L-alpha/H-alpha and H-beta/H-alpha correspond to temperatures from about 9000 to 13,000 K, and hydrogen densities from 10 to the 11th to 10 to the 15th cu cm. The H-alpha and Ly-alpha source functions are thermalized at depths consistent with those inferred from independent studies, although the observed Ly-alpha/H-alpha ratio does not necessarily imply an electron temperature appropriate to the Planck function ratio. It is also shown that the value of Ly-alpha/H-alpha depends on the temperature, hydrogen density, and the optical depth of the emitting chromospheric layer.

Canfield, R. C.↗
NASA NTRS1999

The value of assessing pulmonary venous flow velocity for predicting severity of mitral regurgitation: A quantitative assessment integrating left ventricular function

Although alteration in pulmonary venous flow has been reported to relate to mitral regurgitant severity, it is also known to vary with left ventricular (LV) systolic and diastolic dysfunction. There are few data relating pulmonary venous flow to quantitative indexes of mitral regurgitation (MR). The object of this study was to assess quantitatively the accuracy of pulmonary venous flow for predicting MR severity by using transesophageal echocardiographic measurement in patients with variable LV dysfunction. This study consisted of 73 patients undergoing heart surgery with mild to severe MR. Regurgitant orifice area (ROA), regurgitant stroke volume (RSV), and regurgitant fraction (RF) were obtained by quantitative transesophageal echocardiography and proximal isovelocity surface area. Both left and right upper pulmonary venous flow velocities were recorded and their patterns classified by the ratio of systolic to diastolic velocity: normal (>/=1), blunted (<1), and systolic reversal (<0). Twenty-three percent of patients had discordant patterns between the left and right veins. When the most abnormal patterns either in the left or right vein were used for analysis, the ratio of peak systolic to diastolic flow velocity was negatively correlated with ROA (r = -0.74, P <.001), RSV (r = -0.70, P <.001), and RF (r = -0.66, P <.001) calculated by the Doppler thermodilution method; values were r = -0.70, r = -0.67, and r = -0.57, respectively (all P <.001), for indexes calculated by the proximal isovelocity surface area method. The sensitivity, specificity, and predictive values of the reversed pulmonary venous flow pattern for detecting a large ROA (>0.3 cm(2)) were 69%, 98%, and 97%, respectively. The sensitivity, specificity, and predictive values of the normal pulmonary venous flow pattern for detecting a small ROA (<0.3 cm(2)) were 60%, 96%, and 94%, respectively. However, the blunted pattern had low sensitivity (22%), specificity (61%), and predictive values (30%) for detecting ROA of greater than 0.3 cm(2) with significant overlap with the reversed and normal patterns. Among patients with the blunted pattern, the correlation between the systolic to diastolic velocity ratio was worse in those with LV dysfunction (ejection fraction <50%, r = 0.23, P >.05) than in those with normal LV function (r = -0.57, P <.05). Stepwise linear regression analysis showed that the peak systolic to diastolic velocity ratio was independently correlated with RF (P <.001) and effective stroke volume (P <.01), with a multiple correlation coefficient of 0.71 (P <.001). In conclusion, reversed pulmonary venous flow in systole is a highly specific and reliable marker of moderately severe or severe MR with an ROA greater than 0.3 cm(2), whereas the normal pattern accurately predicts mild to moderate MR. Blunted pulmonary venous flow can be seen in all grades of MR with low predictive value for severity of MR, especially in the presence of LV dysfunction. The blunted pulmonary venous flow pattern must therefore be interpreted cautiously in clinical practice as a marker for severity of MR.

Non-NASA Center↗
NASA NTRS1978

Internal friction Q factor measurements in lunar rocks

In order to better interpret recently reported values for the variation of seismic Q as a function of depth below the lunar surface, we have developed apparatus and made laboratory measurements of Q as a function of hydrostatic pressure, temperature and frequency. Our measurements of the Q associated with shear deformations have demonstrated that the large difference in Q between well outgassed and volatile rich rocks persists to pressures corresponding to a depth of at least 50 km. Here we report new measurements of Q as a function of temperature, on the development of techniques to measure the Q associated with extensional deformations under hydrostatic pressure, on the derivation of theoretical relations between our laboratory Q values and the attenuation coefficient of seismic waves, and on the development of a model for mechanism of adsorption.

Tittmann, B. R.↗
NASA NTRS1993

A function approximation approach to anomaly detection in propulsion system test data

Ground test data from propulsion systems such as the Space Shuttle Main Engine (SSME) can be automatically screened for anomalies by a neural network. The neural network screens data after being trained with nominal data only. Given the values of 14 measurements reflecting external influences on the SSME at a given time, the neural network predicts the expected nominal value of a desired engine parameter at that time. We compared the ability of three different function-approximation techniques to perform this nominal value prediction: a novel neural network architecture based on Gaussian bar basis functions, a conventional back propagation neural network, and linear regression. These three techniques were tested with real data from six SSME ground tests containing two anomalies. The basis function network trained more rapidly than back propagation. It yielded nominal predictions with, a tight enough confidence interval to distinguish anomalous deviations from the nominal fluctuations in an engine parameter. Since the function-approximation approach requires nominal training data only, it is capable of detecting unknown classes of anomalies for which training data is not available.

Whitehead, Bruce A.↗