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NASA NTRS1994

Spectral Methods for Computational Fluid Dynamics

As a tool for large-scale computations in fluid dynamics, spectral methods were prophesized in 1944, born in 1954, virtually buried in the mid-1960's, resurrected in 1969, evangalized in the 1970's, and catholicized in the 1980's. The use of spectral methods for meteorological problems was proposed by Blinova in 1944 and the first numerical computations were conducted by Silberman (1954). By the early 1960's computers had achieved sufficient power to permit calculations with hundreds of degrees of freedom. For problems of this size the traditional way of computing the nonlinear terms in spectral methods was expensive compared with finite-difference methods. Consequently, spectral methods fell out of favor. The expense of computing nonlinear terms remained a severe drawback until Orszag (1969) and Eliasen, Machenauer, and Rasmussen (1970) developed the transform methods that still form the backbone of many large-scale spectral computations. The original proselytes of spectral methods were meteorologists involved in global weather modeling and fluid dynamicists investigating isotropic turbulence. The converts who were inspired by the successes of these pioneers remained, for the most part, confined to these and closely related fields throughout the 1970's. During that decade spectral methods appeared to be well-suited only for problems governed by ordinary diSerential eqllations or by partial differential equations with periodic boundary conditions. And, of course, the solution itself needed to be smooth. Some of the obstacles to wider application of spectral methods were: (1) poor resolution of discontinuous solutions; (2) inefficient implementation of implicit methods; and (3) drastic geometric constraints. All of these barriers have undergone some erosion during the 1980's, particularly the latter two. As a result, the applicability and appeal of spectral methods for computational fluid dynamics has broadened considerably. The motivation for the use of spectral methods in numerical calculations stems from the attractive approximation properties of orthogonal polynomial expansions.

Zang, T. A.↗

NASA NTRS1995

Electric conductivity of plasma in solar wind

One of the most important parameters in MHD description of the solar wind is the electric conductivity of plasma. There exist now two quite different approaches to the evaluation of this parameter. In the first one a value of conductivity taken from the most elaborated current theory of plasma should be used in calculations. The second one deals with the empirical, phenomenological value of conductivity. E.g.: configuration of interplanetary magnetic field, stretched by the expanding corona, depends on the magnitude of electrical conductivity of plasma in the solar wind. Knowing the main empirical features of the field configuration, one may estimate the apparent phenomenological value of resistance. The estimations show that the electrical conductivity should be approximately 10(exp 13) times smaller than that calculated by Spitzer. It must be noted that the empirical value should be treated with caution. Due to the method of its obtaining it may be used only for 'large-scale' description of slow processes like coronal expansion. It cannot be valid for 'quick' processes, changing the state of plasma, like collisions with obstacles, e.g., planets and vehicles. The second approach is well known in large-scale planetary hydrodynamics, stemming from the ideas of phenomenological thermodynamics. It could formulate real problems which should be solved by modern plasma physics, oriented to be adequate for complicated processes in space.

Chertkov, A. D.↗

NASA NTRS1995

Existence of frozen-in coordinate systems

The 'frozen-in' coordinate systems were first introduced in the works on 'reconnection' and 'magnetic barrier' theories (see review by M.l.Pudovkin and V.S.Semenov, Space Sci. Rev. 41,1 1985). The idea was to utilize the mathematical apparatus developed for 'general relativity' theory to simplify obtaining solutions to the ideal MHD equations set. Magnetic field (B), plasma velocity (v), and their vector product were used as coordinate vectors. But there exist no stationary solutions of ideal MHD set that satisfies the required boundary conditions at infinity (A.D.Chertkov, Solar Wind Seven Conf.,Pergamon Press,1992,165) having non-zero vector product of v and B where v and B originate from the same sphere. The existence of a solution is the hidden mine of the mentioned theories. The solution is constructed in the coordinate system, which is unknown and indeterminate before obtaining this solution. A substitution of the final solution must be done directly into the initial MHD set in order to check the method. One can demonstrate that 'solutions' of Petschek's problem, obtained by 'frozen-in' coordinate systems, does not satisfy just the 'frozen-in' equation, i.e. induction equation. It stems from the fact that Petschek's 're-connection' model, treated as a boundary problem, is over determined. This problem was incorrectly formulated.

Chertkov, A. D.↗

NASA NTRS1996

Quantum Probability Cancellation Due to a Single-Photon State

When an N-photon state enters a lossless symmetric beamsplitter from one input port, the photon distribution for the two output ports has the form of Bernouli Binormial, with highest probability at equal partition (N/2 at one outport and N/2 at the other). However, injection of a single photon state at the other input port can dramatically change the photon distribution at the outputs, resulting in zero probability at equal partition. Such a strong deviation from classical particle theory stems from quantum probability amplitude cancellation. The effect persists even if the N-photon state is replaced by an arbitrary state of light. A special case is the coherent state which corresponds to homodyne detection of a single photon state and can lead to the measurement of the wave function of a single photon state.

Ou, Z. Y.↗

NASA NTRS1996

Satellite Angular Rate Estimation From Vector Measurements

This paper presents an algorithm for estimating the angular rate vector of a satellite which is based on the time derivatives of vector measurements expressed in a reference and body coordinate. The computed derivatives are fed into a spacial Kalman filter which yields an estimate of the spacecraft angular velocity. The filter, named Extended Interlaced Kalman Filter (EIKF), is an extension of the Kalman filter which, although being linear, estimates the state of a nonlinear dynamic system. It consists of two or three parallel Kalman filters whose individual estimates are fed to one another and are considered as known inputs by the other parallel filter(s). The nonlinear dynamics stem from the nonlinear differential equation that describes the rotation of a three dimensional body. Initial results, using simulated data, and real Rossi X ray Timing Explorer (RXTE) data indicate that the algorithm is efficient and robust.

Azor, Ruth↗

NASA NTRS1996

Torsional Buckling Tests of a Simulated Solar Array

Spacecraft solar arrays are typically large structures supported by long, thin deployable booms. As such, they may be particularly susceptible to abnormal structural behavior induced by mechanical and thermal loading. One example is the Hubble Space Telescope solar arrays which consist of two split tubes fit one inside the other called BiSTEMs. The original solar arrays on the Hubble Space Telescope were found to be severely twisted following deployment and later telemetry data showed the arrays were vibrating during daylight to night and night to daylight transition. The solar array twist however can force the BiSTEM booms to change in cross-section and cause tile solar arrays to react unpredictably to future loading. The solar arrays were redesigned to correct for tile vibration, however, upon redeployment they again twisted. To assess the influence of boom cross-sectional configuration, experiments were conducted on two types of booms, (1)booms with closed cross-sections, and (2) booms with open cross-sections. Both models were subjected to compressive loading and imposed tip deflections. An existing analytical model by Chung and Thornton was used to define the individual load ranges for each model solar array configuration. The load range for the model solar array using closed cross-section booms was 0-120 Newtons and 0-160 Newtons for the model solar array using open cross-section booms. The results indicate the model solar array with closed cross-section booms buckled only in flexure. However, the results of the experiment with open cross-section booms indicate the model solar array buckled only in torsion and with imposed tip deflections the cross section can degrade by rotation of the inner relative to the outer STEM. For tile Hubble Space Telescope solar arrays the results of these experiments indicate the twisting resulted from the initial mechanical loading of the open cross-section booms.

Thornton, E. A.↗

NASA NTRS1996

NASA Rat Acoustic Tolerance Test 1994-1995: 8 kHz, 16 kHz, 32 kHz Experiments

Adult male Sprague-Dawley rats were exposed to chronic applied sound (74 to 79 dB, SPL) with octave band center frequencies of either 8, 16 or 32 kHz for up to 60 days. Control cages had ambient sound levels of about 62 dB (SPL). Groups of rats (test vs. control; N=9 per group) were euthanized after 0. 5. 14, 30, and 60 days. On each euthanasia day, objective evaluation of their physiology and behavior was performed using a Stress Assessment Battery (SAB) of measures. In addition, rat hearing was assessed using the brain stem auditory evoked potential (BAER) method after 60 days of exposure. No statistically significant differences in mean daily food use could be attributed to the presence of the applied test sound. Test rats used 5% more water than control rats. In the 8 kHz and 32 kHz tests this amount was statistically significant(P less than .05). This is a minor difference of questionable physiological significance. However, it may be an indication of a small reaction to the constant applied sound. Across all test frequencies, day 5 test rats had 6% larger spleens than control rats. No other body or organ weight differences were found to be statistically significant with respect to the application of sound. This spleen effect may be a transient adaptive process related to adaptation to the constant applied noise. No significant test effect on differential white blood cell counts could be demonstrated. One group demonstrated a low eosinophil count (16 kHz experiment, day 14 test group). However this was highly suspect. Across all test frequencies studied, day 5 test rats had 17% fewer total leukocytes than day 5 control rats. Sound exposed test rats exhibited 44% lower plasma corticosterone concentrations than did control rats. Note that the plasma corticosterone concentration was lower in the sound exposed test animals than the control animals in every instance (frequency exposure and number of days exposed).

Mele, Gary D.↗

NASA NTRS1996

Mineralogy

The power of mineralogical analysis as a descriptive or predictive technique stems from the fact that only a few thousand minerals are known to occur in nature as compared to several hundred thousand inorganic compounds. Further, all of the known minerals have specific stability ranges in pressure, temperature, an composition. A specific knowledge of the mineralogy of a planets surface or interior therefore allows one to characterize the present or past conditions under which the minerals were formed or have existed. For the purposes of this paper, a slightly broader definition of mineralogy was adopted by including not only crystalline materials found on planetary surfaces, but also ices and classes that can benefit from in situ types of analyses. Both visual examination and the various spectroscopies available for robotic probes to planetary surfaces are discussed.

Dyar, M. Darby↗

NASA NTRS1996

Quasi-Optimal Schwarz Methods for the Conforming Spectral Element Discretization

Fast methods are proposed for solving the system K(sub N)x = b resulting from the discretization of self-adjoint elliptic equations in three dimensional domains by the spectral element method. The domain is decomposed into hexahedral elements, and in each of these elements the discretization space is formed by polynomials of degree N in each variable. Gauss-Lobatto-Legendre (GLL) quadrature rules replace the integrals in the Galerkin formulation. This system is solved by the preconditioned conjugate gradients method. The conforming finite element space on the GLL mesh consisting of piecewise Q(sub 1) elements produces a stiffness matrix K(sub h) that is spectrally equivalent to the spectral element stiffness matrix K(sub N). The action of the inverse of K(sub h) is expensive for large problems, and is therefore replaced by a Schwarz preconditioner B(sub h) of this finite element stiffness matrix. The preconditioned operator then becomes B(sub h)(exp -l)K(sub N). The technical difficulties stem from the nonregularity of the mesh. Tools to estimate the convergence of a large class of new iterative substructuring and overlapping Schwarz preconditioners are developed. This technique also provides a new analysis for an iterative substructuring method proposed by Pavarino and Widlund for the spectral element discretization.

Casarin, Mario↗

NASA NTRS1996

A Cell-Centered Multigrid Algorithm for All Grid Sizes

Multigrid methods are optimal; that is, their rate of convergence is independent of the number of grid points, because they use a nested sequence of coarse grids to represent different scales of the solution. This nesting does, however, usually lead to certain restrictions of the permissible size of the discretised problem. In cases where the modeler is free to specify the whole problem, such constraints are of little importance because they can be taken into consideration from the outset. We consider the situation in which there are other competing constraints on the resolution. These restrictions may stem from the physical problem (e.g., if the discretised operator contains experimental data measured on a fixed grid) or from the need to avoid limitations set by the hardware. In this paper we discuss a modification to the cell-centered multigrid algorithm, so that it can be used br problems with any resolution. We discuss in particular a coarsening strategy and choice of intergrid transfer operators that can handle grids with both an even or odd number of cells. The method is described and applied to linear equations obtained by discretization of two- and three-dimensional second-order elliptic PDEs.

Gjesdal, Thor↗

NASA NTRS1995

EXPECT: Explicit Representations for Flexible Acquisition

To create more powerful knowledge acquisition systems, we not only need better acquisition tools, but we need to change the architecture of the knowledge based systems we create so that their structure will provide better support for acquisition. Current acquisition tools permit users to modify factual knowledge but they provide limited support for modifying problem solving knowledge. In this paper, the authors argue that this limitation (and others) stem from the use of incomplete models of problem-solving knowledge and inflexible specification of the interdependencies between problem-solving and factual knowledge. We describe the EXPECT architecture which addresses these problems by providing an explicit representation for problem-solving knowledge and intent. Using this more explicit representation, EXPECT can automatically derive the interdependencies between problem-solving and factual knowledge. By deriving these interdependencies from the structure of the knowledge-based system itself EXPECT supports more flexible and powerful knowledge acquisition.

Swartout, BIll↗

NASA NTRS1996

Prediction of the backflow and recovery regions in the backward facing step at various Reynolds numbers

A four-equation model of turbulence is applied to the numerical simulation of flows with massive separation induced by a sudden expansion. The model constants are a function of the flow parameters, and two different formulations for these functions are tested. The results are compared with experimental data for a high Reynolds-number case and with experimental and DNS data for a low Reynolds-number case. The computations prove that the recovery region downstream of the massive separation is properly modeled only for the high Re case. The problems in this case stem from the gradient diffusion hypothesis, which underestimates the turbulent diffusion.

Michelassi, V.↗

NASA NTRS1996

Enhanced Raman Monitor Project

Monitoring of gaseous contaminants stems from the need to ensure a healthy and safe environment. NASA/Ames needs sensors that are able to monitor common atmospheric gas concentrations as well as trace amounts of contaminant gases. To provide an accurate assessment of air quality, a monitoring system would need to be continuous and on-line with full spectrum capabilities, allowing simultaneous detection of all gas components in a sample, including both combustible and non-combustible gases. The system demands a high degree of sensitivity to detect low gas concentrations in the low-ppm and sub-ppm regions. For clean and healthy air ('good' category), criteria established by the EPA requires that contaminant concentrations not exceed 4 ppm of carbon monoxide (CO) in an 8 hour period, 60 ppb of ozone(O3) in a one hour period and 30 ppb of sulfur dioxide (SO2) in a 24 hour period. One step below this is the National Ambient Air Quality Standard ('moderate' category) which requires that contaminant concentrations not exceed 9 ppm of carbon monoxide (CO), 120 ppb of ozone (O3) and 140 ppb of sulfur dioxide (SO2) for their respective time periods. Ideally a monitor should be able to detect the concentrations specified in the 'good' category. To benchmark current abilities of Raman technology in gas phase analysis, laboratory experiments were performed to evaluate the RASCAL II anesthetic gas monitor.

Westenskow, Dwayne↗

NASA NTRS1997

Combustion of PTFE: The Effects of Gravity and Pigmentation on Ultrafine Particle Generation

Ultrafine particles generated during polymer thermodegradation are a major health hazard, owing to their unique pathway of processing in the lung. This hazard in manned spacecraft is poorly understood, because the particulate products of polymer thermodegradation are generated under low gravity conditions. Particulate generated from the degradation of PolyTetraFluoroEthylene (PTFE), insulation coating for 20 AWG copper wire (representative of spacecraft application) under intense ohmic heating were studied in terrestrial gravity and microgravity. Microgravity tests were done in a 1.2-second drop tower at the Colorado School of Mines (CSM). Thermophoretic sampling was used for particulate collection. Transmission Electron Microscopy (TEM) and Scanning Transmission Electron Microscopy (STEM) were used to examine the smoke particulates. Image software was used to calculate particle size distribution. In addition to gravity, the color of PTFE insulation has an overwhelming effect on size, shape and morphology of the particulate. Nanometer-sized primary particles were found in all cases, and aggregation and size distribution was dependent on both color and gravity; higher aggregation occurred in low gravity. Particulates from white, black, red and yellow colored PTFE insulations were studied. Elemental analysis of the particulates shows the presence of inorganic pigments.

McKinnon, J. Thomas↗

NASA NTRS1996

A Potato cDNA Encoding a Homologue of Mammalian Multidrug Resistant P-Glycoprotein

A homologue of the multidrug resistance (MDR) gene was obtained while screening a potato stolon tip cDNA expression library with S-15-labeled calmodulin. The mammalian MDR gene codes for a membrane-bound P-glycoprotein (170-180 kDa) which imparts multidrug resistance to cancerous cells. The potato cDNA (PMDR1) codes for a polypeptide of 1313 amino acid residues (ca. 144 kDa) and its structural features are very similar to the MDR P-glycoprotein. The N-terminal half of the PMDR1-encoded protein shares striking homology with its C-terminal half, and each half contains a conserved ATP-binding site and six putative transmembrane domains. Southern blot analysis indicated that potato has one or two MDR-like genes. PMDR1 mRNA is constitutively expressed in all organs studied with higher expression in the stem and stolon tip. The PMDR1 expression was highest during tuber initiation and decreased during tuber development.

Wang, W.↗

NASA NTRS1995

Calmodulin Gene Family in Potato: Developmental and Touch-Induced Expression of the mRNA Encoding a Novel Isoform

Eight genomic clones of potato calmodulin (PCM1 to 8) were isolated and characterized. Sequence comparisons of different genes revealed that the deduced amino acid sequence of PCM1 had several unique substitutions, especially in the fourth Ca(2+)-binding area. The expression patterns of different genes were studied by northern analysis using the 3'-untranslated regions as probes. The expression of PCM1, 5, and 8 was highest in the stolon tip and it decreased during tuber development. The expression of PCM6 did not vary much in the tissues tested, except in the leaves, where the expression was lower; whereas, the expression of PCM4 was very low in all the tissues. The expression of PCM2 and PCM3 was not detected in any of the tissues tested. Among these genes, only PCM1 showed increased expression following touch stimulation. To study the regulation of PCM1, transgenic potato plants carrying the PCM1 promoter fused to the beta-glucuronidase (GUS) reporter gene were produced. GUS expression was found to be developmentally regulated and touch-responsive, indicating a positive correlation between the expression of PCM1 and GUS mRNAs. These results suggest that the 5'-flanking region of PCM1 controls developmental and touch-induced expression. X-Gluc staining patterns revealed that GUS localization is high in meristematic tissues such as the stem apex, stolon tip, and vascular regions.

Takezawa, D.↗

NASA NTRS1996

Spectra of High-Ionization Seyfert 1 Galaxies: Implications for the Narrow-Line Region

We present line profiles and profile parameters for the Narrow-Line Regions (NLRs) of six Seyfert 1 galaxies with high-ionization lines: MCG 8-11-11, Mrk 79, Mrk 704, Mrk 841, NGC 4151, and NGC 5548. The sample was chosen primarily with the goal of obtaining high-quality [Fe VII] lambda6087 and, when possible, [Fe X] lambda6374 profiles to determine if these lines are more likely formed in a physically distinct 'coronal line region' or are formed throughout the NLR along with lines of lower critical density (n(sub cr)) and/or Ionization Potential (IP). We discuss correlations of velocity shift and width with n(sub cr) and IP. In some objects, lines of high IP and/or n(sub cr) are systematically broader than those of low IP/n(sub cr). Of particular interest, however, are objects that show no correlations of line width with either IP or n(sub cr). In these objects, lines of high and low IP/n(sub cr), are remarkably similar, which is difficult to reconcile with the classical picture of the NLR, in which lines of high and low IP/n(sub cr) are formed in physically distinct regions. We argue for similar spatial extents for the flux in lines with similar profiles. Here, as well as in a modeling-oriented companion paper, we develop further an idea suggested by Moore & Cohen that objects that do and do not show line width correlations with IP/n(sub cr) can both be explained in terms of a single NLR model with only a small difference in the cloud column density distinguishing the two types of object. Overall, our objects do not show correlations between the Full Width at Half-Maximum (FWHM) and IP and/or n(sub cr). The width must be defined by a parameter that is sensitive to extended profile wings in order for the correlations to result. We present models in which FWHM correlations with IP and/or n(sub cr) result only after simulating the lower spectral resolution used in previous observational studies. The models that simulate the higher spectral resolution of our observational study produce line width correlations only if the width is defined by a parameter that is more sensitive to extended profile wings than is the FWHM. Our sample of six objects is in effect augmented by incorporating the larger sample (16 objects) of Veilleux into some of our discussion. This paper focuses on new interpretations of NLR emission-line spectra and line profiles that stem directly from the observations. Paper 2 focuses on modeling and complements this paper by illustrating explicitly the effects that spatial variations in electron density, ionization parameter, and column density have on model profiles. By comparing model profiles with the observed profiles presented here, as well as with those presented by Veilleux, Paper 2 yields insight into how the electron density, ionization parameter, and column density likely vary throughout the NLR.

Moore, David↗

NASA NTRS1995

Plant Roots: The Hidden Half: Calcium and Gravitropism - Chapter 16

Environmental signals such as light and gravity control many aspects of plant growth and development. In higher plants, the directional growth of an organ in response to stimuli such as gravity and light is considered a tropic movement. Such movement could be either positive or negative with respect to a specific stimulus. In general, stems show a positive response to light and negative response to gravity. In contrast, most roots show a positive response to gravity and a negative response to light. Investigations on plant tropism date back a century when Darwin studied the phototropic responses of maize seedlings (Darwin). Although the precise mechanism of signal perception and transduction in roots is not understood, Darwin recognized over 100 years ago that the root cap is the probable site of signal perception. He discovered that the removal of the root cap eliminates the ability of roots to respond to gravity. Other investigators have since confirmed Darwin's observation (Konings; Evans et al.). In recent years, especially with the advent of the U.S. Space Program, there has been a renewed interest in understanding how plants respond to extracellular signals such as gravity (Halstead and Dutcher). Studies on the mechanisms involved in perception and transduction of gravity signal by roots would ultimately help us to better understand gravitropism and also to grow plants under microgravity conditions as in space. In this chapter, we restrict ourselves to the role of calcium in transduction of the gravity signal. In doing so, emphasis is given to the role of calcium-modulated proteins and their role in signal transduction in gravitropism. Detailed reviews on various other aspects of gravitropism (Scott, Torrey, Wilkins, Fim and Digby, Feldman, Pickard, Moore and Evans, Halstead and Dutcher, Poovaiah et al.) and on the role of calcium as a messenger in signal transduction in general have been published (Helper and Wayne, Poovaiah and Reddy, Roberts and Hartnon, Bowler and Chua, Gilroy and Trewavas). Plant roots have been widely used to study the transduction of gravity and light signals (Poovaiah et al., Roux and Serlin). Most roots show positive gravitropic response in either dark or light. However, roots of some varieties of plants (e.g., Zea mays L., cv Merit, and Zea rwvs L., cv Golden Cross Bantam 70) show positive gravitropic response only in light (Feldman, Miyazaki et al.). Investigations from various laboratories indicate that calcium acts as a messenger in transducing gravity and light signals in plant roots(Pickard, Evans et al., Pooviah et al.).

Poovaiah, B. W.↗