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NASA NTRS2007

Anticipating Cycle 24 Minimum and Its Consequences

On the basis of the 12-mo moving average of monthly mean sunspot number (R) through November 2006, cycle 23 has persisted for 126 mo, having had a minimum of 8.0 in May 1996, a peak of 120.8 in April 2000, and an ascent duration of 47 mo. In November 2006, the 12-mo moving average of monthly mean sunspot number was 12.7, a value just outside the upper observed envelope of sunspot minimum values for the most recent cycles 16-23 (range 3.4-12.3), but within the 90-percent prediction interval (7.8 +/- 6.7). The first spotless day during the decline of cycle 23 occurred in January 2004, and the first occurrence of 10 or more and 20 or more spotless days was February 2006 and April 2007, respectively, inferring that sunspot minimum for cycle 24 is imminent. Through May 2007, 121 spotless days have accumulated. In terms of the weighted mean latitude (weighed by spot area) (LAT) and the highest observed latitude spot (HLS) in November 2006, 12-mo moving averages of these parameters measured 7.9 and 14.6 deg, respectively, these values being the lowest values yet observed during the decline of cycle 23 and being below corresponding mean values found for cycles 16-23. As yet, no high-latitude new-cycle spots have been seen nor has there been an upturn in LAT and HLS, these conditions having always preceded new cycle minimum by several months for past cycles. Together, these findings suggest that cycle 24 s minimum amplitude still lies well beyond November 2006. This implies that cycle 23 s period either will lie in the period "gap" (127-134 mo), a first for a sunspot cycle, or it will be longer than 134 mo, thus making cycle 23 a long-period cycle (like cycle 20) and indicating that cycle 24 s minimum will occur after July 2007. Should cycle 23 prove to be a cycle of longer period, a consequence might be that the maximum amplitude for cycle 24 may be smaller than previously predicted.

Wilson, Robert M.↗

NASA NTRS2004

Computationally-Efficient Minimum-Time Aircraft Routes in the Presence of Winds

A computationally efficient algorithm for minimizing the flight time of an aircraft in a variable wind field has been invented. The algorithm, referred to as Neighboring Optimal Wind Routing (NOWR), is based upon neighboring-optimal-control (NOC) concepts and achieves minimum-time paths by adjusting aircraft heading according to wind conditions at an arbitrary number of wind measurement points along the flight route. The NOWR algorithm may either be used in a fast-time mode to compute minimum- time routes prior to flight, or may be used in a feedback mode to adjust aircraft heading in real-time. By traveling minimum-time routes instead of direct great-circle (direct) routes, flights across the United States can save an average of about 7 minutes, and as much as one hour of flight time during periods of strong jet-stream winds. The neighboring optimal routes computed via the NOWR technique have been shown to be within 1.5 percent of the absolute minimum-time routes for flights across the continental United States. On a typical 450-MHz Sun Ultra workstation, the NOWR algorithm produces complete minimum-time routes in less than 40 milliseconds. This corresponds to a rate of 25 optimal routes per second. The closest comparable optimization technique runs approximately 10 times slower. Airlines currently use various trial-and-error search techniques to determine which of a set of commonly traveled routes will minimize flight time. These algorithms are too computationally expensive for use in real-time systems, or in systems where many optimal routes need to be computed in a short amount of time. Instead of operating in real-time, airlines will typically plan a trajectory several hours in advance using wind forecasts. If winds change significantly from forecasts, the resulting flights will no longer be minimum-time. The need for a computationally efficient wind-optimal routing algorithm is even greater in the case of new air-traffic-control automation concepts. For air-traffic-control automation, thousands of wind-optimal routes may need to be computed and checked for conflicts in just a few minutes. These factors motivated the need for a more efficient wind-optimal routing algorithm.

Jardin, Matthew R.↗

NASA NTRS2013

Elemental GCR Observations during the 2009-2010 Solar Minimum Period

Using observations from the Cosmic Ray Isotope Spectrometer (CRIS) onboard the Advanced Composition Explorer (ACE), we present new measurements of the galactic cosmic ray (GCR) elemental composition and energy spectra for the species B through Ni in the energy range approx. 50-550 MeV/nucleon during the record setting 2009-2010 solar minimum period. These data are compared with our observations from the 1997-1998 solar minimum period, when solar modulation in the heliosphere was somewhat higher. For these species, we find that the intensities during the 2009-2010 solar minimum were approx. 20% higher than those in the previous solar minimum, and in fact were the highest GCR intensities recorded during the space age. Relative abundances for these species during the two solar minimum periods differed by small but statistically significant amounts, which are attributed to the combination of spectral shape differences between primary and secondary GCRs in the interstellar medium and differences between the levels of solar modulation in the two solar minima. We also present the secondary-to-primary ratios B/C and (Sc+Ti+V)/Fe for both solar minimum periods, and demonstrate that these ratios are reasonably well fit by a simple "leaky-box" galactic transport model that is combined with a spherically symmetric solar modulation model.

Solar Modulation↗

NASA NTRS2017

The 2014 X-Ray Minimum of Eta Carinae as Seen by Swift

We report on Swift X-ray Telescope observations of Eta Carinae ( Car), an extremely massive, long-period, highly eccentric binary obtained during the 2014.6 X-ray minimumperiastron passage. These observations show that Car may have been particularly bright in X-rays going into the X-ray minimum state, while the duration of the 2014 X-ray minimum was intermediate between the extended minima seen in 1998.0 and 2003.5 by Rossi X-Ray Timing Explorer (RXTE), and the shorter minimum in 2009.0. The hardness ratios derived from the Swift observations showed a relatively smooth increase to a peak value occurring 40.5 days after the start of the X-ray minimum, though these observations cannot reliably measure the X-ray hardness during the deepest part of the X-ray minimum when contamination by the central constant emission component is significant. By comparing the timings of the RXTE and Swift observations near the X-ray minima, we derive an updated X-ray period of P X equals 2023.7 +/- 0.7 days, in good agreement with periods derived from observations at other wavelengths, and we compare the X-ray changes with variations in the He ii lambda 4686 emission. The middle of the Deep Minimum interval, as defined by the Swift column density variations, is in good agreement with the time of periastron passage derived from the He ii 4686 line variations.

binaries: general↗

NASA NTRS2018

Output Feedback Adaptive Control of Non-Minimum Phase Systems Using Optimal Control Modification

This paper describes output feedback adaptive control approaches for non-minimum phase SISO systems with relative degree 1 and non-strictly positive real (SPR) MIMO systems with uniform relative degree 1 using the optimal control modification method. It is well-known that the standard model-reference adaptive control (MRAC) cannot be used to control non-SPR plants to track an ideal SPR reference model. Due to the ideal property of asymptotic tracking, MRAC attempts an unstable pole-zero cancellation which results in unbounded signals for non-minimum phase SISO systems. The optimal control modification can be used to prevent the unstable pole-zero cancellation which results in a stable adaptation of non-minimum phase SISO systems. However, the tracking performance using this approach could suffer if the unstable zero is located far away from the imaginary axis. The tracking performance can be recovered by using an observer-based output feedback adaptive control approach which uses a Luenberger observer design to estimate the state information of the plant. Instead of explicitly specifying an ideal SPR reference model, the reference model is established from the linear quadratic optimal control to account for the non-minimum phase behavior of the plant. With this non-minimum phase reference model, the observer-based output feedback adaptive control can maintain stability as well as tracking performance. However, in the presence of the mismatch between the SPR reference model and the non-minimum phase plant, the standard MRAC results in unbounded signals, whereas a stable adaptation can be achieved with the optimal control modification. An application of output feedback adaptive control for a flexible wing aircraft illustrates the approaches.

Adaptive Contro↗

NASA NTRS2024

High Reliability at Minimum Cost

This paper investigates the minimum cost of improving the reliability of complex technical systems. The two major methods to improve reliability are redesigning the system for higher reliability or providing redundant components to replace failed elements. The costs of redesign for reliability or adding redundancy are estimated. The most cost-effective combination for high reliability can be identified. The cost of increasing the intrinsic reliability of a system can be modeled as cost proportional to 1/(system failure rate) a , where the exponent “a” measures the difficulty of increasing reliability. The “a” exponent can vary from 0.25 to about 2.5. Operational reliability can also be increased by using redundant systems. The failure rate for N parallel redundant units is (system failure rate) N . The cost of redundancy is N times the system cost. The total redundant system cost is proportional to N/(system failure rate) a . The cost of redundancy increases as N gets larger, but larger N allows a higher system failure rate, which reduces the system design cost. There is a certain N, a certain level of redundancy, that has the minimum cost to achieve the required overall redundant system failure rate. The minimum cost for the redundant system is achieved at the optimum level of redundancy. The N for minimum cost is equal to -a ln (redundant system failure rate). The minimum cost of the N redundant systems is proportional to N * (original system failure rate) a . The optimum redesigned individual system failure rate is proportional to exp (-1/a), so the greater the difficulty, the higher the optimum individual system failure rate. Increasing the intrinsic reliability of a system encounters diminishing returns and at some point it becomes more cost-effective to add redundancy. The difficulty of increasing intrinsic system reliability determines the optimum design for high reliability at minimum cost.

reliability↗

NASA NTRSDate not supplied

High Reliability at Minimum Cost

reliability↗

NASA NTRS2005

The Minimum Impulse Thruster

The Minimum Impulse Thruster (MIT) was developed to improve the state-of-the-art minimum impulse capability of hydrazine monopropellant thrusters. Specifically, a new fast response solenoid valve was developed, capable of responding to a much shorter electrical pulse width, thereby reducing the propellant flow time and the minimum impulse bit. The new valve was combined with the Aerojet MR-103, 0.2 lbf (0.9 N) thruster and put through an extensive Delta-qualification test program, resulting in a factor of 5 reduction in the minimum impulse bit, from roughly 1.1 milli-lbf-seconds (5 milliNewton seconds) to - 0.22 milli-lbf-seconds (1 mN-s). To maintain it's extensive heritage, the thruster itself was left unchanged. The Minimum Impulse Thruster provides mission and spacecraft designers new design options for precision pointing and precision translation of spacecraft.

thruster↗

NASA NTRS1972

Minimum distance classification in remote sensing

The utilization of minimum distance classification methods in remote sensing problems, such as crop species identification, is considered. Literature concerning both minimum distance classification problems and distance measures is reviewed. Experimental results are presented for several examples. The objective of these examples is to: (a) compare the sample classification accuracy of a minimum distance classifier, with the vector classification accuracy of a maximum likelihood classifier, and (b) compare the accuracy of a parametric minimum distance classifier with that of a nonparametric one. Results show the minimum distance classifier performance is 5% to 10% better than that of the maximum likelihood classifier. The nonparametric classifier is only slightly better than the parametric version.

Wacker, A. G.↗

NASA NTRS1974

The minimum free-stream wind speed for initiating motion of surface material on Mars

Estimates of the minimum free-stream wind speed that is required for initiating the motion of surficial material on Mars have ranged from 30 to about 200 meters per second. Thus the best value for this quantity is not well established. Graphical comparison of much of the pertinent data taken in the laboratory and in the field on Earth provides a minimum value for the Bagnold coefficient of 0.08 and this in turn provides a minimum value for the threshold friction velocity of 1.3 meters per second for initiating motion of particulate matter on Mars at low elevations where the pressure is 7 millibars. The most appropriate value of the ratio of friction velocity to free-stream velocity for putative unstable condition appears to be 0.026. Thus the minimum free-stream wind speed for initiating motion is obtained as 50 meters per second. If the surface material on Mars, however, is less cohesive than that on earth, the minimum value may be smaller.

Wood, G. P.↗

NASA NTRS1988

Minimum-time pointing control of a two-link manipulator

Minimum-time pointing control for the end-effector of a planar, two-link manipulator is developed. Minimum-time pointing control is a new area of research for multilink manipulators, which can be applied to rapid retargeting control of a multibody spacecraft. The minimum-time control problem of aligning the second link of the two-link manipulator with a given target point is considered. A numerical method called the minimizing-boundary-condition method is used to determine optimal solutions for the two-point boundary-value problem associated with first-order necessary conditions. Minimum-time solutions for different models of pointing systems are compared. The results of the comparison show that a two-link manipulator with two degree-of-freedom performs better than a conventional one-link system for minimum-time pointing.

Wie, Bong↗

NASA NTRS1991

The minimum control authority of a system of actuators with applications to Gravity Probe-B

The forcing capabilities of systems composed of many actuators are analyzed in this paper. Multiactuator systems can generate higher forces in some directions than in others. Techniques are developed to find the force in the weakest direction. This corresponds to the worst-case output and is defined as the 'minimum control authority'. The minimum control authority is a function of three things: the actuator configuration, the actuator controller and the way in which the output of the system is limited. Three output limits are studied: (1) fuel-flow rate, (2) power, and (3) actuator output. The three corresponding actuator controllers are derived. These controllers generate the desired force while minimizing either fuel flow rate, power or actuator output. It is shown that using the optimal controller can substantially increase the minimum control authority. The techniques for calculating the minimum control authority are applied to the Gravity Probe-B spacecraft thruster system. This example shows that the minimum control authority can be used to design the individual actuators, choose actuator configuration, actuator controller, and study redundancy.

Wiktor, Peter↗

NASA NTRS1997

Solar Cycle Predictions Near Sunspot Minimum

Observations of solar magnetic activity and the dynamics of the solar convection zone have produced severe constraints on models of the Sun's magnetic dynamo. These constraints are so severe that, at present, we do not have numerical models that can accept the current conditions and then march forward in time to predict future activity. Given this state of solar dynamo theory we are forced to examine previous behavior to discover patterns and trends that afford us some measure of predictability. Here we examine the behavior of several indicators of solar activity near solar minimum that are well correlated with the amplitude of the following solar maximum to predict the level of solar activity over cycle 23. Sunspot numbers, areas, and positions are useful for characterizing solar cycle behavior due to the extent of the data (12 cycles or more). These data exhibit several patterns that relate future activity to past behavior. With the Odd-Even effect the odd numbered cycles have been larger than their even numbered predecessors for each of the last six cycle pairs. With the Amplitude-Period effect short period cycles have been followed by large amplitude cycles and long period cycles have been followed by small amplitude cycles for 10 of the last 13 cycles. With the Maximum-Minimum effect the sunspot number at minimum is directly correlated with the sunspot number at maximum for a given cycle. The geomagnetic indices aa and Ap are also related to solar activity by the connections between disturbances in the solar wind and variations in the Earth's magnetic field. Like the Maximum-Minimum effect for sunspots, the size of the aa and Ap indices at minimum are directly related to the amplitude of the following maximum. The number of geomagnetically disturbed days (days with Ap >= 25) over the course of a cycle is another indicator for the size of the next cycle. The aa and Ap indices can each be separated into a component in phase with the current sunspot cycle and an "extended cycle" component that is directly related to the following cycle. Individually each of these indicators provides some measure of predictive ability for the amplitudes of previous cycles. Taken in combination we find that the predictions are much more accurate. Our multi-variate analysis indicates that a maximum sunspot number of 160 +/- 20 should occur near the end of 1999 for cycle 23.

Hathaway, David H.↗

NASA NTRS1994

Computed Minimum Energy Pathway for Isomerization in Ketene

A minimum energy pathway for interchange of the CH groups in ketene via a C2v structure has been obtained using complete active space self consistent field (CASSCF) derivative methods with a polarized valence double zeta basis set to define the reaction pathway followed by multi-reference internally contracted configuration interaction (ICCI) calculations with a [3s3p2d/3s2p] basis set to determine the energetics. Qualitatively, the C2v structure is found to be a shallow minimum on the potential energy surface separated from ketene by a small barrier (0.2 kcal/mol), a second minimum, and a larger barrier (3.0 kcal/mol). The minimum energy pathway leading from the C2v minimum to ketene starts by simultaneous rotation of the farther CH group out of the plane and away from the oxygen followed by increase of the CCO angle and subsequent 1,2-migration of the H of the nearer CH group toward the carbon of the farther CH group.

Walch, Stephen P.↗

NASA NTRS2006

Global X-ray Spectral Variation of Eta Carinae through the 2003 X-ray Minimum

We report on the results of the X-ray observing campaign of the massive, evolved star Eta Carinae in 2003 around its recent X-ray Minimum, mainly using data from the XMM-Newton observatory. These imaging observations show that the hard X-ray source associated with the Eta Carinae system does not completely disappear in any of the observations during the Minimum. The variation of the spectral shape revealed two emission components. One newly discovered component did not exhibit any variation on kilo-second to year-long timescales, in a combined analysis with earlier ASCA and ROSAT data, and might represent the collision of a high speed outflow from Eta Carinae with ambient gas clouds. The other emission component was strongly variable in flux but the temperature of the hottest plasma did not vary significantly at any orbital phase. Absorption to the hard emission, was about a factor of three larger than the absorption determined from the cutoff of the soft emission, and reached a maximum of approx.4 x 10(exp 23)/sq cm before the Minimum. The thermal Fe\rm XXV emission line showed significant excesses on both the red and blue sides of the line outside the Minimum and exhibited a large redward excess during the Minimum. This variation in the line profile probably requires an abrupt change in ionization balance in the shocked gas.

Hamaguchi, K.↗

NASA NTRS1974

A model of the trapped electron population for solar minimum

A model is presented of the trapped electron environment of solar minimum conditions. Solar maximum models have been presented for the inner radiation zone (AE-5 1967), and for the outer radiation zone (AE-4 1967). The present solar minimum model consists of an inner zone model (AE-5 1975 Projected) with an epoch of 1975, and an outer zone model with an epoch of 1964. With only minor modifications this latter model is identical to the AE-4 1964 model presented previous. The model, however, has not previously been issued in computer form. AE-4 1964 is based upon satellite data, while the inner zone solar minimum model AE-5 1975 Projected consists entirely of extrapolations from AE-5 1967. While the two components of the solar minimum model have epochs 11 years part, it is assumed that any differences between the successive solar minima are smaller than the model error, and the complete model is associated with an epoch of 1975.

Teague, M. J.↗

NASA NTRS1982

A recent time of minimum for and atmospheric-eclipse in the ultraviolet spectrum of the Wolf-Rayet eclipsing binary V444 Cygni

The 1200-1900 angstrom region and fine error sensor observations in the optical for V444 Cyg were continuously observed. More than half of a primary minimum and almost a complete secondary minimum were observed. It is found that the time of minimum for the secondary eclipse is consistent with that for primary eclipse, and the ultraviolet times of minimum are consistent with the optical ones. The spectrum shows a considerable amount of phase dependence. The general shaps and depths of the light curves for the FES signal and the 1565-1900 angstrom continuum are similar to those for the blue continuum. The FES, however, detected an atmospheric eclipse in line absorption at about the phase the NIV absorption was strongest. It is suggested that there is a source of continuum absorption shortward of 1460 angstrom which exists throughout a large part of the extended atmosphere and which, by implication, must redden considerably the ultraviolet continuua of WN stars. A fairly high degree of ionization for the inner part of the WN star a atmosphere is implied.

Eaton, J. E.↗

NASA NTRS1982

Twenty three year cycle in surface temperatures during the Maunder minimum

Power spectra of Manley's record of central England temperatures for the Maunder minimum have been compared with later periods. It is found that the power in the approximately 23 year cycle is statistically significant in the Maunder minimum portion of this temperature time series. This gives indirect support to the recent suggestion that the solar cycle persisted in the Maunder minimum even though normal sunspot activity was not observed. The results also indicate that the approximately 23 year cycle was stronger during the Maunder minimum than later times in this record.

Hameed, S.↗