Search NASA⌕ Search

SEARCH · Search NASA

Results for “fixed points”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 181 records · Page 10

Water Surface Currents, Short Gravity-Capillary Waves and Radar Backscatter

Despite their importance for air-sea interaction and microwave remote sensing of the ocean surface, intrinsic properties of short gravity-capillary waves are not well established. This is largely due to water surface currents and their effects on the direct measurements of wave parameters conducted at a fixed point. Frequencies of small scale waves propagating on a surface which itself is in motion, are subject to Doppler shifts. Hence, the high frequency tail of the wave spectra obtained from such temporal observations is smeared. Conversion of this smeared measured-frequency spectra to intrinsic-frequency (or wavenumber) spectra requires corrections for the Doppler shifts. Such attempts in the past have not been very successful in particular when field data were used. This becomes evident if the amplitude modulation of short waves by underlying long waves is considered. Microwave radar studies show that the amplitude of a short wave component attains its maximum value near the crests and its minimum in the troughs of the long waves. Doppler-shifted wave data yield similar results but much larger in modulation magnitude, as expected. In general, Doppler shift corrections reduce the modulation magnitude. Overcorrection may result in a negligible modulation or even in a strong modulation with the maximum amplitude in the wave troughs. The latter situation is clearly contradictory to our visual observations as well as the radar results and imply that the advection by currents is overestimated. In this study, a differential-advection approach is used in which small scale waves are advected by the currents evaluated not at the free surface, but at a depth proportional to their wavelengths. Applicability of this approach is verified by the excellent agreement in phase and magnitude of short-wave modulation between results based on radar and on wave-gauge measurements conducted on a lake.

Atakturk, Serhad S.↗

Delay of Turbulent Boundary Layer Detachment by Mechanical Excitation: Application to Rearward-facing Ramp

A vane oscillating about a fixed point at the inlet to a two-dimensional 20 deg rearward-facing ramp proved effective in delaying the detachment of a turbulent boundary layer. Flow-field, surface static pressure, and smoke-wire flow visualization measurements were made. Surface pressure coefficient distributions revealed that two different effects occurred with axial distance along the ramp surface. The surface pressure coefficient varied as a complex function of the vane oscillation frequency and its trailing edge displacement amplitude; that is, it varied as a function of the vane oscillation frequency throughout the entire range of frequencies covered during the test, but it varied over only a limited range of the trailing edge displacement amplitudes covered.The complexity of these findings prompted a detailed investigation, the results of which revealed a combination of phenomena that explain qualitatively how the mechanically generated, periodic, sinusoidal perturbing signal produced by the oscillating vane reacts with the fluid flow to delay the detachment of a turbulent boundary layer experiencing transitory detachment.

McKinzie, Daniel J., Jr.↗

Fast Multigrid Techniques in Total Variation-Based Image Reconstruction

Existing multigrid techniques are used to effect an efficient method for reconstructing an image from noisy, blurred data. Total Variation minimization yields a nonlinear integro-differential equation which, when discretized using cell-centered finite differences, yields a full matrix equation. A fixed point iteration is applied with the intermediate matrix equations solved via a preconditioned conjugate gradient method which utilizes multi-level quadrature (due to Brandt and Lubrecht) to apply the integral operator and a multigrid scheme (due to Ewing and Shen) to invert the differential operator. With effective preconditioning, the method presented seems to require Omicron(n) operations. Numerical results are given for a two-dimensional example.

Oman, Mary Ellen↗

Dynamical System Analysis of Reynolds Stress Closure Equations

In this paper, we establish the causality between the model coefficients in the standard pressure-strain correlation model and the predicted equilibrium states for homogeneous turbulence. We accomplish this by performing a comprehensive fixed point analysis of the modeled Reynolds stress and dissipation rate equations. The results from this analysis will be very useful for developing improved pressure-strain correlation models to yield observed equilibrium behavior.

Girimaji, Sharath S.↗

Reconfigurable Flight Control Designs With Application to the X-33 Vehicle

Two methods for control system reconfiguration have been investigated. The first method is a robust servomechanism control approach (optimal tracking problem) that is a generalization of the classical proportional-plus-integral control to multiple input-multiple output systems. The second method is a control-allocation approach based on a quadratic programming formulation. A globally convergent fixed-point iteration algorithm has been developed to make onboard implementation of this method feasible. These methods have been applied to reconfigurable entry flight control design for the X-33 vehicle. Examples presented demonstrate simultaneous tracking of angle-of-attack and roll angle commands during failures of the right body flap actuator. Although simulations demonstrate success of the first method in most cases, the control-allocation method appears to provide uniformly better performance in all cases.

Burken, John J.↗

Southern Africa Validation of NASA's Earth Observing System (SAVE EOS)

Southern Africa Validation of EOS (SAVE) is 4-year, multidisciplinary effort to validate operational and experimental products from Terra-the flagship satellite of NASA's Earth Observing System (EOS). At test sites from Zambia to South Africa, we are measuring soil, vegetation and atmospheric parameters over a range of ecosystems for comparison with products from Terra, Landsat 7, AVHRR and SeaWiFS. The data are also employed to parameterize and improve vegetation process models. Fixed-point and mobile "transect" sampling are used to collect the ground data. These are extrapolated over larger areas with fine-resolution multispectral imagery. We describe the sites, infrastructure, and measurement strategies developed underSAVE, as well as initial results from our participation in the first Intensive Field Campaign of SAFARI 2000. We also describe SAVE's role in the Kalahari Transect Campaign (February/March 2000) in Zambia and Botswana.

Privette, Jeffrey L.↗

Controlling Chaos Via Knowledge of Initial Condition for a Curved Structure

Nonlinear response of a flexible curved panel exhibiting bifurcation to fully developed chaos is demonstrated along with the sensitivity to small perturbation from the initial conditions. The response is determined from the measured time series at two fixed points. The panel is forced by an external nonharmonic multifrequency and monofrequency sound field. Using a low power time-continuous feedback control, carefully tuned at each initial condition, produces large long-term effects on the dynamics toward taming chaos. Without the knowledge of the initial conditions, control may be achieved by destructive interference. In this case, the control power is proportional to the loading power. Calculation of the correlation dimension and the estimation of positive Lyapunov exponents, in practice, are the proof of chaotic response.

Maestrello, L.↗

Two Reconfigurable Flight-Control Design Methods: Robust Servomechanism and Control Allocation

Two methods for control system reconfiguration have been investigated. The first method is a robust servomechanism control approach (optimal tracking problem) that is a generalization of the classical proportional-plus-integral control to multiple input-multiple output systems. The second method is a control-allocation approach based on a quadratic programming formulation. A globally convergent fixed-point iteration algorithm has been developed to make onboard implementation of this method feasible. These methods have been applied to reconfigurable entry flight control design for the X-33 vehicle. Examples presented demonstrate simultaneous tracking of angle-of-attack and roll angle commands during failures of the fight body flap actuator. Although simulations demonstrate success of the first method in most cases, the control-allocation method appears to provide uniformly better performance in all cases.

Burken, John J.↗

STS-110 Flight Day 8 Highlights

On Flight Day 8 of the STS-110 mission, the combined members of the Atlantis STS-110 crew and the International Space Station (ISS) Expedition 4 crew, Commanders Michael J. Bloomfield and Yury I. Onufrienko, respectively, answer questions posed to them by press members on the ground. Topics covered include: challenges of long term space habitation, adequacy of training for the on-orbit construction of the space station, details on the Mobile Transporter (MT) railcar system. Footage of the MT directly precedes and follows the extended question and answer portion of the video. The MT is seen from a variety of angles, as it slowly moves from Workstation 4 to Workstation 5 in order to test its ability to grapple to a fixed point along the track. The MT will eventually be used as a base for the robot arm in order to perform maintenance and assembly tasks on the ISS.

Source record↗

Some Remarks on GMRES for Transport Theory

We review some work on the application of GMRES to the solution of the discrete ordinates transport equation in one-dimension. We note that GMRES can be applied directly to the angular flux vector, or it can be applied to only a vector of flux moments as needed to compute the scattering operator of the transport equation. In the former case we illustrate both the delights and defects of ILU right-preconditioners for problems with anisotropic scatter and for problems with upscatter. When working with flux moments we note that GMRES can be used as an accelerator for any existing transport code whose solver is based on a stationary fixed-point iteration, including transport sweeps and DSA transport sweeps. We also provide some numerical illustrations of this idea. We finally show how space can be traded for speed by taking multiple transport sweeps per GMRES iteration. Key Words: transport equation, GMRES, Krylov subspace

Patton, Bruce W.↗

Dynamical Chaos in the Wisdom-Holman Integrator: Origins and Solutions

We examine the nonlinear stability of the Wisdom-Holman (WH) symplectic mapping applied to the integration of perturbed, highly eccentric (e-0.9) two-body orbits. We find that the method is unstable and introduces artificial chaos into the computed trajectories for this class of problems, unless the step size chosen 1s small enough that PeriaPse is always resolved, in which case the method is generically stable. This 'radial orbit instability' persists even for weakly perturbed systems. Using the Stark problem as a fiducial test case, we investigate the dynamical origin of this instability and argue that the numerical chaos results from the overlap of step-size resonances; interestingly, for the Stark-problem many of these resonances appear to be absolutely stable. We similarly examine the robustness of several alternative integration methods: a time-regularized version of the WH mapping suggested by Mikkola; the potential-splitting (PS) method of Duncan, Levison, Lee; and two original methods incorporating approximations based on Stark motion instead of Keplerian motion. The two fixed point problem and a related, more general problem are used to conduct a comparative test of the various methods for several types of motion. Among the algorithms tested, the time-transformed WH mapping is clearly the most efficient and stable method of integrating eccentric, nearly Keplerian orbits in the absence of close encounters. For test particles subject to both high eccentricities and very close encounters, we find an enhanced version of the PS method-incorporating time regularization, force-center switching, and an improved kernel function-to be both economical and highly versatile. We conclude that Stark-based methods are of marginal utility in N-body type integrations. Additional implications for the symplectic integration of N-body systems are discussed.

Rauch, Kevin P.↗

A Low Cost Single Chip VDL Compatible Transceiver ASIC

Recent trends in commercial communications system components have focussed almost exclusively on cellular telephone technology. As many of the traditional sources of receiver components have discontinued non-cellular telephone products, the designers of avionics and other low volume radio applications find themselves increasingly unable to find highly integrated components. This is particularly true for low power, low cost applications which cannot afford the lavish current consumption of the software defined radio approach increasingly taken by certified device manufacturers. In this paper, we describe a low power transceiver chip targeting applications from low VHF to low UHF frequencies typical of avionics systems. The chip encompasses a selectable single or double conversion design for the receiver and a low power IF upconversion transmitter. All local oscillators are synthesized and integrated into the chip. An on-chip I-Q modulator and demodulator provide baseband modulation and demodulation capability allowing the use of low power, fixed point signal processing components for signal demodulation. The goal of this program is to demonstrate a low cost VDL mode-3 transceiver using this chip to receive text weather information sent using 4-slot TDMA with no support for voice. The data will be sent from an experimental ground station. This work is funded by NASA Glenn Research Center.

Becker, Robert↗

First Terrestrial Soft X-ray Aurora Observations by Chandra

Northern polar "auroral" regions of Earth was observed by High-Resolution Camera in imaging mode (T32C-I) aboard Chandra X-Ray Observatory (CXO) during mid December 2003 - mid April 2004. Ten CXO observations, each approximately 20 min duration, were made in a non-conventional method (due to CXO technical issues), such that Chandra was aimed at a fixed point in sky and the Earth's polar cusp was allowed to drift through the HRC-I field-of-view. The observations were performed when CXO was near apogee and timed during northern winter mostly near midnight (6 hr), except two observations which occurred around 1200 UT, so that northern polar region is entirely in dark and solar fluoresced x-ray contamination can be avoided. These observations were aimed at searching the Earth's soft x-ray aurora and to do a comparative study with Jupiter's x-ray aurora, where a pulsating x-ray hot-spot near the northern magnetic pole has been observed by Chandra that implies a particle source region near Jupiter's magnetopause, and entry of heavy solar wind ions due to high-latitude reconnection as a viable explanation for the soft x-ray emissions. The first Chandra soft (0.1-2 keV) x-ray observations of Earth's aurora show that it is highly variable (intense arc, multiple arcs, diffuse, at times almost absent). In at least one of the observations an isolated blob of emission is observed where we expect cusp to be: giving indication of solar wind charge-exchange signature in x-rays. We are comparing the Chandra x-ray observations with observations at other wavelengths and particle data from Earth-orbiting satellites and solar wind measurements from near-Earth ACE and SOH0 spacecraft. Preliminary results from these unique CXO-Earth observations will be presented and discussed.

Bhardwaj, Anil↗

Monte Carlo Simulation of THz Multipliers

Schottky Barrier diode frequency multipliers are critical components in submillimeter and Thz space based earth observation systems. As the operating frequency of these multipliers has increased, the agreement between design predictions and experimental results has become poorer. The multiplier design is usually based on a nonlinear model using a form of harmonic balance and a model for the Schottky barrier diode. Conventional voltage dependent lumped element models do a poor job of predicting THz frequency performance. This paper will describe a large signal Monte Carlo simulation of Schottky barrier multipliers. The simulation is a time dependent particle field Monte Carlo simulation with ohmic and Schottky barrier boundary conditions included that has been combined with a fixed point solution for the nonlinear circuit interaction. The results in the paper will point out some important time constants in varactor operation and will describe the effects of current saturation and nonlinear resistances on multiplier operation.

East, J.↗

Single-Scale Retinex Using Digital Signal Processors

The Retinex is an image enhancement algorithm that improves the brightness, contrast and sharpness of an image. It performs a non-linear spatial/spectral transform that provides simultaneous dynamic range compression and color constancy. It has been used for a wide variety of applications ranging from aviation safety to general purpose photography. Many potential applications require the use of Retinex processing at video frame rates. This is difficult to achieve with general purpose processors because the algorithm contains a large number of complex computations and data transfers. In addition, many of these applications also constrain the potential architectures to embedded processors to save power, weight and cost. Thus we have focused on digital signal processors (DSPs) and field programmable gate arrays (FPGAs) as potential solutions for real-time Retinex processing. In previous efforts we attained a 21 (full) frame per second (fps) processing rate for the single-scale monochromatic Retinex with a TMS320C6711 DSP operating at 150 MHz. This was achieved after several significant code improvements and optimizations. Since then we have migrated our design to the slightly more powerful TMS320C6713 DSP and the fixed point TMS320DM642 DSP. In this paper we briefly discuss the Retinex algorithm, the performance of the algorithm executing on the TMS320C6713 and the TMS320DM642, and compare the results with the TMS320C6711.

Hines, Glenn↗

Monitoring a Complex Physical System using a Hybrid Dynamic Bayes Net

The Reverse Water Gas Shift system (RWGS) is a complex physical system designed to produce oxygen from the carbon dioxide atmosphere on Mars. If sent to Mars, it would operate without human supervision, thus requiring a reliable automated system for monitoring and control. The RWGS presents many challenges typical of real-world systems, including: noisy and biased sensors, nonlinear behavior, effects that are manifested over different time granularities, and unobservability of many important quantities. In this paper we model the RWGS using a hybrid (discrete/continuous) Dynamic Bayesian Network (DBN), where the state at each time slice contains 33 discrete and 184 continuous variables. We show how the system state can be tracked using probabilistic inference over the model. We discuss how to deal with the various challenges presented by the RWGS, providing a suite of techniques that are likely to be useful in a wide range of applications. In particular, we describe a general framework for dealing with nonlinear behavior using numerical integration techniques, extending the successful Unscented Filter. We also show how to use a fixed-point computation to deal with effects that develop at different time scales, specifically rapid changes occuring during slowly changing processes. We test our model using real data collected from the RWGS, demonstrating the feasibility of hybrid DBNs for monitoring complex real-world physical systems.

Lerner, Uri↗

Optical Measurements of Axial and Tangential Steady-State Blade Deflections Obtained Simultaneously

Case-mounted fiber-optic sensors have been used by aircraft engine manufacturers mainly to monitor blade vibration in fans and compressors. The simplest probe arrangement is a spot probe where, typically, a center fiber transmits laser light, and the outer fibers collect the reflected light from the blade tips and transmit it to a photodetector. Because the spot of incident light is fixed in space, whereas the blade deflects dynamically, the reflected light will originate from slightly different portions of the blade tip under different operating conditions. Unless corrections are developed to compensate for this effect, some error in vibratory tangential amplitude will occur. For monitoring vibrations, this error is usually not critical. However, when steady-state blade deflections are being measured, it is very important to fix the spot on the blade tip at a particular location because the operating speed blade deflections are evaluated against a low-speed reference run. The change in speed usually implies a significant change in the blade orientation and possibly its shape brought about by the aerodynamic and centrifugal loading. It is most convenient to select the blade s leading and trailing edges as the fixed points for which deflections will be evaluated. To capture the blade edges at various speeds, the light probe must be movable. This was achieved by mounting the probe in an eccentric hole in a bushing that fit the fan case in the region that overlapped the path of the blade edge. The probe was actuated to search for a blade edge while all the blades were viewed on an oscilloscope. The blade edge was considered to be captured when a pulse associated with a particular blade was significantly reduced in magnitude but was clearly distinguishable from the background noise level. By tracing the axial position of either blade edge, one could extend the deflection measurement to two dimensions: axial and tangential. These blade deflection measurements were obtained during a wind tunnel test of a fan prototype.

Kurkov, Anatole P.↗

Analysis of Crossflow Transition Flight Experiment aboard the Pegasus Launch Vehicle

The Pegasus wing-glove flight experiment was designed to provide crossflow transition data at high Mach numbers, specifically to help validate stability based predictions for transition onset in a flight environment. This paper provides an analysis of the flight experiment, with emphasis on computational results for crossflow disturbances and the correlation of disturbance growth factors with in-flight transition locations via the e(sup N) method. Implications of the flight data for attachment line stability are also examined. Analysis of the thermocouple data reveals that transition (from turbulent to laminar flow) was first detected during the ascending flight of the rocket when the free stream Mach number exceeded about 4. Therefore, computations have been performed for flight Mach numbers of 4.13, 4.35, 4.56 and 4.99. Due to continually decreasing unit Reynolds number at higher altitudes, the entire wing-glove boundary layer became laminar at the highest flight Mach number computed above. In contrast, the boundary layer flow over the inboard tile region remained transitional up to and somewhat beyond the time of laminarization over the instrumented glove region. Linear stability predictions confirmed that the tile boundary layer is indeed more unstable to crossflow disturbances than the much colder stainless steel glove boundary layer. The transition locations based on thermocouple data from both the glove and the tile regions are found to correlate with stationary-crossflow N-factors within the range of 7 to 12.4 and with traveling mode N-factors between 7.6 and 14.1. Data from the thermocouples and hot film sensors indicates that transition from turbulent to laminar flow (i.e., laminarization) at a fixed point over the glove is generally completed within a flight time interval of 3 seconds. However, the times at which transition begins and ends as inferred from the hot film sensors are found to differ by about 2 seconds from the corresponding estimates based on the thermocouple data.

Malik, Mujeeb R.↗