Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “EXPECTATION VALUE”

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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Accurate Evaluation of Quantum Integrals

Combining an appropriate finite difference method with Richardson's extrapolation results in a simple, highly accurate numerical method for solving a Schrodinger's equation. Important results are that error estimates are provided, and that one can extrapolate expectation values rather than the wavefunctions to obtain highly accurate expectation values. We discuss the eigenvalues, the error growth in repeated Richardson's extrapolation, and show that the expectation values calculated on a crude mesh can be extrapolated to obtain expectation values of high accuracy.

Galant, D. C.↗
NASA NTRS1974

The Hubble relation for nonstandard candles and the origin of the redshift of quasars

It is shown that the magnitude-log (redshift) relation for brightest quasars can have a slope different from the value expected for standard candles. The value of this slope depends on the luminosity function and its evolution. Therefore the difference of this slope from the expected value cannot be used as evidence against the cosmological origin of the redshift of the quasars. It is shown that the observed variation of the luminosity of the brightest objects with redshift is consistent with the cosmological hypothesis and that it agrees with (and perhaps could be used to complement) the luminosity function obtained from V/Vm analysis. It is also shown that the nonzero slope of the magnitude-log (redshift) relation rules out the local quasar hypothesis, where it is assumed that the sources are nearby (less than 500 Mpc), that the bulk of their redshift is intrinsic, and that there is no dependence on distance of the intrinsic properties of the sources.

Petrosian, V.↗
NASA NTRS1992

Engine monitoring display study

The current study is part of a larger NASA effort to develop displays for an engine-monitoring system to enable the crew to monitor engine parameter trends more effectively. The objective was to evaluate the operational utility of adding three types of information to the basic Boeing Engine Indicating and Crew Alerting System (EICAS) display formats: alphanumeric alerting messages for engine parameters whose values exceed caution or warning limits; alphanumeric messages to monitor engine parameters that deviate from expected values; and a graphic depiction of the range of expected values for current conditions. Ten training and line pilots each flew 15 simulated flight scenarios with five variants of the basic EICAS format; these variants included different combinations of the added information. The pilots detected engine problems more quickly when engine alerting messages were included in the display; adding a graphic depiction of the range of expected values did not affect detection speed. The pilots rated both types of alphanumeric messages (alert and monitor parameter) as more useful and easier to interpret than the graphic depiction. Integrating engine parameter messages into the EICAS alerting system appears to be both useful and preferred.

Hornsby, Mary E.↗
NASA NTRS1989

Probabilities and statistics for backscatter estimates obtained by a scatterometer with applications to new scatterometer design data

The values of the Normalized Radar Backscattering Cross Section (NRCS), sigma (o), obtained by a scatterometer are random variables whose variance is a known function of the expected value. The probability density function can be obtained from the normal distribution. Models for the expected value obtain it as a function of the properties of the waves on the ocean and the winds that generated the waves. Point estimates of the expected value were found from various statistics given the parameters that define the probability density function for each value. Random intervals were derived with a preassigned probability of containing that value. A statistical test to determine whether or not successive values of sigma (o) are truly independent was derived. The maximum likelihood estimates for wind speed and direction were found, given a model for backscatter as a function of the properties of the waves on the ocean. These estimates are biased as a result of the terms in the equation that involve natural logarithms, and calculations of the point estimates of the maximum likelihood values are used to show that the contributions of the logarithmic terms are negligible and that the terms can be omitted.

Pierson, Willard J., Jr.↗
NASA NTRS1972

Parameter uncertainties in control system design.

Development of a design method for including the effects of parameter uncertainties in the design of linear control systems. The approach taken to this problem may be classified as a special case of the stochastic control problem. Thus the formulation is based on the minimization of the expected value of a quadratic performance index defined in terms of the system state vector. The uncertainty in the value of the performance index is the result of the statistical nature of the system parameters rather than a random input signal. It is shown that the expected value of the performance index may be written as a sum of two terms under the assumption of first-order variations of the system state. The first of these terms expresses the nominal performance of the system when the system parameters assume their mean values. The second term represents the effect of the uncertainties on the expected value of the performance index, and is interpreted as an index of system sensitivity.

Palsson, T.↗
NASA NTRS1978

Relative abundance of antiprotons and antihelium in the primary cosmic radiation

The paper reports measurement of the antiproton-to-proton and antihelium-to-helium ratios in the 4-100 GeV/c range. A superconducting magnet spectrophotometer obtained the data during a balloon flight in May 1976. The upper limit value for the antiproton ratio is 0.0005 in the 4.2-12.5 GeV/c range. This value is only slightly higher than the expected value for a leaky box-model and nearly equal to the value expected in the Peter-Westergard model. It is suggested that this upper limit value rules out the closed galaxy model. Upper limit values for the antihelium ratio are 0.000058 in the 4-10 GeV/c range; less than 0.0001 in the 4-33 GeV/c range; and less than 0.01 in the 33-100 GeV/c range. The interpretation of the raw data is explained.

Badhwar, G. D.↗
NASA NTRS1989

Linear canonical transformations of coherent and squeezed states in the Wigner phase space. II - Quantitative analysis

It is possible to calculate expectation values and transition probabilities from the Wigner phase-space distribution function. Based on the canonical transformation properties of the Wigner function, an algorithm is developed for calculating these quantities in quantum optics for coherent and squeezed states. It is shown that the expectation value of a dynamical variable can be written in terms of its vacuum expectation value of the canonically transformed variable. Parallel-axis theorems are established for the photon number and its variant. It is also shown that the transition probability between two squeezed states can be reduced to that of the transition from one squeezed state to vacuum.

Han, D.↗
NASA NTRS1989

Probabilities and statistics for backscatter estimates obtained by a scatterometer

Methods for the recovery of winds near the surface of the ocean from measurements of the normalized radar backscattering cross section must recognize and make use of the statistics (i.e., the sampling variability) of the backscatter measurements. Radar backscatter values from a scatterometer are random variables with expected values given by a model. A model relates backscatter to properties of the waves on the ocean, which are in turn generated by the winds in the atmospheric marine boundary layer. The effective wind speed and direction at a known height for a neutrally stratified atmosphere are the values to be recovered from the model. The probability density function for the backscatter values is a normal probability distribution with the notable feature that the variance is a known function of the expected value. The sources of signal variability, the effects of this variability on the wind speed estimation, and criteria for the acceptance or rejection of models are discussed. A modified maximum likelihood method for estimating wind vectors is described. Ways to make corrections for the kinds of errors found for the Seasat SASS model function are described, and applications to a new scatterometer are given.

Pierson, Willard J., Jr.↗
NASA NTRS2001

Structure and Variability of Water Vapor in the Upper Troposphere and Lower Stratosphere

Upper-tropospheric humidity (UTH) has been synoptically mapped via an algorithm that rejects small-scale undersampled variance, which is intrinsic to asymptotic measurements of water vapor, cloud, and other convective properties. Mapped distributions of UTH have been used, jointly with high-resolution Global Cloud Imagery (GCI), to study how the upper troposphere is humidified. The time-mean distribution of UTH is spatially correlated to the time-mean distribution of cold cloud fraction (eta)(sub c) (T < than 230 K). Regions of large UTH coincide with regions of large eta(sub c), which mark deep convection. They also coincide with regions of reduced vertical stability, in which the vertical gradient of theta is weakened by convective mixing. Coldest cloud cover is attended convective overshoots above the local tropopause, which is simultaneously coldest and highest. Together, these features reflect the upper-troposphere being ventilated by convection, which mixes in moist air from lower levels. Histograms of UTH and eta(sub c) have been applied to construct the joint probability density function, which quantifies the relationship between these properties. The expected value of UTH in convective regions is strongly correlated to the expected value of eta(sub c). In ensembles of asymptotic samples, the correlation between epsilon[UTH] and epsilon[eta(sub c)] exceeds 0.80. As these expectations reflect the most likely values, the strong correlation between epsilon[UTH] and epsilon[eta(sub c)] indicates that the large-scale organization of UTH is strongly shaped by convective pumping of moisture from lower levels. The same relationship holds for unsteady fields - even though, instantaneously, those fields are comprised almost entirely of small-scale convective structure. The spatial autocorrelation of UTH, constructed at high resolution from overpass data along ascending and descending tracks of the orbit, is limited to only a couple of degrees in the horizontal. This mirrors the spatial autocorrelation of eta(sub c), which likewise operates coherently on short scales. The short correlation scale of UTH, which reflects the scale of individual convective systems, is comparable to the spacing of retrievals from MLS. These scales are undersampled in the asynoptic measurements. Despite their prevalence, the mapping algorithm described above successfully recovers synoptic behavior operating coherently on large scales. It reveals eastward migration of anomalous UTH from the Indian ocean to the central Pacific, in association with the modulation of convection by the Madden-Julian oscillation. Additional information is contained in the original extended abstract.

Salby, Murry L.↗
NASA NTRS1980

Galilean satellite eclipse studies. III - Jovian methane abundance

The methane abundance in the lower Jovian stratosphere is measured using the Galilean satellite eclipse technique. The average mixing ratio at the locations measured is larger than the expected value for a solar abundance of carbon with the expected value for a solar abundance of carbon with the possibility of some zenographic variation. Observationally compatible values are found for the South Temperate Zone, the edge of the Great Red Spot and the South Tropical Zone, and the Great Red Spot.

Smith, D. W.↗
NASA NTRS2004

Distributed Control by Lagrangian Steepest Descent

Often adaptive, distributed control can be viewed as an iterated game between independent players. The coupling between the players mixed strategies, arising as the system evolves from one instant to the next, is determined by the system designer. Information theory tells us that the most likely joint strategy of the players, given a value of the expectation of the overall control objective function, is the minimizer of a function o the joint strategy. So the goal of the system designer is to speed evolution of the joint strategy to that Lagrangian mhimbhgpoint,lowerthe expectated value of the control objective function, and repeat Here we elaborate the theory of algorithms that do this using local descent procedures, and that thereby achieve efficient, adaptive, distributed control.

Wolpert, David H.↗
NASA NTRS2006

Impact of Probabilistic Weather on Flight Routing Decisions

Flight delays in the United States have been found to increase year after year, along with the increase in air traffic. During the four-month period from May through August of 2005, weather related delays accounted for roughly 70% of all reported delays, The current weather prediction in tactical (within 2 hours) timeframe is at manageable levels, however, the state of forecasting weather for strategic (2-6 hours) timeframe is still not dependable for long-term planning. In the absence of reliable severe weather forecasts, the decision-making for flights longer than two hours is challenging. This paper deals with an approach of using probabilistic weather prediction for Traffic Flow Management use, and a general method using this prediction for estimating expected values of flight length and delays in the National Airspace System (NAS). The current state-of-the-art convective weather forecasting is employed to aid the decision makers in arriving at decisions for traffic flow and flight planing. The six-agency effort working on the Next Generation Air Transportation System (NGATS) have considered weather-assimilated decision-making as one of the principal foci out of a list of eight. The weather Integrated Product Team has considered integrated weather information and improved aviation weather forecasts as two of the main efforts (Ref. 1, 2). Recently, research has focused on the concept of operations for strategic traffic flow management (Ref. 3) and how weather data can be integrated for improved decision-making for efficient traffic management initiatives (Ref. 4, 5). An overview of the weather data needs and benefits of various participants in the air traffic system along with available products can be found in Ref. 6. Previous work related to use of weather data in identifying and categorizing pilot intrusions into severe weather regions (Ref. 7, 8) has demonstrated a need for better forecasting in the strategic planning timeframes and moving towards a probabilistic description of weather (Ref. 9). This paper focuses on. specified probability in a local region for flight intrusion/deviation decision-making. The process uses a probabilistic weather description, implements that in a air traffic assessment system to study trajectories of aircraft crossing a cut-off probability contour. This value would be useful for meteorologists in creating optimum distribution profiles for severe weather, Once available, the expected values of flight path and aggregate delays are calculated for efficient operations. The current research, however, does not deal with the issue of multiple cell encounters, as well as echo tops, and will be a topic of future work.

Sheth, Kapil↗
NASA NTRS2008

Dawn Ion Propulsion System - Initial Checkout After Launch

The first 80 days after launch of the Dawn mission were dedicated to the checkout of the spacecraft with a major emphasis on the ion propulsion system. All three ion thrusters, all three thruster-gimbal assemblies, both power processor units, both digital interface and control units, and the entire xenon feed system were completely checked out and every component was found to be in good health. Direct thrust measurements agreed well with preflight expected values for all three thrusters over the entire throttle range. Thruster electrical operating parameters and power processor units efficiencies also agreed well with preflight expected values based on acceptance test data. Two of the three ion thrusters were fully checked out within 30 days after launch. Checkout of all three thrusters was completed 64 days after launch. Deterministic thrusting with the IPS began on December 17, 2007.

electric propulsion↗
NASA NTRS2006

Using Quasiparticle Poisoning To Detect Photons

According to a proposal, a phenomenon associated with excitation of quasiparticles in certain superconducting quantum devices would be exploited as a means of detecting photons with exquisite sensitivity. The phenomenon could also be exploited to perform medium-resolution spectroscopy. The proposal was inspired by the observation that Coulomb blockade devices upon which some quantum logic gates are based are extremely sensitive to quasiparticles excited above the superconducting gaps in their leads. The presence of quasiparticles in the leads can be easily detected via the charge states. If quasiparticles could be generated in the leads by absorption of photons, then the devices could be used as very sensitive detectors of electromagnetic radiation over the spectral range from x-rays to submillimeter waves. The devices in question are single-Cooper-pair boxes (SCBs), which are mesoscopic superconducting devices developed for quantum computing. An SCB consists of a small superconducting island connected to a reservoir via a small tunnel junction and connected to a voltage source through a gate capacitor. An SCB is an artificial two-level quantum system, the Hamiltonian of which can be controlled by the gate voltage. One measures the expected value of the charge of the eigenvectors of this quantum system by use of a radio-frequency single-electron transistor. A plot of this expected value of charge as a function of gate voltage resembles a staircase that, in the ideal case, consists of steps of height 2 e (where e is the charge of one electron). Experiments have shown that depending on the parameters of the device, quasiparticles in the form of "broken" Cooper pairs present in the reservoir can tunnel to the island, giving rise to steps of 1 e. This effect is sometimes called "poisoning." Simulations have shown that an extremely small average number of quasiparticles can generate a 1-e periodic signal. In a device according to the proposal, this poisoning would be turned to advantage. Depending on the wavelength, an antenna or other component would be used to couple radiation into the reservoir, wherein the absorption of photons would break Cooper pairs, thereby creating quasiparticles that, in turn, would tunnel to the island, creating a 1-e signal. On the basis of conservative estimates of device parameters derived from experimental data and computational simulations that fit the data, it has been estimated that the noise equivalent power of a device according to the proposal could be as low as 6 10(exp -22) W/Hz(exp 1/2). It has also been estimated that the spectroscopic resolution (photon energy divided by increment of photon energy) of such a device in visible light would exceed 100.

Echternach, Pierre↗
NASA NTRS1993

Spurious symptom reduction in fault monitoring

Previous work accomplished on NASA's Faultfinder concept suggested that the concept was jeopardized by spurious symptoms generated in the monitoring phase. The purpose of the present research was to investigate methods of reducing the generation of spurious symptoms during in-flight engine monitoring. Two approaches for reducing spurious symptoms were investigated. A knowledge base of rules was constructed to filter known spurious symptoms and a neural net was developed to improve the expectation values used in the monitoring process. Both approaches were effective in reducing spurious symptoms individually. However, the best results were obtained using a hybrid system combining the neural net capability to improve expectation values with the rule-based logic filter.

Shontz, William D.↗
NASA NTRS2011

Drop Shapes Versus Fall Velocities in Rain: 2 Contrasting Examples

Rainfall retrievals from polarimetric radar measurements require the knowledge of four fundamental rain microstructure parameters, namely, drop size distribution, drop shape distribution, canting angles and drop fall velocities. Some recent measurements of all four parameters in natural rain are summarized in [1]. In this paper, we perform an in-depth analysis of two events, using two co-located 2D video disdrometers (2DVD; see [2]) both with high calibration accuracy, and a C-band polarimetric radar [3], located 15 km away. The two events, which occurred 7 days apart (on the 18th and the 25th of Dec 2009), had moderate-to-intense rainfall rates, but the second event had an embedded convection line within the storm. The line had passed over the 2DVD site, thus enabling the shapes and fall velocities to be determined as the line crossed the site. The first event was also captured in a similar manner by both the 2DVDs as well as the C-band radar. Drop fall velocity measurements for, say, the 3 mm drops show noticeable differences between the two events. Whereas for the first event, the velocity distribution showed a narrow and symmetric distribution, with a mode at the expected value (7.95 m/s, as given by the formula in [4]), the second event produced a wider distribution with a significant skewness towards lower velocities (although its mode too was close to the expected value). Moreover, the slower 3 mm drops in the second event occurred when the convection line was directly over the 2DVD site (03:35-03:45 utc), and not before nor after. A similar trend was observed in terms of the horizontal dimensions of the 3 mm drops, i.e. large fluctuations during the same time period, but not outside the period. Vertical dimensions of the drops also fluctuated but not to the same extent. Interestingly, the horizontal dimensions tended towards larger values during the 10-minute period, implying an increase in drop oblateness, which in turn indicates the possibility of the horizontal mode oscillation, one of the three fundamental modes of drop oscillations [5], albeit the most difficult one to excite.

Thurai, M.↗
NASA NTRS1994

Infrared to x-ray spectral energy distributions of high redshift quasars

We have observed 14 quasars with z greater than 2.8 with the ROSAT-PSPC, and detected 12 of them, including the z=4.11 quasar 0000-263. We present the first x-ray spectrum of a radio quiet quasar with z greater than 3, 1946+768. Its x-ray spectrum is consistent with a power law with spectral index alpha(sub E)=1.8(sup +2.1, sub -1.4) and no evidence for absorption in excess of the galactic column (alpha(sub E)=1.00(sup +0.28, sub -0.32) assuming N(sub H)=N(sub H)(Gal)). A Position Sensitive Proportional Counter (PSPC) hardness ratio is used to constrain the x-ray spectral properties of the quasars for which there were less than 100 photons detected. For the radio quiet quasars, (alpha(sub E)) approximately equals 1.2, if one assumes that there is no absorption in excess of the galactic column. We combine the x-ray data with new ground based optical and near-IR spectrophotometry obtained at the Steward 2.3 m and Multiple Mirror Telescope, and data from the literature. The spectral energy distributions are compared to those of low redshift objects. For the radio quiet quasars with z greater than 2.5, the mean (alpha(sub ox)) is approximately 1.8. This is larger than the mean for quasars with z less than 2.5, but consistent with the expected value for quasars with the high optical luminosities of the objects in this sample. For the radio-loud quasars, (alpha(sub ox)) is approximately 1.4, independent of redshift. This is smaller than the expected value for the optically luminous, high redshift objects in this sample, if they are mostly GHz peaked radio sources and hence comparable to steep-spectrum, compact radio sources at lower redshift. Finally, we compare the spectral energy distributions of two representative objects to the predicted spectrum of a thin accretion disk in the Kerr geometry, and discuss the uncertainties in deriving black hole masses and mass accretion rates.

Bechtold, Jill↗
NASA NTRS1987

Theoretical study of the dipole moment function of OH(X 2Pi)

A complete theoretical electric dipole moment function mu(r) is computed for OH(X 2Pi) at the full configuration-interaction (FCI) level for DZP + diffuse Gaussian basis set. The energy and dipole moment are also determined with 2d functions on oxygen at seven r values. The following methods are compared to the FCI for both the oxygen 1d and 2d basis sets: single-reference singles-plus-doubles configuration interaction (SDCI), SDCI with Davidson's correction, the coupled pair functional approach (CPF) and a modified form of CPF, CASSCF, and CASSCF-MRSDCI, and the external contracted CI(CCI) method. The dipole moments are evaluated both as an expectation value and by finite-field methods. The results support the superiority of evaluating the dipole moment as an energy derivative rather than as an expectation value.

Langhoff, Stephen R.↗