On the Distribution of the Sum of Independent Doubly Truncated Gamma Variables
Pearson distribution of doubly truncated gamma variables
Lavender, D. E.↗
SEARCH · Engineering Papers
Results for “gamma distribution”
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.
On the bimodal distribution of gamma-ray bursts
Kouveliotou et al. recently confirmed that gamma-ray bursts are bimodal in duration. In this paper we compute the statistical properties of the short (less than or = 2 s) and long (greater than 2 s) bursts using a method of analysis that makes no assumption regarding the location of the bursts, whether in the Galaxy or at a cosmological distance. We find the 64 ms channel on Burst and Transient Source Experiment (BATSE) to be more sensitive to short bursts and the 1024 ms channel to be more sensitive to long bursts. We show that all the currently available data are consistent with the simple hypothesis that both short and long bursts have the same spatial distribution and that within each population the sources are standard candles. The rate of short bursts per unit volume is about 40% of the rate of long bursts. Although the durations of short and long gamma-ray bursts span several orders of magnitude and the total energy of a typical short burst is smaller than that of a typical long burst by a factor of about 20, surprisingly the peak luminosities of the two kinds of bursts are equal to within a factor of about 2.
Mao, Shude↗
The effects of pure density evolution on the brightness distribution of cosmological gamma-ray bursts
In this work, we explore the effects of burst rate density evolution on the observed brightness distribution of cosmological gamma-ray bursts. Although the brightness distribution of gamma-ray bursts observed by the BATSE experiment has been shown to be consistent with a nonevolving source population observed to redshifts of order unity, evolution of some form is likely to be present in the gamma-ray bursts. Additionally, nonevolving models place significant constraints on the range of observed burst luminosities, which are relaxed if evolution of the burst population is present. In this paper, three analytic forms of density evolution are examined. In general, forms of evolution with densities that increase monotonically with redshift require that the BATSE data correspond to bursts at larger redshifts, or to incorporate a wider range of burst luminosities, or both. Independent estimates of the maximum observed redshift in the BATSE data and/or the range of luminosity from which a large fraction of the observed bursts are drawn therefore allow for constraints to be placed on the amount of evolution that may be present in the burst population. Specifically, if recent measurements obtained from analysis of the BATSE duration distribution of the actual limiting redshift in the BATSE data at z(sub lim) = 2 are correct, the BATSE N(P) distribution in a Lambda = 0 universe is inconsistent at a level of approximately 3 alpha with nonevolving gamma-ray bursts and some form of evolution in the population is required. The sense of this required source evolution is to provide a higher density, larger luminosities, or both with increasing redshift.
Horack, J. M.↗
A discrete dislocation dynamics study of precipitate bypass mechanisms in nickel-based superalloys
Order strengthening in nickel-based superalloys is associated with the extra stress required for dislocations to bypass the $\gamma'$ precipitates distributed in the $\gamma$ matrix. Depending on the operating conditions and microstructure, a rich variety of bypass mechanism has been identified, with various shearing and Orowan looping processes gradually giving way to climb bypass as the operating conditions change from the low/intermediate temperatures and high stress regime, to the high temperature and low stress regime. When anti phase boundary (APB) shearing and Orowan looping mechanisms operate, the classical picture is that, at for a given volume fraction, the bypass mechanism changes from shearing to looping with increased particle size and within a broad coexistence size window. Another possibility, which is supported by indirect experimental evidence, is that a third “hybrid” transition mechanism may operate. Here, in this paper we use discrete dislocation dynamics (DDD) simulations to study dislocation bypass mechanisms in Ni-based superalloys. We develop a new method to compute generalized stacking fault forces in DDD simulations, based on a concept borrowed from complex analysis and known as the winding number of a closed curve about a point. We use this method to study the mechanisms of bypass of a square lattice of spherical $\gamma'$ precipitates by $a/2\langle110\rangle$ {111} edge dislocations, as a function of the precipitates volume fraction and size. We show that not only the hybrid mechanism is possible, but also that it operates as the transition mechanism between the shearing and looping regimes over a wide range of precipitates volume fraction and radii. Based on our simulation results, we propose a simple model for the strength of this mechanism. We also consider the effects of a $\gamma$/$\gamma'$ lattice misfit on the bypass mechanisms, which we approximate by an additional precipitate stress computed according to Eshelby’s inclusion theory. We show that in the shearing and hybrid looping-shearing regimes, a lattice misfit generally results in an increased bypass stress. For sufficiently high lattice misfit, the critical bypass configuration in attractive dislocation-precipitates interactions changes dramatically, and the bypass stress is controlled by the pinning of the trailing dislocation on the exit side of the precipitates, similar to what has been reported in the high-temperature creep literature.
36 MATERIALS SCIENCE↗
cdf_normalize
The code performs image intensity normalization. A new intensity normalization method is presented, which works well with images whose pixel intensity distribution follow a Gamma Probability Distribution. Some examples are provided to show the normalization effect. This new intensity normalization method is also compared to some other well-established intensity normalization methods.
Mundhenk, TerrellN.↗
The question of radiation source geometry
Fast neutron and gamma radiation flux distribution from isotropically radiation sources
RADIATION DISTRIBUTION↗
No new limit on the size distribution of gamma-ray bursts
The results of a study (Carter et. al.) of gamma ray bursts using long duration balloon exposure are analyzed. Arguments are presented against the conclusion that the size spectrum extrapolates to a power law with index from -1.0 to -0.5, and that therefore the gamma ray bursts are of galactic origin. It is claimed that the data are consistent with an upper limit over 100 times that proposed, and that therefore no conclusion can be drawn from the measurements regarding the nature or origin of gamma ray bursts. The resulting upper limit to the rate of occurrence of small bursts lies above the -1.5 index power law extrapolation of the size spectrum of known events, i.e., greater than the rate expected from an infinitely extended source region.
Cline, T. L.↗
No new limit on size distribution of gamma-ray bursts
It is argued that the results of Carter et al. (1976), who derived an upper limit to the balloon intensity of small gamma-ray bursts at about 100 below the extrapolated known size spectrum and therefore concluded that the gamma-ray bursts are of galactic origin, are entirely consistent with the -1.5 index power-law extrapolation, so that no conclusion regarding the origin of gamma-ray bursts can be drawn. A reply of Carter et al. is published. Points at issue include: (1) whether a selection criterion of three successive 0.6-sec increases in the gamma-ray count rate ignores a significant or only a small number of events, (2) whether the spectra of all bursts extend below 100 keV, the satellite energy threshold, and (3) the required correction for the distortion of a horizontal, flat detector.
Cline, T. L.↗
Statistical wind profile gust model
A statistical wind profile gust model for the Space Transportation Operations and Trade Studies is developed by using 1800 Jimsphere wind profile data collected at Cape Kennedy during 1965 to 1972. Wind profiles from the surface to 20 km in component form, i.e., zonal and meridional are processed through the digital filters of different wave length ranges bases on the Martin-Graham cosine rolloff model. The residuals obtained from the filtering processes for the data base for the statistical analysis. For each wind component the gust and gust length at a specified reference altitude in a residual profile are defined. A two parameter gamma probability marginal distribution seems to fit the component gust amplitude and the gust length when redefined. The problem of finding an appropriate bivariate joint distribution of the gust amplitude and length remains to be solved. The probability distribution of the modulus of the gust amplitudes was derived under the assumption that they are independently distributed as gamma variates.
Doss, D. C.↗
GRB 050826: A Subluminous Event at z=0.296 Finds Its Place in the Luminosity Distribution of Gamma-Ray Burst Afterglows
We present the optical identification and spectroscopy of the host galaxy of GRB 050826 at redshift z = 0.296 +/- 0.001. Image subtraction among observations obtained on three consecutive nights reveals a fading object 5 hr after the burst, confirming its identification as the optical afterglow of this event. Deep imaging shows that the optical afterglow is offset by 0.4" (1.76 kpc) from the center of its irregular host galaxy, which is typical for long-duration gamma-ray bursts. Combining these results with X-ray measurements acquired by the Swift XRT instrument, we find that GRB 050826 falls entirely within the subluminous, subenergetic group of long gamma-ray bursts at low redshift (z less than or equal to 0.3). The results are discussed in the context of models that possibly account for this trend, including the nature of the central engine, the evolution of progenitor properties as a function of redshift, and incompleteness in current gamma-ray burst samples.
Mirabal, N.↗
The distribution of cosmological gamma-ray bursts
We compare the burst distribution of the Burst and Transient Source Experiment (BATSE)-2B catalog to a cosmological distribution. The observed distribution agrees well with a cosmological one, however, it is insensitive to cosmological parameters such as omega and lambda. The bursts are not necessarily standard candles, and their luminosity can vary by up to a factor of 10. The maximal redshift, z(sub max), of bursts longer than 2 s is 2.1(sup +1)(sub -0.7) (assuming no evolution). The present data is insufficient to determine maximal redshift, z(sub max), of bursts shorter than 2 s.
Cohen, Ehud↗
$\gamma$-ray angular correlations, distributions and linear polarization in tracking arrays
With $\gamma $-ray tracking arrays, the angular correlation and, especially, the linear polarization of $\gamma $ rays can be measured with high precision. However, because of the complexity of these spectrometers, measuring angular distributions is more involved. The techniques and associated formalisms were developed and established in the 1950s. The experimental setups of that era were relatively simple when compared to the advanced $\gamma $-ray tracking arrays available today. This paper aims to review and refine these techniques, unify the nomenclatures and, specifically, adapt them for use with the newest tracking arrays. In addition, new methods for producing the required response functions for these arrays are introduced.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Galactic distribution models of gamma-ray burst sources
The log N-log S relationships for several galactic distribution models of gamma-ray burst sources are derived. The resulting curves are substantially different from the galactic curves usually assumed (slope = -1). There is a relatively weak dependence on the radial distribution assumed but a strong dependence on scale height. Available observational data from several experiments appear to rule out both thin disk distributions and extended halo distributions which have a strong radial density dependence. The prospects are good for obtaining self-consistent distribution data from future large-area detectors.
Fishman, G. J.↗
Drop Size Distribution Measurements Supporting the NASA Global Precipitation Measurement Mission: Infrastructure and Preliminary Results
Global Precipitation Measurement Mission (GPM) retrieval algorithm validation requires datasets that characterize the 4-D structure, variability, and correlation properties of hydrometeor particle size distributions (PSD) and accumulations over satellite fields of view (5 -- 50 km). Key to this process is the combined use of disdrometer and polarimetric radar platforms. Here the disdrometer measurements serve as a reference for up-scaling dual-polarimetric radar observations of the PSD to the much larger volumetric sampling domain of the radar. The PSD observations thus derived provide a much larger data set for assessing DSD variability, and satellite-based precipitation retrieval algorithm assumptions, in all three spatial dimensions for a range of storm types and seasons. As one component of this effort, the GPM Ground Validation program recently acquired five 3rd generation 2D Video disdrometers as part of its Disdrometer and Radar Observations of Precipitation Facility (DROP), currently hosted in northern Alabama by the NASA Marshall Space Flight Center and the University of Alabama in Huntsville. These next-generation 2DVDs were operated and evaluated in different phases of data collection under the scanning domain of the UAH ARMOR C-band dual-polarimetric radar. During this period approximately 7500 minutes of PSD data were collected and processed to create gamma size distribution parameters using a truncated method of moments approach. After creating the gamma parameter datasets the DSDs were then used as input to T-matrix code for computation of polarimetric radar moments at C-band. The combined dataset was then analyzed with two basic objectives in mind: 1) the investigation of seasonal variability in the rain PSD parameters as observed by the 2DVDs; 2) the use of combined polarimetric moments and observed gamma distribution parameters in a functional form to retrieve PSD parameters in 4-D using the ARMOR radar for precipitation occurring in different seasons and for different rain system types. Preliminary results suggest that seasonal variations in the DSD parameters do occur, but are most pronounced when comparing tropical PSDs to either winter or summer convective precipitation. For example the previously documented shift to relatively smaller drop diameters in higher number concentrations for equivalent rain rate bins was observed in tropical storm rainbands occurring over Huntsville. On a more inter seasonal basis empirical fits between parameters such as D0 and ZDR do not appear to exhibit robust seasonal biases- i.e., one fit seems to work for all seasons within acceptable standard error (O[10%]) for estimates of D0. In polarimetric retrievals of the vertical variability in PSD (rain layer) for a tropical rainband we find that the Do varies with height when partitioned by specified precipitation categories (e.g., convective or stratiform, heavy and light stratiform etc.) but this variation is of order 10-20% and is smaller than the difference in D0 observed between the basic delineation of convective and stratiform precipitation types. Currently we are expanding our analysis of the vertical structure of the PSD to include several seasonally and/or dynamically-different storm system types (e.g., winter convection and stratiform events; summer mid-latitude convective etc.) sampled by ARMOR. The study will present the results of our combined analyses.
Petersen, Walter A.↗
Requirements Description of GAMSOR and GAMSRC
This report presents the modeling and simulation capabilities of Argonne National Laboratory’s GAMSOR and GAMSRC code that is used in present reactor analysis activities. These capabilities will then be used to establish the set of verification tasks necessary to verify GAMSOR for use on commercial projects. A similar approach was taken for the PERSENT, REBUS and DIF3D software packages. The GAMSOR program is a modified version of DIF3D used to obtain the coupled neutron gamma flux distributions for a given reactor system. GAMSOR was first developed in the 1980s and its work has progressed in parallel with DIF3D throughout its various development phases. While GAMSOR is compatible with DIF3D-FD and DIF3D-Nodal, DIF3D-VARIANT is most commonly used today and will be the focus of the present verification effort. As covered in [1], GAMSOR was built to provide more accurate heating distributions by explicitly solving for both the gamma and neutron heating distributions. Without this consideration, gamma heat is normally assumed to be deposited locally at the site of gamma production. This is acceptable for modeling some phenomena because the total energy production is preserved, but it can lead to inaccurate approximations of fluence-dependent behaviors such as fuel performance, swelling, cladding embrittlement, radiation induced creep, and power peaking. The outputs from GAMSOR are contained in multiple intermediate and final output files: FIXSRC, VARSRC, GTFLUX, GHFLUX, PWDINT, NPDINT, and GPDINT. DIF3D normally produces a PWDINT file containing power density results, with the assumption that gamma rays are absorbed where they are emitted (i.e., energy deposition is local with no modeled transport). With GAMSOR, neutron power density (NPDINT) and gamma power density (GPDINT) are both produced, with their summed power densities replacing the results in PWDINT for total heating (i.e., recoverable) power density.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Atmospheric gamma ray angle and energy distributions from 2 to 25 MeV
Results are given for gamma ray fluxes in six energy intervals from 2-25 MeV and five zenith angle intervals from 0-50 deg (downward moving) and five from 130-180 deg (upward moving). Observations were obtained with the University of California, Riverside double Compton scatter gamma ray telescope flown on a balloon to a 3.0 g/sq cm residual atmosphere at a geomagnetic cuttoff of 4.5 GV. It was found that the angular distribution of downward moving gamma rays is relatively flat, increasing slowly from 10-40 deg. The angular distribution of the upward moving gamma rays at 4.2 g/sq cm increases with angle from the vertical. Energy distributions of upward and downward moving gamma rays are in good agreement with the results of previous studies.
Ryan, J. M.↗
Internal Luminosity Distribution of Bright Gamma-Ray Bursts and its Relation to Duration and Spectral Hardness
We present first results from a comprehensive investigation into the distribution of luminosity within the 50 brightest cosmic gamma-ray bursts detected by the Burst and Transient Source Experiment (BATSE). The internal luminosity function psi(L) is defined such that the quantity psi(L)dL represents the fraction of total emission time during which the burst possesses a luminosity between L and L + dL. For these brightest bursts, the psi(L) functions are quasi-power-law-like and decrease in amplitude with increasing luminosity. Through investigation of both individual psi(L) distributions and data from the ensemble of bursts, we demonstrate a high probability for correlation between the shape of the internal luminosity function as measured by the average logarithmic slope and the burst duration as measured by the T(sub 90) parameter and, with lower significance, between the shape of psi(L) and the burst photon-fluence spectral index. We furthermore demonstrate a correlation between burst hardness ratio and duration in these brightest bursts which is opposite to that of the entire gamma-ray burst ensemble.
Horack, John M.↗
The Intensity Distribution of Faint Gamma-Ray Bursts Detected with BATSE
We have recently completed a search of 6 years of archival BATSE data for gamma-ray bursts (GRBS) that were too faint to activate the real-time burst detection system running on board the spacecraft. These "nontriggered" bursts can be combined with the "triggered" bursts detected on board to produce a GRB intensity distribution that reaches peak fluxes a factor of approximately 2 lower than could be studied previously. The value of the statistic (in Euclidean space) for the bursts we detect is 0.177 plus or minus 0.006. This surprisingly low value is obtained because we detected very few bursts on the 4.096 s and 8.192 s timescales (where most bursts have their highest signal-to-noise ratio) that were not already detected on the 1.024 s timescale. If allowance is made for a power-law distribution of intrinsic peak luminosities, the extended peak flux distribution is consistent with models in which the redshift distribution of the gamma-ray burst rate approximately traces the star formation history of the universe. We argue that this class of models is preferred over those in which the burst rate is independent of redshift. We use the peak flux distribution to derive a limit of 10% (99% confidence) on the fraction of the total burst rate that could be contributed by a spatially homogeneous (in Euclidean space) subpopulation of burst sources, such as type lb/c supernovae. These results lend support to the conclusions of previous studies predicting that relatively few faint "classical" GRBs will be found below the BATSE onboard detection threshold.
Kommers, Jefferson M.↗