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All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Effective diffusion equation in a random velocity field

The effects are studied of assumed random velocity fields on diffusion in a binary fluid. Random velocity fields can result, for example, from the high-frequency components of residual accelerations onboard spacecraft (often called g-jitter). An effective diffusion equation is derived for an average concentration which includes spatial and temporal correlations induced by the fluctuating velocity fields assumed to be Gaussianly distributed. The resulting equation becomes nonlocal, and if correlations between different components of the velocity field exist, it is also anisotropic. The simple limiting case of short correlation times is discussed and an effective diffusivity is obtained which reflects the enhanced mixing caused by the velocity fields. The results obtained in the limit of short correlation times are valid even if the probability distribution of the velocity field is not Gaussian.

Vinals, Jorge↗
NASA NTRS1993

Optimal thresholds for the estimation of area rain-rate moments by the threshold method

Optimization of the threshold method, achieved by determination of the threshold that maximizes the correlation between an area-average rain-rate moment and the area coverage of rain rates exceeding the threshold, is demonstrated empirically and theoretically. Empirical results for a sequence of GATE radar snapshots show optimal thresholds of 5 and 27 mm/h for the first and second moments, respectively. Theoretical optimization of the threshold method by the maximum-likelihood approach of Kedem and Pavlopoulos (1991) predicts optimal thresholds near 5 and 26 mm/h for lognormally distributed rain rates with GATE-like parameters. The agreement between theory and observations suggests that the optimal threshold can be understood as arising due to sampling variations, from snapshot to snapshot, of a parent rain-rate distribution. Optimal thresholds for gamma and inverse Gaussian distributions are also derived and compared.

Short, David A.↗
NASA NTRS2014

Investigating the Differential Emission Measure and Energetics of Microflares with Combined SDO/AIA and RHESSI Observations

An important question in solar physics is whether solar microflares, the smallest currently observable flare events in X-rays, possess the same energetic properties as large flares. Recent surveys have suggested that microflares may be less efficient particle accelerators than large flares, and hence contribute less non-thermal energy, which may have implications for coronal heating mechanisms. We therefore explore the energetic properties of microflares by combining EUV and X-ray measurements. We present forward-fitting differential emission measure (DEM) analysis of 10 microflares. The fitting is constrained by combining, for the first time, high-temperature Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) observations and flux data from the Solar Dynamics Observatory (SDO) Atmospheric Imaging Assembly (AIA). Two fitting models are tested for the DEM; a Gaussian distribution and a uniform DEM profile. A Gaussian fit proved unable to explain the observations for any of the studied microflares. However, 8 of 10 events studied were reasonably fit by a uniform DEM profile. Hence microflare plasma can be considered to be significantly multi-thermal, and may not be significantly peaked or contain resolvable fine structure, within the uncertainties of the observational instruments. The thermal and non-thermal energy is estimated for each microflare, comparing the energy budget with an isothermal plasma assumption. From the multi-thermal fits the minimum non-thermal energy content was found to average approximately 30% of the estimated thermal energy. By comparison, under an isothermal model the non-thermal and thermal energy estimates were generally comparable. Hence, multi-thermal plasma is an important consideration for solar microflares that substantially alters their thermal and non-thermal energy content.

Sun: flares↗
NASA NTRS1986

Field size distributions for selected agricultural crops in the United States and Canada

Digitized agricultural field boundary taken in the United States and Canada during the LACIE and AgRISTARS programs, in 1977 through 1980, were used to construct histograms showing the distributions of field area, width, and length for crops for which there were data for 700 or more fields per state. The observed distributions of area and width for fields of 10 crops grown in 13 states of the United States and Canada were compared with best-fit inverse Gaussian distributions and with log-normal distributions. For 28 distributions of area and 16 distributions of width there was found to be a probability of greater than .01 of their being inverse Gaussian. There were 10 distributions of area for which there was probability of greater than .005 of their being log-normal. Distributions of area and width stratified by state and crop type appear to be unique. The inverse Gaussian, which represents a wide range of statistical distributions from skewed to almost symmetrical, can provide a useful model for distributions of field area.

Ferguson, M. C.↗
NASA NTRS2023

Sources of L-Band RFI Determined From Kurtosis Using the SMAP Radiometer

Among the parameters of the signal measured by the SMAP radiometer to identify RFI is kurtosis which indicates the departure of the received signal from a gaussian distribution and therefor helpful in identifying RFI. But the kurtosis has the potential to provide additional information. This manuscript reports results of an investigation examining the connection between the level of kurtosis (K) and the characteristics of the source of the RFI. It is shown, for example, that the level of can be used to distinguish the short pulse, relatively wideband RFI associated with radar from the narrow bandwidth signals associated with faulty consumer electronics.

Radio Frequency Interference↗
NASA NTRS1976

A technique for generating correlated X-band weather degradation statistics

It is, known that the X-band noise temperature of DSN receivers can go up from 20 K to over 100 K or more, if the air is heavily laden with water vapor, although that is an uncommon occurrence. It is proposed that the DSN furnish flight projects relying on X-band degradation models, one for each DSN Complex. Such models would be in the form of a random process generator, say in an MBASIC program, that would permit the project to generate X-band degradation data with the right autocorrelations for periods of interest to the Projects. The autocorrelation modeling is especially important because bursts of degradation lasting several days can affect data storage and mission sequence design strategy. One approach which works if the degradation statistics obey a half-gaussian law. That is, the random variables are formed by taking the absolute values of another set of random variables, themselves having a Gaussian distribution. The technique then permits the half-gaussian random variables to have given one and two-step correlation coefficients.

Posner, E. C.↗
NASA NTRS2000

Experience with a Genetic Algorithm Implemented on a Multiprocessor Computer

Numerical experiments were conducted to find out the extent to which a Genetic Algorithm (GA) may benefit from a multiprocessor implementation, considering, on one hand, that analyses of individual designs in a population are independent of each other so that they may be executed concurrently on separate processors, and, on the other hand, that there are some operations in a GA that cannot be so distributed. The algorithm experimented with was based on a gaussian distribution rather than bit exchange in the GA reproductive mechanism, and the test case was a hub frame structure of up to 1080 design variables. The experimentation engaging up to 128 processors confirmed expectations of radical elapsed time reductions comparing to a conventional single processor implementation. It also demonstrated that the time spent in the non-distributable parts of the algorithm and the attendant cross-processor communication may have a very detrimental effect on the efficient utilization of the multiprocessor machine and on the number of processors that can be used effectively in a concurrent manner. Three techniques were devised and tested to mitigate that effect, resulting in efficiency increasing to exceed 99 percent.

Plassman, Gerald E.↗
NASA NTRS2000

Experience with a Genetic Algorithm Implemented on a Multiprocessor Computer

Numerical experiments were conducted to find out the extent to which a Genetic Algorithm (GA) may benefit from a multiprocessor implementation, considering, on one hand, that analyses of individual designs in a population are independent of each other so that they may be executed concurrently on separate processors, and, on the other hand, that there are some operations in a GA that cannot be so distributed. The algorithm experimented with was based on a gaussian distribution rather than bit exchange in the GA reproductive mechanism, and the test case was a hub frame structure of up to 1080 design variables. The experimentation engaging up to 128 processors confirmed expectations of radical elapsed time reductions comparing to a conventional single processor implementation. It also demonstrated that the time spent in the non-distributable parts of the algorithm and the attendant cross-processor communication may have a very detrimental effect on the efficient utilization of the multiprocessor machine and on the number of processors that can be used effectively in a concurrent manner. Three techniques were devised and tested to mitigate that effect, resulting in efficiency increasing to exceed 99 percent.

Plassman, Gerald E.↗
NASA NTRS2011

Constraining the Physical Properties of Meteor Stream Particles by Light Curve Shapes Using the Virtual Meteor Observatory

Different authors have produced models for the physical properties of meteoroids based on the shape of a meteor's light curve, typically from short observing campaigns. We here analyze the height profiles and light curves of approx.200 double-station meteors from the Leonids and Perseids using data from the Virtual Meteor Observatory, to demonstrate that with this web-based meteor database it is possible to analyze very large datasets from different authors in a consistent way. We compute the average heights for begin point, maximum luminosity, and end heights for Perseids and Leonids. We also compute the skew of the light curve, usually called the F-parameter. The results compare well with other author's data. We display the average light curve in a novel way to assess the light curve shape in addition to using the F-parameter. While the Perseids show a peaked light curve, the average Leonid light curve has a more flat peak. This indicates that the particle distribution of Leonid meteors can be described by a Gaussian distribution; the Perseids can be described with a power law. The skew for Leonids is smaller than for Perseids, indicating that the Leonids are more fragile than the Perseids.

Koschny, D.↗
NASA NTRS2022

Study of the Mass-loss Rate from the Sun

We investigate the temporal evolution of the yearly total mass-loss rate (YTMLR) from the Sun through coronal mass ejections (CMEs) over solar cycles 23 and 24. The mass determination of CMEs can be subject to significant uncertainty. To minimize this problem, we have used extensive statistical analysis. For this purpose, we employed data included in the Coordinated Data Analysis Workshop (CDAW) catalog. We estimated the contributions to mass loss from the Sun from different subsamples of CMEs (selected on the basis of their masses, angular widths, and position angles). The temporal variations of the YTMLR were compared to those of the sunspot number (SSN), X-ray flare flux, and the Disturbance Storm Time (Dst) index. We show that the CME mass included in the CDAW catalog reflects with high accuracy the actual mass-loss rate from the Sun through CMEs. Additionally, it is shown that the CME mass distribution in the log-lin representation reflects the Gaussian distribution very well. This means that the CMEs included in the CDAW catalog form one coherent population of ejections that have been correctly identified. Unlike the CME occurrence rate, it turns out that the YTMLR is a very good indicator of solar activity (e.g., SSN) and space weather (e.g., Dst index) consequences. These results are very important, since the YTMLR, unlike the mass loss through solar wind, significantly depends on solar cycles.

the sun↗
NASA NTRS2011

Magnetic Field Strength Fluctuations in the Heliosheath: Voyager 1 Observations during 2009

We analyze the "microscale fluctuations" of the magnetic field strength Beta on a scale of several hours observed by Voyager I (VI) in the heliosheath during 2009. The microscale fluctuations of Beta range from coherent to stochastic structures. The amplitude of microscale fluctuations of Beta during 1 day is measured by the standard deviation (SD) of 48 s averages of B. The distribution of the daily values of SD is lognormal. SD(t) from day of year (DOY) I to 331, 2009, is very intermittent. SD(t) has a 1/f or "pink noise" spectrum on scales from I to 100 days, and it has a broad multi fractal spectrum f(alpha) with 0.57 much < alpha much < 1.39. The time series of increments SD(t + r) - SD(t) has a pink noise spectrum with alpha' = 0.88 +/- 0.14 on scales from 1 to 100 days. The increments have a Tsallis (q-Gaussian) distribution on scales from 1 to 165 days, with an average q = 1.75 +/- 0.12. The skewness S and kurtosis K have Gaussian and lognormal distributions, respectively. The largest spikes in K(t) and Set) are often associated with a change in Beta across a data gap and with identifiable physical structures. The "turbulence" observed by VI during 2009 was weakly compressible on average but still very intermittent, highly variable, and highly compressible at times. The turbulence observed just behind the termination shock by Voyager 2 was twice as strong. These observations place strong constraints on any model of "turbulence" in the heliosheath.

Burlaga, L. F.↗
NASA NTRS2012

Magnetic Field Strength Fluctuations in the Heliosheath: Voyager 1 Observations During 2009

We analyze the microscale fluctuations of the magnetic field strength B on a scale of several hours observed by Voyager1 (V1) in the heliosheath during 2009. The microscale fluctuations of B range from coherent to stochastic structures. The amplitude of microscale fluctuations of B during 1 day is measured by the standard deviation (SD) of 48 s averages of B. The distribution of the daily values of SD is lognormal. SD(t) from day of year (DOY) 1 to 331, 2009, is very intermittent. SD(t) has a 1/f or "pink noise" spectrum on scales from 1 to 100 days, and it has a broad multifractal spectrum f(alpha) with 0.57 less than or equal to alpha less than or equal to 1.39. The time series of increments SD(t + tau) -- SD(t) has a pink noise spectrum with alpha(1) = 0.88 plus or minus 0.14 on scales from 1 to 100 days. The increments have a Tsallis (q-Gaussian) distribution on scales from 1 to 165 days, with an average q = 1.75 plus or minus 0.12. The skewness S and kurtosis K have Gaussian and lognormal distributions, respectively. The largest spikes in K(t) and S(t) are often associated with a change in B across a data gap and with identifiable physical structures. The "turbulence" observed by V1 during 2009 was weakly compressible on average but still very intermittent, highly variable, and highly compressible at times. The turbulence observed just behind the termination shock by Voyager 2 was twice as strong. These observations place strong constraints on any model of turbulence in the heliosheath.

Brulaga, L. F.↗
NASA NTRS1973

Statistics for ionospherically diffracted VHF/UHF signals.

In this paper, a general characterization of the statistics for an ionospherically diffracted, monochromatic plane wave is presented. The main results are restricted to weak scatter, although two possible extensions that accommodate large phase perturbations and multiple scatter are discussed. A detailed discussion of the first-order statistics of amplitude is given. The general Gaussian distribution is discussed together with its Nakagami-distribution approximation and the log-normal distribution. By using a segment of ATS-3 satellite data recorded at Lima, Peru, we show equally good fits to Gaussian and log-normal distributions at least for the limited dynamic range available. The Nakagami distribution provides only a poor approximation.

Rino, C. L.↗
NASA NTRS1982

The influence of varied gravito-inertial fields on the cardiac response of orb-weaving spiders

The Gz transfer function was described for the orb weaving spider A. sericatus. The functional relationship between the heartrate and the intensity of G is linear in the form of: Y = a Log Gz-1 +k. The heartrate in unrestrained animals was recorded by a laser plethysmograph developed specifically for this purpose. Following a control, sample heartrate were taken postrotation between 1.001 and 1.5 Gz in 6 steps. The underlying distribution of heartrates does not appear significantly different from a Gaussian distribution. A method of varnishing the legs of the spider was developed. This was done in order to compromise the lyriform organs, especially those located on the patellae. The lyriform organ is hypothesized to serve the receptor role in the transduction of gravity related stimuli. In preliminary animals the Gz function, post varnishing of the patellae, appears to be changed in the direction of poorer discrimination. We also observed that the resting heartrate following the varnish procedure is substantially increased.

Finck, A.↗
NASA NTRS1987

A new approach to importance sampling for the simulation of false alarms

In this paper a modified importance sampling technique for improving the convergence of Importance Sampling is given. By using this approach to estimate low false alarm rates in radar simulations, the number of Monte Carlo runs can be reduced significantly. For one-dimensional exponential, Weibull, and Rayleigh distributions, a uniformly minimum variance unbiased estimator is obtained. For Gaussian distribution the estimator in this approach is uniformly better than that of previously known Importance Sampling approach. For a cell averaging system, by combining this technique and group sampling, the reduction of Monte Carlo runs for a reference cell of 20 and false alarm rate of lE-6 is on the order of 170 as compared to the previously known Importance Sampling approach.

Lu, D.↗
NASA NTRS1994

Truncated Gaussians as tolerance sets

This work focuses on the use of truncated Gaussian distributions as models for bounded data measurements that are constrained to appear between fixed limits. The authors prove that the truncated Gaussian can be viewed as a maximum entropy distribution for truncated bounded data, when mean and covariance are given. The characteristic function for the truncated Gaussian is presented; from this, algorithms are derived for calculation of mean, variance, summation, application of Bayes rule and filtering with truncated Gaussians. As an example of the power of their methods, a derivation of the disparity constraint (used in computer vision) from their models is described. The authors' approach complements results in Statistics, but their proposal is not only to use the truncated Gaussian as a model for selected data; they propose to model measurements as fundamentally in terms of truncated Gaussians.

Cozman, Fabio↗
NASA NTRS1977

An estimate of field size distributions for selected sites in the major grain producing countries

The field size distributions for the major grain producing countries of the World were estimated. LANDSAT-1 and 2 images were evaluated for two areas each in the United States, People's Republic of China, and the USSR. One scene each was evaluated for France, Canada, and India. Grid sampling was done for representative sub-samples of each image, measuring the long and short axes of each field; area was then calculated. Each of the resulting data sets was computer analyzed for their frequency distributions. Nearly all frequency distributions were highly peaked and skewed (shifted) towards small values, approaching that of either a Poisson or log-normal distribution. The data were normalized by a log transformation, creating a Gaussian distribution which has moments readily interpretable and useful for estimating the total population of fields. Resultant predictors of the field size estimates are discussed.

Podwysocki, M. H.↗
NASA NTRS2010

Sectors and Large-Scale Magnetic Field Strength Fluctuations in the Heliosheath Near 110 AU: Voyager 1,2009

This paper describes observations of daily averages of the magnetic field strength B and the magnetic polarity measured by Voyager 1 (V1) in the heliosheath during 2009 between 108.5 and 112.1 AU and at heliographic latitude 34. . 4. A negative magnetic polarity sector was observed during 2009 DOY 43.255. A positive polarity sector was observed during 2009 DOY 256.365. We offer the hypothesis that the existence of the two sectors is the result of the displacement of the wavy heliospheric current sheet to the position of V1 as a result of northward flow in the heliosheath. The large size of the sectors is caused by the slow radial motion of the flow observed by V1 in the heliosheath. The distribution of B during 2009 was lognormal, in contrast to the Gaussian distributions observed by V1 in the heliosheath prior to 2009. The large-scale fluctuations of B, described by the distribution of increments of daily averages of B, have a Tsallis distribution with q = 1.6. The large-scale fluctuations of B observed by V1 during 2009 have a multifractal spectrum with the same parameters that V1 observed during 2005 close to the termination shock at 94 AU. These results suggest that the large-scale magnetic fluctuations of B are in a metastable equilibrium state in the heliosheath between 94 AU and 112.1 AU.

Burlaga, L. F.↗