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At least 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

On the spline-based wavelet differentiation matrix

The differentiation matrix for a spline-based wavelet basis is constructed. Given an n-th order spline basis it is proved that the differentiation matrix is accurate of order 2n + 2 when periodic boundary conditions are assumed. This high accuracy, or superconvergence, is lost when the boundary conditions are no longer periodic. Furthermore, it is shown that spline-based bases generate a class of compact finite difference schemes.

Jameson, Leland↗
NASA NTRS1993

On the Daubechies-based wavelet differentiation matrix

The differentiation matrix for a Daubechies-based wavelet basis is constructed and superconvergence is proven. That is, it will be proven that under the assumption of periodic boundary conditions that the differentiation matrix is accurate of order 2M, even though the approximation subspace can represent exactly only polynomials up to degree M-1, where M is the number of vanishing moments of the associated wavelet. It is illustrated that Daubechies-based wavelet methods are equivalent to finite difference methods with grid refinement in regions of the domain where small-scale structure is present.

Jameson, Leland↗
NASA NTRS1993

Multigrid methods for differential equations with highly oscillatory coefficients

New coarse grid multigrid operators for problems with highly oscillatory coefficients are developed. These types of operators are necessary when the characters of the differential equations on coarser grids or longer wavelengths are different from that on the fine grid. Elliptic problems for composite materials and different classes of hyperbolic problems are practical examples. The new coarse grid operators can be constructed directly based on the homogenized differential operators or hierarchically computed from the finest grid. Convergence analysis based on the homogenization theory is given for elliptic problems with periodic coefficients and some hyperbolic problems. These are classes of equations for which there exists a fairly complete theory for the interaction between shorter and longer wavelengths in the problems. Numerical examples are presented.

Engquist, Bjorn↗
NASA NTRS1993

On the differentiation matrix for Daubechies-based wavelets on an interval

The differentiation matrix for a Daubechies-based wavlet basis defined on an interval will be constructed. It will be shown that the differentiation matrix based on the currently available boundary constructions does not maintain the superconvergence encountered under periodic boundary conditions.

Jameson, Leland↗
NASA NTRS1993

Differential GPS for air transport: Status

The presentation presents background on what the Global Navigation Satellite System (GNSS) is, desired target dates for initial GNSS capabilities for aircraft operations, and a description of differential GPS (Global Positioning System). The presentation also presents an overview of joint flight tests conducted by LaRC and Honeywell on an integrated differential GPS/inertial reference unit (IRU) navigation system. The overview describes the system tested and the results of the flight tests. The last item presented is an overview of a current grant with Ohio University from LaRC which has the goal of developing a precision DGPS navigation system based on interferometry techniques. The fundamentals of GPS interferometry are presented and its application to determine attitude and heading and precision positioning are shown. The presentation concludes with the current status of the grant.

Hueschen, Richard M.↗
NASA NTRS1993

Differential Scanning Calorimetry (DSC) for planetary surface exploration

Differential Scanning Calorimetry (DSC) is the quantitative measurement of the enthalpic response of a material to a systematic change in temperature. In practice, the heat flow into or outward from a sample is measured as the sample is heated or cooled at a carefully controlled rate. DSC superficially resembles, but is not the same as differential thermal analysis (DTA), which is the measurement of temperature differences between a sample and reference material as the pair is heated or cooled. The fundamental properties measured by DSC are enthalpies and temperatures of phase transitions and constant-pressure heat capacities. Depending on instrument design and the nature of the sample, high-quality DSC analyses can be obtained on only a few milligrams of solid materials. DSC requires direct contact with the sample and generally degrades, if not destroys, the sample as a consequence of heating. In laboratory applications, it is common to subject the gaseous effluent from the DSC to analysis by a separate evolved-gas analyzer (EGA).

Gooding, James L.↗
NASA NTRS1994

Pseudospectral collocation methods for fourth order differential equations

Collocation schemes are presented for solving linear fourth order differential equations in one and two dimensions. The variational formulation of the model fourth order problem is discretized by approximating the integrals by a Gaussian quadrature rule generalized to include the values of the derivative of the integrand at the boundary points. Collocation schemes are derived which are equivalent to this discrete variational problem. An efficient preconditioner based on a low-order finite difference approximation to the same differential operator is presented. The corresponding multidomain problem is also considered and interface conditions are derived. Pseudospectral approximations which are C1 continuous at the interfaces are used in each subdomain to approximate the solution. The approximations are also shown to be C3 continuous at the interfaces asymptotically. A complete analysis of the collocation scheme for the multidomain problem is provided. The extension of the method to the biharmonic equation in two dimensions is discussed and results are presented for a problem defined in a nonrectangular domain.

Malek, Alaeddin↗
NASA NTRS1994

The Mars Observer differential one-way range demonstration

Current methods of angular spacecraft positioning using station differenced range data require an additional observation of an extragalactic radio source (quasar) to estimate the timing offset between the reference clocks at the two Deep Space Stations. The quasar observation is also used to reduce the effects of instrumental and media delays on the radio metric observable by forming a difference with the spacecraft observation (delta differential one-way range, delta DOR). An experiment has been completed using data from the Global Positioning System satellites to estimate the station clock offset, eliminating the need for the quasar observation. The requirements for direct measurement of the instrumental delays that must be made in the absence of a quasar observation are assessed. Finally, the results of the 'quasar-free' differential one-way range, or DOR, measurements of the Mars Observer spacecraft are compared with those of simultaneous conventional delta DOR measurements.

Kroger, P. M.↗
NASA NTRS1994

Morphological Differentiation of Colon Carcinoma Cell Lines in Rotating Wall Vessels

The objectives of this project were to determine whether (1) microgravity permits unique, three-dimensional cultures of neoplastic human colon tissues and (2) this culture interaction produces novel intestinal growth and differentiation factors. The initial phase of this project tested the efficacy of simulated microgravity for the cultivation and differentiation of human colon carcinoma in rotating wall vessels (RWV's) on microcarrier beads. The RWV's simulate microgravity by randomizing the gravity vector in an aqueous medium under a low shear stress environment in unit gravity. This simulation achieves approximately a one-fifth g environment that allows cells to 'float' and form three-dimensional relationships with less shear stress than in other stirred aqueous medium bioreactors. In the second phase of this project we assessed the ability of human colon carcinoma lines to adhere to various substrates because adhesion is the first event that must occur to create three-dimensional masses. Finally, we tested growth factor production in the last phase of this project.

Jessup, J. M.↗
NASA NTRS1994

Mass analysis addition to the Differential Ion Flux Probe (DIFP) study

The objective of this study is to develop a technique to measure the characteristics of space plasmas under highly disturbed conditions; e.g., non-Maxwellian plasmas with strong drifting populations and plasmas contaminated by spacecraft outgassing. The approach, conducted in conjunction with current MSFC activities, is to extend the capabilities of the Differential Ion Flux Probe (DIFP) to include a high throughput mass measurement that does not require either high voltage or contamination sensitive devices such as channeltron electron multipliers or microchannel plates. This will significantly reduce the complexity and expense of instrument fabrication, testing, and integration of flight hardware compared to classical mass analyzers. The feasibility of the enhanced DIFP has been verified by using breadboard test models in a controlled plasma environment. The ability to manipulate particles through the instrument regardless of incident angle, energy, or ionic component has been amply demonstrated. The energy analysis mode is differential and leads directly to a time-of-flight mass measurement. With the new design, the DIFP will separate multiple ion streams and analyze each stream independently for ion flux intensity, velocity (including direction of motion), mass, and temperature (or energy distribution). In particular, such an instrument will be invaluable on follow-on electrodynamic TSS missions and, possibly, for environmental monitoring on the space station.

Wright, K. H., Jr.↗
NASA NTRS1994

Differential GPS and system integration of the Low Visibility Landing and Surface Operations (LVLASO) demonstration

The LVLASO Flight Demonstration of ASTA concepts (FDAC) integrates NASA-Langley's electronic moving map display and Transport Systems Research Vehicle (TSRV) (a modified Boeing 737 aircraft); ARINC's VHF data link, GPS ground station, and automated controller workstation; and Norden's surface radar/airport movement safety system. Aircraft location is shown on the electronic map display in the cockpit. An approved taxi route as well as other aircraft and surface traffic are also displayed. An Ashtech Z12 Global Positioning System (GPS) receiver on the TSRV estimates the aircraft's position. In Differential mode (DSPS), the Ashtech receiver accepts differential C/A code pseudorange corrections from a GPS ground station. The GPS ground station provides corrections up to ten satellites. The corrections are transmitted on a VHF data link at a 1 Hz. rate using the RTCM-104 format. DGPS position estimates will be within 5 meters of actual aircraft position. DGPS position estimates are blended with position, velocity, acceleration, and heading data from the TSRV Air Data/Inertial Reference System (ADIRS). The ADIRS data is accurate in the short-term, but drifts over time. The DGPS data is used to keep the ADIRS position accurate. Ownship position, velocity, heading, and turn rate are sent at a 20 Hz. rate to the electronic map display. Airport traffic is detected by the airport surface radar system. Aircraft and vehicles such as fuel trucks and baggage carts are detected. The traffic's location, velocity, and heading are sent to the TSRV. To prevent traffic symbology from jumping each second when a location update arrives, velocity and heading are used to predict a new traffic location for each display update. Possible runway incursions and collisions can be shown on the electronic map. Integrating the different systems used in the FDAC requires attention to the underlying coordinate systems. The airport diagram displayed on the electronic map is obtained from published navigational charts. The charts reference the North American Datum of 1927 (NAD27) or a local state-plane coordinate system. GPS uses the World Geodetic Standard of 1984 (WGS84). Both NAD27 and WGS84 model the Earth as an ellipsoid, however, they use a different origin and different size ellipsoids. Latitudes and longitudes given in these systems can be converted to a Cartesian system with the origin at the Earth's center. The surface radar detects traffic in a locally-level, rho-theta coordiante system. The electronic airport diagram is stored using a flat XY coordinate system. The map origin is at the tower and is referenced as True North up. All ownship and other traffic positions must be converted to the electronic map's frame of reference for display.

Rankin, James M.↗
NASA NTRS1994

A brief survey of constrained mechanics and variational problems in terms of differential forms

There has been considerable interest recently in constrained mechanics and variational problems. This is in part due to applied interests (such as 'non-holonomic mechanics in robotics') and in other part due to the fact that several schools of 'pure' mathematics have found that this classical subject is of importance for what they are trying to do. I have made various attempts at developing these subjects since my Lincoln lab days of the late 1950's. In this Chapter, I will sketch a Unified point of view, using Cartan's approach with differential forms. This has the advantage from the C-O-R viewpoint being developed in this Volume that the extension from 'smooth' to 'generalized' data is very systematic and algebraic. (I will only deal with the 'smooth' point of view in this Chapter; I will develop the 'generalized function' material at a later point.) The material presented briefly here about Variational Calculus and Constrained Mechanics can be found in more detail in my books, 'Differential Geometry and the Calculus of Variations', 'Lie Algebras and Quantum Mechanics', and 'Geometry, Physics and Systems'.

Hermann, Robert↗
NASA NTRS1995

Automatic differentiation evaluated as a tool for rotorcraft design and optimization

This paper investigates the use of automatic differentiation (AD) as a means for generating sensitivity analyses in rotorcraft design and optimization. This technique transforms an existing computer program into a new program that performs sensitivity analysis in addition to the original analysis. The original FORTRAN program calculates a set of dependent (output) variables from a set of independent (input) variables, the new FORTRAN program calculates the partial derivatives of the dependent variables with respect to the independent variables. The AD technique is a systematic implementation of the chain rule of differentiation, this method produces derivatives to machine accuracy at a cost that is comparable with that of finite-differencing methods. For this study, an analysis code that consists of the Langley-developed hover analysis HOVT, the comprehensive rotor analysis CAMRAD/JA, and associated preprocessors is processed through the AD preprocessor ADIFOR 2.0. The resulting derivatives are compared with derivatives obtained from finite-differencing techniques. The derivatives obtained with ADIFOR 2.0 are exact within machine accuracy and do not depend on the selection of step-size, as are the derivatives obtained with finite-differencing techniques.

Walsh, Joanne L.↗
NASA NTRS1995

Dynamical Approach Study of Spurious Steady-State Numerical Solutions of Nonlinear Differential Equations: Global Asymptotic Behavior of Time Discretizations - 2

The global asymptotic nonlinear behavior of 1 1 explicit and implicit time discretizations for four 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODES) is analyzed. The objectives are to gain a basic understanding of the difference in the dynamics of numerics between the scalars and systems of nonlinear autonomous ODEs and to set a baseline global asymptotic solution behavior of these schemes for practical computations in computational fluid dynamics. We show how 'numerical' basins of attraction can complement the bifurcation diagrams in gaining more detailed global asymptotic behavior of time discretizations for nonlinear differential equations (DEs). We show how in the presence of spurious asymptotes the basins of the true stable steady states can be segmented by the basins of the spurious stable and unstable asymptotes. One major consequence of this phenomenon which is not commonly known is that this spurious behavior can result in a dramatic distortion and, in most cases, a dramatic shrinkage and segmentation of the basin of attraction of the true solution for finite time steps. Such distortion, shrinkage and segmentation of the numerical basins of attraction will occur regardless of the stability of the spurious asymptotes, and will occur for unconditionally stable implicit linear multistep methods. In other words, for the same (common) steady-state solution the associated basin of attraction of the DE might be very different from the discretized counterparts and the numerical basin of attraction can be very different from numerical method to numerical method. The results can be used as an explanation for possible causes of error, and slow convergence and nonconvergence of steady-state numerical solutions when using the time-dependent approach for nonlinear hyperbolic or parabolic PDES.

Yee, H. C.↗
NASA NTRS1995

Dynamical Approach Study of Spurious Steady-State Numerical Solutions of Nonlinear Differential Equations: Global Asymptotic Behavior of Time Discretizations - Part 2

The global asymptotic nonlinear behavior of 11 explicit and implicit time discretizations for four 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODEs) is analyzed. The objectives are to gain a basic understanding of the difference in the dynamics of numerics between the scalars and systems of nonlinear autonomous ODEs and to set a baseline global asymptotic solution behavior of these schemes for practical computations in computational fluid dynamics. We show how 'numerical' basins of attraction can complement the bifurcation diagrams in gaining more detailed global asymptotic behavior of time discretizations for nonlinear differential equations (DEs). We show how in the presence of spurious asymptotes the basins of the true stable steady states can be segmented by the basins of the spurious stable and unstable asymptotes. One major consequence of this phenomenon which is not commonly known is that this spurious behavior can result in a dramatic distortion and, in most cases, a dramatic shrinkage and segmentation of the basin of attraction of the true solution for finite time steps. Such distortion, shrinkage and segmentation of the numerical basins of attraction will occur regardless of the stability of the spurious asymptotes, and will occur for unconditionally stable implicit linear multistep methods. In other words, for the same (common) steady-state solution the associated basin of attraction of the DE might be very different from the discretized counterparts and the numerical basin of attraction can be very different from numerical method to numerical method. The results can be used as an explanation for possible causes of error, and slow convergence and nonconvergence of steady-state numerical solutions when using the time-dependent approach for nonlinear hyperbolic or parabolic PDEs.

Yee, H. C.↗
NASA NTRS1998

Turbulent Compressible Convection with Rotation: Mean Flows and Differential Rotation - 2

The effects of rotation on turbulent, compressible convection within stellar envelopes are studied through three-dimensional numerical simulations conducted within a local f-plane model. This work seeks to understand the types of differential rotation that can be established in convective envelopes of stars like the Sun, for which recent helioseismic observations suggest an angular velocity profile with depth and latitude at variance with many theoretical predictions. This paper analyzes the mechanisms that are responsible for the mean (horizontally averaged) zonal and meridional flows that are produced by convection influenced by Coriolis forces. The compressible convection is considered for a range of Rayleigh, Taylor, and Prandtl (and thus Rossby) numbers encompassing both laminar and turbulent flow conditions under weak and strong rotational constraints. When the nonlinearities are moderate, the effects of rotation on the resulting laminar cellular convection leads to distinctive tilts of the cell boundaries away from the vertical. These yield correlations between vertical and horizontal motions that generate Reynolds stresses that can drive mean flows, interpretable as differential rotation and meridional circulations. Under more vigorous forcing, the resulting turbulent convection involves complicated and contorted fluid particle trajectories, with few clear correlations between vertical and horizontal motions, punctuated by an evolving and intricate downflow network that can extend over much of the depth of the layer. Within such networks are some coherent structures of vortical downflow that tend to align with the rotation axis. These yield a novel turbulent alignment mechanism, distinct from the laminar tilting of cellular boundaries, that can provide the principal correlated motions and thus Reynolds stresses and subsequently mean flows. The emergence of such coherent structures that can persist amidst more random motions is a characteristic of turbulence with symmetries broken by rotation and stratification. Such structure is here found to play a crucial role in defining the mean zonal and meridional flows that coexist with the convection. Though they are subject to strong inertial oscillations, the strength and type of the mean flows are determined by a combination of the laminar tilting and the turbulent alignment mechanisms. Varying the parameters produces a wide range of mean motions. Among these, some turbulent solutions exhibit a mean zonal velocity profile that is nearly constant with depth, much as deduced by helioseismology at midlatitudes within the Sun. The solutions exhibit a definite handedness, with the direction of the persistent mean flows often prescribing a spiral with depth near the boundaries, also in accord with helioseismic deductions. The mean helicity has a profile that is positive in the upper portion of the domain and negative in the lower portion, a property bearing on magnetic dynamo processes that may be realized within such rotating layers of turbulent convection.

Brummell, Nicholas H.↗
NASA NTRS1997

Low Differential Pressure Generator

A method and apparatus for evaluating low differential pressure transducers includes a pressure generator in the form of a piston-cylinder assembly having a piston that may be manually positioned precisely within the cylinder to change the volume and thus the pressure at respective sides of the piston. At one side of the piston the cylinder communicates with a first chamber and at the other side of the piston the cylinder communicates with a second chamber, the first and second chambers being formed within a common tank by a partition wall. The chambers each communicate with the transducer to be evaluated and a standard pre-calibrated transducer the transducers being connected fluidly in parallel so that a pressure differential between air in the two chambers resulting from movement of the piston within the cylinder is communicated to both the transducer to be evaluated and the standard transducer, and the outputs of the transducers is observed and recorded.

Stout, Stephen J.↗
NASA NTRS1996

Atmospheric Pre-Corrected Differential Absorption Techniques to Retrieve Columnar Water Vapor: Theory and Simulations

Two different approaches exist to retrieve columnar water vapor from imaging spectrometer data: (1) Differential absorption techniques based on: (a) Narrow-Wide (N/W) ratio between overlapping spectrally wide and narrow channels; (b) Continuum Interpolated Band Ratio (CIBR) between a measurement channel and the weighted sum of two reference channels. (2) Non-linear fitting techniques which are based on spectral radiative transfer calculations. The advantage of the first approach is computational speed and of the second, improved retrieval accuracy. Our goal was to improve the accuracy of the first technique using physics based on radiative transfer. Using a modified version of the Duntley equation, we derived an "Atmospheric Pre-corrected Differential Absorption" (APDA) technique and described an iterative scheme to retrieve water vapor on a pixel-by-pixel basis. Next we compared both, the CIBR and the APDA using the Duntley equation for MODTRAN3 computed irradiances, transmissions and path radiance (using the DISORT option). This simulation showed that the CIBR is very sensitive to reflectance effects and that the APDA performs much better. An extensive data set was created with the radiative transfer code 6S over 379 different ground reflectance spectra. The calculated relative water vapor error was reduced significantly for the APDA. The APDA technique had about 8% (vs. over 35% for the CIBR) of the 379 spectra with a relative water vapor error of greater than +5%. The APDA has been applied to 1991 and 1995 AVIRIS scenes which visually demonstrate the improvement over the CIBR technique.

Borel, Christoph C.↗