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At least 37 records · Page 2

Modeling and simulation of a Stewart platform type parallel structure robot

The kinematics and dynamics of a Stewart Platform type parallel structure robot (NASA's Dynamic Docking Test System) were modeled using the method of kinematic influence coefficients (KIC) and isomorphic transformations of system dependence from one set of generalized coordinates to another. By specifying the end-effector (platform) time trajectory, the required generalized input forces which would theoretically yield the desired motion were determined. It was found that the relationship between the platform motion and the actuators motion was nonlinear. In addition, the contribution to the total generalized forces, required at the actuators, from the acceleration related terms were found to be more significant than the velocity related terms. Hence, the curve representing the total required actuator force generally resembled the curve for the acceleration related force. Another observation revealed that the acceleration related effective inertia matrix I sub dd had the tendency to decouple, with the elements on the main diagonal of I sub dd being larger than the off-diagonal elements, while the velocity related inertia power array P sub ddd did not show such tendency. This tendency results in the acceleration related force curve of a given actuator resembling the acceleration profile of that particular actuator. Furthermore, it was indicated that the effective inertia matrix for the legs is more decoupled than that for the platform. These observations provide essential information for further research to develop an effective control strategy for real-time control of the Dynamic Docking Test System.

Lim, Gee Kwang↗

SPACE: the SPectroscopic, All-Sky Cosmic Explorer

We describe the scientific motivations, the mission concept and the instrumentation of SPACE, a class-M mission proposed for concept study at the first call of the ESA Cosmic-Vision 2015-2025 planning cycle. SPACE aims at producing the largest three-dimensional evolutionary map of the Universe over the past 10 billion years by taking near-IR spectra and measuring redshifts of more than half a billion galaxies at 0 < z < 2 down to AB approximately 23 over 37r sr of the sky. In addition, SPACE will also target a smaller sky field, performing a deep spectroscopic survey of millions of galaxies to AB approximately 26 and at 2 < z < l0+. Owing to the depth, redshift range, volume coverage and quality of its spectra, SPACE will reveal with unique sensitivity most of the fundamental cosmological signatures, including the power spectrum of density fluctuations and its turnover, the baryonic acoustic oscillations imprinted when matter and radiation decoupled, the distance-luminosity relation of cosmological supernovae, the evolution of the cosmic expansion rate, the growth rate of cosmic large-scale structure, the large scale distribution of galaxies. The datasets from the SPACE mission will represent a long lasting legacy that will be data mined for many years to come.

Cimatti, A.↗

Indexing system for optical beam steering

This paper describes the design and testing of an indexing system for optical-beam steering. The cryogenic beam-steering mechanism is a 360-degree rotation device capable of discrete, high-precision alignment positions. It uses low-precision components for its rough alignment and kinematic design to meet its stringent repeatability and stability requirements (of about 5 arcsec). The principal advantages of this design include a decoupling of the low-precision, large angular motion from the high-precision alignment, and a power-off alignment position that potentially extends the life or hold time of cryogenic systems. An alternate design, which takes advantage of these attributes while reducing overall motion, is also presented. Preliminary test results show the kinematic mount capable of sub-arc second repeatability.

Sullivan, Mark T.↗

An extension of the Lighthill theory of jet noise to encompass refraction and shielding

A formalism for jet noise prediction is derived that includes the refractive 'cone of silence' and other effects; outside the cone it approximates the simple Lighthill format. A key step is deferral of the simplifying assumption of uniform density in the dominant 'source' term. The result is conversion to a convected wave equation retaining the basic Lighthill source term. The main effect is to amend the Lighthill solution to allow for refraction by mean flow gradients, achieved via a frequency-dependent directional factor. A general formula for power spectral density emitted from unit volume is developed as the Lighthill-based value multiplied by a squared 'normalized' Green's function (the directional factor), referred to a stationary point source. The convective motion of the sources, with its powerful amplifying effect, also directional, is already accounted for in the Lighthill format: wave convection and source convection are decoupled. The normalized Green's function appears to be near unity outside the refraction dominated 'cone of silence', this validates our long term practice of using Lighthill-based approaches outside the cone, with extension inside via the Green's function. The function is obtained either experimentally (injected 'point' source) or numerically (computational aeroacoustics). Approximation by unity seems adequate except near the cone and except when there are shrouding jets: in that case the difference from unity quantifies the shielding effect. Further extension yields dipole and monopole source terms (cf. Morfey, Mani, and others) when the mean flow possesses density gradients (e.g., hot jets).

Ribner, Herbert S.↗

Feasibility study for convertible engine torque converter

The feasibility study has shown that a dump/fill type torque converter has excellent potential for the convertible fan/shaft engine. The torque converter space requirement permits internal housing within the normal flow path of a turbofan engine at acceptable engine weight. The unit permits operating the engine in the turboshaft mode by decoupling the fan. To convert to turbofan mode, the torque converter overdrive capability bring the fan speed up to the power turbine speed to permit engagement of a mechanical lockup device when the shaft speed are synchronized. The conversion to turbofan mode can be made without drop of power turbine speed in less than 10 sec. Total thrust delivered to the aircraft by the proprotor, fan, and engine during tansient can be controlled to prevent loss of air speed or altitude. Heat rejection to the oil is low, and additional oil cooling capacity is not required. The turbofan engine aerodynamic design is basically uncompromised by convertibility and allows proper fan design for quiet and efficient cruise operation. Although the results of the feasibility study are exceedingly encouraging, it must be noted that they are based on extrapolation of limited existing data on torque converters. A component test program with three trial torque converter designs and concurrent computer modeling for fluid flow, stress, and dynamics, updated with test results from each unit, is recommended.

Source record↗

Progress Toward a Compact 0.05 K Magnet Refrigerator Operating from 10 K

Much of the most interesting information regarding our universe is hidden in the sub-millimeter, infrared, and x-rays bands of the spectrum, to which our atmosphere is largely opaque. Thus, missions exploring these bands are a very important part of NASA s Space Science program. Coincidentally, the most sensitive detectors in these spectral regions operate at extremely low temperatures, typically 0.05 - 0.10 K. Generally these temperatures will be achieved using magnetic refrigerators, also know as Adiabatic Demagnetization Refrigerators, or ADRs. Current ADRs, such as the one used in the XRS-II instrument on the Astro-E2 satellite, use a single-stage to cool detectors from 1.3 K to 0.06 K. The ADR is designed so that it can absorb the heat on the detector stage for at least 24 hours before it must stop, warm up to the helium bath temperature (1.3 K), and dump the accumulated heat. Future detector arrays will be much larger and will have higher heat dissipation. Furthermore, future missions will use mechanical cryocoolers to provide upper stage cooling, but they can only reach 4 - 10 K. Trying to scale heavy (-15 kg) single stage ADRs up to the higher heat loads and higher heat rejection temperatures required leads to unacceptably large systems. The GSFC Cryogenics Branch has developed the Continuous ADR (CADR) to solve this problem. The CADR consists of a series of ADR stages that sequentially pass heat from the load up to the high temperature heat sink. The stage connected to the load remains at a constant temperature. The continuous stage effectively decouples detector operation from ADR operation, allowing the ADR stages to be cycled much more rapidly. Rapid cycling leads to higher cooling power density. The cascading, multistage arrangement allows the magnetic refrigerant of each stage to be optimized for its own temperature swing. In the past year, we have made good progress toward a 0.05 to 10K system. A four-stage system that operates from 4.2 K was demonstrated. Magnetic shielding was added to eliminate inter-stage coupling. Improvements were made to superconducting and passive gas-gap heat switches. A second type of passive gas gap switch, one meant for use at higher temperature, was demonstrated. The presentation will focus primarily on these recent design improvements, and on the challenges that remain on the progress toward a system that will operate from 10 K or higher.

Canavan, Edgar↗

Development of Superconducting Transition Edge Sensors Based on Electron-Phonon Decoupling

We have successfully fabricated a superconducting transition edge sensor (TES), bolometer that centers on the use of electron-phonon decoupling (EPD) for thermal isolation. We have selected a design approach that separates the two functions of far-infrared and THz radiative power absorption and temperature measurement, allowing separate optimization of the performance of each element. We have integrated molybdenum/gold (Mo/Au) bilayer TES and ion assisted thermally evaporated (IAE) bismuth (Bi) films as radiation absorber coupled to a low-loss microstripline from niobium (Nb) ground plane to a twin-slot antenna structure. The thermal conductance (G) and the time constant for the different geometry device have been measured. For one such device, the measured G is 1.16 x 10(exp -10) W/K (plus or minus 0.61 x 10(exp- 10) W/K) at 60 mK, which corresponds to noise equivalent power (NEP) = 1.65 X 10(exp -18)W/vHz and time constant of approximately 5 microseconds.

Jethava, Nikhil↗

Predictive momentum management for the Space Station

Space station control moment gyro momentum management is addressed by posing a deterministic optimization problem with a performance index that includes station external torque loading, gyro control torque demand, and excursions from desired reference attitudes. It is shown that a simple analytic desired attitude solution exists for all axes with pitch prescription decoupled, but roll and yaw coupled. Continuous gyro desaturation is shown to fit neatly into the scheme. Example results for pitch axis control of the NASA power tower Space Station are shown based on predictive attitude prescription. Control effector loading is shown to be reduced by this method when compared to more conventional momentum management techniques.

Hatis, P. D.↗

The Role of Convection and Growth Competition in Phase Selection in Microgravity: Controlled Convection in the Containerless Processing of Steel Alloys

Containerless processing using electromagnetic levitation (EML) is a powerful technique in the investigation of reactive molten metal systems. On ground, the power required to overcome the weight of the sample is sufficient to cause significant heating and induce substantial melt convection. In microgravity, the heating and positioning fields may be decoupled and the field strength may be varied to achieve the desired level of convection within the limits set by the geometry of the levitation coil and the sample size. From high-speed digital images of the double recalescence behavior of Fe-Cr-Ni alloys in ground-based testing and in reduced-gravity aboard the NASA KC-135 parabolic aircraft, we have shown that phase selection can be predicted based on a growth competition model. An important parameter in this model is the delay time between primary nucleation and subsequent nucleation of the stable solid within the liquid/metastable solid array. This delay time is a strong function of composition and a weak function of the undercooling of the melt below the metastable liquidus. From the results obtained during the first Microgravity Sciences Laboratory (MSL-1) mission, we also know that convection may significantly influence the delay time, especially at low undercoolings. Currently, it is unclear what mechanism controls the formation of a heterogeneous site that allows nucleation of the austenitic phase on the pre-existing ferrite skeleton. By examining the behavior of the delay time under different convective conditions, we hypothesize that we can differentiate between several of these mechanisms to gain an understanding of how to control microstructural. evolution. We will anchor these predictions by examining samples quenched at different times following primary recalescence in microgravity. A second important parameter in the growth competition model is the identification of the growth rate of the stable phase into the semi-solid array that formed during primary recalescence. Current dendritic growth theory is inadequate in predicting solidification behavior under these conditions as metallographic analyses show that stable phase growth proceeds along the interface between the metastable solid and residual liquid. Since growth velocity is independent of the initial undercooling relative to the metastable liquidus, we hypothesize that purely thermal effects can be separated from other important growth model parameters by careful selection of the liquid composition in a ternary system.

Matson, D. M.↗

Head-eye tracking in two-dimensional pursuit tasks

The neurological control systems for the eye and head are studied by investigating dynamic eye and head rotations in two degrees of freedom using bandlimited, white noise stimuli, nominally wide field of view stimulus presentations of + or - 10 deg and power spectral analysis of the data to produce input/output transfer and coherence functions. Determined were frequency response characteristics of these systems, the linearity of the transfer functions in both coupled and decoupled vertical and horizontal stimulus/response reference axes and the amount of cross axis coupling present in system responses. A comparative study was also conducted to assess the differences in response characteristics between single axis and dual axis visual stimulation for the same subject.

Shirachi, D. K.↗

Series Elastic Tether Management for Rappelling Rovers

The Axel rappelling rover was designed to enable access to intriguing and important science sites that lie in difficult terrains that are inaccessible to conventional rovers. Extended autonomous rappelling calls for careful control of tethertension,precisemanagementoftetherspooling,andsome measure of shock tolerance. This paper covers the design and testing of a first-generation tether management system (TMS) for Axel. The system uses a double bull-wheel capstan driven by a low-stiffness series elastic actuator (SEA) to provide tension control and decouple internal spooling tension from external tether tension. The benefit of the series elastic actuator is two-fold. First, it permits closed-loop tether tension control with lower mass and power consumption than a comparable torque motor. Second, it improves the shock/drop tolerance of the rappelling system both while moving and when the system is inactive with the motors locked. Experiments on the new TMS show that this design performs well in keeping nearly constant spooling tension while rejecting large dynamic disturbances at the output. While the SEA is very effective at maintaining a given tension contribution, the additional effects of friction and the unique mechanical properties of the tether result in substantial errors in the measured output tension. Upcoming field trials will be used to evaluate the effectiveness and sufficiency of this system when integrated in Axel.

Nesnas, Issa↗

Rolling Bearing Life Prediction, Theory, and Application

A tutorial is presented outlining the evolution, theory, and application of rolling-element bearing life prediction from that of A. Palmgren, 1924; W. Weibull, 1939; G. Lundberg and A. Palmgren, 1947 and 1952; E. Ioannides and T. Harris, 1985; and E. Zaretsky, 1987. Comparisons are made between these life models. The Ioannides-Harris model without a fatigue limit is identical to the Lundberg-Palmgren model. The Weibull model is similar to that of Zaretsky if the exponents are chosen to be identical. Both the load-life and Hertz stress-life relations of Weibull, Lundberg and Palmgren, and Ioannides and Harris reflect a strong dependence on the Weibull slope. The Zaretsky model decouples the dependence of the critical shear stress-life relation from the Weibull slope. This results in a nominal variation of the Hertz stress-life exponent. For 9th- and 8th-power Hertz stress-life exponents for ball and roller bearings, respectively, the Lundberg- Palmgren model best predicts life. However, for 12th- and 10th-power relations reflected by modern bearing steels, the Zaretsky model based on the Weibull equation is superior. Under the range of stresses examined, the use of a fatigue limit would suggest that (for most operating conditions under which a rolling-element bearing will operate) the bearing will not fail from classical rolling-element fatigue. Realistically, this is not the case. The use of a fatigue limit will significantly overpredict life over a range of normal operating Hertz stresses. Since the predicted lives of rolling-element bearings are high, the problem can become one of undersizing a bearing for a particular application.

Zaretsky, Erwin V.↗

Rolling Bearing Life Prediction, Theory, and Application

A tutorial is presented outlining the evolution, theory, and application of rolling-element bearing life prediction from that of A. Palmgren, 1924; W. Weibull, 1939; G. Lundberg and A. Palmgren, 1947 and 1952; E. Ioannides and T. Harris, 1985; and E. Zaretsky, 1987. Comparisons are made between these life models. The Ioannides-Harris model without a fatigue limit is identical to the Lundberg-Palmgren model. The Weibull model is similar to that of Zaretsky if the exponents are chosen to be identical. Both the load-life and Hertz stress-life relations of Weibull, Lundberg and Palmgren, and Ioannides and Harris reflect a strong dependence on the Weibull slope. The Zaretsky model decouples the dependence of the critical shear stress-life relation from the Weibull slope. This results in a nominal variation of the Hertz stress-life exponent. For 9th- and 8th-power Hertz stress-life exponents for ball and roller bearings, respectively, the Lundberg-Palmgren model best predicts life. However, for 12th- and 10th-power relations reflected by modern bearing steels, the Zaretsky model based on the Weibull equation is superior. Under the range of stresses examined, the use of a fatigue limit would suggest that (for most operating conditions under which a rolling-element bearing will operate) the bearing will not fail from classical rolling-element fatigue. Realistically, this is not the case. The use of a fatigue limit will significantly overpredict life over a range of normal operating Hertz stresses. (The use of ISO 281:2007 with a fatigue limit in these calculations would result in a bearing life approaching infinity.) Since the predicted lives of rolling-element bearings are high, the problem can become one of undersizing a bearing for a particular application. Rules had been developed to distinguish and compare predicted lives with those actually obtained. Based upon field and test results of 51 ball and roller bearing sets, 98 percent of these bearing sets had acceptable life results using the Lundberg- Palmgren equations with life adjustment factors to predict bearing life. That is, they had lives equal to or greater than that predicted. The Lundberg-Palmgren model was used to predict the life of a commercial turboprop gearbox. The life prediction was compared with the field lives of 64 gearboxes. From these results, the roller bearing lives exhibited a load-life exponent of 5.2, which correlated with the Zaretsky model. The use of the ANSI/ABMA and ISO standards load-life exponent of 10/3 to predict roller bearing life is not reflective of modern roller bearings and will underpredict bearing lives.

Life prediction↗

164-GHz MMIC HEMT Frequency Doubler

A monolithic microwave integrated circuit (MMIC) that includes a high-electron-mobility transistor (HEMT) has been developed as a prototype of improved frequency doublers for generating signals at frequencies greater than 100 GHz. Signal sources that operate in this frequency range are needed for a variety of applications, notably including general radiometry and, more specifically, radiometric remote sensing of the atmosphere. Heretofore, it has been common practice to use passive (diode-based) frequency multipliers to obtain frequencies greater than 100 GHz. Unfortunately, diode-based frequency multipliers are plagued by high DC power consumption and low conversion efficiency. Moreover, multiplier diodes are not easily integrated with such other multiplier-circuit components as amplifiers and oscillators. The goals of developing the present MMIC HEMT frequency doubler were (1) to utilize the HEMT as an amplifier to increase conversion efficiency (more precisely, to reduce conversion loss), thereby increasing the output power for a given DC power consumption or, equivalently, reducing the DC power consumption for a given output power; and (2) to provide for the integration of amplifier and oscillator components on the same chip. The MMIC frequency doubler (see Figure 1) contains an AlInAs/GaInAs/InP HEMT biased at pinch-off to make it function as a class-B amplifier (meaning that it conducts in half-cycle pulses). Grounded coplanar waveguides (GCPWs) are used as impedance-matching transmission lines. Air bridges are placed at discontinuities to suppress undesired slot electromagnetic modes. Another combination of GCPWs also serves both as a low-pass filter to suppress undesired oscillations at frequencies below 60 GHz and as a DC blocker. Large decoupling capacitors and epitaxial resistors are added in the drain and gate lines to suppress bias oscillations. At the output terminal, the fundamental frequency is suppressed by a quarter-wave open stub, which presents a short circuit at the fundamental frequency and an open circuit at the second harmonic. At an input power of 7 mW, the output power and conversion loss at an output frequency of 164 GHz were found to be 5 dBm (approximately equal to 3.2 mW) and 2 dB, respectively, with a 3-dB output-power bandwidth of 14 GHz. This is the best performance reported to date for an MMIC HEMT frequency doubler above 100 GHz.

Samoska, Lorene↗

Decoupling the Effects of Anthropogenic Emission Reductions from the Meteorology and Natural Emissions in TROPOMI NO 2 Retrievals During the 2020 COVID-19 Lockdowns

Satellite measurements during the COVID-19 lockdowns that began in 2020 revealed unprecedented reductions in NO 2 tropospheric vertical column densities (VCD). These reductions have largely been attributed to reduced anthropogenic emissions associated with abrupt decreases in road traffic and other power consuming business activities. Although decreased emissions tended to be the main contributor to the observed NO 2 VCD reduction, meteorological variability also played a role. Whereas the observed VCD changes were predominantly negative in places where public health policies were strictly enforced, meteorology had both positive and negative effects over short time intervals. Here, we present results from a global study of the NO 2 reductions aimed at disentangling the meteorological and natural emission variability from the anthropogenic emissions over the world’s most populated megacities. For this study, NASA’s TROPOMI NO 2 algorithm was used in conjunction with the Global Modeling Initiative (GMI) chemical transport model to separate the contributions due emissions and meteorology. A priori NO 2 profiles were generated from two GMI simulations performed for 2020 at a resolution of 0.25° longitude x 0.25° latitude. The first simulation used updated, COVID-impacted NOX emissions based on Forster et al. (2020), while the second simulation used the 2019 emissions with the 2020 meteorology, referred to here as 2020BAU. The 2020BAU data set allowed for the decoupling of the emission component from the meteorology. When compared to the same period in 2019, NO 2 column amounts during the lockdowns were reduced in 35 out of 36 cities. While reduced emissions contributed most to the observed total change in NO 2 during the lockdowns, the effects of meteorology were significant, ranging between 40% (Chennai) and 15% (Beijing). In China, an increase in NO 2 levels due to meteorology were observed in five out of the seven cities considered in the study. Use of different a-priori NO 2 profiles from the two simulations in our TROPOMI retrievals allowed for a determination of retrieval errors that ranged from -1.7% to -11.0%. We used the quality assurance flag > 0.75 to select the highest quality scenes in the study period. Using the GMI, we estimated the sampling biases to be in the range -11% to 10% of the total change for the cities in our study.

Brad Fisher↗

CF6 fan performance improvement

A significant portion of the NASA-sponsored Performance Improvement Program for the CF6 engine was the development of an improved fan concept. This involved aerodynamic redesign of the CF6 fan blade to increase fan efficiency while retaining the mechanical integrity, operability, and acoustic characteristics of the existing blade. A further improvement in performance was obtained by adding a fan case stiffener ring to decouple blade-case vibrational characteristics, permitting a significant reduction in running tip clearance. Engine testing was performed to establish the performance, mechanical and acoustic properties of the new design relative to the current fan, and to establish power management characteristics for the CF6-50C2/E2 engine. A significant improvement in cruise power SFC of 1.8 percent was demonstrated in Sea Level testing projected to altitude flight conditions.

Patt, R. F.↗

Analysis of multiple pulse NMR in solids. III

The paper introduces principles which greatly simplify the process of designing and analyzing compound pulse cycles. These principles are demonstrated by applying them to the design and analysis of several cycles, including a 52-pulse cycle; this pulse cycle combines six different REV-8 cycles and has substantially more resolving power than previously available techniques. Also, a new 24-pulse cycle is introduced which combines three different REV-8 cycles and has a resolving ability equivalent to that of the 52-pulse cycle. The principle of pulse-cycle decoupling provides a method for systematically combining pulse groups into compound cycles in order to achieve enhanced performance. This method is illustrated by a logical development from the two-pulse solid echo sequence to the WAHUHA (Waugh et al., 1968), the REV-8, and the new 24-pulse and 52-pulse cycles, along with the 14-pulse and 12-pulse cycles. Proton chemical shift tensor components for several organic solids, measured by using the 52-pulse cycle, are reported without detailed discussion.

Burum, D. P.↗

First Year Wilkinson Microwave Anisotropy Probe (WMAP)Observations: Preliminary Maps and Basic Results

We present full sky microwave maps in five frequency bands (23 to 94 GHz) from the WMAP first year sky survey. Calibration errors are less than 0.5% and the low systematic error level is well specified. The cosmic microwave background (CMB) is separated from the foregrounds using multifrequency data. The sky maps are consistent with the 7 in. full-width at half-maximum (FWHM) Cosmic Background Explorer (COBE) maps. We report more precise, but consistent, dipole and quadrupole values. The CMB anisotropy obeys Gaussian statistics with -58 less than f(sub NL) less than 134 (95% CL). The 2 less than or = l less than or = 900 anisotropy power spectrum is cosmic variance limited for l less than 354 with a signal-to-noise ratio greater than 1 per mode to l = 658. The temperature-polarization cross-power spectrum reveals both acoustic features and a large angle correlation from reionization. The optical depth of reionization is tau = 0.17 +/- 0.04, which implies a reionization epoch of t(sub r) = 180(sup +220, sub -80) Myr (95% CL) after the Big Bang at a redshift of z(sub r) = 20(sup +10, sub -9) (95% CL) for a range of ionization scenarios. This early reionization is incompatible with the presence of a significant warm dark matter density. A best-fit cosmological model to the CMB and other measures of large scale structure works remarkably well with only a few parameters. The age of the best-fit universe is t(sub 0) = 13.7 +/- 0.2 Gyr old. Decoupling was t(sub dec) = 379(sup +8, sub -7)kyr after the Big Bang at a redshift of z(sub dec) = 1089 +/- 1. The thickness of the decoupling surface was Delta(sub z(sub dec)) = 195 +/- 2. The matter density of the universe is Omega(sub m)h(sup 2) = 0.135(sup +0.008, sub -0.009) the baryon density is Omega(sub b)h(sup 2) = 0.0224 +/- 0.0009, and the total mass-energy of the universe is Omega(sub tot) = 1.02 +/- 0.02. There is progressively less fluctuation power on smaller scales, from WMAP to fine scale CMB measurements to galaxies and finally to the Ly-alpha forest. This is accounted for with a running spectral index, significant at the approx. 2(sigma) level. The spectral index of scalar fluctuations is fit as n(sub s) = 0.93 +/-0.03 at wavenumber k(sub o) = 0.05/Mpc ((sub eff) approx. = 700), with a slope of dn(sub s)/d I(sub nk) = -0.031(sup + 0.016, sub -0.018) in the best-fit model.

Bennett, C. L.↗