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NASA NTRS1996

Numerical Algorithms Based on Biorthogonal Wavelets

Wavelet bases are used to generate spaces of approximation for the resolution of bidimensional elliptic and parabolic problems. Under some specific hypotheses relating the properties of the wavelets to the order of the involved operators, it is shown that an approximate solution can be built. This approximation is then stable and converges towards the exact solution. It is designed such that fast algorithms involving biorthogonal multi resolution analyses can be used to resolve the corresponding numerical problems. Detailed algorithms are provided as well as the results of numerical tests on partial differential equations defined on the bidimensional torus.

Ponenti, Pj.↗
NASA NTRS2004

Quantifying Square Membrane Wrinkle Behavior Using MITC Shell Elements

For future membrane based structures, quantified predictions of membrane wrinkling behavior in terms of amplitude, angle and wavelength are needed to optimize the efficiency and integrity of such structures, as well as their associated control systems. For numerical analyses performed in the past, limitations on the accuracy of membrane distortion simulations have often been related to the assumptions made while using finite elements. Specifically, this work demonstrates that critical assumptions include: effects of gravity. supposed initial or boundary conditions, and the type of element used to model the membrane. In this work, a 0.2 square meter membrane is treated as a structural material with non-negligible bending stiffness. Mixed Interpolation of Tensorial Components (MTTC) shell elements are used to simulate wrinkling behavior due to a constant applied in-plane shear load. Membrane thickness, gravity effects, and initial imperfections with respect to flatness were varied in numerous nonlinear analysis cases. Significant findings include notable variations in wrinkle modes for thickness in the range of 50 microns to 1000 microns, which also depend on the presence of an applied gravity field. However, it is revealed that relationships between overall strain energy density for cases with differing initial conditions are independent of assumed initial con&tions. In addition, analysis results indicate that the relationship between amplitude scale (W/t) and structural scale (L/t) is linear in the presence of a gravity field.

Jacobson, Mindy B.↗
NASA NTRS2007

Minnowbrook I: 1993 Workshop on End-Stage Boundary Layer Transition

This volume contains materials presented at the Minnowbrook I-1993 Workshop on End-Stage Boundary Layer Transition, held at the Syracuse University Minnowbrook Conference Center, New York, from August 15 to 18, 1993. This volume was previously published as a Syracuse University report edited by John E. LaGraff. The workshop organizers were John E. LaGraff (Syracuse University), Terry V. Jones (Oxford University), and J. Paul Gostelow (University of Technology, Sydney). The workshop focused on physical understanding of the late stages of transition from laminar to turbulent flows, with the specific goal of contributing to improving engineering design of turbomachinery and wing airfoils. The workshop participants included academic researchers from the United States and abroad, and representatives from the gas-turbine industry and U.S. government laboratories. To improve interaction and discussions among the participants, no formal papers were required. The physical mechanisms discussed were related to natural and bypass transition, wake-induced transition, effects of freestream turbulence, turbulent spots, hairpin vortices, nonlinear instabilities and breakdown, instability wave interactions, intermittency, turbulence, numerical simulation and modeling of transition, heat transfer in boundary-layer transition, transition in separated flows, laminarization, transition in turbomachinery compressors and turbines, hypersonic boundary-layer transition, and other related topics. This volume contains abstracts and copies of the viewgraphs presented, organized according to the workshop sessions. The workshop summary and the plenary discussion transcript clearly outline future research needs.

LaGraff, John E.↗
NASA NTRS2011

Future Opportunities and Challenges in Remote Sensing of Drought

The value of satellite remote sensing for drought monitoring was first realized more than two decades ago with the application of Normalized Difference Index (NDVI) data from the Advanced Very High Resolution Radiometer (AVHRR) for assessing the effect of drought on vegetation. Other indices such as the Vegetation Health Index (VHI) were also developed during this time period, and applied to AVHRR NDVI and brightness temperature data for routine global monitoring of drought conditions. These early efforts demonstrated the unique perspective that global imagers such as AVHRR could provide for operational drought monitoring through their near-daily, global observations of Earth's land surface. However, the advancement of satellite remote sensing of drought was limited by the relatively few spectral bands of operational global sensors such as AVHRR, along with a relatively short period of observational record. Remote sensing advancements are of paramount importance given the increasing demand for tools that can provide accurate, timely, and integrated information on drought conditions to facilitate proactive decision making (NIDIS, 2007). Satellite-based approaches are key to addressing significant gaps in the spatial and temporal coverage of current surface station instrument networks providing key moisture observations (e.g., rainfall, snow, soil moisture, ground water, and ET) over the United States and globally (NIDIS, 2007). Improved monitoring capabilities will be particularly important given increases in spatial extent, intensity, and duration of drought events observed in some regions of the world, as reported in the International Panel on Climate Change (IPCC) report (IPCC, 2007). The risk of drought is anticipated to further increase in some regions in response to climatic changes in the hydrologic cycle related to evaporation, precipitation, air temperature, and snow cover (Burke et al., 2006; IPCC, 2007; USGCRP, 2009). Numerous national, regional, and global efforts such as the Famine and Early Warning System (FEWS), National Integrated Drought Information System (NIDIS), and Group on Earth Observations (GEO), as well as the establishment of regional drought centers (e.g., European Drought Observatory) and geospatial visualization and monitoring systems (e.g, NASA SERVIR) have been undertaken to improve drought monitoring and early warning systems throughout the world. The suite of innovative remote sensing tools that have recently emerged will be looked upon to fill important data and knowledge gaps (NIDIS, 2007; NRC, 2007) to address a wide range of drought-related issues including food security, water scarcity, and human health.

Wardlow, Brian D.↗
NASA NTRS1977

Data simulation studies for field programs, satellite system tests, and regional weather prediction

In the present paper, the status of the Drexel/NCAR regional numerical weather forecast system is summarized to show the extent of our experience and our immediate requirements for data within the United States on scales smaller than rawinsonde spacing (approximately 300 km). Preliminary experiments are described, and data assimilation problems are examined. It is shown that data requirements, assimilation methods, and forecast sensitivity differ for regional and large-scale models. Forecast verification statistics suggest that middle-troposphere temperature is well known but relative humidity is not. In some cases, regional forecasts require much better humidity data than available from rawinsondes. Numerics, lateral boundary conditions, model physics, and computing power are adequate for near real-time experimental regional prediction with horizontal mesh sizes down to 35 km. Subsynoptic data and assimilation are the primary challenges facing regional NWP.

Kreitzberg, C. W.↗
NASA NTRS2005

Dependence of Ru2O3 Activity on Composition of Silicate Melts: Using Statistical Correlations to Infer Thermodynamic Behavior in the Melt

Understanding variations in activity with composition is an essential step in improving prediction of partition coefficients during magma evolution. Variations in activity with composition are complex and do not generally exhibit ideal behavior relative to a traditional melt-component set. Although deviations from component ideality can be modeled numerically by simply fitting to compositional variables (such as in a regular or subregular solution model), such models have not been particularly successful for describing variations in trace component activities. A better approach might be to try to identify components that do a better job of describing the behavior of the species in the melt. Electrochemical Measurement of Ru2O3 activities: Electrodes were inserted into silicate melt beads of various compositions (Table 1) suspended on Ptwire loops in a 1-atm gas mixing furnace. An electrical potential was imposed between the electrodes, the imposed potential increasing along a step ramp with a pulse imposed on each step (Fig. 1). Current flows between electrodes when electroactive species in the melt are oxidized or reduced at the electrodes. The resulting current was measured at the top and bottom of the voltage pulse, and the difference (the differential current) was plotted against potential. The peak of the resulting curve is related to the activity coefficient for the particular electroactive species (Ru2O3) in the melt [1, 2, 3]. A significant part of the nonideal contribution to activity is due not to intrinsic properties of the component in the melt, but to our ignorance about the state and mixing properties of the component in the melt.

Colson, R. O.↗
NASA NTRS2006

Constraining Numerical Geodynamo Modeling with Surface Observations

Numerical dynamo solutions have traditionally been generated entirely by a set of self-consistent differential equations that govern the spatial-temporal variation of the magnetic field, velocity field and other fields related to dynamo processes. In particular, those solutions are obtained with parameters very different from those appropriate for the Earth s core. Geophysical application of the numerical results therefore depends on correct understanding of the differences (errors) between the model outputs and the true states (truth) in the outer core. Part of the truth can be observed at the surface in the form of poloidal magnetic field. To understand these differences, or errors, we generate new initial model state (analysis) by assimilating sequentially the model outputs with the surface geomagnetic observations using an optimal interpolation scheme. The time evolution of the core state is then controlled by our MoSST core dynamics model. The final outputs (forecasts) are then compared with the surface observations as a means to test the success of the assimilation. We use the surface geomagnetic data back to year 1900 for our studies, with 5-year forecast and 20-year analysis periods. We intend to use the result; to understand time variation of the errors with the assimilation sequences, and the impact of the assimilation on other unobservable quantities, such as the toroidal field and the fluid velocity in the core.

Kuang, Weijia↗
NASA NTRS1995

On the Utility of the Molecular Oxygen Dayglow Emissions as Proxies for Middle Atmospheric Ozone

Molecular oxygen dayglow emissions arise in part from processes related to the Hartley band photolysis of ozone. It is therefore possible to derive daytime ozone concentrations from measurements of the volume emission rate of either dayglow. The accuracy to which the ozone concentration can be inferred depends on the accuracy to which numerous kinetic and spectroscopic rate constants are known, including rates which describe the excitation of molecular oxygen by processes that are not related to the ozone concentration. We find that several key rate constants must be known to better than 7 percent accuracy in order to achieve an inferred ozone concentration accurate to 15 percent from measurements of either dayglow. Currently, accuracies for various parameters typically range from 5 to 100 percent.

Mlynczak, Martin G.↗
NASA NTRS1995

Global precipitation estimates based on a technique for combining satellite-based estimates, rain gauge analysis, and NWP model precipitation information

The 'satellite-gauge model' (SGM) technique is described for combining precipitation estimates from microwave satellite data, infrared satellite data, rain gauge analyses, and numerical weather prediction models into improved estimates of global precipitation. Throughout, monthly estimates on a 2.5 degrees x 2.5 degrees lat-long grid are employed. First, a multisatellite product is developed using a combination of low-orbit microwave and geosynchronous-orbit infrared data in the latitude range 40 degrees N - 40 degrees S (the adjusted geosynchronous precipitation index) and low-orbit microwave data alone at higher latitudes. Then the rain gauge analysis is brougth in, weighting each field by its inverse relative error variance to produce a nearly global, observationally based precipitation estimate. To produce a complete global estimate, the numerical model results are used to fill data voids in the combined satellite-gauge estimate. Our sequential approach to combining estimates allows a user to select the multisatellite estimate, the satellite-gauge estimate, or the full SGM estimate (observationally based estimates plus the model information). The primary limitation in the method is imperfections in the estimation of relative error for the individual fields. The SGM results for one year of data (July 1987 to June 1988) show important differences from the individual estimates, including model estimates as well as climatological estimates. In general, the SGM results are drier in the subtropics than the model and climatological results, reflecting the relatively dry microwave estimates that dominate the SGM in oceanic regions.

Huffman, George J.↗
NASA NTRS1993

Antenna pattern control using impedance surfaces

A hybrid numerical technique is developed for electrically large pyramidal horn antennas radiating in free space. A stepped-waveguide method is used to analyze the interior surfaces of the horn transition. The Electric Field Integral Equation (EFIE) is employed on the outer surfaces of the pyramidal horn including the radiating aperture. Meanwhile, the Magnetic Field Integral Equation (MFIE) is used on the aperture to relate the aperture fields and those in the horn transition. The resultant hybrid field integral equation (HFIE) is solved numerically by the method of moments. This formulation is both accurate and numerically stable so that high-gain microwave pyramidal horns can be analyzed rigorously. Far-field radiation patterns, both computed and measured, are presented for three electrically-large x-band horn antennas. The comparisons demonstrate that this method is accurate enough to predict the fine pattern structure at wide angles and in the back region. Computed far-field patterns and aperture field distribution of two smaller x-band horns are also presented along with a discussion on the validity of the approximate aperture field distributions routinely used in the analysis and design of pyramidal horns.

Balanis, Constantine A.↗
NASA NTRS2011

Determining the Local Abundance of Martian Methane and its 13-C/l2-C and D/H Isotopic Ratios for Comparison with Related Gas and Soil Analysis on the 2011 Mars Science Laboratory (MSL) Mission

Understanding the origin of Martian methane will require numerous complementary measurements from both in situ and remote sensing investigations and laboratory work to correlate planetary surface geophysics with atmospheric dynamics and chemistry. Three instruments (Quadrupole Mass Spectrometer (QMS), Gas Chromatograph (GC) and Tunable Laser Spectrometer (TLS)) with sophisticated sample handling and processing capability make up the Sample Analysis at Mars (SAM) analytical chemistry suite on NASA s 2011 Mars Science Laboratory (MSL) Mission. Leveraging off the SAM sample and gas processing capability that includes methane enrichment, TLS has unprecedented sensitivity for measuring absolute methane (parts-per-trillion), water, and carbon dioxide abundances in both the Martian atmosphere and evolved from heated soil samples. In concert with a wide variety of associated trace gases (e.g. SO2, H2S, NH3, higher hydrocarbons, organics, etc.) and other isotope ratios measured by SAM, TLS will focus on determining the absolute abundances of methane, water and carbon dioxide, and their isotope ratios: 13C/12C and D/H in methane; 13C/12C and 18O/17O/16O in carbon dioxide; and 18O/17O/16O and D/H in water. Measurements near the MSL landing site will be correlated with satellite (Mars Express, Mars 2016) and ground-based observations.

Webster, Christopher R.↗
NASA NTRS1986

Optimization methods and silicon solar cell numerical models

The goal of this project is the development of an optimization algorithm for use with a solar cell model. It is possible to simultaneously vary design variables such as impurity concentrations, front junction depth, back junctions depth, and cell thickness to maximize the predicted cell efficiency. An optimization algorithm has been developed and interfaced with the Solar Cell Analysis Program in 1 Dimension (SCAPID). SCAPID uses finite difference methods to solve the differential equations which, along with several relations from the physics of semiconductors, describe mathematically the operation of a solar cell. A major obstacle is that the numerical methods used in SCAPID require a significant amount of computer time, and during an optimization the model is called iteratively until the design variables converge to the value associated with the maximum efficiency. This problem has been alleviated by designing an optimization code specifically for use with numerically intensive simulations, to reduce the number of times the efficiency has to be calculated to achieve convergence to the optimal solution. Adapting SCAPID so that it could be called iteratively by the optimization code provided another means of reducing the cpu time required to complete an optimization. Instead of calculating the entire I-V curve, as is usually done in SCAPID, only the efficiency is calculated (maximum power voltage and current) and the solution from previous calculations is used to initiate the next solution.

Girardini, K.↗
NASA NTRS1984

A numerical scheme for the identification of hybrid systems describing the vibration of flexible beams with tip bodies

A cubic spline based Galerkin-like method is developed for the identification of a class of hybrid systems which describe the transverse vibration to flexible beams with attached tip bodies. The identification problem is formulated as a least squares fit to data subject to the system dynamics given by a coupled system of ordnary and partial differential equations recast as an abstract evolution equation (AEE) in an appropriate infinite dimensional Hilbert space. Projecting the AEE into spline-based subspaces leads naturally to a sequence of approximating finite dimensional identification problems. The solutions to these problems are shown to exist, are relatively easily computed, and are shown to, in some sense, converge to solutions to the original identification problem. Numerical results for a variety of examples are discussed.

Rosen, I. G.↗
NASA NTRS1992

Numerical simulations of cometary dust

Most observations of comets are done photometrically or spectrophotometrically. The interpretation of the aperture-averaged flux is relatively simple for an isotropic, radially expanding coma of infinite extent - the canonical model. However, the interpretation of the observations is not so clear when the motion of the dust is affected by radiation pressure, or when the emission is time-varying and anisotropic. For example, in a sample of CCD images of 10 comets, Jewitt and Meech (1987, Ap.J. 317, 992) found that the photometric profiles of only three comets were consistent, within the observational errors, with the profiles predicted form the canonical model. Photometric observations with large apertures, however, seem to suggest that the canonical model may be quite adequate (c.f. Osip, Schleicher, and Millis, 1992, Icarus 98, 115). The dust itself is characterized by a size distribution, with size dependencies on the expansion velocity, the scattered and thermal radiation, the response to radiation pressure, and probably the density. How good then are the approximations normally used in determining the production rates of the dust when these effects are present? As part of a program to better understand the dynamics of cometary dust and gas, a computer program has been developed which numerically simulates the emission of both dust and gas from a tilted rotating nucleus.

Lien, David J.↗
NASA NTRS2016

Trajectories for Flyby Sample Return at Saturn's Moons

Ballistic trajectories are computed which would enable a sample return mission to Titan or Enceladus without capturing, descending, or landing. The low-cost mission concept utilizes a free return trajectory that also involves a close flyby of the moon. This work extends the concept, and related trajectory analysis methodology, previously applied to a Europa mission. Specifically, a broad search algorithm is employed to systematically locate potentially feasible itineraries over an entire Saturn period. High-quality approximate solutions are then optimized to be continuous using high-fidelity dynamics. Techniques and software from the Europa analysis, were readily adapted and able to find numerous mission enabling trajectories. A direct mission to Titan is possible with flight time under 16 years and Earth-relative speeds below 11.0 km/sec. The VEEGA option is shown to substantially reduce launch C3, but flight times exceed 21 years. Unfortunately, an Enceladus mission requires a flight time of 25 years or more, and incurs fairly high relative speeds. Nevertheless, an optimized reference mission is computed.

Jones, Drew Ryan↗
NASA NTRS1996

Relativity Parameters Determined from Lunar Laser Ranging

Analysis of 24 years of lunar laser ranging data is used to test the principle of equivalence, geodetic precession, the PPN parameters beta and gamma, and G/G. Recent data can be fitted with a rms scatter of 3 cm. (a) Using the Nordtvedt effect to test the principle of equivalence, it is found that the Moon and Earth accelerate alike in the Sun's field. The relative accelerations match to within 5 x 10(exp -13) . This limit, combined with an independent determination of y from planetary time delay, gives beta. Including the uncertainty due to compositional differences, the parameter beta differs from unity by no more than 0.0014; and, if the weak equivalence principle is satisfied, the difference is no more than 0.0006. (b) Geodetic precession matches its expected 19.2 marc sec/yr rate within 0.7%. This corresponds to a 1% test of gamma. (c) Apart from the Nordtvedt effect, beta and gamma can be tested from their influence on the lunar orbit. It is argued theoretically that the linear combination 0.8(beta) + 1.4(gamma) can be tested at the 1% level of accuracy. For solutions using numerically derived partial derivatives, higher sensitivity is found. Both 6 and y match the values of general relativity to within 0.005, and the linear combination beta+ gamma matches to within 0,003, but caution is advised due to the lack of theoretical understanding of these sensitivities. (d) No evidence for a changing gravitational constant is found, with absolute value of G/G less than or equal to 8 x lO(exp -12)/yr. There is significant sensitivity to G/G through solar perturbations on the lunar orbit.

Williams, J. G.↗
NASA NTRS1975

An interdisciplinary analysis of multispectral satellite data for selected cover types in the Colorado Mountains, using automatic data processing techniques

The author has reported the following significant results. A data set containing SKYLAB, LANDSAT, and topographic data has been overlayed, registered, and geometrically corrected to a scale of 1:24,000. After geometrically correcting both sets of data, the SKYLAB data were overlayed on the LANDSAT data. Digital topographic data were then obtained, reformatted, and a data channel containing elevation information was then digitally overlayed onto the LANDSAT and SKYLAB spectral data. The 14,039 square kilometers involving 2,113, 776 LANDSAT pixels represents a relatively large data set available for digital analysis. The overlayed data set enables investigators to numerically analyze and compare two sources of spectral data and topographic data from any point in the scene. This capability is new and it will permit a numerical comparison of spectral response with elevation, slope, and aspect. Utilization of the spectral and topographic data together to obtain more accurate classifications of the various cover types present is feasible.

Hoffer, R. M.↗
NASA NTRS1976

Random vibration of compliant wall

The paper is concerned with the realistic case of two-dimensional random motion of a membrane with bending stiffness supported on a viscoelastic spring substrate and on an elastic base plate under both subsonic and supersonic boundary layer turbulence. The cross-power spectral density of surface displacements is solved in terms of design variables of the compliant wall - such as the dimensions and material properties of the membrane (Mylar), substrate (PVC foam), and panel (aluminum) - so that a sensitivity analysis can be made to examine the influence of each design variable on the surface response statistics. Three numerical examples typical of compliant wall design are worked out and their response statistics in relation to wave drag and roughness drag are assessed. The results can serve as a guideline for experimental investigation of the drag reduction concept through the use of a compliant wall.

Yang, J.-N.↗