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NASA NTRS1986

Partial and Interaction Spline Models for the Semiparametric Estimation of Functions of Several Variables

A partial spline model is a model for a response as a function of several variables, which is the sum of a smooth function of several variables and a parametric function of the same plus possibly some other variables. Partial spline models in one and several variables, with direct and indirect data, with Gaussian errors and as an extension of GLIM to partially penalized GLIM models are described. Application to the modeling of change of regime in several variables is described. Interaction splines are introduced and described and their potential use for modeling non-linear interactions between variables by semiparametric methods is noted. Reference is made to recent work in efficient computational methods.

Wahba, Grace↗
NASA NTRS1989

The implementation and operation of a variable-response electronic throttle control system for a TF-104G aircraft

During some flight programs, researchers have encountered problems in the throttle response characteristics of high-performance aircraft. To study and to help solve these problems, the National Aeronautics and Space Administration Ames Research Center's Dryden Flight Research Facility (Ames-Dryden) conducted a study using a TF-104G airplane modified with a variable-response electronic throttle control system. Ames-Dryden investigated the effects of different variables on engine response and handling qualities. The system provided transport delay, lead and lag filters, second-order lags, command rate and position limits, and variable gain between the pilot's throttle command and the engine fuel controller. These variables could be tested individually or in combination. Ten research flights were flown to gather data on engine response and to obtain pilot ratings of the various system configurations. The results should provide design criteria for engine-response characteristics. The variable-response throttle components and how they were installed in the TF-104G aircraft are described. How the variable-response throttle was used in flight and some of the results of using this system are discussed.

Neal, Bradford↗
NASA NTRS1994

Joint for a variable geometry truss and method of constructing same

A joint and a method of constructing a joint for a variable geometry truss having a variable number of planes of variable length battens connected together in a triangular configuration, each plane being connected by six fixed length longerons in a Stewart platform configuration, are presented. The variable length battens allow the orientation of one end plane of the variable geometry truss to be changed to the other end plane in a controlled manner by selectively adjusting the lengths of the variable length battens. A main pivot joint pivotally connects two battens about a pivotal axis. A universal joint is pivotally connected to the main joint such that the pivotal axis of the universal joint is coextensive with the pivotal axis at the main joint. Two longerons are pivotally connected to the universal joint. Each longeron is thereby provided with three intersecting axes of rotation. Each longeron may include a revolute joint, allowing rotation about the longitudinal axis of the longeron.

Horner, Garnett C.↗
NASA NTRS1994

ROSAT all-sky survey observations of X-ray variability in cool giant stars

We have identified 24 active late-type giant stars, including 11 RS CVn systems, with soft X-ray count rates high enough to allow the detection of statistically significant variability on a Roentgen Satellite (ROSAT) orbital timescale (96 minutes) as observed by the Position Sensitive Proportional Counter (PSPC) during the all-sky survey. Our sensitivity typically lies in the range of 10% - 25%, depending on the source count rate. Comparison is made to the daily, nonflare solar soft X-ray variability as observed by the Solrad satellites during solar minimum in 1969 and solar maximum in 1975. Seven of the 24 stars show significant variability; in two of these cases (HR 3922 and HR 8448) major flares were observed in which the peak count rate is enhanced by at least a factor of 3 above quiescent. While HR 3922 (G5 III) is not (yet) classified as an RS CVn star, its flare is more energetic (3 x 10(exp 31) ergs/s) than previously observed RS CVn flares. The apparently single giant HR 8167 (G8 III) also shows two flares. While one might expect to find an anticorrelation between saturated coronae and variability, we find no evidence of this: the two stars in our sample with the highest ratio of f(sub x)/f(sub v) both show variability. We also point out that Capella (G6 III + F9 III) is one of the stars manifesting variability.

Haisch, Bernhard↗
NASA NTRS1994

Evidence for X-ray flux and spectral modulation by absorption in NGC 6814. 1: The nature of the most rapid variability

The Seyfert 1 galaxy NGC 6814 was observed using the Japanese X-ray astronomy satellite Ginga in 1990 April and October. The rapid variability characteristically associated with this source was reconfirmed. Specifically, three dips were found in the April observation in which the flux dropped to nearly zero in approximately 300 s. The doubling timescale was approximately 50 s. A similar but separated drop and rise in flux was observed in the October data, different in that the flux did not decrease completely to zero. A detailed analysis of the data around the structures of most rapid variability found spectral variability and lags in flux between different energy bands. Lags were on the order of a few to tens of seconds for the April data, and on the order of tens to a couple of hundred seconds for the October data. The sense of the lags was such that during flux decreases the hard flux lagged, while during flux increases the soft flux lagged. Associated significant apparent hardening of the spectrum at low flux was observed in the April data. Apparent hardening of the spectrum also occurred in the October flux decrease, to a photon index of GAMMA = 0.85; however, the spectrum softened at lowest flux to the index of the predecrease level, GAMMA = 1.54. In the April dips, the line flux was found to decrease significantly. A marginal decrease in line flux was also observed in the October data. The variability of the line flux reconfirmed the result of Kunieda et al. (1990), who found that the line production region must be within approximately 300 light-seconds from the source. To explain the observational results, a variable-absorption model was proposed, in which the column density was assumed to vary as a function of time. Other physical processes, including intrinsic spectral changes and warm absorber models, which could account for the fastest variability, could be ruled out by the results of the data analysis. A primary constraint found for geometrical models is that the material which is doing the absorption must have relatively low ionization (xi less than 100). This result leads to severe constraints on a general orbiting cloud model, requiring high densities (n approximately 10(exp 16)/cu cm) and sheetlike geometry.

Leighly, Karen↗
NASA NTRS1994

Sea level variability in the eastern tropical Pacific as observed by TOPEX and Tropical Ocean-Global Atmosphere Tropical Atmosphere-Ocean Experiment

Sea surface height measurements from the TOPEX altimeter and dynamic height from Tropical Ocean-Global Atmosphere Tropical Atmosphere-Ocean (TOGA TAO) moorings are used to explore sea level variability in the northeastern tropical Pacific Ocean. Afetr the annual harmonic is removed, there are two distinct bands of variability: one band is centered at 5 deg N to 7 deg N and extends from 165 deg W to 110 deg W, and the other band is centered at 10 deg N to 12 deg N and extends from 120 deg W to the coast of Central America. The correspondence between the two independent observation data sets at 5 deg N is excellent with correlations of about 90%. The variability at 5 deg-7 deg N is identified as instability waves formed just south of the North Equatorial Countercurrent during the months of July and March. Wave amplitudes are largest in the range of longitudes 160 deg-140 deg W, where they can exceed 10 cm. The waves disappear when the equatorial current system weakens, during the months of March and May. The variability at 11 deg N in 1993 has the form of anticyclone eddies. These eddies propagate westward at a speed of about 17 cm/s, consistent with the dispersion characteristics of free Rossby waves. The eddies are shown to have their origin near the coast of central America during northern fall and winter. Their formation seems to result from intense wind bursts across the Gulfs of Tehuantepec and Papagayo which generate strong anticyclonic ocean eddies. The disappearance of the eddies in the summer of 1993 coincidences with the seasonal intensification of equatorial currents. Thus the variability at 11 deg N has very little overlap in time with the variability at 5 deg N.

Giese, Benjamin S.↗
NASA NTRS1984

Selection of Slow and Fast Variables in the Three-Dimensional Flight Dynamics

A transformation from the altitude and velocity state variables of three-dimensional flight mechanics to a new set of more desirable variables is found. The new variables provide a greater time-scale separation, decrease system coupling, and give better estimates of the fast-variable values along the reduced solution. One of the new variables is the often-used specific energy, whereas the other variable changes along a given trajectory, depending on the nature of the local reduced solution. Numerical examples are included.

Ardema, M.↗
NASA NTRS2000

A Systematic Search for Short-term Variability of EGRET Sources

The 3rd EGRET Catalog of High-energy Gamma-ray Sources contains 170 unidentified sources, and there is great interest in the nature of these sources. One means of determining source class is the study of flux variability on time scales of days; pulsars are believed to be stable on these time scales while blazers are known to be highly variable. In addition, previous work has demonstrated that 3EG J0241-6103 and 3EG J1837-0606 are candidates for a new gamma-ray source class. These sources near the Galactic plane display transient behavior but cannot be associated with any known blazers. Although, many instances of flaring AGN have been reported, the EGRET database has not been systematically searched for occurrences of short-timescale (approximately 1 day) variability. These considerations have led us to conduct a systematic search for short-term variability in EGRET data, covering all viewing periods through proposal cycle 4. Six 3EG catalog sources are reported here to display variability on short time scales; four of them are unidentified. In addition, three non-catalog variable sources are discussed.

Wallace, P. M.↗
NASA NTRS2000

First-Order Model Management With Variable-Fidelity Physics Applied to Multi-Element Airfoil Optimization

First-order approximation and model management is a methodology for a systematic use of variable-fidelity models or approximations in optimization. The intent of model management is to attain convergence to high-fidelity solutions with minimal expense in high-fidelity computations. The savings in terms of computationally intensive evaluations depends on the ability of the available lower-fidelity model or a suite of models to predict the improvement trends for the high-fidelity problem, Variable-fidelity models can be represented by data-fitting approximations, variable-resolution models. variable-convergence models. or variable physical fidelity models. The present work considers the use of variable-fidelity physics models. We demonstrate the performance of model management on an aerodynamic optimization of a multi-element airfoil designed to operate in the transonic regime. Reynolds-averaged Navier-Stokes equations represent the high-fidelity model, while the Euler equations represent the low-fidelity model. An unstructured mesh-based analysis code FUN2D evaluates functions and sensitivity derivatives for both models. Model management for the present demonstration problem yields fivefold savings in terms of high-fidelity evaluations compared to optimization done with high-fidelity computations alone.

Alexandrov, N. M.↗
NASA NTRS1998

Modeling the Variability of the BL Lacertae Object PKS 2155-304

The bright X-ray-selected BL Lacertae object PKS 2155-304 has been the target of two intense multi-wavelength campaigns in 1991 November and in 1994 May. Although the spectral energy distributions at both epochs were quite similar, the source exhibited two very distinct variability patterns that cannot be easily reconciled with homogeneous one-zone C7 jet models. During the first epoch the variability was almost achromatic in amplitude, with a time lag between X-rays and ultraviolet radiation (UV) of approximately three hours, while during the second epoch the variability amplitude increased as a function of wavelength with the EUV flare peaking approximately one day after the X-ray flare. We model the source using a time-dependent inhomogeneous accelerating jet model. We reproduce the general characteristics of the different variability signatures by assuming that plasma disturbances with different physical properties propagate downstream in an underlying jet characterized by the same set of physical parameters at both epochs. A time delay of approximately one day between the hardening of the UV spectral index and the UV flux present at both epochs is modeled with stochastic fluctuations in the particle acceleration manifested through small variations of the maximum energy of the injected electrons. We predict that similar time delays will be present in future observations even in the absence of strong variability event. We stress the importance of observations at neighboring frequencies as a diagnostic tool for the structure of the quiescent jet in blazars especially in the seemingly dull case in which strong variability is absent.

Georganopuolos, Markos↗
NASA NTRS2001

Enhancing the Remote Variable Operations in NPSS/CCDK

Many scientific applications in aerodynamics and solid mechanics are written in Fortran. Refitting these legacy Fortran codes with distributed objects can increase the code reusability. The remote variable scheme provided in NPSS/CCDK helps programmers easily migrate the Fortran codes towards a client-server platform. This scheme gives the client the capability of accessing the variables at the server site. In this paper, we review and enhance the remote variable scheme by using the operator overloading features in C++. The enhancement enables NPSS programmers to use remote variables in much the same way as traditional variables. The remote variable scheme adopts the lazy update approach and the prefetch method. The design strategies and implementation techniques are described in details. Preliminary performance evaluation shows that communication overhead can be greatly reduced.

Sang, Janche↗
NASA NTRS2001

The Variability of the Horizontal Circulation in the Troposphere and Stratosphere: A Comparison

The variability of the horizontal circulation in the stratosphere and troposphere of the Northern Hemisphere (NH) is compared by using various approaches. Spatial degrees of freedom (dof) on different time scales were derived. Modes of variability were computed in geopotential height fields at the tropospheric and stratospheric pressure levels by applying multivariate statistical approaches. Features of the spatial and temporal variability of the winterly zonal wind were studied with the help of recurrence and persistence analyses. The geopotential height and zonally-averaged zonal wind at the 50-, 500- and 1000-hPa level are used to investigate the behavior of the horizontal circulation in the lower stratosphere, mid-troposphere and at the near surface level, respectively. It is illustrated that the features of the variability of the horizontal circulation are very similar in the mid-troposphere and at the near surface level. Due to the filtering of tropospheric disturbances by the stratospheric and upper tropospheric zonal mean flow, the variability of the stratospheric circulation exhibits less spatial complexity than the circulation at tropospheric pressure levels. There exist enormous differences in the number of degrees of freedom (or free variability modes) between both atmospheric layers. Results of the analyses clearly show that the concept of a zonally symmetric AO with a simple structure in the troposphere similar to the one in the stratosphere is not valid. It is concluded that the spatially filtered climate change signal can be detected earlier in the stratosphere than in the mid-troposphere or at the near surface level.

Perlwitz, Judith↗
NASA NTRS2001

Variable Iron K(alpha) Lines in Seyfert 1 Galaxies

We find that variability of the iron K alpha line is common in Seyfert 1 galaxies. Using data from the ASCA archive for objects that have been observed more than once during the mission, we study the time-averaged spectra from individual observations, thereby probing variability on timescales that range from days to years. Since the statistics of the data do not warrant searches for line variability in terms of a complex physical model, we use a simple Gaussian to model the gross shape of the line and then use the centroid energy, intensity, and equivalent width as robust indicators of changes in the line profile. We find that approximately 70% of Seyfert 1 galaxies (10 out of 15) show variability in at least one of these parameters: the centroid energy, intensity, and equivalent width vary in six, four, and eight sources, respectively. Because of the low signal-to-noise ratio, limited sampling, and time averaging, we consider these results to represent lower limits to the rate of incidence of variability. In most cases changes in the line do not appear to track changes in the continuum. In particular, we find no evidence for variability of the line intensity in NGC 4151, suggesting an origin in a region larger than the putative accretion disk, where most of the iron line has been thought to originate. Mrk 279 is investigated on short timescales. The time-averaged effective line energy (as measured by the Gaussian center energy, which is weighted by emission in the entire line profile) is 6.5 keV in the galaxy rest frame. As the continuum flux increases by 20% in a few hours, the Fe K line responds within approximately 10,000 seconds with the effective line energy increasing by 0.22 keV (approximately 10,500 kilometers per second). We also examine the ROSAT PSPC spectrum of Mrk 279 but find inconsistencies with ASCA. Problems with the ASCA and ROSAT calibration that affect simultaneous spectral fits at low energies are discussed in an appendix.

Weaver, K. A.↗
NASA NTRS2003

HST Snapshot Study of Variable Stars in Globular Clusters: Inner Region of NGC 6441

We present the results of a Hubble Space Telescope snapshot program to survey the inner region of the metal-rich globular cluster NGC 6441 for its variable stars. A total of 57 variable stars was found including 38 RR Lyrae stars, 6 Population II Cepheids, and 12 long period variables. Twenty-four of the RR Lyrae stars and all of the Population II Cepheids were previously undiscovered in ground-based surveys. Of the RR Lyrae stars observed in h s survey, 26 are pulsating in the fundamental mode with a mean period of 0.753 d and 12 are first-overtone mode pulsators with a mean period of 0.365 d. These values match up very well with those found in ground-based surveys. Combining all the available data for NGC 6441, we find mean periods of 0.759 d and 0.375 d for the RRab and RRc stars, respectively. We also find that the RR Lyrae in this survey are located in the same regions of a period-amplitude diagram as those found in ground-based surveys. The overall ratio of RRc to total RR Lyrae is 0.33. Although NGC 6441 is a metal-rich globular cluster and would, on that ground, be expected either to have few RR Lyrae stars, or to be an Oosterhoff type I system, its RR Lyrae more closely resemble those in Oosterhoff type II globular clusters. However, even compared to typical Oosterhoff type II systems, the mean period of its RRab stars is unusually long. We also derived I-band period-luminosity relations for the RR Lyrae stars. Of the six Population II Cepheids, five are of W Virginis type and one is a BL Herculis variable star. This makes NGC 6441, along with NGC 6388, the most metal-rich globular cluster known to contain these types of variable stars. Another variable, V118, may also be a Population II Cepheid given its long period and its separation in magnitude from the RR Lyrae stars. We examine the period-luminosity relation for these Population II Cepheids and compare it to those in other globular clusters and in the Large Magellanic Cloud. We argue that there does not appear to be a change in the period-luminosity relation slope between the BL Herculis and W Virginis stars, but that a change of slope does occur when the RV Tauri stars are added to the period-luminosity relation.

Pritzl, Barton J.↗
NASA NTRS1998

Gait variability and basal ganglia disorders: stride-to-stride variations of gait cycle timing in Parkinson's disease and Huntington's disease

The basal ganglia are thought to play an important role in regulating motor programs involved in gait and in the fluidity and sequencing of movement. We postulated that the ability to maintain a steady gait, with low stride-to-stride variability of gait cycle timing and its subphases, would be diminished with both Parkinson's disease (PD) and Huntington's disease (HD). To test this hypothesis, we obtained quantitative measures of stride-to-stride variability of gait cycle timing in subjects with PD (n = 15), HD (n = 20), and disease-free controls (n = 16). All measures of gait variability were significantly increased in PD and HD. In subjects with PD and HD, gait variability measures were two and three times that observed in control subjects, respectively. The degree of gait variability correlated with disease severity. In contrast, gait speed was significantly lower in PD, but not in HD, and average gait cycle duration and the time spent in many subphases of the gait cycle were similar in control subjects, HD subjects, and PD subjects. These findings are consistent with a differential control of gait variability, speed, and average gait cycle timing that may have implications for understanding the role of the basal ganglia in locomotor control and for quantitatively assessing gait in clinical settings.

Non-NASA Center↗
NASA NTRS2005

Spinning Spacecraft Attitude Estimation Using Markley Variables: Filter Implementation And Results

Attitude estimation is often more difficult for spinning spacecraft than for three-axis stabilized platforms due to the need to follow rapidly-varying state vector elements and the lack of three-axis rate measurements from gyros. The estimation problem simplifies when torques are negligible and nutation has damped out, but the general case requires a sequential filter with dynamics propagation. This paper describes the implementation and test results for an extended Kalman filter for spinning spacecraft attitude and rate estimation based on a novel set of variables suggested in a paper by Markley [AAS93-3301 (referred to hereafter as Markley variables). Markley has demonstrated that the new set of variables provides a superior parameterization for numerical integration of the attitude dynamics for spinning or momentum-biased spacecraft. The advantage is that the Markley variables have fewer rapidly-varying elements than other representations such as the attitude quaternion and rate vector. A filter based on these variables was expected to show improved performance due to the more accurate numerical state propagation. However, for a variety of test cases, it has been found that the new filter, as currently implemented, does not perform significantly better than a quaternion-based filter that was developed and tested in parallel. This paper reviews the mathematical background for a filter based on Markley variables. It also describes some features of the implementation and presents test results. The test cases are based on a mission using magnetometer and Sun sensor data and gyro measurements on two axes normal to the spin axis. The orbit and attitude scenarios and spacecraft parameters are modeled after one of the THEMIS (Time History of Events and Macroscale Interactions during Substorms) probes. Several tests are presented that demonstrate the filter accuracy and convergence properties. The tests include torque-free motion with various nutation angles, large constant-torque attitude slews, sensor misalignments, large initial attitude and rate errors, and cases with low data frequency. It is found that the convergence is rapid, the radius of convergence is large, and the results are reasonably accurate even in the presence of unmodeled perturbations.

Sedlak, Joseph E.↗
NASA NTRS2006

Image-Subtraction Photometry of Variable Stars in the Globular Clusters NGC 6388 and NGC 6441

We have applied Alard's image subtraction method (ISIS v2.1) to the observations of the globular clusters NGC 6388 and NGC 6441 previously analyzed using standard photometric techniques (DAOPHOT, ALLFRAME). In this reanalysis of observations obtained at CTIO, besides recovering the variables previously detected on the basis of our ground-based images, we have also been able to recover most of the RR Lyrae variables previously detected only in the analysis of Hubble Space Telescope WFPC2 observations of the inner region of NGC 6441. In addition, we report five possible new variables not found in the analysis of the EST observations of NGC 6441. This dramatically illustrates the capabilities of image subtraction techniques applied to ground-based data to recover variables in extremely crowded fields. We have also detected twelve new variables and six possible variables in NGC 6388 not found in our previous groundbased studies. Revised mean periods for RRab stars in NGC 6388 and NGC 6441 are 0.676 day and 0.756 day, respectively. These values are among the largest known for any galactic globular cluster. Additional probable type II Cepheids were identified in NGC 6388, confirming its status as a metal-rich globular cluster rich in Cepheids.

Corwin, Michael T.↗
NASA NTRS2002

Dynamical and chemical contributions to variability in microwave limb sounder Arctic stratoshperic column ozone

Analyses of column ozone above 100 hPa (Col100) derived from Upper Atmosphere Research Satellite Microwave Limb Sounder (MLS) data in February/March 1992-1998 show that about half of the interannual variability in Col100 in the Arctic polar vortex in late winter results from interannual variability in chemical loss. A majority of the remainder results from interannual variability in day-to-day dynamical motions including adiabatic warming/cooling and poleward advection of underlying upper tropospheric subtropical air on short timescales, rather than from variations in descent rates and large-scale transport over the winters. The morphology of Col100 from MLS remains very similar to that in the dynamical models even in the years with most chemical ozone loss. The amount and character of day-to-day variability in dynamical models closely follows that in MLS Col100. Although the morphology of and day-to-day variability in Arctic column ozone are controlled by dynamical processes, chemical ozone loss was a major factor in producing both the low values of and the large interannual variability in Arctic column ozone observed during the 1990s.

Arctic ozone loss↗