SEARCH · Engineering Papers

Results for “Differentiability”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 991 records · Page 55

All sources NASA NTRS DOE OSTI

NASA NTRS1988

Discriminating late volcanic differentiates commonly associated with precious metal deposits, using Landsat Thematic Mapper imagery

The magmatic differentiates emplaced late in volcanotectonic cycles (which when highly evolved commonly occur as domes, flow-dome complexes, and shallow intrusive porphyries) are typically more silicic and felsic than their earlier counterparts and exhibit unusually steep spectral curves from about 1.5 to 2.2 microns. This spectral characteristic emerges in the form of relatively high Landsat TM band 7 DN values and low 5/7 values, as well as dark-contrast or enhanced 5/7 images. These evolved late-phase differentiates are commonly associated both temporally and spatially with precious metal deposits, furnishing site-specific exploration targets as well as guides to caldera margins and other late-stage volcanotectonic structures.

Spatz, David M.↗

NASA NTRS1989

Classical geometries defined by exterior differential systems on higher frame bundles

Exterior differential ideals are discussed, and sets of invariant generators presented, for Reimannian, conformal and projective geometries, and for specializations such as Ricci-flat, self-dual and Einstein-Maxwell theories. The Cartan characteristic integers are explicitly calculated, and involutory basis forms found, for each of these (specialized to four dimensions), exposing their algebraic structure and showing how they generate well-posed sets of partial differential equations.

Estabrook, Frank B.↗

NASA NTRS1989

Photoacoustic measurement of differential broadening of the Lambda doublets in NO(X 2Pi 1/2,v = 2-0) by Ar

A differential broadening of the Lambda doublets in the v = 2-0 overtone band of the 2pi1/2 ground electronic state of NO in an Ar buffer gas has been observed by photoacoustic spectroscopy using a tunable color-center laser. The broadening coefficients for the f symmetry components are larger than for the e symmetry components by up to about 6 percent for J of about 16.5. This differential depends on J and vanishes at low J, implicating the anisotropy of the unpaired electron Pi orbital in the plane of rotation. The 2Pi3/2 transitions are slightly broader than the 2Pi1/2 as a result of spin-flipping collisional relaxation. The observed line shapes also exhibit collisional or Dicke narrowing due to velocity-changing collisions.

Pine, A. S.↗

NASA NTRS1989

Principles and procedures for determining absolute differential electron-molecule (atom) scattering cross sections

Procedures and calibration techniques for measuring the absolute elastic and inelastic differential cross sections (DCS) for electron impact on molecular (atomic) species are described and illustrated by examples. The elastic DCS for the molecule under study is first determined by calibration against helium using the relative flow technique. The second step involves the production of energy-loss spectra for the instrument response function, the unfolding of overlapping inelastic structures and the normalization of inelastic intensities to the elastic cross sections. It is concluded that this method of determining absolute differential electron-molecule (atom) scattering cross sections is generally applicable and provides reliable results.

Nickel, J. C.↗

NASA NTRS1989

A relationship between peak temperature drop and velocity differential in a microburst

Results from numerical microburst simulations using the Terminal Area Simulation System (Proctor, 1987) are used to develop a relationship between wind velocity differential and peak temperature drop. The numerical model and the relationships derived from the model are described. The relationship between peak temperature drop and differential wind velocity is shown to be valid during microburst development, for all precipitation shaft intensities and diameters. It is found that the relationship is not valid for low-reflectivity microburst events or in the presence of ground-based stable layers. The use of the relationship in IR wind shear detection systems is considered.

Proctor, Fred H.↗

NASA NTRS1987

Guidance simulation and test support for differential GPS flight experiment

Three separate tasks which supported the test preparation, test operations, and post test analysis of the NASA Ames flight test evaluation of the differential Global Positioning System (GPS) are presented. Task 1 consisted of a navigation filter design, coding, and testing to optimally make use of GPS in a differential mode. The filter can be configured to accept inputs from external censors such as an accelerometer and a barometric or radar altimeter. The filter runs in real time onboard a NASA helicopter. It processes raw pseudo and delta range measurements from a single channel sequential GPS receiver. The Kalman filter software interfaces are described in detail, followed by a description of the filter algorithm, including the basic propagation and measurement update equations. The performance during flight tests is reviewed and discussed. Task 2 describes a refinement performed on the lateral and vertical steering algorithms developed on a previous contract. The refinements include modification of the internal logic to allow more diverse inflight initialization procedures, further data smoothing and compensation for system induced time delays. Task 3 describes the TAU Corp participation in the analysis of the real time Kalman navigation filter. The performance was compared to that of the Z-set filter in flight and to the laser tracker position data during post test analysis. This analysis allowed a more optimum selection of the parameters of the filter.

Geier, G. J.↗

NASA NTRS1990

Differential equation based method for accurate approximations in optimization

A method to efficiently and accurately approximate the effect of design changes on structural response is described. The key to this method is to interpret sensitivity equations as differential equations that may be solved explicitly for closed form approximations, hence, the method is denoted the Differential Equation Based (DEB) method. Approximations were developed for vibration frequencies, mode shapes and static displacements. The DEB approximation method was applied to a cantilever beam and results compared with the commonly-used linear Taylor series approximations and exact solutions. The test calculations involved perturbing the height, width, cross-sectional area, tip mass, and bending inertia of the beam. The DEB method proved to be very accurate, and in most cases, was more accurate than the linear Taylor series approximation. The method is applicable to simultaneous perturbation of several design variables. Also, the approximations may be used to calculate other system response quantities. For example, the approximations for displacements are used to approximate bending stresses.

Pritchard, Jocelyn I.↗

NASA NTRS1990

Differential equation based method for accurate approximations in optimization

This paper describes a method to efficiently and accurately approximate the effect of design changes on structural response. The key to this new method is to interpret sensitivity equations as differential equations that may be solved explicitly for closed form approximations, hence, the method is denoted the Differential Equation Based (DEB) method. Approximations were developed for vibration frequencies, mode shapes and static displacements. The DEB approximation method was applied to a cantilever beam and results compared with the commonly-used linear Taylor series approximations and exact solutions. The test calculations involved perturbing the height, width, cross-sectional area, tip mass, and bending inertia of the beam. The DEB method proved to be very accurate, and in msot cases, was more accurate than the linear Taylor series approximation. The method is applicable to simultaneous perturbation of several design variables. Also, the approximations may be used to calculate other system response quantities. For example, the approximations for displacement are used to approximate bending stresses.

Pritchard, Jocelyn I.↗

NASA NTRS1990

Minimal parameter solution of the orthogonal matrix differential equation

As demonstrated in this work, all orthogonal matrices solve a first order differential equation. The straightforward solution of this equation requires n sup 2 integrations to obtain the element of the nth order matrix. There are, however, only n(n-1)/2 independent parameters which determine an orthogonal matrix. The questions of choosing them, finding their differential equation and expressing the orthogonal matrix in terms of these parameters are considered. Several possibilities which are based on attitude determination in three dimensions are examined. It is shown that not all 3-D methods have useful extensions to higher dimensions. It is also shown why the rate of change of the matrix elements, which are the elements of the angular rate vector in 3-D, are the elements of a tensor of the second rank (dyadic) in spaces other than three dimensional. It is proven that the 3-D Gibbs vector (or Cayley Parameters) are extendable to other dimensions. An algorithm is developed emplying the resulting parameters, which are termed Extended Rodrigues Parameters, and numerical results are presented of the application of the algorithm to a fourth order matrix.

Bar-Itzhack, Itzhack Y.↗

NASA NTRS1990

Vertex implications of stability for a class of delay-differential interval system

Although vertex implication in parameter space does not hold for stability of general delay-differential interval systems, it is shown that in an important special case when the characteristic equation of the system is describable by certain quasi-polynomials the vertex implication for stability does hold. It is also pointed out that vertex implication for stability does not hold in general for delay-differential systems with interval delay.

Kim, K. D.↗

NASA NTRS1991

Asymptotic integration algorithms for nonhomogeneous, nonlinear, first order, ordinary differential equations

New methods for integrating systems of stiff, nonlinear, first order, ordinary differential equations are developed by casting the differential equations into integral form. Nonlinear recursive relations are obtained that allow the solution to a system of equations at time t plus delta t to be obtained in terms of the solution at time t in explicit and implicit forms. Examples of accuracy obtained with the new technique are given by considering systems of nonlinear, first order equations which arise in the study of unified models of viscoplastic behaviors, the spread of the AIDS virus, and predator-prey populations. In general, the new implicit algorithm is unconditionally stable, and has a Jacobian of smaller dimension than that which is acquired by current implicit methods, such as the Euler backward difference algorithm; yet, it gives superior accuracy. The asymptotic explicit and implicit algorithms are suitable for solutions that are of the growing and decaying exponential kinds, respectively, whilst the implicit Euler-Maclaurin algorithm is superior when the solution oscillates, i.e., when there are regions in which both growing and decaying exponential solutions exist.

Walker, K. P.↗

NASA NTRS1991

Doppler-corrected differential detection system

Doppler in a communication system operating with a multiple differential phase-shift-keyed format (MDPSK) creates an adverse phase shift in an incoming signal. An open loop frequency estimation is derived from a Doppler-contaminated incoming signal. Based upon the recognition that, whereas the change in phase of the received signal over a full symbol contains both the differentially encoded data and the Doppler induced phase shift, the same change in phase over half a symbol (within a given symbol interval) contains only the Doppler induced phase shift, and the Doppler effect can be estimated and removed from the incoming signal. Doppler correction occurs prior to the receiver's final output of decoded data. A multiphase system can operate with two samplings per symbol interval at no penalty in signal-to-noise ratio provided that an ideal low pass pre-detection filter is employed, and two samples, at 1/4 and 3/4 of the symbol interval T sub s, are taken and summed together prior to incoming signal data detection.

Simon, Marvin K.↗

NASA NTRS1991

From differential to difference equations for first order ODEs

When constructing an algorithm for the numerical integration of a differential equation, one should first convert the known ordinary differential equation (ODE) into an ordinary difference equation. Given this difference equation, one can develop an appropriate numerical algorithm. This technical note describes the derivation of two such ordinary difference equations applicable to a first order ODE. The implicit ordinary difference equation has the same asymptotic expansion as the ODE itself, whereas the explicit ordinary difference equation has an asymptotic that is similar in structure but different in value when compared with that of the ODE.

Freed, Alan D.↗

NASA NTRS1989

A study of microstructural characteristics and differential thermal analysis of Ni-based superalloys

The objective of this work is to correlate the mechanical properties of the Ni-based superalloy MAR M246(Hf) used in the Space Shuttle Main Engine with its structural characteristics by systematic study of optical photomicrographs and differential thermal analysis. The authors developed a method of predicting the liquidus and solidus temperature of various nickel based superalloys (MAR-M247, Waspaloy, Udimet-41, polycrystalline and single crystals of CMSX-2 and CMSX-3) and comparing the predictions with the experimental differential thermal analysis (DTA) curves using Perkin-Elmer DTA 1700. The method of predicting these temperatures is based on the additive effect of the components dissolved in nickel. The results were compared with the experimental values.

Aggarwal, M. D.↗

NASA NTRS1991

Using trees to compute approximate solutions to ordinary differential equations exactly

Some recent work is reviewed which relates families of trees to symbolic algorithms for the exact computation of series which approximate solutions of ordinary differential equations. It turns out that the vector space whose basis is the set of finite, rooted trees carries a natural multiplication related to the composition of differential operators, making the space of trees an algebra. This algebraic structure can be exploited to yield a variety of algorithms for manipulating vector fields and the series and algebras they generate.

Grossman, Robert↗

NASA NTRS1991

Evolutionary models of halo stars with rotation. I - Evidence for differential rotation with depth in stars

Evolutionary models of metal-poor stars are computed including the effects of rotation, and their properties are compared with observations. The models rotate slowly at the surface, in agreement with the observed upper limits on the rotation velocity at main-sequence turnoff; they also have substantial differential rotation with depth. This differential rotation preserves a sufficient amount of internal angular momentum to explain the rapid rotation of evolved horizontal-branch stars. These results hold for a wide range of angular momentum loss and transport parameter values. Differences and similarities between the surface and internal rotation of solar metallicity and metal-poor models are discussed. Rigidly rotating models are found to be incompatible with the observations once giant branch mass loss is taken into account. Horizontal-branch rotation velocity measurements as a function of color are proposed as a test of the rotation law enforced in convection zones, and their dependence on cluster age and metallicity are discussed.

Pinsonneault, Marc H.↗

NASA NTRS1991

Early mantle differentiation and its thermal consequences

This paper discusses early events (i.e., pre-3.8 Ga) leading to the mantle differentiation. Arguments are presented in favor of a pre-3.8 Ga basaltic crust covering the earth to balance the depletion of the mantle source of Archean continental crust. It is shown that isotopic and chemical considerations of surviving Archean rocks require the existence of a region enriched in Nd throughout much of the early and middle Archean, which was distinct from the continental crust. Data are presented on the essential mass balance for Nd between the depleted mantle and the enriched reservoir, showing that the enriched reservoir must have contained a large (about 30-70 percent) fraction of the total Nd inventory of the differentiated crust-mantle system at 3.8 Ga.

Galer, S. J. G.↗

NASA NTRS1992

Differential Current Source

Circuit acts as voltage-controlled current source having high-impedance floating differential output. Maintains commanded current in load, regardless of changes in load impedance and regardless of any common-mode voltages on load. Provides constant excitation current to germanium resistance thermometer or other transducer, output voltage of which sensed by differential voltage amplifier.

Sutton, John F.↗