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NASA NTRS1985

Computation of Normal Modes from Identified Complex Modes

A technique is presented to compute a set of normal modes from a set of measured (damped) complex modes. The number of elements in the modal vectors, which is equal to the number of measurements, can be larger than the number of modes under consideration. It is also shown in this paper that the practice of normal mode approximation to complex modes can lead to considerably large errors when the modes are too complex. A numerical example and a simulated experiment are presented to illustrate the concepts discussed and to support the theory presented.

Ibrahim, S. R.↗

NASA NTRS1985

Atmospheric and Science Complexity Effects on Surface Bidirectional Reflectance

Among the tools used in passive remote sensing of Earth resources in the visible and near-infrared spectral regions are measurements of spectral signature and bidirectional reflectance functions (BDRFs). Determination of surface properties using these observables is complicated by a number of factors, including: (1) mixing of surface components, such as soil and vegetation, (2) multiple reflections of radiation due to complex geometry, such as in crop canopies, and (3) atmospheric effects. In order to bridge the diversity in these different approaches, there is a need for a fundamental physical understanding of the influence of the various effects and a quantiative measure of their relative importance. In particular, we consider scene complexity effects using the example of reflection by vegetative surfaces. The interaction of sunlight with a crop canopy and interpretation of the spectral and angular dependence of the emergent radiation is basically a multidimensional radiative transfer problem. The complex canopy geometry, underlying soil cover, and presence of diffuse as well as collimated illumination will modify the reflectance characteristics of the canopy relative to those of the individual elements.

Diner, D. J.↗

NASA NTRS1985

The method of complex characteristics for transonic airfoil design, with an application to compressors

The use of mathematical models to study physical problems of current interest to aeronautical engineers has been made possible by the development of numerical techniques to compute solutions of the differential equations of transonic aerodynamics. These advances have encouraged the improvement of supercritical wing technology. A method to determined steady, shockless flow of an inviscid, compressible fluid past a cascade of airfoils in the (x,y)-plane is considered, taking into account also the case of an isolated airfoil. The method of complex characteristics solves the equations in the hodograph plane by extending all variables into the complex domain, where the notion of type is no longer significant. Attention is given to the mathematical background, the method of complex characteristics, and numerical calculations.

Bledsoe, M.↗

NASA NTRS1986

Description and operational status of the National Transonic Facility computer complex

This paper describes the National Transonic Facility (NTF) computer complex and its support of tunnel operations. The capabilities of the research data acquisition and reduction are discussed along with the types of data that can be acquired and presented. Pretest, test, and posttest capabilities are also outlined along with a discussion of the computer complex to monitor the tunnel control processes and provide the tunnel operators with information needed to control the tunnel. Planned enhancements to the computer complex for support of future testing are presented.

Boyles, G. B., Jr.↗

NASA NTRS1986

Multiband far-infrared observations of the NGC 6334 complex

Multiband far-infrared (20-155 microns) observations of the large H II region/molecular cloud complex NGC 6334 are presented. The observations were performed simultaneously in four bands with effective wavelengths 21, 42, 71, and 134 microns. Eight far-infrared sources were detected which cover the range from sources with little of no continuum radio emission to well-developed H II regions. Maps of dust temperature and far-infrared optical depth of the complex are presented which reveal large-scale variations in the color temperature and optical depth. Star formation in the complex is discussed and it is concluded that a Rayleigh-Taylor instability generated by the gravitational attraction of the galactic plane can explain the regular separation of the far-IR sources.

Loughran, L.↗

NASA NTRS1986

A new VLSI complex integer multiplier which uses a quadratic-polynomial residue system with Fermat numbers

A quadratic-polynomial Fermat residue number system (QFNS) has been used to compute complex integer multiplications. The advantage of such a QFNS is that a complex integer multiplication requires only two integer multiplications. In this article, a new type Fermat number multiplier is developed which eliminates the initialization condition of the previous method. It is shown that the new complex multiplier can be implemented on a single VLSI chip. Such a chip is designed and fabricated in CMOS-pw technology.

Truong, T. K.↗

NASA NTRS1986

Clump 1 - An unusual molecular cloud complex near the Galactic center

The properties of the (C-12)O and (C-13)O emission from Clump I, a complex of molecular clouds which shows the largest noncircular velocities of any molecular material known in the Milky Way, are studied. Observations of the J = 1-0 rotational transitions of the above molecules are reported, and the large-scale distribution and kinematics of the molecular gas in the direction of Clump I are discussed. The small-scale structure is described based on one arcmin resolution of (C-13)O data. Physical properties of the molecular material are derived, and the dynamics of the Clump I clouds are discussed in the context of their stability against Galactic tidal forces. It is concluded that all the clouds in the complex are gravitationally bound, although their outer envelopes may be tidally disrupted by the Galactic potential. The relative motion of the clouds is qualitatively similar to giant molecular cloud complexes in spiral arms of the outer Galactic disk, but the velocities are higher.

Bania, T. M.↗

NASA NTRS1987

A new VLSI complex integer multiplier which uses a quadratic-polynomial residue system with Fermat numbers

Shyu, H. C.↗

NASA NTRS1988

The N2-P3 complex of the evoked potential and human performance

The N2-P3 complex and other endogenous components of human evoked potential provide a set of tools for the investigation of human perceptual and cognitive processes. These multidimensional measures of central nervous system bioelectrical activity respond to a variety of environmental and internal factors which have been experimentally characterized. Their application to the analysis of human performance in naturalistic task environments is just beginning. Converging evidence suggests that the N2-P3 complex reflects processes of stimulus evaluation, perceptual resource allocation, and decision making that proceed in parallel, rather than in series, with response generation. Utilization of these EP components may provide insights into the central nervous system mechanisms modulating task performance unavailable from behavioral measures alone. The sensitivity of the N2-P3 complex to neuropathology, psychopathology, and pharmacological manipulation suggests that these components might provide sensitive markers for the effects of environmental stressors on the human central nervous system.

Odonnell, Brian F.↗

NASA NTRS1987

10.7-cm solar radio flux and the magnetic complexity of active regions

During sunspot cycles 20 and 21, the maximum in smoothed 10.7-cm solar radio flux occurred about 1.5 yr after the maximum smoothed sunspot number, whereas during cycles 18 and 19 no lag was observed. Thus, although 10.7-cm radio flux and Zurich sunspot number are highly correlated, they are not interchangeable, especially near solar maximum. The 10.7-cm flux more closely follows the number of sunspots visible on the solar disk, while the Zurich sunspot number more closely follows the number of sunspot groups. The number of sunspots in an active region is one measure of the complexity of the magnetic structure of the region, and the coincidence in the maxima of radio flux and number of sunspots apparently reflects higher radio emission from active regions of greater magnetic complexity. The presence of a lag between sunspot-number maximum and radio-flux maximum in some cycles but not in others argues that some aspect of the average magnetic complexity near solar maximum must vary from cycle to cycle. A speculative possibility is that the radio-flux lag discriminates between long-period and short-period cycles, being another indicator that the solar cycle switches between long-period and short-period modes.

Wilson, Robert M.↗

NASA NTRS1989

Measurements of complex permittivity of microwave substrates in the 20 to 300 K temperature range from 26.5 to 40.0 GHz

A knowledge of the dielectric properties of microwave substrates at low temperatures is useful in the design of superconducting microwave circuits. Results are reported for a study of the complex permittivity of sapphire (Al2O3), magnesium oxide (MgO), silicon oxide (SiO2), lanthanum aluminate (LaAlO3), and zirconium oxide (ZrO2), in the 20 to 300 Kelvin temperature range, at frequencies from 26.5 to 40.0 GHz. The values of the real and imaginary parts of the complex permittivity were obtained from the scattering parameters, which were measured using a HP-8510 automatic network analyzer. For these measurements, the samples were mounted on the cold head of a helium gas closed cycle refrigerator, in a specially designed vacuum chamber. An arrangement of wave guides, with mica windows, was used to connect the cooling system to the network analyzer. A decrease in the value of the real part of the complex permittivity of these substrates, with decreasing temperature, was observed. For MgO and Al2O3, the decrease from room temperature to 20 K was of 7 and 15 percent, respectively. For LaAlO3, it decreased by 14 percent, for ZrO2 by 15 percent, and for SiO2 by 2 percent, in the above mentioned temperature range.

Miranda, Felix A.↗

NASA NTRS1989

Thermodynamic cost of computation, algorithmic complexity and the information metric

Algorithmic complexity is discussed as a computational counterpart to the second law of thermodynamics. It is shown that algorithmic complexity, which is a measure of randomness, sets limits on the thermodynamic cost of computations and casts a new light on the limitations of Maxwell's demon. Algorithmic complexity can also be used to define distance between binary strings.

Zurek, W. H.↗

NASA NTRS1990

Unbound molecular complexes in M33

The HI content of the nearby spiral galaxy M33 (d approx. 0.8 Mpc) has been the subject of many detailed studies (most recently Deul and van der Hulst 1987), but similar data on the molecular gas component has been lacking. This galaxy is currently undergoing vigorous high-mass star formation, as evidenced by the many OB associations and HII regions, and so is expected to possess at least some molecular gas. Interferometric studies have detected molecular clouds similar to Galactic Giant Molecular Clouds (GMCs) (Boulanger et al. 1988; Wilson et al. 1988). Researchers have recently mapped the nuclear region of M33 in the CO J=1-0 line with a 12 m telescope (half power beam width 55 inches approx. 210 pc) out to a radius of 3.5 minutes in order to trace the detailed distribution of the molecular gas. The resulting map reveals six large complexes with diameters of 200 to 400 pc. Interferometer observations of these regions have resolved them into individual molecular clouds similar to Galactic GMCs (Wilson et al. 1988). The complexes shown are much larger than individual Galactic GMCs (Sanders, Scoville, and Solomon 1985), but are somewhat smaller on average than the large associations seen in the grand-design spiral galaxy M51 (Rand and Kulkarni 1989). If we extend the velocity-diameter relation observed for Galactic GMCs to these larger structures, the predicted velocity widths are a factor of 1.5 to 3 times greater than the observed full-width half-maximum velocities (13 to 29 km (s-1). The peak brightness temperatures are approx. 0.2 K, at least a factor of 10 lower than what is observed for Galactic GMCs. If these large structures are made up of objects similar to Galactic GMCs, the area filling factor of the small clouds is roughly 10 percent. These results suggest that these complexes are not very large GMCs, but rather are associations of many individual GMCs or GMCs embedded in a diffuse gas component.

Wilson, Christine D.↗

NASA NTRS1991

Application of a solution adaptive grid scheme, SAGE, to complex three-dimensional flows

A new three-dimensional (3D) adaptive grid code based on the algebraic, solution-adaptive scheme of Nakahashi and Deiwert is developed and applied to a variety of problems. The new computer code, SAGE, is an extension of the same-named two-dimensional (2D) solution-adaptive program that has already proven to be a powerful tool in computational fluid dynamics applications. The new code has been applied to a range of complex three-dimensional, supersonic and hypersonic flows. Examples discussed are a tandem-slot fuel injector, the hypersonic forebody of the Aeroassist Flight Experiment (AFE), the 3D base flow behind the AFE, the supersonic flow around a 3D swept ramp and a generic, hypersonic, 3D nozzle-plume flow. The associated adapted grids and the solution enhancements resulting from the grid adaption are presented for these cases. Three-dimensional adaption is more complex than its 2D counterpart, and the complexities unique to the 3D problems are discussed.

Davies, Carol B.↗

NASA NTRS1990

Measurements of complex permittivity of microwave substrates in the 20 to 300 K temperature range from 26.5 to 40.0 GHz

A knowledge of the dielectric properties of microwve substrates at low temperatures is useful in the design of superconducting microwave circuits. Results are reported for a study of the complex permittivity of sapphire (Al2O3), magnesium oxide (MgO), silicon oxide (SiO2), lanthanum aluminate (LaAlO3), and zirconium oxide (ZrO2), in the 20 to 300 Kelvin temperature range, at frequencies from 26.5 to 40.0 GHz. The values of the real and imaginary parts of the complex permittivity were obtained from the scattering parameters, which were measured using an HP-8510 automatic network analyzer. For these measurements, the samples were mounted on the cold head of a helium gas closed cycle refrigerator, in a specially designated vacuum chamber. An arrangement of wave guides, with mica windows, was used to connect the cooling system to the network analyzer. A decrease in the value of the real part of the complex permittivity of these substrates, with decreasing temperature, was observed. For MgO and Al2O3, the decrease from room temperature to 20 K was of 7 and 15 percent, respectively. For LaAlO3, it decreased by 14 percent, for ZrO2 by 15 percent, and for SiO2 by 2 percent, in the above mentioned temperature range.

Miranda, Felix A.↗

NASA NTRS1991

Decision paths in complex tasks

Complex real world action and its prediction and control has escaped analysis by the classical methods of psychological research. The reason is that psychologists have no procedures to parse complex tasks into their constituents. Where such a division can be made, based say on expert judgment, there is no natural scale to measure the positive or negative values of the components. Even if we could assign numbers to task parts, we lack rules i.e., a theory, to combine them into a total task representation. We compare here two plausible theories for the amalgamation of the value of task components. Both of these theories require a numerical representation of motivation, for motivation is the primary variable that guides choice and action in well-learned tasks. We address this problem of motivational quantification and performance prediction by developing psychophysical scales of the desireability or aversiveness of task components based on utility scaling methods (Galanter 1990). We modify methods used originally to scale sensory magnitudes (Stevens and Galanter 1957), and that have been applied recently to the measure of task 'workload' by Gopher and Braune (1984). Our modification uses utility comparison scaling techniques which avoid the unnecessary assumptions made by Gopher and Braune. Formula for the utility of complex tasks based on the theoretical models are used to predict decision and choice of alternate paths to the same goal.

Galanter, Eugene↗

NASA NTRS1993

Estimation of full modal damping matrices from complex test modes

This paper describes the refinements of a previously published method for estimating a full modal damping matrix from complex test modes. It also documents application of the refined method to a structure where complex test modes were derived by the ERA method from multi-input random vibration test data. A numerical example based on simulated test data is presented to demonstrate the validity of the method. The application using real data was not successful, presumably because of noise in the small phase angles of the measured complex modes. Alternative test and data reduction procedures are suggested as possible remedies to the problem. A careful analysis of measurement and data processing errors should be made to examine basic feasibility before implementing the alternative procedures. The ability to estimate a full modal damping matrix is considered important for the preflight estimation of on-orbit damping, and for the synthesis of structural damping from substructure tests.

Hasselman, T. K.↗

NASA NTRS1991

Full complex modulation with two one-parameter SLMs

Although the action of a spatial light modulator (SLM) is usually restricted to certain locations on the operating curve of the complex plane, NASA is planning to use architectures that allow two continuously variable SLMs to function jointly so as to access the full interior of a closed curve in the complex plane. This paper describes three fundamental methods for attaining full complex modulation. The mathematics for two of these methods is presented, and signal decomposition in their terms is outlined.

Juday, Richard D.↗