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NASA NTRS1990

Run-time parallelization and scheduling of loops

Run time methods are studied to automatically parallelize and schedule iterations of a do loop in certain cases, where compile-time information is inadequate. The methods presented involve execution time preprocessing of the loop. At compile-time, these methods set up the framework for performing a loop dependency analysis. At run time, wave fronts of concurrently executable loop iterations are identified. Using this wavefront information, loop iterations are reordered for increased parallelism. Symbolic transformation rules are used to produce: inspector procedures that perform execution time preprocessing and executors or transformed versions of source code loop structures. These transformed loop structures carry out the calculations planned in the inspector procedures. Performance results are presented from experiments conducted on the Encore Multimax. These results illustrate that run time reordering of loop indices can have a significant impact on performance. Furthermore, the overheads associated with this type of reordering are amortized when the loop is executed several times with the same dependency structure.

Saltz, Joel H.↗

NASA NTRS1992

System identification from closed-loop data with known output feedback dynamics

This paper presents a procedure to identify the open loop systems when it is operating under closed loop conditions. First, closed loop excitation data are used to compute the system open loop and closed loop Markov parameters. The Markov parameters, which are the pulse response samples, are then used to compute a state space representation of the open loop system. Two closed loop configurations are considered in this paper. The closed loop system can have either a linear output feedback controller or a dynamic output feedback controller. Numerical examples are provided to illustrate the proposed closed loop identification method.

Phan, Minh↗

NASA NTRS1992

Acquisition performance of various QPSK carrier tracking loops

The frequency and phase acquisition performance of three quadrature phase shift keying (QPSK) carrier tracking loops, the MAP estimation loop, the Costas crossover loop, and the generalized Costas loop, is described. Acquisition time and probability of acquisition as a function of both loop signal-to-noise ratio and frequency offset to loop bandwidth ratio are obtained via computer simulations for type II and III loops. It is shown that the MAP loop, which results in the smallest squaring loss for all signal-to-noise ratios, is sometimes outperformed by the other two loops in terms of acquisition time and acquisition probability.

Hinedi, S.↗

NASA NTRS1994

Coalescence of two current loops with a kink instability simulated by a three-dimensional electromagnetic particle code

We have studied the dynamics of a coalescence of current loops using three-dimensional electromagnetic (EM) particle simulation code. Our focus is the investigation of such kinetic processes as energy trasnfer, heating particles, and electromagnetic emissions associated with a current loop coalescence which cannot be studied by MHD simulations. First, the two loops undergo a pinching oscillation due to a pressure imbalance between the inside and outside of the current loop. During the pinching oscillation, a kinetic kink instability is excited and electrons in the loops are heated perpendicularly to an ambient magnetic field. Next, the two current loops collide and coalesce, while at the same time a helical structure grows further. Subsequently, the perturbed current, which is due to these helically bunched electrons, can drive a whistler instability. It should be noted in this case that the whistler wave is excited by the kinetic kink instability and not a beam instability. After the coalescence of two helical loops, tilting motions can be observed in the direction of left-hand rotation, and the helical structure will relax resulting in strong plasma heating mostly in the direction perpendicular to the ambient magnetic field. It is also shown that high-frequency electromagnetic waves can be emitted from the region where the two loops coalesce and propagate strongly in the direction of the electron drift velocity. These processes may be important in understanding heating mechansims for coronal loops as well as radio wave emission mechanisms from active regions of solar plasmas.

Nishikawa, K.-I.↗

NASA NTRS1998

3D-Stereoscopic Analysis of Solar Active Region Loops: I: SoHo/EIT Observations at Temperatures of 1.0-1.5 MK

The three-dimensional (3D) structure of solar active region NOAA 7986 observed on 1996 August 30 with the Extrem-ultraviolet Imaging Telescope (EIT) onboard the Solar and Heliospheric Observatory (SoHO) is analyzed. We develop a new method of Dynamic Stereoscopy to reconstruct the 3D geometry of dynamically changing loops, which allows us to determine the orientation of the loop plane with respect to the line-of-sight, a prerequisite to correct properly for projection effects in 3D loop models. With this method and the filter-ratio technique applied to EIT 171 A and 195 A images we determine the 3D coordinates (x(s), y(s), z(s)), the loop width) w(s), the electron density n(sub e)(s), and the electron temperature T(sub e)(s) as function of the loop length s for 30 loop segments. Fitting the loop densities with an exponential density model n(sub e)(h) we find that the so inferred scale height temperatures, T(sub e)(sup lambda) = 1.22 +/- 0.23 MK, match closely the EIT filter-ratio temperatures, T(sub e)(sup FIT) = 1.21 +/- 0.06 MK. We conclude that these rather large-scale loops (with heights of h approx. equals 50 - 200 Mm) that dominate EIT 171 A images are close to thermal equilibrium. Most of the loops show no significant thickness variation w(s), but many exhibit a trend of increasing temperature (dT/ds greater than 0) above the footpoint.

Aschwanden, Markus J.↗

NASA NTRS2001

An Experimental Study of the Operating Temperature in a Loop Heat Pipe with Two Evaporators and Two Condensers

This paper presents a comprehensive experimental study of the loop operating temperature in a loop heat pipe (LHP) which has two parallel evaporators and two parallel condensers. In a single evaporator LHP, it is well known that the loop operating temperature is a function of the heat load, the sink temperature and the ambient temperature. The objective of the present study emphasizes on the stability of the loop operating temperature and parameters that affects the loop operation. Tests results show that the loop operating temperature is a function of the total system heat load, sink temperature, ambient temperature, and beat load distribution between the two evaporators. Under most conditions, only one compensation chamber (CC) contains two-phase fluid and controls the loop operating temperature, and the other CC is completely filled with liquid. Moreover, as the test condition changes, control of the loop operating temperature often shifted from one CC to another. In spite of complex interactions between various components, the test loop has demonstrated very robust operation even during fast transients.

Ku, Jentung↗

NASA NTRS2014

Simulated Time Lags of Hinode/XRT and SDO/AIA Lightcurves as an Indication of Loop Heating Scenario

The precise nature of the heating mechanism (location, duration) in coronal loops is still a matter of enormous research. We present results from a one-dimensional (1D) hydrodynamic loop simulation of a coronal loop which was run using different parameters such as loops length (50, 200 and 500 light-seconds), maximum temperature reached (3 million degrees Kelvin and 10 million degrees Kelvin), and abundances. For each scenario the model outputs were used to calculate the corresponding lightcurves as seen by X-ray telescope/Be-thin filter and various Extreme Ultra Violet Atmospheric Imaging Assembly channels. The lag time between the peak of these lightcurves was computed using cross-correlation and plotted as a function of loop length. Additional results were computed using the zero-dimensional Enthalpy-Based Thermal Evolution of Loops (EBTEL) code in order to test the compatibility of the two codes and to investigate additional loop lengths. Initial results indicate that the long (greater than 5000 seconds) lags observed in the approximately 100 light-seconds loops of active regions can only be reproduced using photospheric abundances and much longer loop lengths. This result suggests that the observed time lags cannot be completely explained by impulsive heating.

nanoflares↗

NASA NTRS2016

Suppression of Heating of Coronal Loops Rooted in Opposite Polarity Sunspot Umbrae

EUV observations of active region (AR) coronae reveal the presence of loops at different temperatures. To understand the mechanisms that result in hotter or cooler loops, we study a typical bipolar AR, near solar disk center, which has moderate overall magnetic twist and at least one fully developed sunspot of each polarity. From AIA 193 and 94 Å images we identify many clearly discernible coronal loops that connect plage or a sunspot of one polarity to an opposite-polarity plage region. The AIA 94 Å images show dim regions in the umbrae of the spots. To see which coronal loops are rooted in a dim umbral area, we performed a non-linear force‐free field (NLFFF) modeling using photospheric vector magnetic field measurements obtained with the Heliosesmic Magnetic Imager (HMI) onboard SDO. The NLFFF model, validated by comparison of calculated model field lines with observed loops in AIA 193 and 94 Å, specifies the photospheric roots of the model field lines. Some model coronal magnetic field lines arch from the dim umbral area of the positive-polarity sunspot to the dim umbral area of a negative-polarity sunspot. Because these coronal loops are not visible in any of the coronal EUV and X-ray images of the AR, we conclude they are the coolest loops in the AR. This result suggests that the loops connecting opposite polarity umbrae are the least heated because the field in umbrae is so strong that the convective braiding of the field is strongly suppressed.

sunspot↗

NASA NTRS2014

Improving Coverage of Test Cases Generated by Symbolic PathFinder for Programs with Loops

Symbolic execution is a program analysis technique that is used for many purposes, one of which is test-case generation. For loop-free programs, this generates a test-set that achieves path coverage. Program loops, however, imply exponential growth of the number of paths in the best case and non-termination in the worst case. In practice, the number of loop unwindings needs to be bounded for analysis. We consider symbolic execution in the context of the tool Symbolic Pathfinder. This tool extends the model-checker Java Pathfinder and relies on its bounded state-space exploration for termination. We present an implementation of k-bounded loop unwinding, which increases the amount of user-control over the symbolic execution of loops. Bounded unwinding can be viewed as a naive way to prune paths through loops. When using symbolic execution for test-case generation, naively pruning paths is likely at the cost of coverage. In order to improve coverage of branches within a loop body, we present a technique that semi-automatically concretizes variables used in a loop. The basic technique is limited and we therefore present annotations to manually steer symbolic execution towards certain branches, as well as ideas on how the technique can be extended to be more widely applicable.

Programs With Loops↗

NASA NTRS1975

The temperature structure and pressure balance of magnetic loops in active regions

EUV observations show many active region loops in lines formed at temperatures between 10,000 and 2,000,000 K. The brightest loops are associated with flux tubes leading to the umbrae of sunspots. It is shown that the high visibility of certain loops in transition region lines is due principally to a sharp radial decrease of temperature to chromospheric values toward the loop axis. The plasma density of these cool loops is not significantly greater than in the hot gas immediately surrounding it. Consequently, the internal gas pressure of the cool material is clearly lower. The hot material immediately surrounding the cool loops is generally denser than the external corona by a factor 3-4. When the active region is examined in coronal lines, this hot high pressure plasma shows up as loops that are generally parallel to the cool loops but significantly displaced laterally.

Foukal, P.↗

NASA NTRS1977

Physics of an active region loop system

The structure of the active region loops is investigated by the study of a loop complex which undergoes a dramatic evacuation of most of the mass it contains. The need for continual energy deposition in loops is emphasized by the apparent cessation of energy input to the loops studied and their subsequent behavior. Estimates are made of the energy necessary to form and to maintain the loops, and of the relative importance of radiation and thermal conduction as energy loss mechanisms. Models based on the observed EUV emission are used to place limits on the size of loops seen in various lines and on the density and temperature structure. It is found that the cool cores of active region loops are likely to be no more than a few hundred kilometers in radius and that several such cool threads may be imbedded in a common hot outer sheath. The primary energy loss on a large scale is radiation with thermal conduction contributing to local disturbances. There is a tendency for the development of apparently unstable condensations or knots along the length of a loop.

Levine, R. H.↗

NASA NTRS1982

The thermal structure of solar coronal loops and implications for physical models of coronae

EUV spectra of three active region loops observed above the solar limb with the SO55 spectrometer on Skylab are analyzed. It is noted that the lengths, peak temperatures, and pressures of the loops are typical of the X-ray coronal loops to which static models have been applied. It is found that the physical parameters of the coronal loop plasma derived from EUV spectra and raster pictures are not well represented by the static models. Although the loops also contain a significant quantity of cool plasma, no physical reason is found to differentiate them from other active region loops of similar length, pressure, and temperature. Several line ratios in the loop spectrum suggest departures from ionization equilibrium caused by rapid cooling. The source of this cooling material is discussed with reference to several models of loop dynamics.

Raymond, J. C.↗

NASA NTRS1987

A linear quadratic Gaussian with loop transfer recovery proximity operations autopilot for spacecraft

An automatic control scheme for spacecraft proximity operations is presented. The controller is capable of holding the vehicle at a prescribed location relative to a target, or maneuvering it to a different relative position using straight line-of-sight translations. The autopilot uses a feedforward loop to initiate and terminate maneuvers, and for operations at nonequilibrium set-points. A multivariate feedback loop facilitates precise position and velocity control in the presence of sensor noise. The feedback loop is formulated using the Linear Quadratic Gaussian (LQG) with Loop Transfer Recovery (LTR) design procedure. Linear models of spacecraft dynamics, adapted from Clohessey-Wiltshire Equations, are augmented and loop shaping techniques are applied to design a target feedback loop. The loop transfer recovery procedure is used to recover the frequency domain properties of the target feedback loop. The resulting compensator is integrated into an autopilot which is tested in a high fidelity Space Shuttle Simulator. The autopilot performance is evaluated for a variety of proximity operations tasks envisioned for future Shuttle flights.

Chen, George T.↗

NASA NTRS1989

Control-structure interaction in precision pointing servo loops

The control-structure interaction problem is addressed via stability analysis of a generic linear servo loop model. With the plant described by the rigid body mode and a single elastic mode, structural flexibility is categorized into one of three types: (1) appendage, (2) in-the-loop minimum phase, and (3) in-the-loop nonminimum phase. Closing the loop with proportional-derivative (PD) control action and introducing sensor roll-off dynamics in the feedback path, stability conditions are obtained. Trade studies are conducted with modal frequency, modal participation, modal damping, loop bandwidth, and sensor bandwidth treated as free parameters. Results indicate that appendage modes are most likely to produce instability if they are near the sensor rolloff, whereas in-the-loop modes are most dangerous near the loop bandwidth. The main goal of this paper is to provide a fundamental understanding of the control-structure interaction problem so that it may benefit the design of complex spacecraft and pointing system servo loops. In this framework, the JPL Pathfinder gimbal pointer is considered as an example.

Spanos, John T.↗

NASA NTRS1991

Run-time parallelization and scheduling of loops

Run-time methods are studied to automatically parallelize and schedule iterations of a do loop in certain cases where compile-time information is inadequate. The methods presented involve execution time preprocessing of the loop. At compile-time, these methods set up the framework for performing a loop dependency analysis. At run-time, wavefronts of concurrently executable loop iterations are identified. Using this wavefront information, loop iterations are reordered for increased parallelism. Symbolic transformation rules are used to produce: inspector procedures that perform execution time preprocessing, and executors or transformed versions of source code loop structures. These transformed loop structures carry out the calculations planned in the inspector procedures. Performance results are presented from experiments conducted on the Encore Multimax. These results illustrate that run-time reordering of loop indexes can have a significant impact on performance.

Saltz, Joel H.↗

NASA NTRS1992

Tracking performance and cycle slipping in the all-digital symbol synchronizer loop of the block 5 receiver

Computer simulated noise performance of the symbol synchronizer loop (SSL) in the Block 5 receiver is compared with the theoretical noise performance. Good agreement is seen at the higher loop SNR's (SNR(sub L)'s), with gradual degradation as the SNR(sub L) is decreased. For the different cases simulated, cycle slipping is observed (within the simulation time of 10(exp 4) seconds) at SNR(sub L)'s below different thresholds, ranging from 6 to 8.5 dB, comparable to that of a classical phase-locked loop. An important point, however, is that to achieve the desired loop SNR above the seemingly low threshold to avoid cycle slipping, a large data-to-loop-noise power ratio, P(sub D)/(N(sub 0)B(sub L)), is necessary (at least 13 dB larger than the desired SNR(sub L) in the optimum case and larger otherwise). This is due to the large squaring loss (greater than or equal to 13 dB) inherent in the SSL. For the special case of symbol rates approximately equaling the loop update rate, a more accurate equivalent model accounting for an extra loop update period delay (characteristic of the SSL phase detector design) is derived. This model results in a more accurate estimation of the noise-equivalent bandwidth of the loop.

Aung, M.↗

NASA NTRS2006

Understanding X-Ray Source Motions in a Solar Flare Loop

RHESSI images of a solar flare on 2002 November 28 showed a 3-6 keV hard X-ray source that was initially located at the flare loop top, split and propagated to the foot points of the loop during the flare rise phase, and then propagated back up to the loop top during the declining phase of the flare (Sai, Holman, & Dennis 2006). Higher energy X-ray sources were located lower in the legs of the loop during this period of source evolution, with X-rays above 25 keV seen only at the foot points. Sui, Holman, & Dennis suggested that this spatial evolution reflected the evolution of the spectral index and low-energy cutoff to the distribution of accelerated electrons in the flare. We construct a model flare loop and electron distribution injected at the top of this loop to reproduce the source evolution of the November 28 flare. We determine the constraints on the loop model and the evolution of the accelerated electron distribution. We also study the implications of the model for energy deposition into the loop plasma, and the integrated and imaged X-ray spectra. This work is supported in part by the RHESSI Project and the NASA Guest Investigator Program.

Holman, Gordon D.↗

NASA NTRS2008

Similarity Metrics for Closed Loop Dynamic Systems

To what extent and in what ways can two closed-loop dynamic systems be said to be "similar?" This question arises in a wide range of dynamic systems modeling and control system design applications. For example, bounds on error models are fundamental to the controller optimization with modern control design methods. Metrics such as the structured singular value are direct measures of the degree to which properties such as stability or performance are maintained in the presence of specified uncertainties or variations in the plant model. Similarly, controls-related areas such as system identification, model reduction, and experimental model validation employ measures of similarity between multiple realizations of a dynamic system. Each area has its tools and approaches, with each tool more or less suited for one application or the other. Similarity in the context of closed-loop model validation via flight test is subtly different from error measures in the typical controls oriented application. Whereas similarity in a robust control context relates to plant variation and the attendant affect on stability and performance, in this context similarity metrics are sought that assess the relevance of a dynamic system test for the purpose of validating the stability and performance of a "similar" dynamic system. Similarity in the context of system identification is much more relevant than are robust control analogies in that errors between one dynamic system (the test article) and another (the nominal "design" model) are sought for the purpose of bounding the validity of a model for control design and analysis. Yet system identification typically involves open-loop plant models which are independent of the control system (with the exception of limited developments in closed-loop system identification which is nonetheless focused on obtaining open-loop plant models from closed-loop data). Moreover the objectives of system identification are not the same as a flight test and hence system identification error metrics are not directly relevant. In applications such as launch vehicles where the open loop plant is unstable it is similarity of the closed-loop system dynamics of a flight test that are relevant.

Whorton, Mark S.↗