Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Differential”

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 1,729 records · Page 96
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Solution of elliptic partial differential equations by fast Poisson solvers using a local relaxation factor. 1: One-step method

An algorithm for solving a large class of two- and three-dimensional nonseparable elliptic partial differential equations (PDE's) is developed and tested. It uses a modified D'Yakanov-Gunn iterative procedure in which the relaxation factor is grid-point dependent. It is easy to implement and applicable to a variety of boundary conditions. It is also computationally efficient, as indicated by the results of numerical comparisons with other established methods. Furthermore, the current algorithm has the advantage of possessing two important properties which the traditional iterative methods lack; that is: (1) the convergence rate is relatively insensitive to grid-cell size and aspect ratio, and (2) the convergence rate can be easily estimated by using the coefficient of the PDE being solved.

Chang, S. C.↗
NASA NTRS1984

Specification of a NAVSTAR Global Positioning System (GPS) receiver for a differential GPS ground system

One step towards the successful completion of a functional ground unit for the Differential Global Positioning System (DGPS) will be in choosing a currently available GPS receiver that will accurately measure the propagation times of the satellite signals and have the capability to be electrically interfaced with and controlled by a Digital Equipment Corporation (DEC) PDP-11/34A computer. The minimum requirements and characteristics of a NAVSTAR Global Positioning System (GPS) receiver are described. The specific technical specifications addressed include data accuracies and resolutions, receiver interface/external control, enclosure dimensions and mounting requirements, receiver operation, and environmental specifications.

Mccall, D. L.↗
NASA NTRS1986

Theory and operation of the real-time data acquisition system for the NASA-LaRC differential absorption lidar (DIAL)

The improvement of computer hardware and software of the NASA Multipurpose Differential Absorption Lidar (DIAL) system is documented. The NASA DIAL system is undergoing development and experimental deployment at NASA Langley Research Center for the remote measurement of atmospheric trace gas concentrations from ground and aircraft platforms. A viable DIAL system was developed capable of remotely measuring O3 and H2O concentrations from an aircraft platform. Test flights of the DIAL system were successfully performed onboard the NASA Goddard Flight Center Electra aircraft from 1980 to 1985. The DIAL Data Acquisition System has undergone a number of improvements over the past few years. These improvements have now been field tested. The theory behind a real time computer system as it applies to the needs of the DIAL system is discussed. This report is designed to be used as an operational manual for the DIAL DAS.

Butler, C.↗
NASA NTRS1985

Low-angle normal faults-low differential stress at mid crustal levels

A simple model for frictional slip on pre-existing faults that considers the local stress state near the fault and the effect of non-hydrostatic fluid pressures predicts that low-angle normal faulting is restricted to areas of the crust characterized by low differential stress and nearly lithostatic fluid pressures. The model considers frictional slip on a cohesionless low-angle normal fault governed by the failure criterion tau = mu sub f (sigma (*) sub n) =mu sub f (sigma sub n - P sub f) where tau and sigma sub n are the shear and normal stresses across the fault plane, mu sub f is the static coefficient of friction, and P sub f is the pore fluid pressure. As a first approximation, the model considers a vertical greatest principal compressive stress, sigma sub 1. It is apparent that if slip on low-angle normal faults is governed by the avove frictional failure criterion, slip on the low-angle normal fault occurs only if the least effective principal stress, sigma (*) sub 3 = sigma sub 3 - P sub f, is tensile, whenever tan superscrip -1(mu sub f d, where d is the dip of the fault. If detachment faulting occurs at any significant depth in the crust, P sub f sigma sub 3 is required. In light of this conclusion I allow P sub f to vary as necessary to allow slip on the low-angle normal fault.

Power, W. L.↗
NASA NTRS1985

Differential photometry of magnetic faculae

New observations extending the differential continuum photometry technique to the near-infrared are presented which demonstrate that the main factor determining the facular visibility near the solar disk center is the difference in H(-) opacity (and thus in penetration depth) between the continuum passbands. It is shown how the difference signal obtained depends on the temperature gradient difference between the two faculae and photosphere. The measured facular temperature gradient is compared with that given by empirical facular models based on Fraunhofer line observations, and with theoretical predictions. An explanation for the enhanced visibility of faculae against granular noise in the difference signal is suggested.

Foukal, P.↗
NASA NTRS1985

Instrument for differential on flux vector measurements on Spacelab 2

The DIF (differential ion flux) probe used on the Spacelab-2 mission as part of the PDP (plasma diagnostic package) as well as the DIF design, operational characteristics and data reduction procedures required to obtain plasma properties are described. The basic principles, the sensor head design, and the electronics design are discussed. Plasma properties such as ion drift energy and temperature, ion flow direction, and ion flux density are explained, and in addition, calibration procedures and calibration data on detection of multiple ion streams and detection of ion streams superimposed on an isotropic plasma are analyzed. Finally, the mounting and role of the DIF probe on the PDP are briefly reviewed. Schematics of the instrument and of its control logic are included.

Stone, N. H.↗
NASA NTRS1986

Differential excitation cross section of atomic oxygen by electron impact - (3P-1D transition)

Results of an electron impact experiment in which a crossed-beam method was used to determine the differential excitation cross sections of atomic oxygen (3P-1D transition) are reported. The measurements cover energies of 7, 10, 15, 20, and 30 eV, with the angular range varying from 30 to 150 deg in 15-deg increments. The results are consistent, both in shape and in magnitude, with theoretical predictions, providing a direct confirmation of the theoretical total excitation cross sections of O(1D) state. Details of the experimental equipment and procedure are given.

Shyn, T. W.↗
NASA NTRS1985

Solution of partial differential equations on vector and parallel computers

The present status of numerical methods for partial differential equations on vector and parallel computers was reviewed. The relevant aspects of these computers are discussed and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. Application areas utilizing these computers are briefly discussed.

Ortega, J. M.↗
NASA NTRS1986

Viscoplasticity based on overstress with a differential growth law for the equilibrium stress

Two coupled, nonlinear differential equations are proposed for the modeling of the elastic and rate (time) dependent inelastic behavior of structural metals in the absence of recovery and aging. The structure of the model is close to the unified theories but contains essential differences. It is shown that the model reproduces almost elastic regions upon initial loading and in the unloading regions of the hysteresis loop. Under loading, unloading and reloading in strain control the model simulated the experimentally observed sharp transition from nearly elastic to inelastic behavior. When a formulation akin to existing unified theories is adopted the almost elastic regions reduce the points and the transition upon reloading is very gradual. For different formulations the behavior under sudden in(de)creases of the strain rate by two orders of magnitude is simulated by numerical experiments and differences are noted. The model represents cyclically neutral behavior and contains three constants and two positive, decreasing functions. The determination of constants and functions from monotonic loading with strain rate changes and relaxation periods is described.

Krempl, E.↗
NASA NTRS1985

On optimal strategies in event-constrained differential games

Combat games are formulated as zero-sum differential games with unilateral event constraints. An interior penalty function approach is employed to approximate optimal strategies for the players. The method is very attractive computationally and possesses suitable approximation and convergence properties.

Heymann, M.↗
NASA NTRS1986

Differential Very Long Baseline Interferometry for 50 nanoradian deep space navigation - Results from quasar pair experiments

Deep space tracking experiments completed at JPL have demonstrated a 50-nanoradian angular positioning accuracy with wideband differential Very Long Baseline Interferometry (delta VLBI). This meets the stringent navigation requirements of NASA's Galileo mission, scheduled for launch in May 1986 and for encounter with Jupiter in December 1988. Pairs of extragalactic radio sources (quasars) with well-known coordinates were used to simulate deep space navigation passes in which quasar-spacecraft pairs are observed. This paper discusses the accuracy of the delta VLBI technique and how it is affected by source separations, source elevations, source strengths, solar plasma and ionosphere. Several observation strategies are discussed and one is shown to be especially effective in minimizing these major error sources.

Trinkle, B. K.↗
NASA NTRS1985

Legendre-tau approximation for functional differential equations. III - Eigenvalue approximations and uniform stability

The stability and convergence properties of the Legendre-tau approximation for hereditary differential systems are analyzed. A characteristic equation is derived for the eigenvalues of the resulting approximate system. As a result of this derivation the uniform exponential stability of the solution semigroup is preserved under approximation. It is the key to obtaining the convergence of approximate solutions of the algebraic Riccati equation in trace norm.

Ito, K.↗
NASA NTRS1986

Tracking Landsat-5 by a differential GPS technique

As part of an international campaign to develop precise geodetic applications of the Global Positioning System (GPS), the Jet Propulsion Laboratory is conducting a demonstration of differential GPS tracking using Landsat-5. Two strategies have been investigated: one in which only the Landsat-5 orbit is estimated, and one in which both the Landsat-5 and GPS orbits are estimated together. Error studies show that under the limited conditions of the experiment, three-dimensional Landsat-5 position accuracies of about 5 m with the first strategy and 2 m with the second strategy can be achieved over a 20-min period of good observing geometry. Orbit determination results using a version of the first strategy appear to achieve the 5 m goal. This is supported by various formal error measures and independent comparisons. The more powerful strategy has yet to be carried out.

Yunck, T. P.↗
NASA NTRS1987

Parallel Algorithm Solves Coupled Differential Equations

Numerical methods adapted to concurrent processing. Algorithm solves set of coupled partial differential equations by numerical integration. Adapted to run on hypercube computer, algorithm separates problem into smaller problems solved concurrently. Increase in computing speed with concurrent processing over that achievable with conventional sequential processing appreciable, especially for large problems.

Hayashi, A.↗
NASA NTRS1986

Global collocation methods for approximation and the solution of partial differential equations

Polynomial interpolation methods are applied both to the approximation of functions and to the numerical solutions of hyperbolic and elliptic partial differential equations. The derivative matrix for a general sequence of the collocation points is constructed. The approximate derivative is then found by a matrix times vector multiply. The effects of several factors on the performance of these methods including the effect of different collocation points are then explored. The resolution of the schemes for both smooth functions and functions with steep gradients or discontinuities in some derivative are also studied. The accuracy when the gradients occur both near the center of the region and in the vicinity of the boundary is investigated. The importance of the aliasing limit on the resolution of the approximation is investigated in detail. Also examined is the effect of boundary treatment on the stability and accuracy of the scheme.

Solomonoff, A.↗
NASA NTRS1986

Solution of elliptic partial differential equations by fast Poisson solvers using a local relaxation factor. 2: Two-step method

A two-step semidirect procedure is developed to accelerate the one-step procedure described in NASA TP-2529. For a set of constant coefficient model problems, the acceleration factor increases from 1 to 2 as the one-step procedure convergence rate decreases from + infinity to 0. It is also shown numerically that the two-step procedure can substantially accelerate the convergence of the numerical solution of many partial differential equations (PDE's) with variable coefficients.

Chang, S. C.↗
NASA NTRS1986

Survey of the status of finite element methods for partial differential equations

The finite element methods (FEM) have proved to be a powerful technique for the solution of boundary value problems associated with partial differential equations of either elliptic, parabolic, or hyperbolic type. They also have a good potential for utilization on parallel computers particularly in relation to the concept of domain decomposition. This report is intended as an introduction to the FEM for the nonspecialist. It contains a survey which is totally nonexhaustive, and it also contains as an illustration, a report on some new results concerning two specific applications, namely a free boundary fluid-structure interaction problem and the Euler equations for inviscid flows.

Temam, Roger↗
NASA NTRS1987

Doubly differential cross sections for galactic heavy-ion fragmentation

An abrasion-ablation T-matrix formulation is applied to the calculation of double differential-cross sections in projectile fragmentation of 2.1 GeV/nucleon O-16 on Be-9 and 86 MeV/nucleon C-12 on C-12 and Ag-108. An exponential parameterization of the ablation T-matrix is used and the total width of the intermediate states is taken as a parameter. Fitted values of the total width to experimental results are used to predict the lifetime of the ablation stage and indicate a decay time on the order of 10 to the -19th power sec.

Cucinotta, Francis A.↗