Results for “sufficient statistics” — Page 18

NASA NTRS1982

Acoustic modal analysis of a full-scale annular combustor

An acoustic modal decomposition of the measured pressure field in a full scale annular combustor installed in a ducted test rig is described. The modal analysis, utilizing a least squares optimization routine, is facilitated by the assumption of randomly occurring pressure disturbances which generate equal amplitude clockwise and counter-clockwise pressure waves, and the assumption of statistical independence between modes. These assumptions are fully justified by the measured cross spectral phases between the various measurement points. The resultant modal decomposition indicates that higher order modes compose the dominant portion of the combustor pressure spectrum in the range of frequencies of interest in core noise studies. A second major finding is that, over the frequency range of interest, each individual mode which is present exists in virtual isolation over significant portions of the spectrum. Finally, a comparison between the present results and a limited amount of data obtained in an operating turbofan engine with the same combustor is made. The comparison is sufficiently favorable to warrant the conclusion that the structure of the combustor pressure field is preserved between the component facility and the engine.

Karchmer, A. M.↗

NASA NTRS1983

Acoustic modal analysis of a full-scale annular combustor

An acoustic modal decomposition of the measured pressure field in a full scale annular combustor installed in a ducted test rig is described. The modal analysis, utilizing a least squares optimization routine, is facilitated by the assumption of randomly occurring pressure disturbances which generate equal amplitude clockwise and counter-clockwise pressure waves, and the assumption of statistical independence between modes. These assumptions are fully justified by the measured cross spectral phases between the various measurement points. The resultant modal decomposition indicates that higher order modes compose the dominant portion of the combustor pressure spectrum in the range of frequencies of interest in core noise studies. A second major finding is that, over the frequency range of interest, each individual mode which is present exists in virtual isolation over significant portions of the spectrum. Finally, a comparison between the present results and a limited amount of data obtained in an operating turbofan engine with the same combustor is made. The comparison is sufficiently favorable to warrant the conclusion that the structure of the combustor pressure field is preserved between the component facility and the engine. Previously announced in STAR as N83-21896

Karchmer, A. M.↗

NASA NTRS1994

The 1991 WMO ozone sonde intercomparison

The WMO ozone sonde intercomparison was held at Vanscoy, Saskatchewan from May 13 to May 24, 1991. The purpose of the intercomparison is to evaluate the performance of various ozone sonde types used operationally in the Global Ozone Observing System and to ensure that the accuracy and precision of the measurements are sufficient to detect long-term trends in stratospheric ozone. The intercomparison was sponsored by WMO and hosted by the Atmospheric Environment Service (AES) of Canada. It was attended by scientists from six countries: Canada, Finland, Germany, India, Japan and USA. A total of 10 balloon payloads were launched each carrying 7 or 8 sondes for a total of 67 successful ozone sonde flights. The payloads were carried to altitudes between 35 and 40 km where the flights terminated by balloon burst. Results of the profile measurements made during the series of the profile measurements made during the series of flight are used to determine statistically meaningful evaluations of the different sonde types. A description of the payload and the different ozone sondes is given. Preliminary results of the profile measurements and an evaluation of the performance of the sonde types are presented.

Kerr, James B.↗

NASA NTRS2012

Complex Decision-Making Applications for the NASA Space Launch System

The Space Shuttle program is ending and elements of the Constellation Program are either being cancelled or transitioned to new NASA exploration endeavors. The National Aeronautics and Space Administration (NASA) has worked diligently to select an optimum configuration for the Space Launch System (SLS), a heavy lift vehicle that will provide the foundation for future beyond low earth orbit (LEO) large-scale missions for the next several decades. Thus, multiple questions must be addressed: Which heavy lift vehicle will best allow the agency to achieve mission objectives in the most affordable and reliable manner? Which heavy lift vehicle will allow for a sufficiently flexible exploration campaign of the solar system? Which heavy lift vehicle configuration will allow for minimizing risk in design, test, build and operations? Which heavy lift vehicle configuration will be sustainable in changing political environments? Seeking to address these questions drove the development of an SLS decision-making framework. From Fall 2010 until Spring 2011, this framework was formulated, tested, fully documented, and applied to multiple SLS vehicle concepts at NASA from previous exploration architecture studies. This was a multistep process that involved performing figure of merit (FOM)-based assessments, creating Pass/Fail gates based on draft threshold requirements, performing a margin-based assessment with supporting statistical analyses, and performing sensitivity analysis on each. This paper discusses the various methods of this process that allowed for competing concepts to be compared across a variety of launch vehicle metrics. The end result was the identification of SLS launch vehicle candidates that could successfully meet the threshold requirements in support of the SLS Mission Concept Review (MCR) milestone.

Lyles, Garry↗

NASA NTRS2017

It's All Relative: A Validation of Radiation Quality Comparison Metrics

The difference between high-LET and low-LET radiation is quantified by a measure called relative biological effectiveness (RBE). RBE is defined as the ratio of the dose of a reference radiation to that of a test radiation to achieve the same effect level, and thus, is described either as an iso-effector dose-to-dose ratio. A single dose point is not sufficient to calculate an RBE value; therefore, studies with only one dose point usually calculate an effect-to-effect ratio. While not formally used in radiation protection, these iso-dose values may still be informative. Shuryak, et al 2017 investigated the use of an iso-dose metric termed "radiation effects ratio" (RER) and used both RBE and RER to estimate high-LET risks. To apply RBE or RER to risk prediction, the selected metric must be uniquely defined. That is, the calculated value must be consistent within a model given a constant set of constraints and assumptions, regardless of how effects are defined using statistical transformations from raw endpoint data. We first test the RBE and the RER to determine whether they are uniquely defined using transformations applied to raw data. Then, we test whether both metrics can predict heavy ion response data after simulated effect size scaling between human populations or when converting animal to human endpoints.

Chappell, Lori J.↗

NASA NTRS1979

Optimized multisectioned acoustic liners

A critical examination is presented of the use of optimized axially segmented acoustic liners to increase the attenuation of a liner. New calculations show that segmenting is most efficient at high frequencies with relatively long duct lengths where the attenuation is low for both uniform and segmented liners. Statistical considerations indicate little advantage in using optimized liners with more than two segments while the bandwidth of an optimized two-segment liner is shown to be nearly equal to that of a uniform liner. Multielement liner calculations show a large degradation in performance due to changes in assumed input modal structure. Finally, in order to substantiate previous and future analytical results, in-house (finite difference) and contractor (mode matching) programs are used to generate theoretical attenuations for a number of liner configurations for liners in a rectangular duct with no mean flow. Overall, the use of optimized multisectioned liners (sometimes called phased liners) fails to offer sufficient advantage over a uniform liner to warrant their use except in low frequency single mode application.

Baumeister, K. J.↗

NASA NTRS2005

Improved Compression of Wavelet-Transformed Images

A recently developed data-compression method is an adaptive technique for coding quantized wavelet-transformed data, nominally as part of a complete image-data compressor. Unlike some other approaches, this method admits a simple implementation and does not rely on the use of large code tables. A common data compression approach, particularly for images, is to perform a wavelet transform on the input data, and then losslessly compress a quantized version of the wavelet-transformed data. Under this compression approach, it is common for the quantized data to include long sequences, or runs, of zeros. The new coding method uses prefixfree codes for the nonnegative integers as part of an adaptive algorithm for compressing the quantized wavelet-transformed data by run-length coding. In the form of run-length coding used here, the data sequence to be encoded is parsed into strings consisting of some number (possibly 0) of zeros, followed by a nonzero value. The nonzero value and the length of the run of zeros are encoded. For a data stream that contains a sufficiently high frequency of zeros, this method is known to be more effective than using a single variable length code to encode each symbol. The specific prefix-free codes used are from two classes of variable-length codes: a class known as Golomb codes, and a class known as exponential-Golomb codes. The codes within each class are indexed by a single integer parameter. The present method uses exponential-Golomb codes for the lengths of the runs of zeros, and Golomb codes for the nonzero values. The code parameters within each code class are determined adaptively on the fly as compression proceeds, on the basis of statistics from previously encoded values. In particular, a simple adaptive method has been devised to select the parameter identifying the particular exponential-Golomb code to use. The method tracks the average number of bits used to encode recent runlengths, and takes the difference between this average length and the code parameter. When this difference falls outside a fixed range, the code parameter is updated (increased or decreased). The Golomb code parameter is selected based on the average magnitude of recently encoded nonzero samples. The coding method requires no floating- point operations, and more readily adapts to local statistics than other methods. The method can also accommodate arbitrarily large input values and arbitrarily long runs of zeros. In practice, this means that changes in the dynamic range or size of the input data set would not require a change to the compressor. The algorithm has been tested in computational experiments on test images. A comparison with a previously developed algorithm that uses large code tables (generated via Huffman coding on training data) suggests that the data-compression effectiveness of the present algorithm is comparable to the best performance achievable by the previously developed algorithm.

Kiely, Aaron↗

NASA NTRS2015

The Impact of Assimilating Precipitation-affected Radiance on Cloud and Precipitation in Goddard WRF-EDAS Analyses

High-frequency TMI and AMSR-E radiances, which are sensitive to precipitation over land, are assimilated into the Goddard Weather Research and Forecasting Model- Ensemble Data Assimilation System (WRF-EDAS) for a few heavy rain events over the continental US. Independent observations from surface rainfall, satellite IR brightness temperatures, as well as ground-radar reflectivity profiles are used to evaluate the impact of assimilating rain-sensitive radiances on cloud and precipitation within WRF-EDAS. The evaluations go beyond comparisons of forecast skills and domain-mean statistics, and focus on studying the cloud and precipitation features in the jointed rainradiance and rain-cloud space, with particular attentions on vertical distributions of height-dependent cloud types and collective effect of cloud hydrometers. Such a methodology is very helpful to understand limitations and sources of errors in rainaffected radiance assimilations. It is found that the assimilation of rain-sensitive radiances can reduce the mismatch between model analyses and observations by reasonably enhancing/reducing convective intensity over areas where the observation indicates precipitation, and suppressing convection over areas where the model forecast indicates rain but the observation does not. It is also noted that instead of generating sufficient low-level warmrain clouds as in observations, the model analysis tends to produce many spurious upperlevel clouds containing small amount of ice water content. This discrepancy is associated with insufficient information in ice-water-sensitive radiances to address the vertical distribution of clouds with small amount of ice water content. Such a problem will likely be mitigated when multi-channel multi-frequency radiances/reflectivity are assimilated over land along with sufficiently accurate surface emissivity information to better constrain the vertical distribution of cloud hydrometers.

WRF-EDAS Analyses↗

NASA NTRS2014

The Moving Group Targets of the Seeds High-Contrast Imaging Survey of Exoplanets and Disks: Results and Observations from the First Three Years

We present results from the first three years of observations of moving group (MG) targets in the Strategic Exploration of Exoplanets and Disks with Subaru (SEEDS) high-contrast imaging survey of exoplanets and disks using the Subaru telescope. We achieve typical contrasts of (is) approximately10(exp 5) at 1" and (is) approximately 10(exp 6) beyond 2" around 63 proposed members of nearby kinematic MGs. We review each of the kinematic associations to which our targets belong, concluding that five, beta Pictoris ((is) approximately 20 Myr), AB Doradus ((is) approximately 100 Myr), Columba ((is) approximately 30 Myr), Tucana-Horogium ((is) approximately 30 Myr), and TW Hydrae ((is) approximately 10 Myr), are sufficiently well-defined to constrain the ages of individual targets. Somewhat less than half of our targets are high-probability members of one of these MGs. For all of our targets, we combine proposed MG membership with other age indicators where available, including Ca ii HK emission, X-ray activity, and rotation period, to produce a posterior probability distribution of age. SEEDS observations discovered a substellar companion to one of our targets, kappa And, a late B star. We do not detect any other substellar companions, but do find seven new close binary systems, of which one still needs to be confirmed. A detailed analysis of the statistics of this sample, and of the companion mass constraints given our age probability distributions and exoplanet cooling models, will be presented in a forthcoming paper.

SEEDS high-contrast imaging survey of exoplanets↗

NASA NTRS2025

A Minority Report Submitted as an Addendum to the Report of the Mars 2020 Organic Contamination Panel

This Minority Report (MR) presents seven findings in addition to or contrary to the main OCP report: 1. Contamination control for the Mars 2020 cache must be strict. Mars’ surface is known to be organics-poor from laboratory studies, Mars meteorite analyses, and from four previous NASA missions. It is imperative that contamination control measures are enacted that enable reliable and robust detection of potential biomarker compounds at the ppb level. 2. Since Mars 2020 is a sample return mission and analyses of samples in the returnable cache are expected to occur after return to Earth, positive controls are not recommended for flight on Mars 2020 unless a compelling case can be made for their use. 3. The findings of previous panels dedicated to organic compound analysis in Martian samples (OCSSG, ND-SAG, SDT) recommend TOC limits between 10-40 ppb. The MR finds that the lower limit of 10 ppb is recommended and that insufficient justification is given by the OCP Panel Report (PR) to raise the TOC limit to 40 ppb. 4. Analytical capability is sufficiently advanced that analytical capability is an irrelevant consideration with respect to differentiating between 10 and 40 ppb TOC. 5. Perceived contamination control challenges are an irrelevant consideration for raising the TOC contamination limit from 10 to 40 ppb since those challenges, and the procedures to ameliorate them, will exist regardless of whether the limit is 10 or 40 ppb. 6. The “dilution cleaning” method has not been adequately proven for utilization on the Mars 2020 mission. Shortcomings have been identified in terms of peer review, method verification, analytical and testing approach, application to space flight hardware, and performance under Martian conditions. The method should be revisited and independently tested using statistically and analytically robust methods, and scrutinized in a rigorous peer review process. 7. The Mars 2020 mission claims considerable heritage from the Mars Science Laboratory (MSL) mission, but MSL contamination control efforts contain significant errors and implementation discrepancies that would imperil the Mars 2020 caching mission were they repeated. A standing contamination control panel should be formed to provide independent oversight for the Mars 2020 mission.

Mars Sample Return↗

NASA NTRS2003

Low Earth Orbit Plasma Variability Model

The empirical International Reference Ionosphere is a widely used model for estimating low Earth orbit plasma characteristics for use in spacecraft design and mission analysis. The climatological model provides mean values of plasma density, temperature, composition, and other ionospheric parameters that can be used to estimate the average magnitude of spacecraft charging, current collection for electrodynamic tethers, and other effects on spacecraft design. Mean IRI parameters are not adequate to answer questions such as what is the maximum or minimum value of the spacecraft potential, does the maximum spacecraft potential exceed a program requirement, will an electrodynamic tether provide adequate drag to deorbit a satellite at end of life, and will the tether provide sufficient thrust to reboost a spacecraft at any time in the solar cycle. These questions require estimates of the variability of the ionospheric environment about the mean values. This presentation describes the status of work at MSFC to develop an empirical ionospheric variability model that can be used in conjunction with the climatological IRI model to provide both mean ionospheric parameters and variations of the environment about the mean. Our technique will use an extensive database of satellite and radar observations of the electron density and temperature to derive variances of the data about the model values. The variances will then be incorporated into Fortran wrapper software that calls the IRI-2001 model and provides statistical estimates of the deviation of the environment about the mean IRI values. We will provide an update on the state of the database development and provide examples of analysis and modeling efforts completed specifically for an International Space Station application.

Minow, Joseph I.↗

NASA NTRS2013

Stratified Magnetically Driven Accretion-Disk Winds and Their Relations To Jets

We explore the poloidal structure of two-dimensional magnetohydrodynamic (MHD) winds in relation to their potential association with the X-ray warm absorbers (WAs) and the highly ionized ultra-fast outflows (UFOs) in active galactic nuclei (AGNs), in a single unifying approach. We present the density n(r, theta), ionization parameter xi(r, theta), and velocity structure v(r, theta) of such ionized winds for typical values of their fluid-to-magnetic flux ratio, F, and specific angular momentum, H, for which wind solutions become super-Alfvenic. We explore the geometrical shape of winds for different values of these parameters and delineate the values that produce the widest and narrowest opening angles of these winds, quantities necessary in the determination of the statistics of AGN obscuration. We find that winds with smaller H show a poloidal geometry of narrower opening angles with their Alfv´en surface at lower inclination angles and therefore they produce the highest line of sight (LoS) velocities for observers at higher latitudes with the respect to the disk plane. We further note a physical and spatial correlation between the X-ray WAs and UFOs that form along the same LoS to the observer but at different radii, r, and distinct values of n, xi, and v consistent with the latest spectroscopic data of radio-quiet Seyfert galaxies. We also show that, at least in the case of 3C 111, the winds' pressure is sufficient to contain the relativistic plasma responsible for its radio emission. Stratified MHD disk winds could therefore serve as a unique means to understand and unify the diverse AGN outflows.

accretion↗

NASA NTRS2019

Atmospheric Correction of Satellite Ocean-Color Imagery During the PACE Era

The Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) mission will carry into space the Ocean Color Instrument (OCI), a spectrometer measuring at 5 nm spectral resolution in the ultraviolet (UV) to near infrared (NIR) with additional spectral bands in the shortwave infrared (SWIR), and two multi-angle polarimeters that will overlap the OCI spectral range and spatial coverage, i. e., the Spectrometer for Planetary Exploration (SPEXone) and the Hyper-Angular Rainbow Polarimeter (HARP2). These instruments, especially when used in synergy, have great potential for improving estimates of water reflectance in the post Earth Observing System (EOS) era. Extending the top-of-atmosphere (TOA) observations to the UV, where aerosol absorption is effective, adding spectral bands in the SWIR, where even the most turbid waters are black and sensitivity to the aerosol coarse mode is higher than at shorter wavelengths, and measuring in the oxygen A-band to estimate aerosol altitude will enable greater accuracy in atmospheric correction for ocean color science. The multi-angular and polarized measurements, sensitive to aerosol properties (e.g., size distribution, index of refraction), can further help to identify or constrain the aerosol model, or to retrieve directly water reflectance. Algorithms that exploit the new capabilities are presented, and their ability to improve accuracy is discussed. They embrace a modern, adapted heritage two-step algorithm and alternative schemes (deterministic, statistical) that aim at inverting the TOA signal in a single step. These schemes, by the nature of their construction, their robustness, their generalization properties, and their ability to associate uncertainties, are expected to become the new standard in the future. A strategy for atmospheric correction is presented that ensures continuity and consistency with past and present ocean-color missions while enabling full exploitation of the new dimensions and possibilities. Despite the major improvements anticipated with the PACE instruments, gaps/issues remain to be filled/tackled. They include dealing properly with whitecaps, taking into account Earth-curvature effects, correcting for adjacency effects, accounting for the coupling between scattering and absorption, modeling accurately water reflectance, and acquiring a sufficiently representative dataset of water reflectance in the UV to SWIR. Dedicated efforts, experimental and theoretical, are in order to gather the necessary information and rectify inadequacies. Ideas and solutions are put forward to address the unresolved issues. Thanks to its design and characteristics, the PACE mission will mark the beginning of a new era of unprecedented accuracy in ocean-color radiometry from space.

Robert J Frouin↗

NASA NTRS2019

Atmospheric Correction of Satellite Ocean-Color Imagery During the PACE Era

The Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) mission will carry into space the Ocean Color Instrument (OCI), a spectrometer measuring at 5 nm spectral resolution in the ultraviolet (UV) to near infrared (NIR) with additional spectral bands in the shortwave infrared (SWIR), and two multi-angle polarimeters that will overlap the OCI spectral range and spatial coverage, i. e., the Spectrometer for Planetary Exploration (SPEXone) and the Hyper-Angular Rainbow Polarimeter (HARP2). These instruments, especially when used in synergy, have great potential for improving estimates of water reflectance in the post Earth Observing System (EOS) era. Extending the top-of-atmosphere (TOA) observations to the UV, where aerosol absorption is effective, adding spectral bands in the SWIR, where even the most turbid waters are black and sensitivity to the aerosol coarse mode is higher than at shorter wavelengths, and measuring in the oxygen A-band to estimate aerosol altitude will enable greater accuracy in atmospheric correction for ocean color science. The multi-angular and polarized measurements, sensitive to aerosol properties (e.g., size distribution, index of refraction), can further help to identify or constrain the aerosol model, or to retrieve directly water reflectance. Algorithms that exploit the new capabilities are presented, and their ability to improve accuracy is discussed. They embrace a modern, adapted heritage two-step algorithm and alternative schemes (deterministic, statistical) that aim at inverting the TOA signal in a single step. These schemes, by the nature of their construction, their robustness, their generalization properties, and their ability to associate uncertainties, are expected to become the new standard in the future. A strategy for atmospheric correction is presented that ensures continuity and consistency with past and present ocean-color missions while enabling full exploitation of the new dimensions and possibilities. Despite the major improvements anticipated with the PACE instruments, gaps/issues remain to be filled/tackled. They include dealing properly with whitecaps, taking into account Earth-curvature effects, correcting for adjacency effects, accounting for the coupling between scattering and absorption, modeling accurately water reflectance, and acquiring a sufficiently representative dataset of water reflectance in the UV to SWIR. Dedicated efforts, experimental and theoretical, are in order to gather the necessary information and rectify inadequacies. Ideas and solutions are put forward to address the unresolved issues. Thanks to its design and characteristics, the PACE mission will mark the beginning of a new era of unprecedented accuracy in ocean-color radiometry from space.

ocean color↗

NASA NTRS1999

Comets after Hyakutake and Hale-Bopp

Being icy, cometary nuclei are the most easily modified bodies in the solar system - even modest heating is sufficient to induce significant weight loss. This sublimative loss and longterm storage far from the sun protect the nucleus against internal warming and ensure that cometary nuclei today contain the least processed material remaining from the early nebula - or perhaps from the natal cloud. The chemical compositions of ices, low temperature-refractory organics, and refractory minerals (and their physical states) provide sensitive probes of the origin and history of this material. The fortunate appearance of Hyakutake and Hale-Bopp has provided a wealth of information on these Oort cloud comets, obtained with a wide range of astronomical approaches. I will review certain key results for these comets, such as chemical abundances, isotopic abundance ratios, nuclear spin statistics, and nuclear vs extended production of "parent volatiles", and will illustrate how these test the origins of cometary material. A comparison with 1P/Halley--a third comet from the giant planet nebular region--will be discussed in the context of heterogeneity among these bodies.

Mumma, Michael J.↗

NASA NTRS1987

Measurements of the free stream fluctuations above a turbulent boundary layer

This paper investigates the velocity fluctuations in the free stream above an incompressible turbulent boundary layer developing at constant pressure. It is assumed that the fluctuations receive contributions from three statistically independent sources: (1) one-dimensional unsteadiness, (2) free stream turbulence, and (3) the potential motion induced by the turbulent boundary layer. Measurements were made in a wind tunnel with a root-mean-square level of the axial velocity fluctuations of about 0.2 percent. All three velocity components were measured using an X-wire probe. The unsteadiness was determined from the spanwise covariance of the axial velocity, measured using two single wire probes. The results show that it is possible to separate the contributions to the r.m.s. level of the velocity fluctuations, without resorting to the dubious technique of high-pass filtering. The separation could be extended to the spectral densities of the contributions, if measurements of sufficient accuracy were available. The Appendix provides a general guide for the measurement of small free stream fluctuation levels.

Wood, David H.↗

NASA NTRS1977

Short-term variations of the galactic cosmic ray intensity - 1964-1967

A statistical analysis of time variations in ground-level nucleonic cosmic-ray intensity for the interval from 1964 to 1967 is presented which incorporates synoptic observations of the solar white-light corona as well as indices of photospheric and chromospheric activity. Correlation analysis of solar activity and short-term modulation reveals that all indices vary significantly on time scales near the solar rotation period and that the correlation function exhibits a quasi-sinusoidal variation that maximizes near zero lag. It is found that 27-day variations of the indices were most pronounced in 1966-1967, that recurrent cosmic-ray depressions occurred in conjunction with observed solar-wind disturbances, and that two categories of interplanetary disturbance are sufficient to account for the large recurrent cosmic-ray depressions in 1966-1967. It is suggested that flare-generated shocks were the main source of these recurrent cosmic-ray variations and that the contribution of corotating cosmic-ray disturbances to the observed recurrent modulation was probably very small. This hypothesis is tested against the correlation functions of solar and cosmic-ray indices.

Parker, G. D.↗

NASA NTRS1991

Non-Gaussian microwave background fluctuations from nonlinear gravitational effects

Whether the statistics of primordial fluctuations for structure formation are Gaussian or otherwise may be determined if the Cosmic Background Explorer (COBE) Satellite makes a detection of the cosmic microwave-background temperature anisotropy delta T(sub CMB)/T(sub CMB). Non-Gaussian fluctuations may be generated in the chaotic inflationary model if two scalar fields interact nonlinearly with gravity. Theoretical contour maps are calculated for the resulting Sachs-Wolfe temperature fluctuations at large angular scales (greater than 3 degrees). In the long-wavelength approximation, one can confidently determine the nonlinear evolution of quantum noise with gravity during the inflationary epoch because: (1) different spatial points are no longer in causal contact; and (2) quantum gravity corrections are typically small-- it is sufficient to model the system using classical random fields. If the potential for two scalar fields V(phi sub 1, phi sub 2) possesses a sharp feature, then non-Gaussian fluctuations may arise. An explicit model is given where cold spots in delta T(sub CMB)/T(sub CMB) maps are suppressed as compared to the Gaussian case. The fluctuations are essentially scale-invariant.

Salopek, D. S.↗