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NASA NTRS1984

Multiple spacecraft observations of interplanetary shocks Shock-normal oscillations and their effects

Observations of interplanetary shocks with multiple spacecraft and multiple instruments has permitted the determination of their average shock normals with unprecedented accuracy. Nevertheless, there are still local deviations from the best-fit normal. These deviations in general appear to be less than 5 deg but on occasion can be of the order of 20 deg or more. These fluctuating normals and the fluctuating upstream field can cause variations in the downstream field strength even when the upstream field strength is constant. This behavior has important consequences for the appearance of quasi-parallel shocks. Precursor waves which stand on the shock ramp and do not propagate or are not convected across the shock front do not affect the downstream field.

Russell, C. T.↗

NASA NTRS1985

Black hole normal modes - A semianalytic approach

A new semianalytic technique for determining the complex normal mode frequencies of black holes is presented. The method is based on the WKB approximation. It yields a simple analytic formula that gives the real and imaginary parts of the frequency in terms of the parameters of the black hole and of the field whose perturbation is under study, and in terms of the quantity (n + 1/2), where n = 0, 1, 2,... and labels the fundamental mode, first overtone mode, and so on. In the case of the fundamental gravitational normal modes of the Schwarzschild black hole, the WKB estimates agree with numerical results to better than 7 percent in the real part of the frequency and 0.7 percent in the imaginary part, with the relative agreement improving with increasing angular harmonic. Carried to higher order the method may provide an accurate and systematic means to study black hole normal modes.

Schutz, B. F.↗

NASA NTRS1985

Resistive wave dissipation on magnetic inhomogeneities Normal modes and phase mixing

Numerical solutions of the linearized, resistive MHD equations indicate the presence of two characteristic forms of wave decay on magnetic inhomogeneities. Solutions for relatively long-wavelength disturbances and large values of the resistivity have the behavior of decaying normal modes. In the opposite limits, phase mixing becomes important, with the eventual build-up of large spatial gradients in which the resistive terms dominate. This composite behavior is shown to be conceptually consistent with analytic results, which predict that the complete solution consists of the sum of collective and noncollective contributions. The numerical simulations go beyond analytic theory by defining where each contribution prevails and computing wave decay when phase mixing is effective. The dispersion relation in the normal-mode regime is also determined analytically, with some approximations, and is in good agreement with the numerical solution. The decay time of the normal modes varies with Lundquist number at S1/6, while the phase-mixed decay time scales as S1/3.

Steinolfson, R. S.↗

NASA NTRS1985

Resistive Alfven normal modes in a non-uniform plasma

Resistive normal mode solutions of the MHD equations are found numerically in a smooth, nonuniform, magnetic field. The (alpha, S) boundary within which normal mode solutions exist is explicitly computed, where alpha is the normalized wavenumber and S the Lundquist number. As an extension of previous analytic results of Mok and Einaudi (1985), the damping rate of these modes is computed to a higher accuracy, and is found to have an a + bS exp -1/3 dependence, where a and b are independent of S.

Einaudi, G.↗

NASA NTRS1986

Normal basis of finite field GF(2 super m)

Massey and Omura (1981) recently developed a new multiplication algorithm for Galois fields based on the normal basis representation. This algorithm shows a much simpler way to perform multiplication in finite field than the conventional method. The necessary and sufficient conditions are presented for an element to generate a normal basis in the field GF(2 super m), where m = 2 super k p super n and p super n has two as a primitive root. This result provides a way to find a normal basis in the field.

Pei, D. Y.↗

NASA NTRS1986

A comparison of the bounded derivative and the normal-mode initialization methods using real data

Application of the bounded-derivative and normal-mode methods to a simple linear barotropic model at a typical middle latitude shows that the two methods lead to identical constraints up to a certain degree of approximation. Beyond this accuracy the two methods may differ from each other. When applied to a global nonlinear barotropic model using real data, again the two methods lead to similar balanced initial states. The gravity oscillations in the unbalanced height field, which have amplitudes of up to 60 m with a dominant periodicity of about 5 to 6 h, are practically eliminated by both initialization methods. The rotational wind component is smooth even for the unbalanced initial state. The small-scale spatial features of the irrotational wind component are drastically reduced by initialization. Both the nonlinear normal-mode and the bounded-derivative initialization methods yield similar divergence fields centered around the areas of highest orography. The comparison shows that there is no significant loss of information in the mass and momentum fields, despite the fact that the bounded-derivative method employs only the original, rotational wind component to construct a balanced initial state compared to the normal-mode method, which, in addition, makes use of the unbalanced divergent wind and height fields.

Semazzi, F. H. M.↗

NASA NTRS1987

Optical region elemental abundance analyses of B and A stars. VI - The normal stars HR 6559 (A7 IV) and Eta Leporis (F0 IV)

Abundance analyses using optical region data and fully line-blanketed model atmospheres have been performed for the sharp-lined superficially normal stars HR 6559 (A7 IV) and Eta Leporis (F0 IV), consistent with previous studies of middle B through early A type stars. HR 6559 and Eta Lep are slightly metal-weak in general. Their analyses and that of Theta Leo (A2 V) support the suggestion of Smith (1974) that sharp-lined normal A stars do not necessarily have photospheric abundances identical with those of normal middle to late B stars.

Adelman, S. J.↗

NASA NTRS1987

IRAS far-infrared colours of normal stars

The analysis of IRAS observations at 12, 25, 60 and 100 microns of bright stars of spectral type O to M is presented. The objective is to identify the 'normal' stellar population and to characterize it in terms of the relationships between (B-V) and (V-/12/), between (R-I) and (V-/12/), and as a function of spectral type and luminosity class. A well-defined relation is found between the color of normal stars in the visual (B-V), (R-I) and in the IR, which does not depend on luminosity class. Using the (B-V), (V-/12/) relation for normal stars, it is found that B and M type stars show a large fraction of deviating stars, mostly with IR excess that is probably caused by circumstellar material. A comparison of IRAS colors with the Johnson colors as a function of spectral type shows good agreement except for the K0 to M5 type stars. The results will be useful in identifying the deviating stars detected with IRAS.

Waters, L. B. F. M.↗

NASA NTRS1987

Interseismic deformation for normal fault earthquakes

Comparison between the coseismic vertical deformation associated with normal fault earthquakes and permanent deformation indicated by geologic structure indicates that large deformation must occur during the period between earthquakes. When sufficient geodetic and geologic information is available it is possible to estimate the spatial character of this interseismic deformation. A case in point is the 1983 Borah Peak, Idaho earthquake. This normal fault earthquake produced roughly 5 times as much basin subsidence as it did uplift of the adjacent mountain ranges. In contrast, geophysical and geological observations show that the basin is roughly as deep as the bounding range is high. A similar normal fault event in the Basin and Range, the 1959 Hebgen Lake earthquake, was also accompanied by substantially larger subsidence than uplift. In this case, postseismic geodetic measurements show broad regional uplift with a spatial pattern which is roughly consistent with that proposed for the Borah Peak event. Modeling suggests that postseismic viscoelastic relaxation and strain accumulation in an elastic lithosphere overlying a viscoelastic asthenosphere are possible physical mechanisms to generate interseismic uplift. These mechanisms may be the contemporary expression of those processes responsible for the high elevation of the Basin and Range Province.

Reilinger, Robert↗

NASA NTRS1987

A new method to real-normalize measured complex modes

A time domain subspace iteration technique is presented to compute a set of normal modes from the measured complex modes. By using the proposed method, a large number of physical coordinates are reduced to a smaller number of model or principal coordinates. Subspace free decay time responses are computed using properly scaled complex modal vectors. Companion matrix for the general case of nonproportional damping is then derived in the selected vector subspace. Subspace normal modes are obtained through eigenvalue solution of the (M sub N) sup -1 (K sub N) matrix and transformed back to the physical coordinates to get a set of normal modes. A numerical example is presented to demonstrate the outlined theory.

Wei, Max L.↗

NASA NTRS1988

Information processing deficits in psychiatric populations: Implications for normal workload assessment

In one study, schizophrenics, bipolar manics, and mentally normal individuals were administered a digit recall task. The total performance of schizophrenics looked much like that of a normal processor under a higher load level. The manics' performance was intermediate. Primary performance was particularly poor among the mentally ill subjects. In a second study, three groups in the same populations as in the first study were asked to shadow and recall verbatim eight descriptive text passages. Distraction effects were found for schizophrenics only in the areas of percentage of words correctly shadowed and recall variables; the two areas were not correlated, however. It appears that, for schizophrenics, distraction disrupts the ability to effectively shadow information to a greater extent than it disrupts the ability to encode information for recall. The two studies imply that capacity-carrying abnormalities that affect the quantity but not the quality of information processing can be useful in pointing to information processing of normal humans under high load conditions.

Harvey, Philip D.↗

NASA NTRS1986

Normal incidence reflection multilayer optics for solar soft X-ray/extreme ultraviolet (XUV) observations

In preparation for a solar X-ray/XUV sounding-rocket observation in late 1986 utilizing normal-incidence reflection X-ray optics, several multilayer coatings were deposited on concave and convex spherical surfaces. The coatings are tungsten-carbon and molybdenum-silicon mutilayers and are designed for normal-incidence reflection at wavelengths ranging from 44 to 304 A. The multilayers have been characterized in the laboratory in normal and glancing incidence modes using 1.54-114-A radiation. In addition to measuring spectral resolution and absolute reflectivities, multilayer-coated optics have been successfully tested in the imaging mode. This paper reviews the measured characteristics of the multilayer coatings and optics and describes the optical configurations for the solar observation.

Lindblom, Joakim F.↗

NASA NTRS1989

Effect of adhesive interleaving and discontinuous plies on failure of composite laminates subject to transverse normal loads

Results of a series of tests to determine the effects of adhesive interleaving and discontinuous plies (plies with end-to-end gaps) on the displacements, failure loads and failure modes of graphite-epoxy laminates subjected to transverse normal loads are presented. Adhesive interleaving can be used to contain local damage within a group of plies, i.e., to arrest crack propagation on the interlaminate level, and it can increase the amount of normal displacement the laminate can withstand before failure. However, the addition of adhesive interleaving to a laminate does not significantly increase its load carrying capability. A few discontinuous plies in a laminate can reduce the normal displacement and load at failure by 10 to 40 percent compared to a laminate with no discontinuous plies, but the presence of the ply discontinuities does not generally change the failure location or the failure mode of the laminate.

Jegley, Dawn C.↗

NASA NTRS1989

Design of optimally normal minimum gain controllers by continuation method

A measure of the departure from normality is investigated for system robustness. An attractive feature of the normality index is its simplicity for pole placement designs. To allow a tradeoff between system robustness and control effort, a cost function consisting of the sum of a norm of weighted gain matrix and a normality index is minimized. First- and second-order necessary conditions for the constrained optimization problem are derived and solved by a Newton-Raphson algorithm imbedded into a one-parameter family of neighboring zero problems. The method presented allows the direct computation of optimal gains in terms of robustness and control effort for pole placement problems.

Lim, K. B.↗

NASA NTRS1989

MHD surface waves in high- and low-beta plasmas. I - Normal-mode solutions

Since the first paper by Barston (1964) on electrostatic oscillations in inhomogeneous cold plasmas, it has been commonly accepted that all finite layers with a continuous profile in pressure, density and magnetic field cannot support normal surface waves but instead the waves always decay through phase mixing (also called resonant absorption). The problem is reanalyzed by studying a compressible current sheet of a general structure with rotation of the magnetic field included. All inhomogeneous layers considered in the high-beta plasma limit do not support normal modes. However, in the limit of a low-beta plasma there are some cases when normal-mode solutions are recovered. The latter means that the process of resonant absorption is not common for all inhomogeneous layers.

Musielak, Z. E.↗

NASA NTRS1989

An algorithm to design finite field multipliers using a self-dual normal basis

The concept of using a self-dual normal basis to design the Massey-Omura finite-field multiplier is presented. An algorithm is given to locate a self-dual normal basis for GF(2m) for odd m. A method to construct the product function for designing the Massey-Omura multiplier is developed. It is shown that the construction of the product function based on a self-dual basis is simpler than that based on an arbitrary normal basis.

Wang, Charles C.↗

NASA NTRS1989

Design of a normal incidence multilayer imaging X-ray microscope

Normal incidence multilayer Cassegrain X-ray telescopes were flown on the Stanford/MSFC Rocket X-ray Spectroheliograph. These instruments produced high spatial resolution images of the sun and conclusively demonstrated that doubly reflecting multilayer X-ray optical systems are feasible. The images indicated that aplanatic imaging soft X-ray/EUV microscopes should be achievable using multilayer optics technology. A doubly reflecting normal incidence multilayer imaging X-ray microscope based on the Schwarzschild configuration has been designed. The design of the microscope and the results of the optical system ray trace analysis are discussed. High resolution aplanatic imaging X-ray microscopes using normal incidence multilayer X-ray mirrors should have many important applications in advanced X-ray astronomical instrumentation, X-ray lithography, biological, biomedical, metallurgical, and laser fusion research.

Shealy, David L.↗

NASA NTRS1989

The effect of solidity on propeller normal force

Propeller normal force is a major contributor to pitch and yaw stability on propeller driven aircraft. While it is well known that propeller normal force is a function of the number of blades, there are no published data for the high numbers of blades that are used in the new designs such as the UDF. This paper presents the results of a test conducted in the NASA Langley 14- x 22-foot Subsonic Tunnel using a sting-mounted counter-rotation propeller and nacelle. The configurations tested were combinations of 0, 4, and 8 blades per hub. Tests were conducted for blade angle settings of 31.34, 36.34, and 41.34 deg over an angle-of-attack range from -10 to 90 deg and over a range of advance ratios from 0.8 to 1.4. The results show that propeller normal force varies with both solidity and angle of attack.

Dunham, Dana Morris↗