Flight path optimization with multiple time scales
Flight path optimization with multiple time scales, discussing decoupling of high order three dimensional aircraft flight problem into several low order problems
Kelley, H. J.↗
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Time scales and variability of area-averaged tropical oceanic rainfall
A statistical analysis of time series of area-averaged rainfall over the oceans has been conducted around the diurnal time scale. The results of this analysis can be applied directly to the problem of establishing the magnitude of expected errors to be incurred in the estimation of monthly area-averaged rain rate from low orbiting satellites. Such statistics as the mean, standard deviation, integral time scale of background red noise, and spectral analyses were performed on time series of the GOES precipitation index taken at 3-hour intervals during the period spanning December 19, 1987 to March 31, 1988 over the central and eastern tropical Pacific. The analyses have been conducted on 2.5 x 2.5 deg and 5 x 5 deg grid boxes, separately. The study shows that rainfall measurements by a sun-synchronous satellite visiting a spot twice per day will include a bias due to the existence of the semidiurnal cycle in the SPCZ ranging from 5 to 10 percentage points. The bias in the ITCZ may be of the order of 5 percentage points.
Shin, Kyung-Sup↗
Short time-scale variability of chromospheric Ca II in late-type stars
The short time-scale variability of singly ionized calcium chromospheric emission has been investigated in a few late-type stars. Emission-line variations with time scales of a few minutes to hours are seen in Alpha Tau (K5 III), Lambda And (G8 III-IV), and Epsilon Eri (K2 V). The existence of substantial chromospheric flux changes (10 to the 30th to 10 to the 32nd ergs) over short periods of time suggests that the calcium emission arises from a few small, coherent regions. Frequencies present in the data are discussed in the context of acoustic wave predictions and estimated acoustic cutoff frequencies for giants and dwarfs.
Baliunas, S. L.↗
Universal time scalings of sensitivity in Markovian quantum metrology
Assuming Markovian time evolution of a quantum sensing system, we study the general characterization of the optimal sensitivity scalings with time, under most general quantum control protocols. We allow the estimated parameter to influence both the Hamiltonian as well as the dissipative part of the quantum master equation and focus on the asymptotic-time along with the short-time sensitivity scalings. We find that via simple algebraic conditions (in terms of the Hamiltonian, the jump operators as well as their parameter derivatives), one can characterize the four classes of metrological models that represent: quadratic-linear, quadratic-quadratic, linear-linear, and linear-quadratic time scalings. We also investigate the relevant time scales on which the transition between the two regimes appears. Additionally, we provide universal numerical methods to obtain quantitative bounds on sensitivity that are the tightest that exist in the literature. Simplicity and universality of our results make it suitable for diverse applications in quantum metrology.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Evidence for two distinct morphological classes of gamma-ray bursts from their short time scale variability
We have analyzed the 241 bursts for which peak counts (C)max exist in the publicly available Burst and Transient Source Experiment (BATSE) catalog. Introducing peak counts in 1024 ms as a measure of burst brightness B and the ratio of peak counts in 64 and 1024 ms as a measure of short timescale variability V, we find a statistically significant correlation between the brightness and the short time scale variability of gamma-ray bursts. The bursts which are smoother on short time scales are both faint and bright, while the bursts which are variable on short time scales are faint only, suggesting the existence of two distinct morphological classes of bursts.
Lamb, D. Q.↗
A multiple-time-scale turbulence model based on variable partitioning of turbulent kinetic energy spectrum
A multiple-time-scale turbulence model of a single point closure and a simplified split-spectrum method is presented. In the model, the effect of the ratio of the production rate to the dissipation rate on eddy viscosity is modeled by use of the multiple-time-scales and a variable partitioning of the turbulent kinetic energy spectrum. The concept of a variable partitioning of the turbulent kinetic energy spectrum and the rest of the model details are based on the previously reported algebraic stress turbulence model. Example problems considered include: a fully developed channel flow, a plane jet exhausting into a moving stream, a wall jet flow, and a weakly coupled wake-boundary layer interaction flow. The computational results compared favorably with those obtained by using the algebraic stress turbulence model as well as experimental data. The present turbulence model, as well as the algebraic stress turbulence model, yielded significantly improved computational results for the complex turbulent boundary layer flows, such as the wall jet flow and the wake boundary layer interaction flow, compared with available computational results obtained by using the standard kappa-epsilon turbulence model.
Kim, S.-W.↗
THE HELMHOLTZ-KELVIN TIME SCALE FOR STARS OF VERY LOW MASS
Helmholtz-kelvin time scale for stars of very low mass
STAR↗
Time scale algorithms for an inhomogeneous group of atomic clocks
Through the past 17 years, the time scale requirements at the National Research Council (NRC) have been met by the unsteered output of its primary laboratory cesium clocks, supplemented by hydrogen masers when short-term stability better than 2 x 10(exp -12)tau(sup -1/2) has been required. NRC now operates three primary laboratory cesium clocks, three hydrogen masers, and two commercial cesium clocks. NRC has been using ensemble averages for internal purposes for the past several years, and has a realtime algorithm operating on the outputs of its high-resolution (2 x 10(exp -13) s at 1 s) phase comparators. The slow frequency drift of the hydrogen masers has presented difficulties in incorporating their short-term stability into the ensemble average, while retaining the long-term stability of the laboratory cesium frequency standards. We report on this work on algorithms for an inhomogeneous ensemble of atomic clocks, and on our initial work on time scale algorithms that could incorporate frequency calibrations at NRC from the next generation of Zacharias fountain cesium frequency standards having frequency accuracies that might surpass 10(exp -15), or from single-trapped-ion frequency standards (Ba+, Sr+,...) with even higher potential accuracies. The requirements for redundancy in all the elements (including the algorithms) of an inhomogeneous ensemble that would give a robust real-time output of the algorithms are presented and discussed.
Jacques, C.↗
A multiple-time-scale turbulence model based on variable partitioning of the turbulent kinetic energy spectrum
A multiple-time-scale turbulence model of a single point closure and a simplified split-spectrum method is presented. In the model, the effect of the ratio of the production rate to the dissipation rate on eddy viscosity is modeled by use of the multiple-time-scales and a variable partitioning of the turbulent kinetic energy spectrum. The concept of a variable partitioning of the turbulent kinetic energy spectrum and the rest of the model details are based on the previously reported algebraic stress turbulence model. Example problems considered include: a fully developed channel flow, a plane jet exhausting into a moving stream, a wall jet flow, and a weakly coupled wake-boundary layer interaction flow. The computational results compared favorably with those obtained by using the algebraic stress turbulence model as well as experimental data. The present turbulence model, as well as the algebraic stress turbulence model, yielded significantly improved computational results for the complex turbulent boundary layer flows, such as the wall jet flow and the wake boundary layer interaction flow, compared with available computational results obtained by using the standard kappa-epsilon turbulence model.
Kim, S.-W.↗
Zonal contributions to global momentum variations on intraseasonal through interannual time scales
The variability in a 13-year time series of daily values of the relative angular momentum of the atmosphere (M) is separated into three frequency bands: intraseasonal, seasonal, and interannual. Two methods are used to achieve this separation, and the amount of variance attributable to intraseasonal fluctuations, in particular, is sensitive to the choice made. Seasonal time scales clearly dominate the global momentum series; included in this frequency band is a notable dip in the series early in almost every calendar year. To localize the sources of the frequency band-dependent fluctuations in M, the data were decomposed into series of angular momentum values within each of 46 equal-area zonal belts over the globe and covariances were formed between these belt series and M. Seasonal variations in M represent the residual of opposing contributions from the subtropical jets of the Northern and the Southern Hemispheres. Both intraseasonal and interannual variations in M result mostly from behavior in the tropics.
Rosen, Richard D.↗
Reusable Launch Vehicle Control in Multiple Time Scale Sliding Modes
A reusable launch vehicle control problem during ascent is addressed via multiple-time scaled continuous sliding mode control. The proposed sliding mode controller utilizes a two-loop structure and provides robust, de-coupled tracking of both orientation angle command profiles and angular rate command profiles in the presence of bounded external disturbances and plant uncertainties. Sliding mode control causes the angular rate and orientation angle tracking error dynamics to be constrained to linear, de-coupled, homogeneous, and vector valued differential equations with desired eigenvalues placement. The dual-time scale sliding mode controller was designed for the X-33 technology demonstration sub-orbital launch vehicle in the launch mode. 6DOF simulation results show that the designed controller provides robust, accurate, de-coupled tracking of the orientation angle command profiles in presence of external disturbances and vehicle inertia uncertainties. It creates possibility to operate the X-33 vehicle in an aircraft-like mode with reduced pre-launch adjustment of the control system.
Shtessel, Yuri↗
Reusable Launch Vehicle Control In Multiple Time Scale Sliding Modes
A reusable launch vehicle control problem during ascent is addressed via multiple-time scaled continuous sliding mode control. The proposed sliding mode controller utilizes a two-loop structure and provides robust, de-coupled tracking of both orientation angle command profiles and angular rate command profiles in the presence of bounded external disturbances and plant uncertainties. Sliding mode control causes the angular rate and orientation angle tracking error dynamics to be constrained to linear, de-coupled, homogeneous, and vector valued differential equations with desired eigenvalues placement. Overall stability of a two-loop control system is addressed. An optimal control allocation algorithm is designed that allocates torque commands into end-effector deflection commands, which are executed by the actuators. The dual-time scale sliding mode controller was designed for the X-33 technology demonstration sub-orbital launch vehicle in the launch mode. Simulation results show that the designed controller provides robust, accurate, de-coupled tracking of the orientation angle command profiles in presence of external disturbances and vehicle inertia uncertainties. This is a significant advancement in performance over that achieved with linear, gain scheduled control systems currently being used for launch vehicles.
Shtessel, Yuri↗
IUE program SUGSD: Varability time scale of H Ly-alpha from Uranus
The scientific motivation for this program was to determine the time scale for the variability of the H Lyman-alpha emission from Uranus. The purpose of this series of observation is to determine its variability on shorter time scales. A series of observations was carried out in coordination with ESA to cover as completely as possible one 24 hour period of the Uranian H Lyman-alpha emission. The observations were obtained on April 23 and 24. Two additional ovservations on April 25 and 26 were obtained to search for longer term trends. A small modulation in the brightness was observed and the results presented.
Durrance, Samuel T.↗
Multiple-Time-Scale Concepts in Turbulent Transport Modeling
Progress in developing a turbulence closure employing two or more independently calculated time scales with which to characterize the rates of progress of different turbulent interactions is reported. The energy containing part of the spectrum is divided into two regions which respond at different rates and in different ways to changes in the environment. The scheme may be regarded as providing an intermediate level of approximation between the relatively simple, but fallible, single-point closures and the vastly more elaborate two-point closures which have so far been applied only to simulating homogeneous flows. The proposed approach requires only slightly more computational effort than single-scale schemes. Computational results are reported for several thin shear flows which show striking improvement in the level of agreement with experiment over that obtained with models employing only one time scale.
Hanjalic, K.↗
Time scales for molecule formation by ion-molecule reactions
Analytical solutions are obtained for nonlinear differential equations governing the time-dependence of molecular abundances in interstellar clouds. Three gas-phase reaction schemes are considered separately for the regions where each dominates. The particular case of CO, and closely related members of the Oh and CH families of molecules, is studied for given values of temperature, density, and the radiation field. Nonlinear effects and couplings with particular ions are found to be important. The time scales for CO formation range from 100,000 to a few million years, depending on the chemistry and regime. The time required for essentially complete conversion of C(+) to CO in the region where the H3(+) chemistry dominates is several million years. Because this time is longer than or comparable to dynamical time scales for dense interstellar clouds, steady-state abundances may not be observed in such clouds.
Langer, W. D.↗
The earth's angular momentum budget on subseasonal time scales
Irregular length of day (LOD) fluctuations on time scales of less than a few years are largely produced by atmospheric torques on the underlying planet. Significant coherence is found between the respective time series of LOD and atmospheric angular momentum (AAM) determinations at periods down to 8 days, with lack of coherence at shorter periods caused by the declining signal-to-measurement noise ratios of both data types. Refinements to the currently accepted model of tidal earth rotation variations are required, incorporating in particular the nonequilibrium effect of the oceans. The remaining discrepancies between LOD and AAM in the 100- to 10-day period range may be due to either a common error in the AAM data sets from different meteorological centers, or another component of the angular momentum budget.
Dickey, J. O.↗
Temporal variations of cosmic rays over a variety of time scales
The variation of the intensity of Galactic cosmic rays in the inner solar system over a wide variety of time scales is discussed, and the generally accepted physical model which can account quantitatively for these modulations is reviewed. The use of direct measurements and of nuclear reactions to study the temporal intensity variations is summarized. It is demonstrated that all of the observed variations could easily be the result of solar variations on long and short time scales.
Jokipii, J. R.↗
Stratospheric effects of solar ultraviolet variations on the solar rotation time scale
A summary is presented of some current work on measurement and interpretation of stratospheric ozone and temperature responses to observed short term solar ultraviolet variations. Although some studies have yielded provisional evidence for a nearly in-phase ozone-solar cycle relationship, they extend at most over only one or two 11 year cycles so the statistical significance of the correlations is not large. Similarly, the relatively short lengths of individual satellite data sets combined with the problem of estimating the effect of changes in instrument sensitivity (drift) during the observing period have complicated attempts to infer long term or solar cycle ozone trends. The solar rotation and active region development time scale provides an alternate time scale for which detailed studies of middle atmospheric ozone and temperature responses to solar ultraviolet variability are currently possible using available satellite data sets. At tropical latitudes where planetary wave amplitudes are relatively small, clear correlative evidence for the existence of middle atmospheric ozone and temperature responses to short term solar ultraviolet variations has been obtained in recent years. These measurements will ultimately allow improved empirical and theoretical calculations of longer term solar induced ozone and temperature variations at low and middle latitudes.
Hood, L. L.↗