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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 397 records · Page 22
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NASA NTRS1977

Boundary-fitted curvilinear coordinate systems for solution of partial differential equations on fields containing any number of arbitrary two-dimensional bodies

A method is presented for automatic numerical generation of a general curvilinear coordinate system with coordinate lines coincident with all boundaries of a general multi-connected two-dimensional region containing any number of arbitrarily shaped bodies. No restrictions are placed on the shape of the boundaries, which may even be time-dependent, and the approach is not restricted in principle to two dimensions. With this procedure the numerical solution of a partial differential system may be done on a fixed rectangular field with a square mesh with no interpolation required regardless of the shape of the physical boundaries, regardless of the spacing of the curvilinear coordinate lines in the physical field, and regardless of the movement of the coordinate system in the physical plane. A number of examples of coordinate systems and application thereof to the solution of partial differential equations are given. The FORTRAN computer program and instructions for use are included.

Thompson, J. F.↗
NASA NTRS1977

MACSYMA's symbolic ordinary differential equation solver

The MACSYMA's symbolic ordinary differential equation solver ODE2 is described. The code for this routine is delineated, which is of interest because it is written in top-level MACSYMA language, and may serve as a good example of programming in that language. Other symbolic ordinary differential equation solvers are mentioned.

Golden, J. P.↗
NASA NTRS1964

Analytical Solutions for Non-Linear Differential Equations with the Help of a Digital Computer

A technique was developed with the help of a digital computer for analytic (algebraic) solutions of autonomous and nonautonomous equations. Two operational transform techniques have been programmed for the solution of these equations. Only relatively simple nonlinear differential equations have been considered. In the cases considered it has been possible to assimilate the secular terms into the solutions. For cases where f(t) is not a bounded function, a direct series solution is developed which can be shown to be an analytic function. All solutions have been checked against results obtained by numerical integration for given initial conditions and constants. It is evident that certain nonlinear differential equations can be solved with the help of a digital computer.

Cromwell, P. C.↗
NASA NTRS1977

The effect of temperature and pressure on the distribution of iron group elements between metal and olivine phases in the process of differentiation of protoplanetary material

The distribution patterns of Ni, Co, Mn, and Cr were studied in olivines of various origins: from meteorites (chondrites, achondrites, pallasites), which are likely analogs of the protoplanetary material, to peridotite inclusions in kimberlite pipes, which are analogs of mantle material. According to X-ray microanalysis data, nickel is concentrated in peridotite olivines, while manganese is concentrated in meteoritic olivines. The maximum chromium content was found in ureilites, which were formed under reducing conditions. Experiments at pressures of 20 to 70 kbar and temperatures of 1100 to 2000 C have shown that in a mixture of olivine and Ni metal or NiO, nickel enters the silicate phase, displacing Fe into the metallic phase. Equilibrium temperatures were estimated from the Fe, Ni distribution coefficients between the metal and olivine: 1500 K for pallasites, 1600 K for olivine-bronzite H6 chondrites, 1200 K for olivine-hypersthene L6, 900 K for LL6, and 1900 K for ureilites (at P = 1 atm). The equilibrium conditions of peridotites are close to T = 1800 K and P over 100 kbar. It is concluded that there is a sharp difference between the conditions of differentiation of the protoplanetary material at the time meteorites were formed and the conditions of differentiation of the planets into concentric layers.

Vinogradov, A. P.↗
NASA NTRS1977

Mechanical processess affecting differentiation of protolunar material

Mechanisms prior to lunar formation are sought to account for the loss of volatiles, the depletion of iron, and the enrichment of plagioclase. Some of the same mechanisms are necessary to account for achondritic, stony-iron, and iron meteorites. Collisions seem marginally capable of providing the heat to accomplish the differentiation into iron, magnesian silicates, and plagioclase. Once this differentiation is accomplished, the subsequent mechanical history should have been sufficient to sort material according to composition in the protolunar circumterrestrial cloud. Effects operating include the correlation of body size with mechanical strength; the lesser ability of the cloud to trap the larger, denser infalling bodies; the more rapid drawing into the Earth of the larger moonlets; and the higher energy orbits for dominantly plagioclase smaller pieces broken off by collision.

Kaula, W. M.↗
NASA NTRS1978

Differential optoacoustic absorption detector

A differential optoacoustic absorption detector employed two tapered cells in tandem or in parallel. When operated in tandem, two mirrors were used at one end remote from the source of the beam of light directed into one cell back through the other, and a lens to focus the light beam into the one cell at a principal focus half way between the reflecting mirror. Each cell was tapered to conform to the shape of the beam so that the volume of one was the same as for the other, and the volume of each received maximum illumination. The axes of the cells were placed as close to each other as possible in order to connect a differential pressure detector to the cells with connecting passages of minimum length. An alternative arrangement employed a beam splitter and two lenses to operate the cells in parallel.

Shumate, M. S.↗
NASA NTRS1977

Coplanar tail-chase aerial combat as a differential game

A reduced-order version of the one-on-one aerial combat problem is studied as a pursuit-evasion differential game. The coplanar motion takes place at given speeds and given maximum available turn rates, and is described by three state equations which are equivalent to the range, bearing, and heading of one aircraft relative to the other. The purpose of the study is to determine those relative geometries from which either aircraft can be guaranteed a win, regardless of the maneuver strategies of the other. Termination is specified by the tail-chase geometry, at which time the roles of pursuer and evader are known. The roles are found in general, together with the associated optimal turn maneuvers, by solution of the differential game of kind. For the numerical parameters chosen, neither aircraft can win from the majority of possible initial conditions if the other turns optimally in certain critical geometries.

Merz, A. W.↗
NASA NTRS1977

Boolean differentiation and integration using Karnaugh maps

Algorithms are presented for differentiation and integration of Boolean functions by means of Karnaugh maps. The algorithms are considered simple when the number of variables is six or less; in this case Boolean differentiation and integration is said to be as easy as the Karnaugh map method of simplifying switching functions. It is suggested that the algorithms would be useful in the analysis of faults in combinational systems and in the synthesis of asynchronous sequential systems which utilize edge-sensitive flip-flops.

Tucker, J. H.↗
NASA NTRS1977

ALSEP-quasar differential VLBI

A program of ALSEP-quasar very-long-baseline interferometry (VLBI) is being carried out. These observations employ primarily a 'four-antenna' technique whereby simultaneous observations with two antennas at each end of an intercontinental baseline are used to derive the differential interferometric phase between a compact extragalactic radio source (usually a quasar) and a number of ALSEP transmitters on the lunar surface. A continuous ALSEP-quasar differential phase history over a period of a few hours will lead to milliarcsecond angular accuracy in measuring the lunar position against the quasar reference frame if suitable calibration measurements are obtained. Development of this application of the four-antenna technique has been underway for more than a year and is producing high-quality data utilizing Deep Space Network stations. These high-accuracy observations are of value to tie the lunar ephemeris to a nearly inertial extragalactic reference frame, to test gravitational theories, and to measure the earth-moon tidal friction interaction.

Slade, M. A.↗
NASA NTRS1977

Compositional variation in late-stage differentiates in mare lavas, as indicated by silicate melt inclusions

Questions regarding an interpretation of data from silicate melt inclusions are considered, taking into account the fragmental nature of the record, the possible effects of cooling rate on late-stage melt composition, and the crystallization of the trapped melt. New data related to 484 new analyses are provided in a separate table. Textural and mineralogical features and bulk chemical composition for an overall characterization of late-stage differentiates are discussed. A description is presented of a grouping and recognition of rock types on the basis of late-stage inclusion analyses. Attention is given to the bimodality of potassium values and the delineation of differentiation trends. It is found that many of the problems in interpretation and much of the scatter found in the composition of silicate melt inclusions in lunar samples can be attributed to the incomplete nature of the record and to crystallization after trapping.

Roedder, E.↗
NASA NTRS1975

Rb-Sr study of a lunar dunite and evidence for early lunar differentiates

An Rb-Sr study of Boulder 3 from Station 2 sampled during the Apollo 17 mission is reported. The investigated boulder is a metaclastic rock, inferred to have come from the South Massif, and contains a variety of lithic clasts. Since the rock type may be critical in understanding lunar differentiation processes, an extensive investigation was carried out of the dunite clast and other clasts as well as of the fine-grained matrix. The investigation had the purpose to define the age of crystallization of the dunite and to determine the extent to which later metamorphism of the host rock may have effected the isotopic systematics of this clast. The isochron determined yielded an age of 4.55 plus or minus 0.10 AE for the dunite. This result demonstrates that differentiation began close to the time of formation of the moon and that relics of this process are preserved.

Papanastassiou, D. A.↗
NASA NTRS1978

Differential laser absorption monitoring of the atmosphere

In the airborne detection system of atmospheric constituents and pollutants described, double-ended differential absorption measurement is accomplished by rapidly current tuning the wavelength of a PbSSe diode laser across a single line of the species under consideration. As the laser wavelength sweeps periodically across the absorption line, the laser beam is amplitude modulated and is then synchronously detected. With this technique, a minimum detectable differential transmission of 0.02 percent is obtained for a 1-sec integration time.

Rubin, B.↗
NASA NTRS1978

Model potentials for electron scattering - Converged close coupling calculations for the differential cross section for e/-/N2 at 30-50 eV

A calculation has been made of the elastic scattering and rotational excitation cross sections for e(-)-N2 scattering at 30 and 50 eV using quantum chemical techniques specially designed to be applicable to elastic and inelastic electron scattering by general polyatomic molecules. The angle dependence of the sum of the elastic and rotational excitation differential cross sections is in good agreement with experiment at all scattering angles at both energies, but at 50 eV the difference from experiment exceeds the experimental uncertainty at small scattering angles and near the minimum of the differential cross section. At large scattering angles the rotational excitation cross sections are predicted to exceed the elastic scattering cross sections. The absolute cross sections agree with experiment at some angles but at other angles are as much as 51% (30 eV) or 90% (50 eV) higher; this may be due at least in part to the difficulty of putting the experimental results on an absolute scale.

Onda, K.↗
NASA NTRS1978

Numerical method for solution of systems of non-stationary spatially one-dimensional nonlinear differential equations

A computational scheme and a standard program is proposed for solving systems of nonstationary spatially one-dimensional nonlinear differential equations using Newton's method. The proposed scheme is universal in its applicability and its reduces to a minimum the work of programming. The program is written in the FORTRAN language and can be used without change on electronic computers of type YeS and BESM-6. The standard program described permits the identification of nonstationary (or stationary) solutions to systems of spatially one-dimensional nonlinear (or linear) partial differential equations. The proposed method may be used to solve a series of geophysical problems which take chemical reactions, diffusion, and heat conductivity into account, to evaluate nonstationary thermal fields in two-dimensional structures when in one of the geometrical directions it can take a small number of discrete levels, and to solve problems in nonstationary gas dynamics.

Morozov, S. K.↗
NASA NTRS1979

Characteristics of differential charging of ATS-6

Thirteen days of data collected by the Auroral Particle Experiment onboard the ATS 6 were analyzed emphasizing peculiarities in the electron data attributed to differential charging. On one of these days the satellite was eclipsed by the earth at local midnight. Spectrograms were used to examine the data. It is concluded that differential charging is responsible for returning photoelectrons to the spacecraft up to a couple hundred eV, depending on the spacecraft charge. It is believed that the Minnesota experiment on ATS 6 is largely responsible for producing a potential barrier that returns particles and produces intense spon spots in the count rates.

Johnson, B.↗
NASA NTRS1973

Program for solution of ordinary differential equations

A program for the solution of linear and nonlinear first order ordinary differential equations is described and user instructions are included. The program contains a new integration algorithm for the solution of initial value problems which is particularly efficient for the solution of differential equations with a wide range of eigenvalues. The program in its present form handles up to ten state variables, but expansion to handle up to fifty state variables is being investigated.

Sloate, H.↗
NASA NTRS1978

Voltage tunable differential heterodyne spectroscopy in the far-infrared with Josephson junctions

The basic methods of differential heterodyne spectroscopy with Josephson junctions are described. A technique is outlined for bridging the gap between a local oscillator frequency and a signal frequency through the use of a voltage-tunable internal oscillation frequency in a Josephson junction structure. It is shown that an intermediate frequency can be converted to a conveniently low frequency by double frequency conversion carried out directly in a Josephson junction. The expected conversion efficiency is estimated qualitatively. Experiments are discussed in which the differential heterodyne frequency-conversion technique was demonstrated at a wavelength of 0.4 mm and a voltage-tunable oscillation in a double Josephson junction structure was observed, with oscillation line widths as narrow as 0.5 Hz, for a resistance of 3.3 nanohms and an estimated inductance of the order of 1 nH.

Ulrich, B. T.↗
NASA NTRS1978

Stochastic partial differential equations in turbulence related problems

The theory of stochastic partial differential equations (PDEs) and problems relating to turbulence are discussed by employing the theories of Brownian motion and diffusion in infinite dimensions, functional differential equations, and functional integration. Relevant results in probablistic analysis, especially Gaussian measures in function spaces and the theory of stochastic PDEs of Ito type, are taken into account. Linear stochastic PDEs are analyzed through linearized Navier-Stokes equations with a random forcing. Stochastic equations for waves in random media as well as model equations in turbulent transport theory are considered. Markovian models in fully developed turbulence are discussed from a stochastic equation viewpoint.

Chow, P.-L.↗