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At least 1,621 records · Page 90
All sourcesNASA NTRSDOE OSTI
NASA NTRS1978

Characterization of oriented cracks with differential strain analysis

Linear strain of a rock sample as a function of hydrostatic pressure can be measured with a precision of 2 millionths. Such high-precision data for three orthogonal directions allow calculation of the distribution function for the porosity due to cracks' closing completely at a given pressure. Such data for at least six independent directions yield the zero-pressure strain tensor due to cracks' closing completely at a given pressure. The principal values and axes of this tensor distribution function provide information about the orientation of cracks as a function of closure pressure. The mathematical basis for the technique is developed, and the technique is illustrated with differential strain data for two samples, the Westerly (Rhode Island) granite and the Twin Sisters (Washington) dunite. Strain-tensor calculations reveal that each of these samples has a different type of anisotropic crack distribution.

Siegfried, R.↗
NASA NTRS1977

Differential altimetry for satellite orbit determination

Differential altimetry is concerned with the employment of differenced satellite altimeter measurements at orbit ground trace intersections. The employment of this procedure makes it possible to eliminate two of the major error sources found in direct altimetry. Previous applications have not included the appropriate dynamic constraints required to account for correlations due to satellite orbit motion. A description is given of an investigation in which these correlations are included. The methodology produced is consistent with the dynamic environment. The regional or local limitations of previous approaches are overcome by extending the technique to the global scale. Attention is given to the description of the data type, the geometric topography height, altimeter errors, discretization errors, an approximate orbit determination problem, and a comparison of differenced altimeter measurements for retrograde and prograde orbits.

Hagar, H., Jr.↗
NASA NTRS1978

Lunar initial Nd-143/Nd-144 - Differential evolution of the lunar crust and mantle

The Sm-Nd evolution of Apollo 15 green glass is discussed. The ICE age (intercept with chondritic evolution) of 3.8 + or - 0.4 eons overlaps the range of reported (Ar-39)-(Ar-40) ages and implies a distinct source region for green glass, characterized by very low and unfractionated REE abundances. Evidence is presented that LINd (lunar initial Nd) is compatible with a 'chondritic'-type Nd isotopic evolution as observed in the Juvinas meteorite. This normalization is used to study the Sm-Nd system of various lunar rock types. The results obtained from a limited number of rocks clearly indicate differential Sm-Nd evolution for the lunar crust and mantle. High-Ti basalts returned by the Apollo 11 and 17 missions were derived from distinct source regions. The Nd-143 evolution in KREEP requires a source region which is clearly distinct from any mantle reservoir.

Lugmair, G. W.↗
NASA NTRS1978

Error behaviour of multistep methods applied to unstable differential systems

The problem of modelling a dynamic system described by a system of ordinary differential equations which has unstable components for limited periods of time is discussed. It is shown that the global error in a multistep numerical method is the solution to a difference equation initial value problem, and the approximate solution is given for several popular multistep integration formulae. Inspection of the solution leads to the formulation of four criteria for integrators appropriate to unstable problems. A sample problem is solved numerically using three popular formulae and two different stepsizes to illustrate the appropriateness of the criteria.

Brown, R. L.↗
NASA NTRS1977

Trace element geochemistry and the early lunar differentiation

The results are considered of experiments in which thermal neutron activation analysis was used to measure the halogens, U, Te, Ru, Os, and Hg in lunar samples. A calorimetric method was used for P2O5. Three Apollo 17 basalts, one Apollo 11 basalt, and one Apollo 15 basalt were used for the Ru-Os study. Os and Ru were measured in seven samples of breccia 14305 in a series of experiments to check an apparent anomaly in the isotopic composition of the Hg which it contains. A lunar model for Ru-Os partition is discussed. It is suggested that Ru and Os were partitioned and fractionated in the original differentiation of the lunar surface ocean. Fractionation among near-surface materials was less than a factor of 2 according to the lithic breccia data. Fractionations among basaltic sources were very large, exceeding 100, and primarily due to Ru. A clue to Ru and Os distributions at the depths from which mare basalts were derived may be provided by the relative ages of the basalts. These are interpreted as being related to partial melting in response to temperature increases at depth with time.

Jovanovic, S.↗
NASA NTRS1975

Long-term differential energy spectrum for solar-flare iron-group particles

A long-term solar-flare differential energy spectrum for iron-group nuclei from approximately 0.1 to approximately 600 MeV/amu is derived from track density profile measurements in sample 64455 and sample 68815. Measurements from uneroded surfaces were obtained from quench crystals of plagioclase in 64455, and a Kr-81/Kr method indicates that the exposure age of this sample is 2,010,000 yrs. The power laws which best fit the normalized track density data are reported; the energy spectrum consists of two power law curves smoothly joined together which in turn are smoothly connected to a modulated galactic cosmic-ray spectrum. Standard track production versus depth profiles can be used to determine solar-flare track exposure ages and erosion rates for lunar samples.

Blanford, G. E.↗
NASA NTRS1978

A comparison of the Method of Lines to finite difference techniques in solving time-dependent partial differential equations

Steady state solutions to two time dependent partial differential systems have been obtained by the Method of Lines (MOL) and compared to those obtained by efficient standard finite difference methods: (1) Burger's equation over a finite space domain by a forward time central space explicit method, and (2) the stream function - vorticity form of viscous incompressible fluid flow in a square cavity by an alternating direction implicit (ADI) method. The standard techniques were far more computationally efficient when applicable. In the second example, converged solutions at very high Reynolds numbers were obtained by MOL, whereas solution by ADI was either unattainable or impractical. With regard to 'set up' time, solution by MOL is an attractive alternative to techniques with complicated algorithms, as much of the programming difficulty is eliminated.

Kurtz, L. A.↗
NASA NTRS1979

Differential spectrophone

Sensitivity and measuring capability of optoacoustic gas analyzer (spectrophone) are enhanced by combining differential monitoring stark modulation.

Margolis, J. S.↗
NASA NTRS1980

Low-common-mode differential amplifier

Outputs of differential amplifier are excellently matched in phase and amplitude over wide range of frequencies. Common mode feedback loop offsets differences between two signal paths. Possible applications of circuit are in oscilloscopes, integrated circuit logic tester, and other self contained instruments.

Morrison, S.↗
NASA NTRS1979

Propulsion-free separation and rendezvous of small shuttle free-flyers using controlled differential drag

A natural successor in the Shuttle era to many sounding rocket flights is the free-flyer mode of operation, in which the Shuttle Orbiter releases a subsatellite (with payloads), effects a desired separation, and approaches and retrieves the free-layer. The propulsive maneuvers required of the Orbiter by equivalent relative motions obtained through controlled differential drag (via changes in free-layer effective area and/or Orbiter attitude changes) are replaced. Simplified analytical techniques are developed and feasibility is verified.

King, J. C.↗
NASA NTRS1979

Solar p-mode oscillations as a tracer of radial differential rotation

Photoelectric observations of solar p-modes obtained with improved wavenumber and frequency resolution are presented. The observations are compared with model calculations of the p-modes, and the degree of spatial and temporal coherence of the observed wave pattern is investigated. It is found that the p-mode oscillations pervade the visible surface of the sun with a high degree of coherence in space and time, so that the whole complex pattern of standing waves with its nodes and antinodes can be regarded as a fixed pattern corotating with the solar surface layers. The p-modes are introduced as a tracer of solar rotational flow velocities. The equatorial differential rotation is estimated as a function of effective depth on the basis of the theoretical contribution functions for the p-modes recently derived by Ulrich et al. (1978). The results strongly indicate that the angular speed of rotation is not uniform even in the relatively shallow layer extending about 20,000 km below the photosphere.

Deubner, F.-L.↗
NASA NTRS1979

Propulsion-free separation and rendezvous of small Shuttle free-flyers using controlled differential drag

A natural successor in the Shuttle era to many sounding rocket flights is the free-flyer mode of operation, in which the Shuttle Orbiter releases a subsatellite (with payload), effects a desired separation, and finally approaches and retrieves the free-flyer. This paper proposes replacing, to the maximum extent feasible, the propulsive maneuvers required for the Orbiter by equivalent relative motions obtained through controlled differential drag (via changes in free-flyer effective area and/or Orbiter attitude changes). Simplified analytical techniques are developed and feasibility is verified. Several illustrative examples are specified (e.g., a 3-km separation in 1 day, with 4-day return).

King, J. C.↗
NASA NTRS1979

Energy conserving norms for the solution of hyperbolic systems of partial differential equations

The hyperbolic system of partial differential equations with a real constant square coefficient matrix A is considered. The problem of finding an energy conserving norm for the solution of the system is reduced to the problem of characterizing those matrices appearing in the boundary conditions which satisfy two specific matrix equations. Necessary and sufficient conditions on the coefficient matrix A and the matrices appearing in boundary conditions are derived for an energy conserving norm. The conditions serve as criteria on a given system which determine whether or not the solution will have its energy conserved in some norm. Examples of specific systems and boundary conditions are also provided.

Gunzburger, M. D.↗
NASA NTRS1978

The decrease in effective photocurrents due to saddle points in electrostatic potentials near differentially charged spacecraft

The reported investigation had the objective to illustrate the presence of important multidimensional effects in spacecraft charging. Two-dimensional codes have been under development by Parker (1976). A description is presented of a calculation which was performed using the three-dimensional NASA Charging Analyzer Program (NASCAP). NASCAP was run to calculate the electrostatic potentials on the surface of, and in the space surrounding, a sunlit Teflon-coated sphere. Currents to the sunlit surfaces were determined on the basis of an approximate photosheath model for strong differential charging.

Mandell, M. J.↗
NASA NTRS1979

Stability of sequences generated by nonlinear differential systems

A local stability analysis is presented for both the analytic and numerical solutions of the initial value problem for a system of ordinary differential equations. It is shown that, using a proper choice of Liapunov function, a connected region of stable initial values of both the analytic solution and the one-leg k-step numerical solution can be approximated. Attention is given to the example of the two-dimensional problem involving the stability of the longitudinal equations of motion of a gliding jet aircraft.

Brown, R. L.↗
NASA NTRS1978

An assessment of crustal thickness variations on the lunar near side - Models, uncertainties, and implications for crustal differentiation

The paper presents a series of models for the structure of lunar nearside crust which are consistent with the observed gravity and topography. Each crustal model is derived subject to a specific set of constraints and assumptions. The assumptions/constraints considered include strict isostatic equilibrium, pure Airy compensation mechanism, pure Pratt compensation mechanism, assignment of assumed fixed values for mare basalt thickness, and attribution of all superisostatic mass in the maria to basalt fill. The resulting models are used to assess the degree and mechanism of isostasy, and to investigate the thickness of the mare basalt. Details of the lateral variations in crustal thickness or density and in the degree of isostatic compensation bear strongly on the mode of early crustal differentiation and on the subsequent thermal history of the moon.

Thurber, C. H.↗
NASA NTRS1978

Numerical solutions of a control problem governed by functional differential equations

A numerical procedure is proposed for solving optimal control problems governed by linear retarded functional differential equations. The procedure is based on the idea of 'averaging approximations', due to Banks and Burns (1975). For illustration, numerical results generated on an IBM 370/158 computer, which demonstrate the rapid convergence of the method are presented.

Banks, H. T.↗