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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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1974

An analytic method to account for drag in the Vinti Satellite theory

To retain separability in the Vinti theory of earth satellite motion when a nonconservative force such as air drag is considered, a set of variational equations for the orbital elements are introduced, and expressed as functions of the transverse, radial, and normal components of the nonconservative forces acting on the system. In this approach, the Hamiltonian is preserved in form, and remains the total energy, but the initial or boundary conditions and hence the Jacobi constants of the motion advance with time through the variational equations. In particular, the atmospheric density profile is written as a fitted exponential function of the eccentric anomaly, which adheres to tabular data at all altitudes and simultaneously reduced the variational equations to indefinite integrals with closed form evaluations. The values of the limits for any arbitrary time interval are obtained from the Vinti program.

Watson, J. S.↗
NASA NTRS1986

On the analytical determination of relaxation modulus of viscoelastic materials by Prony's interpolation method

A computer implementation to Prony's curve fitting by exponential functions is presented. The method, although more than one hundred years old, has not been utilized to its fullest capabilities due to the restriction that the time range must be given in equal increments in order to obtain the best curve fit for a given set of data. The procedure used in this paper utilizes the 3-dimensional capabilities of the Interactive Graphics Design System (I.G.D.S.) in order to obtain the equal time increments. The resultant information is then input into a computer program that solves directly for the exponential constants yielding the best curve fit. Once the exponential constants are known, a simple least squares solution can be applied to obtain the final form of the equation.

Rodriguez, Pedro I.↗
NASA NTRS1982

Numerical computation of exponential matrices using the Cayley-Hamilton theorem

A method for computing exponential matrices, which often arise naturally in the solution of systems of linear differential equations, is developed. An exponential matrix is generated as a linear combination of a finite number (equal to the matrix order) of matrices, the coefficients of which are scalar infinite sums. The method can be generalized to apply to any formal power series of matrices. Attention is focused upon the exponential function, and the matrix exponent is assumed tri-diagonal in form. In such cases, the terms in the coefficient infinite sums can be extracted, as recursion relations, from the characteristic polynomial of the matrix exponent. Two numerical examples are presented in some detail: (1) the three dimensional infinitesimal rotation rate matrix, which is skew symmetric, and (2) an N-dimensional tri-diagonal and symmetric finite difference matrix which arises in the numerical solution of the heat conduction partial differential equation. In the second example, the known eigenvalues and eigenvectors of the finite difference matrix permit an analytical solution for the exponential matrix, through the theory of diagonalization and similarity transformations, which is used for independent verification. The convergence properties of the scalar infinite summations are investigated for finite difference matrices of various orders up to ten, and it is found that the number of terms required for convergence increases slowly with the order of the matrix.

Walden, H.↗
NASA NTRS1973

Regression of altitude-produced cardiac hypertrophy.

The rate of regression of cardiac hypertrophy with time has been determined in adult male albino rats. The hypertrophy was induced by intermittent exposure to simulated high altitude. The percentage hypertrophy was much greater (46%) in the right ventricle than in the left (16%). The regression could be adequately fitted to a single exponential function with a half-time of 6.73 plus or minus 0.71 days (90% CI). There was no significant difference in the rates of regression for the two ventricles.

Sizemore, D. A.↗
NASA NTRS1974

Experimental determination of turbulence in a GH2-GOX rocket combustion chamber

The intensity of turbulence and the Lagrangian correlation coefficient for a gaseous rocket combustion chamber have been determined from the experimental measurements of the tracer gas diffusion. A combination of Taylor's turbulent diffusion theory and Spalding's numerical method for solving the conservation equations of fluid mechanics was used to calculate these quantities. Taylor's theory was extended to consider the inhomogeneity of the turbulence field in the axial direction of the combustion chamber. An exponential function was used to represent the Lagrangian correlation coefficient. The results indicate that the maximum value of the intensity of turbulence is about 15% and the Lagrangian correlation coefficient drops to about 0.12 in one inch of the chamber length.

Tou, P.↗
NASA NTRS1974

Infrared maser emission from interstellar hydroxyl molecules

The energy structure and transition rates of the OH radical were studied in rotational and vibrational energies to provide the basis for studies of the population distributions under various exciting mechanisms. The absorption of ultra-violet or near infrared radiation which might explain the microwave emission was examined, as well as the absorption of low temperature blackbody radiation and collisions with molecular hydrogen. The results of the population studies were applied to the transfer equation, and a model of a uniform spherical cloud of OH was used with the pumping process which occurs uniformly throughout the region. The emission is unsaturated and the intensity is an exponential function of the size of the cloud for high pumping rates, and the region of unsaturated emission shrinks for lower pumping rates until the entire region is saturated, the intensity then becoming a linear function of the size of the emitting cloud.

Pelzmann, R. F., Jr.↗
NASA NTRS1975

Solution of the equation of heat conduction with time dependent sources: Programmed application to planetary thermal history

A computer program (Program SPHERE) solving the inhomogeneous equation of heat conduction with radiation boundary condition on a thermally homogeneous sphere is described. The source terms are taken to be exponential functions of the time. Thermal properties are independent of temperature. The solutions are appropriate to studying certain classes of planetary thermal history. Special application to the moon is discussed.

Conel, J. E.↗
NASA NTRS1975

An analytic method to account for drag in the Vinti satellite theory

A quadrature algorithm is presented which employs analytical expressions for the variations of satellite orbital elements caused by air drag. The Hamiltonian is formally preserved and the Jacobi constants of the motion are advanced with time through the variational equations. The atmospheric density profile is written as a fitted exponential function of the eccentric anomaly, which adheres to tabulated data at all altitudes and simultaneously reduces the variational equations to definite integrals with closed form evaluations, whose limits are in terms of the eccentric anomaly. Results are given for two intense air drag satellites and indicate that the satellite ephemerides produced by this method in conjunction with the Vinti program are of very high accuracy.

Watson, J. S.↗
NASA NTRS1975

Exact solution of the Lifshitz equations governing the growth of fluctuations in cosmology

The exact solution of the Lifshitz equations governing the cosmological evolution of an initial fluctuation is presented. Lifshitz results valid for squares of the sound velocity equal to zero and 1/3 are extended in closed form to any equation of state where the pressure equals the total energy density times the square of the sound velocity. The solutions embody all the results found previously for special cases of the square of the sound velocity. It is found that the growth of any initial fluctuation is only an exponential function of time with an exponent of not more than 4/3 and is insufficient to produce galaxies unless the initial fluctuation is very large. A possible way to produce very large initial fluctuations by modifying the equation of state by including gravitational interactions is also examined. It is found that a phase transition can occur at baryonic density of 1 nucleon per cubic Planck length or equivalently, at a time of about 10 to the -43rd power sec. At those early times, the masses allowed by causality requirements are too small to be of interest in galaxy formation.

Adams, P. J.↗
NASA NTRS1976

Mathematical modeling of inhalation exposure

The paper presents a mathematical model of inhalation exposure in which uptake, distribution and excretion are described by exponential functions, while rate constants are determined by tissue volumes, blood perfusion and by the solubility of vapors (partition coefficients). In the model, tissues are grouped into four pharmokinetic compartments. The model is used to study continuous and interrupted chronic exposures and is applied to the inhalation of Forane and methylene chloride.

Fiserova-Bergerova, V.↗
NASA NTRS1978

Development of a winter wheat adjustable crop calendar model

The author has identified the following significant results. After parameter estimation, tests were conducted with variances from the fits, and on independent data. From these tests, it was generally concluded that exponential functions have little advantage over polynomials. Precipitation was not found to significantly affect the fits. The Robertson's triquadratic form, in general use for spring wheat, was found to show promise for winter wheat, but special techniques and care were required for its use. In most instances, equations with nonlinear effects were found to yield erratic results when utilized with daily environmental values as independent variables.

Baker, J. R.↗
NASA NTRS1978

Theoretical study of HSiO/+/ and HOSi/+/

Results are reported for quantum-mechanical studies of the ions HSiO(+) and HOSi(+). The equilibrium geometries, rotation constants, and relative stabilities of these ions are determined using the matrix Hartree-Fock model with a basis set of Slater exponential functions. Optimum bond lengths are calculated, and an empirical correction to the computed bond lengths is introduced. The isomer HOSi(+) is found to be more stable than HSiO(+). A frequency of 35.77 GHz is obtained for the J = 1-0 transition of HOSi(+) by assuming that the vibration-rotation interaction constants for this isomer are the same as those for HCP.

Wilson, S.↗
NASA NTRS1978

Measurement of the turbulence in a gaseous rocket combustion chamber

The intensity of turbulence and the Lagrangian correlation coefficient in a gaseous hydrogen (GH2)-gaseous oxygen (GOX) rocket combustion chamber are studied. A helium tracer gas was injected at an upstream point on the combustion chamber centerline. Samples collected downstream were analyzed for the spreading of the tracer gas concentration. Using Taylor's turbulent diffusion theory and Gosman's numerical method, turbulence parameters were found. In order to evaluate turbulence field inhomogeneity in the axial direction, Taylor's theory was extended. An exponential function was used to approximate the Lagrangian correlation coefficient. It was found that turbulence intensity varies from 15% near the injector to 4% at the nozzle entrance, and that the Lagrangian coefficient rapidly decreases when the dispersion time difference increases.

Tou, P. P.↗
NASA NTRS1979

Ocean Chlorophyll Studies from a U-2 Aircraft Platform

Chlorophyll gradient maps of large ocean areas were generated from U-2 ocean color scanner data obtained over test sites in the Pacific and Atlantic Oceans. The delineation of oceanic features using the upward radiant intensity relies on an analysis method which presupposes that radiation backscattered from the atmosphere and ocean surface can be properly modeled using a measurement made at 778 nm. An estimation of the chlorophyll concentration was performed by properly ratioing radiances measured at 472 nm and 548 nm after removing the atmospheric effects. The correlation between the remotely sensed data and in-situ surface chlorophyll measurements was validated in two sets of data. The results show that the correlation between the in-situ measured chlorophyll and the derived quantity is a negative exponential function and the correlation coefficient was calculated to be -0.965.

Kim, H. H.↗
NASA NTRS1980

Implicit model following and parameter identification of unstable aircraft

A transformation in the s-plane is described which has utility in implicit model-following optimal control design application and in estimation or parameter identification problems. The objective of the transformation is, for the control problem, to achieve an unstable closed-loop system, and, for the estimation problem, to alleviate algorithm convergence problems that may arise in identifying unstable systems. For the control problem, the transformation is a shift along the real (sigma) axis of the plant and model poles and zeros. This transformation is shown to be equivalent to a modified performance index but offers the advantage of compatibility with existing optimal control solution algorithms. For the estimation problem, the data are multiplied by an exponential function and the assumed measurement and process noise covariances are appropriately modified. Examples of both control and estimation applications are presented.

Lebacqz, J. V.↗
NASA NTRS1980

Ocean chlorophyll studies from a U-2 aircraft platform

Chlorophyll gradient maps of large ocean areas were generated from U-2/OCS data obtained over test sites in the Pacific and the Atlantic Oceans. The delineation of oceanic features using the upward radiant intensity relies on an analysis method which presupposes that radiation backscattered from the atmosphere and the ocean surface can be properly modeled by using a measurement made at 778 nm. The calculation of atmospheric radiance was performed by using a method developed by Dave. An estimation of the chlorophyll concentration is performed by properly ratioing radiances measured at 472 and 548 nm after removing the atmospheric effects. The correlation between the remotely sensed data and the in situ surface chlorophyll measurements has been validated in two sets of data. The results show that the correlation between the in situ measured chlorophyll and the derived quantity is a negative exponential function, and the correlation coefficient was calculated to be -0.965.

Kim, H. H.↗
NASA NTRS1982

Observation of gamma-ray bursts from 10 keV to 9 MeV

Time histories and count-rate spectra of some of the gamma-ray bursts detected by the spectrometer on the Solar Maximum Mission between Feb. 20, 1980, and May 1981 are presented. Individual peaks observed in some of the bursts are found to differ significantly in hardness from one another. The similarity in the time profiles in the different energy bands is seen as suggesting that photons spanning two decades in energy are produced by the same mechanism. It is noted that all of the bursts are detected to energies greater than approximately 1 MeV. Two of the spectra presented are seen as being well fit by single power laws; the indices, however, are strikingly different. The other two sepctra require either two power laws or an exponential function. No clear evidence is found for the existence of narrow line features in any of the bursts.

Share, G. H.↗
NASA NTRS1984

Finite-analytic numerical method for unsteady two-dimensional Navier-Stokes equations

A finite analytic (FA) numerical solution is developed for unsteady two-dimensional Navier-Stokes equations. The FA method utilizes the analytic solution in a small local element to formulate the algebraic representation of partial differential equations. The combination of linear and exponential functions that satisfy the governing equation is adopted as the boundary function, thereby improving the accuracy of the finite analytic solution. Two flows, one a starting cavity flow and the other a vortex shedding flow behind a rectangular block, are solved by the FA method. The starting square cavity flow is solved for Reynolds number of 400, 1000, and 2000 to show the accuracy and stability of the FA solution. The FA solution for flow over a rectangular block (H x H/4) predicts the Strouhal number for Reynolds numbers of 100 and 500 to be 0.156 and 0.125. Details of the flow patterns are given. In addition to streamlines and vorticity distribution, rest-streamlines are given to illustrate the vortex motion downstream of the block.

Chen, C.-J.↗