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NASA NTRS1992

Domain decomposition: A bridge between nature and parallel computers

Domain decomposition is an intuitive organizing principle for a partial differential equation (PDE) computation, both physically and architecturally. However, its significance extends beyond the readily apparent issues of geometry and discretization, on one hand, and of modular software and distributed hardware, on the other. Engineering and computer science aspects are bridged by an old but recently enriched mathematical theory that offers the subject not only unity, but also tools for analysis and generalization. Domain decomposition induces function-space and operator decompositions with valuable properties. Function-space bases and operator splittings that are not derived from domain decompositions generally lack one or more of these properties. The evolution of domain decomposition methods for elliptically dominated problems has linked two major algorithmic developments of the last 15 years: multilevel and Krylov methods. Domain decomposition methods may be considered descendants of both classes with an inheritance from each: they are nearly optimal and at the same time efficiently parallelizable. Many computationally driven application areas are ripe for these developments. A progression is made from a mathematically informal motivation for domain decomposition methods to a specific focus on fluid dynamics applications. To be introductory rather than comprehensive, simple examples are provided while convergence proofs and algorithmic details are left to the original references; however, an attempt is made to convey their most salient features, especially where this leads to algorithmic insight.

Keyes, David E.↗

NASA NTRS1991

The 3-D description of vertical current sheets with application to solar flares

Following a brief review of the processes which have been suggested for explaining the occurrence of solar flares we suggest a new scenario which builds on the achievements of the previous suggestion that the current sheets, which develop naturally in 3-D cases with gravity from impacting independent magnetic structures (i.e., approaching current systems), do not consist of horizontal currents but are instead predominantly vertical current systems. This suggestion is based on the fact that as the subphotospheric sources of the magnetic field displace the upper photosphere and lower chromosphere regions, where plasma beta is near unity, will experience predominantly horizontal mass motions which will lead to a distorted 3-D configurations of the magnetic field having stored free energy. In our scenario, a vertically flowing current sheet separates the plasma regions associated with either of the subphotospheric sources. This reflects the balanced tension of the two stressed fields which twist around each other. This leads naturally to a metastable or unstable situation as the twisted field emerges into a low beta region where vertical motions are not inhibited by gravity. In our flare scenario the impulsive energy release occurs, initially, not by reconnection but mainly by the rapid change of the magnetic field which has become unstable. During the impulsive phase the field lines contort in such way as to realign the electric current sheet into a minimum energy horizontal flow. This contortion produces very large electric fields which will accelerate particles. As the current evolves to a horizontal configuration the magnetic field expands vertically, which can be accompanied by eruptions of material. The instability of a horizontal current is well known and causes the magnetic field to undergo a rapid outward expansion. In our scenario, fast reconnection is not necessary to trigger the flare, however, slow reconnection would occur continuously in the current layer at the locations of potential flaring. During the initial rearrangement of the field strong plasma turbulence develops. Following the impulsive phase, the final current sheet will experience faster reconnection which we believe responsible for the gradual phase of the flare. The reconnection will dissipate part of the current and will produce sustained and extended heating in the flare region and in the postflare loops.

Fontenla, Juan M.↗

NASA NTRS1992

Planar laser-induced fluorescence imaging of OH in the exhaust of a bi-propellant thruster

Planar laser-induced fluorescence imaging of the hydroxyl radical has been performed on the flow produced by the exhaust of a subscale H2/O2 fueled bi-propellant rocket engine. Measurements were made to test the feasibility of OH (0,0) and (3,0) excitation strategies by using injection seeded XeCl and KrF excimer lasers, respectively. The flow is produced with hydrogen and oxygen reacting at a combustor chamber pressure of 5 atm which then exhausts to the ambient. The hydroxyl concentration in the exhaust flow is approximately 8 percent. Fluorescence images obtained by pumping the Q1(3) transition in the (0,0) band exhibited very high signals but also showed the effect of laser beam absorption. To obtain images when pumping the P1(8) transition in the (3,0) band it was necessary to use exceptionally fast imaging optics and unacceptably high intensifier gains. The result was single-shot images which displayed a signal-to-noise ratio of order unity or less when measured on a per pixel basis.

Paul, Phillip H.↗

NASA NTRS1993

Close-up analysis of aircraft ice accretion

Various types of ice formation have been studied by analysis of high magnification video observations. All testing was conducted in the NASA Lewis Icing Research Tunnel (IRT). A faired 8.9 cm (3.5 in.) diameter metal-clad cylinder and a 5.1 (2 in.) aluminum cylinder were observed by close-up and overview video cameras for several wind tunnel conditions. These included close-up grazing angle, close-up side view, as well as overhead and side overview cameras. Still photographs were taken at the end of each spray along with tracings of the subsequent ice shape. While in earlier tests only the stagnation region was observed, the entire area from the stagnation line to the horn region of glaze ice shapes was observed in this test. The modes or horn formation have been identified within the range of conditions observed. In the horn region, Horn Type A ice is formed by 'dry' feather growth into the flow direction and Horn Type B is formed by a 'wet' growth normal to the surface. The feather growth occurs when the freezing fraction is near unity and roughness elements exist to provide an initial growth site.

Hansman, R. John↗

NASA NTRS1992

Homogeneous quantum electrodynamic turbulence

The electromagnetic field equations and Dirac equations for oppositely charged wave functions are numerically time-integrated using a spatial Fourier method. The numerical approach used, a spectral transform technique, is based on a continuum representation of physical space. The coupled classical field equations contain a dimensionless parameter which sets the strength of the nonlinear interaction (as the parameter increases, interaction volume decreases). For a parameter value of unity, highly nonlinear behavior in the time-evolution of an individual wave function, analogous to ideal fluid turbulence, is observed. In the truncated Fourier representation which is numerically implemented here, the quantum turbulence is homogeneous but anisotropic and manifests itself in the nonlinear evolution of equilibrium modal spatial spectra for the probability density of each particle and also for the electromagnetic energy density. The results show that nonlinearly interacting fermionic wave functions quickly approach a multi-mode, dynamic equilibrium state, and that this state can be determined by numerical means.

Shebalin, John V.↗

NASA NTRS1992

Modeling and measurement of a micro-optic beam deflector

The use is studied of a unity-magnification micro-optic beam deflector. The defelector consists of two arrays of positively powered lenslets. The lenslets on each array are arranged in a square grid. Design criteria are based on usefulness in optical data storage devices. The deflector is designed to operate over a + or - 1.6 range of deflection angles. Modeling results are compared with interferometric analysis of the wavefront from a single lenslet pair. The results indicate that the device is nearly diffraction limited, but there are substantial wavefront errors at the edges and corners of the lenslets.

Milster, Tom D.↗

NASA NTRS1993

Soft x ray properties of the Geminga pulsar

The ROSAT soft x ray spectrum and pulse profile of the Geminga pulsar are analyzed and interpreted in terms of thermal emission from the surface of the neutron star. The x ray spectrum appears to consist of two blackbody components with T(sub 1) = (5.2 +/- 1.0) x 10 (exp 5) K and T(sub 2) approximately 3 x 10(exp 6) K, respectively. The inferred ratio of surface areas, A(sub 2)/A(sub 1), is approximately 3 x 10(exp -5). Both components are highly modulated at the pulsar rotation period, but the harder x ray pulse is narrower, and leads the main (soft) x ray pulse by about 105 deg of phase. The soft x ray component is interpreted as photospheric cooling of much of the neutron star's surface area, while the small, hot region could be part of the much smaller polar cap heated by energetic particles flowing inward from the magnetospheric accelerator which is responsible for the production of Geminga's gamma rays. Geminga's gamma ray emission is consistent with outer-magnetosphere accelerator models for highly inclined dipoles. These predict the beaming of energetic gamma rays close enough to the star to give copious e(+/-) production in the stellar magnetic field and a large circumstellar pair density from pair inflow toward the surface. These pairs may quench radio emission, and also reflect most of the hard polar cap x rays back to the stellar surface by cyclotron resonance scattering. They are then reemitted from that much larger area at the lower temperature T(sub 1). The single-peaked nature of the x ray pulse and its energy-dependent phase suggest an off-center dipole geometry for the surface magnetic field. Under the assumption that the soft x ray emission comes from the full surface of a neutron star of radius R = 10 km, a distance estimate of (150-400) pc is derived. This range is consistent with the fit interstellar column density of (1.5 +/- 0.5) x 10(exp 20) cm(exp -2). Distances less than 150 pc are probably ruled out both by the lower limit on the column density, and also by the requirement that the Rayleigh-Jeans extrapolation of the soft x ray spectrum not exceed the observed blue flux of the faint optical counterpart. This distance estimate implies that Geminga's efficiency for converting spindown power into gamma-rays is near unity, and that there may be significant beaming of the gamma rays as well. These results tend to bolster the prospect that most of the unidentified high-energy gamma ray sources in the Galactic plane are pulsars, some of which may be radio quiet.

Halpern, J. P.↗

NASA NTRS1992

Possibility expectation and its decision making algorithm

The fuzzy integral has been shown to be an effective tool for the aggregation of evidence in decision making. Of primary importance in the development of a fuzzy integral pattern recognition algorithm is the choice (construction) of the measure which embodies the importance of subsets of sources of evidence. Sugeno fuzzy measures have received the most attention due to the recursive nature of the fabrication of the measure on nested sequences of subsets. Possibility measures exhibit an even simpler generation capability, but usually require that one of the sources of information possess complete credibility. In real applications, such normalization may not be possible, or even desirable. In this report, both the theory and a decision making algorithm for a variation of the fuzzy integral are presented. This integral is based on a possibility measure where it is not required that the measure of the universe be unity. A training algorithm for the possibility densities in a pattern recognition application is also presented with the results demonstrated on the shuttle-earth-space training and testing images.

Keller, James M.↗

NASA NTRS1993

Target fragmentation in radiobiology

Nuclear reactions in biological systems produce low-energy fragments of the target nuclei seen as local high events of linear energy transfer (LET). A nuclear-reaction formalism is used to evaluate the nuclear-induced fields within biosystems and their effects within several biological models. On the basis of direct ionization interaction, one anticipates high-energy protons to have a quality factor and relative biological effectiveness (RBE) of unity. Target fragmentation contributions raise the effective quality factor of 10 GeV protons to 3.3 in reasonable agreement with RBE values for induced micronuclei in bean sprouts. Application of the Katz model indicates that the relative increase in RBE with decreasing exposure observed in cell survival experiments with 160 MeV protons is related solely to target fragmentation events. Target fragment contributions to lens opacity given an RBE of 1.4 for 2 GeV protons in agreement with the work of Lett and Cox. Predictions are made for the effective RBE for Harderian gland tumors induced by high-energy protons. An exposure model for lifetime cancer risk is derived from NCRP 98 risk tables, and protraction effects are examined for proton and helium ion exposures. The implications of dose rate enhancement effects on space radiation protection are considered.

Wilson, John W.↗

NASA NTRS1993

Quaternion normalization in spacecraft attitude determination

Attitude determination of spacecraft usually utilizes vector measurements such as Sun, center of Earth, star, and magnetic field direction to update the quaternion which determines the spacecraft orientation with respect to some reference coordinates in the three dimensional space. These measurements are usually processed by an extended Kalman filter (EKF) which yields an estimate of the attitude quaternion. Two EKF versions for quaternion estimation were presented in the literature; namely, the multiplicative EKF (MEKF) and the additive EKF (AEKF). In the multiplicative EKF, it is assumed that the error between the correct quaternion and its a-priori estimate is, by itself, a quaternion that represents the rotation necessary to bring the attitude which corresponds to the a-priori estimate of the quaternion into coincidence with the correct attitude. The EKF basically estimates this quotient quaternion and then the updated quaternion estimate is obtained by the product of the a-priori quaternion estimate and the estimate of the difference quaternion. In the additive EKF, it is assumed that the error between the a-priori quaternion estimate and the correct one is an algebraic difference between two four-tuple elements and thus the EKF is set to estimate this difference. The updated quaternion is then computed by adding the estimate of the difference to the a-priori quaternion estimate. If the quaternion estimate converges to the correct quaternion, then, naturally, the quaternion estimate has unity norm. This fact was utilized in the past to obtain superior filter performance by applying normalization to the filter measurement update of the quaternion. It was observed for the AEKF that when the attitude changed very slowly between measurements, normalization merely resulted in a faster convergence; however, when the attitude changed considerably between measurements, without filter tuning or normalization, the quaternion estimate diverged. However, when the quaternion estimate was normalized, the estimate converged faster and to a lower error than with tuning only. In last years, symposium we presented three new AEKF normalization techniques and we compared them to the brute force method presented in the literature. The present paper presents the issue of normalization of the MEKF and examines several MEKF normalization techniques.

Deutschmann, J.↗

NASA NTRS1993

Variable-speed Generators with Flux Weakening

A cost-competitive, permanent-magnet 20 kW generator is designed such that the following criteria are satisfied: an (over) load capability of at least 30 kW over the entire speed range of 60-120 rpm, generator weight of about 550 lbs with a maximum radial stator flux density of 0.82 T at low speed, unity power factor operation, acceptably small synchronous reactances and operation without a gear box. To justify this final design four different generator designs are investigated: the first two designs are studied to obtain a speed range from 20 to 200 rpm employing rotor field weakening, and the latter two are investigated to obtain a maximum speed range of 40 to 160 rpm based on field weakening via the stator excitation. The generator reactances and induced voltages are computed using finite element/difference solutions. Generator losses and efficiencies are presented for all four designs at rated temperature of Tr=120C.

Fardoun, A. A.↗

NASA NTRS1993

The large-scale morphology of IRAS galaxies

At present, visual inspection is the only method for comparing the large-scale morphologies in the distribution of galaxies to those in model universes generated by N-body simulations. To remedy the situation, we have developed a set of three structure functions (S1, S2, S3) that quantify the degree of large-scale prolateness, oblateness, and sphericity/uniformity of a 3-D particle distribution and have applied them to a volume-limited (less than = 4000 km/s) sample of 699 IRAS galaxies with f sub 60 greater than 1.2 Jy. To determine the structure functions, we randomly select 500 galaxies as origins of spherical windows of radius R sub w, locate the centroid of the galaxies in the window (assuming all galaxies have equal mass) and then, compute the principal moments of inertia (I sub 1, I sub 2, I sub 3) about the centroid. Each S sub i is a function of (I sub 2)/(I sub 1) and (I sub 3)/I sub 1). S1, S2, and S3 tend to unity for highly prolate, oblate, and uniform distributions, respectively and tend to zero otherwise. The resulting 500 values of S sub i at each scale R sub w are used to construct a histogram.

Babul, Arif↗

NASA NTRS1993

Probing the optical depth of spiral galaxies using multi-waveband observations

The questions of the optical depth and extinction of galaxies obviously have far-reaching implications; from determining the true stellar content and baryonic mass of galaxies to the origin of the major component of their far infrared radiation. We have investigated whether the reddening of stars can be used to determine the amount and extent of obscuring dust. We find that the amount of reddening is very sensitive to the assumed geometry. The usually assumed case of a screen of dust between the observer and the star produces, for a given optical depth, the maximum amount of reddening. However, for external galaxies such a geometry is clearly wrong. More realistic geometries where the dust and stars are uniformly mixed (a 'slab') or where the dust is sandwiched by unobscured stars (a 'sandwich') produce significantly less reddening. For the slab geometry of the reddening rises to a maximum value as the optical depth is increased, and for a sandwich geometry the reddening will actually decrease as the optical depth becomes larger. The reddening vectors produced by these realistic geometries are compared to multi-waveband observations of individual regions of a sample of eight galaxies. We find evidence for significant optical depths in the central regions of some of these galaxies, but optical depths of less than unity at approx. 2 scale lengths from the centers. The optical depths derived are in good agreement with other tests such as the measured hydrogen column densities and the far infrared to blue light ratios. However, whereas these two latter approaches are insensitive to the relative distributions of the stars and the dust, the amount of reddening seen in these eight galaxies suggests that the dust to stellar scale height ratio xi is greater than or equal to 0.5. We find typical blue band extinctions of A(sub B) = 0.75-1.0, a factor of 3-4 higher than the RC2 value.

Evans, Rhodri↗

NASA NTRS1993

Spokes in ring galaxies

We examine the response of self-gravitating primary galaxies consisting of dark matter halos and disks containing both stars and gas to collisions with less massive companions. The primaries were constructed using a technique which makes it possible to realize multi-component systems that are stable and virtually in precise equilibrium. A total of 65,536 particles were employed to represent the primary and 4096 to represent the companion. Half the particles in the primary comprise its halo and the other half its disk. Gas makes up 10 percent of the disk mass and is represented by 8192 of the disk particles. A system of units is used where the gravitational constant, total disk mass, and disk exponential scale length are unity. The primary motivation of the present study is to determine whether effects associated with dissipation and self-gravity can account for the unusual morphology of the Cartwheel galaxy.

Hernquist, Lars↗

NASA NTRS1993

Novel properties of the q-analogue quantized radiation field

The 'classical limit' of the q-analog quantized radiation field is studied paralleling conventional quantum optics analyses. The q-generalizations of the phase operator of Susskind and Glogower and that of Pegg and Barnett are constructed. Both generalizations and their associated number-phase uncertainty relations are manifestly q-independent in the n greater than g number basis. However, in the q-coherent state z greater than q basis, the variance of the generic electric field, (delta(E))(sup 2) is found to be increased by a factor lambda(z) where lambda(z) greater than 1 if q not equal to 1. At large amplitudes, the amplitude itself would be quantized if the available resolution of unity for the q-analog coherent states is accepted in the formulation. These consequences are remarkable versus the conventional q = 1 limit.

Nelson, Charles A.↗

NASA NTRS1993

Using harmonic oscillators to determine the spot size of Hermite-Gaussian laser beams

The similarity of the functional forms of quantum mechanical harmonic oscillators and the modes of Hermite-Gaussian laser beams is illustrated. This functional similarity provides a direct correlation to investigate the spot size of large-order mode Hermite-Gaussian laser beams. The classical limits of a corresponding two-dimensional harmonic oscillator provide a definition of the spot size of Hermite-Gaussian laser beams. The classical limits of the harmonic oscillator provide integration limits for the photon probability densities of the laser beam modes to determine the fraction of photons detected therein. Mathematica is used to integrate the probability densities for large-order beam modes and to illustrate the functional similarities. The probabilities of detecting photons within the classical limits of Hermite-Gaussian laser beams asymptotically approach unity in the limit of large-order modes, in agreement with the Correspondence Principle. The classical limits for large-order modes include all of the nodes for Hermite Gaussian laser beams; Sturm's theorem provides a direct proof.

Steely, Sidney L.↗

NASA NTRS1992

Reflectance spectroscopy and GEX simulation of palagonite and iron-rich montmorillonite clay mixtures: Implications for the surface composition of Mars

Because of the power of remote sensing reflectance spectroscopy in determining mineralogy, it has been used as the major method of identifying a possible mineral analogue of the martian surface. A summary of proposed martian surface compositions from reflectance spectroscopy before 1979 was presented by Singer et al. Since that time, iron-rich montmorillonite clay, nanocrystalline or nanophase hematite, and palagonite have been suggested as Mars soil analogue materials. Palagonite in petrological terms is best described as an amorphous, hydrated, ferric iron, silica gel. Montmorillonite is a member of the smectite clay group, and its structure is characterized by an octahedral sheet in coordination with two tetrahedral sheets in which oxygen atoms are shared. The crystal unity of montmorillonite is well defined in contrast to palagonite where it is considered amorphous or poorly crystalline at best. Because of the absence of the diagnostic strong 2.2-micron reflectance band characteristic of clays in the near-infrared (NIR) spectrum of Mars and palagonite and based upon a consideration of wide wavelength coverage (0.3-50 microns), Roush et al. concluded that palagonite is a more likely Mars surface analogue. In spite of the spectral agreement of palagonite and the Mars reflectance spectrum in the 2.2-micron region, palagonite shows poor correspondence with the results of the Viking LR experiment. In contrast, iron-rich montmorillonite clays show relatively good agreement with the results of the Viking LR experiment. This spectral study was undertaken to evaluate the spectral properties of mixtures of palagonite and Mars analogue iron-rich montmorillonite clay (16-18 wt. percent Fe as Fe2O3) as a Mars surface mineralogical model. Mixtures of minerals as Mars surface analogue materials have been studied before, but the mixtures were restricted to crystalline clays and iron oxides.

Orenberg, J. B.↗

NASA NTRS1992

Pressure dependence of the oxygen reduction reaction at the platinum microelectrode/nafion interface - Electrode kinetics and mass transport

The investigation of oxygen reduction kinetics at the platinum/Nafion interface is of great importance in the advancement of proton-exchange-membrane (PEM) fuel-cell technology. This study focuses on the dependence of the oxygen reduction kinetics on oxygen pressure. Conventional Tafel analysis of the data shows that the reaction order with respect to oxygen is unity at both high and low current densities. Chronoamperometric measurements of the transport parameters for oxygen in Nafion show that oxygen dissolution follows Henry's isotherm. The diffusion coefficient of oxygen is invariant with pressure; however, the diffusion coefficient for oxygen is lower when air is used as the equilibrating gas as compared to when oxygen is used for equilibration. These results are of value in understanding the influence of O2 partial pressure on the performance of PEM fuel cells and also in elucidating the mechanism of oxygen reduction at the platinum/Nafion interface.

Parthasarathy, Arvind↗