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NASA NTRS1982

Effect of differential spectral reflectance on DIAL measurements using topographic targets

Differential absorption lidar (DIAL) measurements of atmospheric gases and temperature made using topographic targets to provide the backscattered signal are subject to errors from the differential spectral reflectance of the target materials. The magnitude of this effect is estimated for a number of DIAL measurements reported in the literature. Calculations are presented for several topographic targets. In general the effect on a DIAL measurement increases directly with increasing wavelength and laser line separation, and inversely with differential absorption coefficient and distance to the target. The effect can be minimized by using tunable or isotope lasers to reduce the laser line separation or by using additional reference wavelengths to determine the surface differential spectral reflectance.

Grant, W. B.↗

NASA NTRS1983

Simulation and analysis of differential global positioning system for civil helicopter operations

A Differential Global Positioning System (DGPS) computer simulation was developed, to provide a versatile tool for assessing DGPS referenced civil helicopter navigation. The civil helicopter community will probably be an early user of the GPS capability because of the unique mission requirements which include offshore exploration and low altitude transport into remote areas not currently served by ground based Navaids. The Monte Carlo simulation provided a sufficiently high fidelity dynamic motion and propagation environment to enable accurate comparisons of alternative differential GPS implementations and navigation filter tradeoffs. The analyst has provided the capability to adjust most aspects of the system, the helicopter flight profile, the receiver Kalman filter, and the signal propagation environment to assess differential GPS performance and parameter sensitivities. Preliminary analysis was conducted to evaluate alternative implementations of the differential navigation algorithm in both the position and measurement domain. Results are presented to show that significant performance gains are achieved when compared with conventional GPS but that differences due to DGPS implementation techniques were small. System performance was relatively insensitive to the update rates of the error correction information.

Denaro, R. P.↗

NASA NTRS1984

Differential, integral, and momentum-transfer cross sections for elastic electron scattering by neon - 5 to 100 eV

Relative elastic-scattering differential cross sections were measured in the 5-100-eV impact energy and 10-145 deg angular ranges. Normalization of these cross sections was achieved by utilizing accurate total electron-scattering cross sections. A phase-shift analysis of the angular distributions in terms of real phase shifts has been carried out. From the differential cross sections, momentum-transfer cross sections were obtained and the values of the critical energy and angle were established (associated with the lowest value of the differential cross section) as 62.5 + or - 2.5 eV and 101.7 deg + or - 1.5 deg, respectively. The present phase shifts, the critical parameters, and differential, integral, and momentum-transfer cross sections are compared to previous experimental and theoretical results. The error associated with the present data is about 10 percent.

NASA NTRS1985

The evolution of partially differentiated planetesimals Evidence from iron meteorite groups IAB and IIICD

Some of the properties of IAB and IIICD iron meteorites thought to be derived from partially differentiated planetesimals are summarized, and the physical aspects that may have controlled parent body differentiation and affected the composition of the sulfide melt are outlined. The chemical evolution of the parent body is then discussed, and observations supporting the partial differentiation model are examined. Finally, an attempt is made to reinterpret barometric and chronometric data in light of the partial differentiation model, and tentative conclusions are presented.

Kracher, A.↗

NASA NTRS1985

Civil helicopter flight operations using differential GPS

The results of NASA flight trials of a dual-receiver differential global positioning system (DGPS) for civilian helicopter navigation applications, are presented. The three principal components of the DGPS system are described, including the GPS ground-reference system, a range tracking system, and an on-board sequential GPS receiver. The ground-based receiver in the DGPS operates at a known fixed location and receives C/A code signals from NAVSTAR satellites. System bias errors in the ground receiver are subtracted from the airborne solution for the navigational fix. Calculations of the differential bias error are carried out using an on-board PDP-11/34 M research computer. The ground-reference differential corrections for satellites are given in a table. It is shown that the differential correction signal of the DGPS contains only a small (0.1 rad/sec) high-frequency component which can be attributed to system error. A schematic diagram of the DGPS postflight data processing routine is provided.

Edwards, F. G.↗

NASA NTRS1986

Differential GPS approaches to orbit determination of high-altitude earth satellites

Orbit determination of earth satellites using conventional (up-looking) differential GPS is limited to lower altitudes due to the finite antenna beamwidth and altitude of GPS satellites. Higher user satellites suffer from having short GPS view period; at sufficiently high altitudes, up-looking GPS visibility becomes so poor that no differential measurements are possible. For such higher user satellites, two alternative differential GPS approaches are suggested. A covariance analysis is performed investigating the capabilities of these approaches at various user satellite altitudes. Best differential GPS data types are identified for satellites within different altitude ranges. Error sources and other factors affecting the orbit determination accuracy are examined. Relative merits of these approaches are compared. When applied to QUASAT, the proposed earth orbiting radio telescope with an elliptical orbit, a sub-meter orbit determination accuracy is expected.

Wu, S.-C.↗

NASA NTRS1987

Spectral differential imaging detection of planets about nearby stars

Direct ground-based optical imaging of planets in orbit about nearby stars may be accomplished by spectral differential imaging using multiple passband acoustooptic filters with a CCD. This technique provides two essential results. First, it provides a means to modulate the stellar flux reflected from a planet while leaving the flux from the star and other sources in the same field of view unmodulated. Second, spectral differential imaging enables the CCD detector to achieve a sufficiently high dynamic range to locate planets near a star in spite of an integrated brightness differential of 5 x 10 to the 8th. Spectral differential imaging at nearby diffraction limited imaging conditions with telescope apodization can reduce the time to conduct a sensitive planetary search to a few hours in some cases. The feasibility of this idea is discussed here and shown to provide, in principle, the discrimination and sensitivity to detect a Jovian-class planet about stars at distances of about 10 parsecs. The detection of brown dwarfs is shown to be feasible as well.

Smith, W. Hayden↗

NASA NTRS1991

Computations involving differential operators and their actions on functions

The algorithms derived by Grossmann and Larson (1989) are further developed for rewriting expressions involving differential operators. The differential operators involved arise in the local analysis of nonlinear dynamical systems. These algorithms are extended in two different directions: the algorithms are generalized so that they apply to differential operators on groups and the data structures and algorithms are developed to compute symbolically the action of differential operators on functions. Both of these generalizations are needed for applications.

Crouch, Peter E.↗

NASA NTRS1991

An edge preserving differential image coding scheme

Differential encoding techniques are fast and easy to implement. However, a major problem with the use of differential encoding for images is the rapid edge degradation encountered when using such systems. This makes differential encoding techniques of limited utility especially when coding medical or scientific images, where edge preservation is of utmost importance. We present a simple, easy to implement differential image coding system with excellent edge preservation properties. The coding system can be used over variable rate channels which makes it especially attractive for use in the packet network environment.

Rost, Martin C.↗

NASA NTRS1992

A nanoradian differential VLBI tracking demonstration

The shift due to Jovian gravitational deflection in the apparent angular position of the radio source P 0201+113 was measured with very long baseline interferometry (VLBI) to demonstrate a differential angular tracking technique with nanoradian accuracy. The raypath of the radio source P 0201+113 passed within 1 mrad of Jupiter (approximately 10 Jovian radii) on 21 Mar. 1988. Its angular position was measured 10 times over 4 hours on that date, with a similar measurement set on 2 Apr. 1988, to track the differential angular gravitational deflection of the raypath. According to general relativity, the expected gravitational bend of the raypath averaged over the duration of the March experiment was approximately 1.45 nrad projected onto the two California-Australia baselines over which it was measured. Measurement accuracies on the order of 0.78 nrad were obtained for each of the ten differential measurements. The chi(exp 2) per degree of freedom of the data for the hypothesis of general relativity was 0.6, which suggests that the modeled dominant errors due to system noise and tropospheric fluctuations fully accounted for the scatter in the measured angular deflections. The chi(exp 2) per degree of freedom for the hypothesis of no gravitational deflection by Jupiter was 4.1, which rejects the no-deflection hypothesis with greater than 99.999 percent confidence. The system noise contributed about 0.34 nrad per combined-baseline differential measurement and tropospheric fluctuations contributed about 0.70 nrad. Unmodeled errors were assessed, which could potentially increase the 0.78 nrad error by about 8 percent. The above chi(exp 2) values, which result from the full accounting of errors, suggest that the nanoradian gravitational deflection signature was successfully tracked.

Treuhaft, R. N.↗

NASA NTRS1992

An edge preserving differential image coding scheme

Differential encoding techniques are fast and easy to implement. However, a major problem with the use of differential encoding for images is the rapid edge degradation encountered when using such systems. This makes differential encoding techniques of limited utility, especially when coding medical or scientific images, where edge preservation is of utmost importance. A simple, easy to implement differential image coding system with excellent edge preservation properties is presented. The coding system can be used over variable rate channels, which makes it especially attractive for use in the packet network environment.

Rost, Martin C.↗

NASA NTRS1993

Differentiation of magma oceans and the thickness of the depleted layer on Venus

Various arguments suggest that Venus probably has no asthenosphere, and it is likely that beneath the crust there is a highly depleted and highly viscous mantle layer which was probably formed in the early history of the planet when it was partially or completely molten. Models of crystallization of magma oceans suggest that just after crystallization of a hypothetical magma ocean, the internal structure of Venus consists of a crust up to about 70 km thickness, a depleted layer up to about 500 km, and an enriched lower layer which probably consists of an undepleted 'lower mantle' and heavy enriched accumulates near the core-mantle boundary. Partial or even complete melting of Venus due to large impacts during the formation period eventually results in differentiation. However, the final result of such a differentiation can vary from a completely differentiated mantle to an almost completely preserved homogeneous mantle depending on competition between convection and differentiation: between low viscosity ('liquid') convection and crystal settling at small crystal fractions, or between high viscosity ('solid') convection and percolation at large crystal fractions.

Solomatov, V. S.↗

NASA NTRS1993

Description and use of LSODE, the Livermore Solver for Ordinary Differential Equations

LSODE, the Livermore Solver for Ordinary Differential Equations, is a package of FORTRAN subroutines designed for the numerical solution of the initial value problem for a system of ordinary differential equations. It is particularly well suited for 'stiff' differential systems, for which the backward differentiation formula method of orders 1 to 5 is provided. The code includes the Adams-Moulton method of orders 1 to 12, so it can be used for nonstiff problems as well. In addition, the user can easily switch methods to increase computational efficiency for problems that change character. For both methods a variety of corrector iteration techniques is included in the code. Also, to minimize computational work, both the step size and method order are varied dynamically. This report presents complete descriptions of the code and integration methods, including their implementation. It also provides a detailed guide to the use of the code, as well as an illustrative example problem.

Radhakrishnan, Krishnan↗

NASA NTRS1994

An Efficient Spectral Method for Ordinary Differential Equations with Rational Function Coefficients

We present some relations that allow the efficient approximate inversion of linear differential operators with rational function coefficients. We employ expansions in terms of a large class of orthogonal polynomial families, including all the classical orthogonal polynomials. These families obey a simple three-term recurrence relation for differentiation, which implies that on an appropriately restricted domain the differentiation operator has a unique banded inverse. The inverse is an integration operator for the family, and it is simply the tridiagonal coefficient matrix for the recurrence. Since in these families convolution operators (i.e. matrix representations of multiplication by a function) are banded for polynomials, we are able to obtain a banded representation for linear differential operators with rational coefficients. This leads to a method of solution of initial or boundary value problems that, besides having an operation count that scales linearly with the order of truncation N, is computationally well conditioned. Among the applications considered is the use of rational maps for the resolution of sharp interior layers.

Coutsias, Evangelos A.↗

NASA NTRS1996

Development of an Automatic Differentiation Version of the FPX Rotor Code

The ADIFOR2.0 automatic differentiator is applied to the FPX rotor code along with the grid generator GRGN3. The FPX is an eXtended Full-Potential CFD code for rotor calculations. The automatic differentiation version of the code is obtained, which provides both non-geometry and geometry sensitivity derivatives. The sensitivity derivatives via automatic differentiation are presented and compared with divided difference generated derivatives. The study shows that automatic differentiation method gives accurate derivative values in an efficient manner.

Hu, Hong↗

NASA NTRS2003

Fidelity and enhanced sensitivity of differential transcription profiles following linear amplification of nanogram amounts of endothelial mRNA

Although mRNA amplification is necessary for microarray analyses from limited amounts of cells and tissues, the accuracy of transcription profiles following amplification has not been well characterized. We tested the fidelity of differential gene expression following linear amplification by T7-mediated transcription in a well-established in vitro model of cytokine [tumor necrosis factor alpha (TNFalpha)]-stimulated human endothelial cells using filter arrays of 13,824 human cDNAs. Transcriptional profiles generated from amplified antisense RNA (aRNA) (from 100 ng total RNA, approximately 1 ng mRNA) were compared with profiles generated from unamplified RNA originating from the same homogeneous pool. Amplification accurately identified TNFalpha-induced differential expression in 94% of the genes detected using unamplified samples. Furthermore, an additional 1,150 genes were identified as putatively differentially expressed using amplified RNA which remained undetected using unamplified RNA. Of genes sampled from this set, 67% were validated by quantitative real-time PCR as truly differentially expressed. Thus, in addition to demonstrating fidelity in gene expression relative to unamplified samples, linear amplification results in improved sensitivity of detection and enhances the discovery potential of high-throughput screening by microarrays.

Evaluation Studies↗

NASA NTRS2001

Chemical differentiation in regions of massive star formation

We have reexamined the origin of the apparent differentiation between nitrogen-bearing molecules and complex oxygen-bearing molecules that is observed in hot molecular cores associated with massive protostars. Observations show that methanol is an ubiquitous and abundant component of protostellar ices. Recent observations suggest that ammonia may constitute an appreciable fraction of the ices toward some sources. In contrast to previous theories that suggested that N/O differentiation was caused by an anticorrelation between methanol and ammonia in the precursor grain mantles, we show that the presence of ammonia in mantles and the core temperature are key quantities in determining N/O differentiation. Calculations are presented which show that when large amounts of ammonia are evaporated alkyl cation transfer reactions are suppressed and the abundances of complex O-bearing organic molecules greatly reduced. Cooler cores (100 K) eventually evolve to an oxygen-rich chemical state similar to that attained when no ammonia was injected, but on a timescale that is an order of magnitude longer (~10(5) yr). Hotter cores (300 K) never evolve an O-rich chemistry unless ammonia is almost absent from the mantles. In this latter case, a complex O-rich chemistry develops on a timescale of ~10(4) yr, as in previous models, but disappears in about 2 x 10(5) yr, after which time the core is rich in NH3, HCN, and other N-bearing molecules. There are thus two ways in which N-rich cores can occur. We briefly discuss the implications for the determination of hot-core ages and for explaining N/O differentiation in several well-studied sources.

NASA Center ARC↗

NASA NTRS1987

Influence of microgravity on cellular differentiation in root caps of Zea mays

We launched imbibed seeds of Zea mays into outer space aboard the space shuttle Columbia to determine the influence of microgravity on cellular differentiation in root caps. The influence of microgravity varied with different stages of cellular differentiation. Overall, microgravity tended to 1) increase relative volumes of hyaloplasm and lipid bodies, 2) decrease the relative volumes of plastids, mitochondria, dictyosomes, and the vacuome, and 3) exert no influence on the relative volume of nuclei in cells comprising the root cap. The reduced allocation of dictyosomal volume in peripheral cells of flight-grown seedlings correlated positively with their secretion of significantly less mucilage than peripheral cells of Earth-grown seedlings. These results indicate that 1) microgravity alters the patterns of cellular differentiation and structures of all cell types comprising the root cap, and 2) the influence of microgravity on cellular differentiation in root caps of Zea mays is organelle specific.

NASA Program Space Biology↗