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This final report is a study of gamma-ray luminosity function of radio pulsars. The goal is to constrain certain parameters in order to address such diverse issues as the high energy emission mechanism in pulsars and the fraction of the Galaxy's gamma ray emission attributable to these objects.
Developing high-speed variable accuracy method for computing ordered sequences of incomplete gamma function
A beta distribution is specified by range parameters a b, and two shape parameters alpha and beta 0. The computer program presented calculates any desired probability and/or fractile point for specified values of a, b, alpha, and beta. This program additionally computes gamma function values for integer and noninteger arguments.
We present charge coupled device (CCD) photometry and spectroscopy for stars in Lucke-Hodge 58, an isolated OB association in the Large Magellanic Cloud (LMC) northwest of 30 Doradus. The photometric catalog contains 839 stars with UBV magnitudes complete to V approximately = 19. We have obtained spectra and classified 35 stars; combined with previous published spectral types, we find 22 O-type stars. The earliest type is O3-4 V, and there are three Wolf-Rayet (WR) stars in the association. The slope of the initial mass function, Gamma = -1.7 +/- 0.3, is in good agreement with other LMC associations. The presence of several evolved supergiants with masses about 15-25 solar mass suggests that some star formation took place as early as 10 million years ago, but the majority of stars formed coevally within the past few million years.
A new technique for measuring cloud liquid water, mean droplet radius and droplet number density is outlined. The technique is based on simultaneously measuring Raman and Mie scattering from cloud liquid droplets using a Raman lidar. Laboratory experiments on liquid micro-spheres have shown that the intensity of Raman scattering is proportional to the amount of liquid present in the spheres. This fact is used as a constraint on calculated Mie intensity assuming a gamma function particle size distribution. The resulting retrieval technique is shown to give stable solutions with no false minima. It is tested using Raman lidar data where the liquid water signal was seen as an enhancement to the water vapor signal. The general relationship of retrieved average radius and number density is consistent with traditional cloud physics models. Sensitivity to the assumed maximum cloud liquid water amount and the water vapor mixing ratio calibration are tested. Improvements to the technique are suggested.
Calculations of reaction rates for the third-order QED process of photon splitting gamma yields gamma.gamma in strong magnetic fields traditionally have employed either the effective Lagrangian method or variants of Schwinger's proper-time technique. Recently, Mentzel, Berg and Wunner [1] presented an alternative derivation via an S-matrix formulation in the Landau representation. Advantages of such a formulation include the ability to compute rates near pair resonances above pair threshold. This paper presents new developments of the Landau representation formalism as applied to photon splitting, providing significant, advances beyond the work of [1] by summing over the spin quantum numbers of the electron propagators, and analytically integrating over the component of momentum of the intermediate states that is parallel to field. The ensuing tractable expressions for the scattering amplitudes are satisfyingly compact, and of an appearance familiar to S-matrix theory applications. Such developments can facilitate numerical computations of splitting considerably both below and above pair threshold. Specializations to two regimes of interest are obtained, namely the limit of highly supercritical fields and the domain where photon energies are far inferior to that for the threshold of single-photon pair creation. In particular, for the first time the low-frequency amplitudes are simply expressed in terms of the Gamma function, its integral and its derivatives. In addition, the equivalence of the asymptotic forms in these two domains to extant results from effective Lagrangian/proper- time formulations is demonstrated.
Observations by the airborne X-band Doppler radar (EDOP) and the NCAR S-band polarimetric (S-POL) radar from two field experiments are used to evaluate the Surface ref'ercnce technique (SRT) for measuring the path integrated attenuation (PIA) and to study attenuation in deep convective storms. The EDOP, flying at an altitude of 20 km, uses a nadir beam and a forward pointing beam. It is found that over land, the surface scattering cross-section is highly variable at nadir incidence but relatively stable at forward incidence. It is concluded that measurement by the forward beam provides a viable technique for measuring PIA using the SRT. Vertical profiles of peak attenuation coefficient are derived in vxo deep convective storms by the dual-wavelength method. Using the measured Doppler velocity, the reflectivities at. the two wavelengths, the differential reflectivity and the estimated attenuation coefficients, it is shown that: supercooled drops and dry ice particles probably co-existed above the melting level in regions of updraft, that water-coated partially melted ice particles probably contributed to high attenuation below the melting level, and that the data are not readil~ explained in terms of a gamma function raindrop size distribution.
Although most parameterizations of the drop size distributions (DSD) use the gamma function, there are several advantages to the log-normal form, particularly if we want to characterize the large scale space-time variability of the DSD and rain rate. The advantages of the distribution are twofold: the logarithm of any moment can be expressed as a linear combination of the individual parameters of the distribution; the parameters of the distribution are approximately normally distributed. Since all radar and rainfall-related parameters can be written approximately as a moment of the DSD, the first property allows us to express the logarithm of any radar/rainfall variable as a linear combination of the individual DSD parameters. Another consequence is that any power law relationship between rain rate, reflectivity factor, specific attenuation or water content can be expressed in terms of the covariance matrix of the DSD parameters. The joint-normal property of the DSD parameters has applications to the description of the space-time variation of rainfall in the sense that any radar-rainfall quantity can be specified by the covariance matrix associated with the DSD parameters at two arbitrary space-time points. As such, the parameterization provides a means by which we can use the spaceborne radar-derived DSD parameters to specify in part the covariance matrices globally. However, since satellite observations have coarse temporal sampling, the specification of the temporal covariance must be derived from ancillary measurements and models. Work is presently underway to determine whether the use of instantaneous rain rate data from the TRMM Precipitation Radar can provide good estimates of the spatial correlation in rain rate from data collected in 5(sup 0)x 5(sup 0) x 1 month space-time boxes. To characterize the temporal characteristics of the DSD parameters, disdrometer data are being used from the Wallops Flight Facility site where as many as 4 disdrometers have been used to acquire data over a 2 km path. These data should help quantify the temporal form of the covariance matrix at this site.
We have employed a Hamiltonian model based on a self-consistent Gaussian appoximation to examine the unfolding process of proteins in external - both mechanical and thermal - force elds. The motivation was to investigate the unfolding pathways of proteins by including only the essence of the important interactions of the native-state topology. Furthermore, if such a model can indeed correctly predict the physics of protein unfolding, it can complement more computationally expensive simulations and theoretical work. The self-consistent Gaussian approximation by Micheletti et al. has been incorporated in our model to make the model mathematically tractable by signi cantly reducing the computational cost. All thermodynamic properties and pair contact probabilities are calculated by simply evaluating the values of a series of Incomplete Gamma functions in an iterative manner. We have compared our results to previous molecular dynamics simulation and experimental data for the mechanical unfolding of the giant muscle protein Titin (1TIT). Our model, especially in light of its simplicity and excellent agreement with experiment and simulation, demonstrates the basic physical elements necessary to capture the mechanism of protein unfolding in an external force field.
Use of dual-wavelength radar, with properly chosen wavelengths, will significantly lessen the ambiguities in the retrieval of microphysical properties of hydrometeors. In this paper, a dual-wavelength algorithm is described to estimate the characteristic parameters of the snow size distributions. An analysis of the computational results, made at X and Ka bands (T-39 airborne radar) and at S and X bands (CP-2 ground-based radar), indicates that valid estimates of the median volume diameter of snow particles, D(sub 0), should be possible if one of the two wavelengths of the radar operates in the non-Rayleigh scattering region. However, the accuracy may be affected to some extent if the shape factors of the Gamma function used for describing the particle distribution are chosen far from the true values or if cloud water attenuation is significant. To examine the validity and accuracy of the dual-wavelength radar algorithms, the algorithms are applied to the data taken from the Convective and Precipitation-Electrification Experiment (CaPE) in 1991, in which the dual-wavelength airborne radar was coordinated with in situ aircraft particle observations and ground-based radar measurements. Having carefully co-registered the data obtained from the different platforms, the airborne radar-derived size distributions are then compared with the in-situ measurements and ground-based radar. Good agreement is found for these comparisons despite the uncertainties resulting from mismatches of the sample volumes among the different sensors as well as spatial and temporal offsets.
FATIG computes fatigue damage/fatigue life using the stress rms (root mean square) value, the total number of cycles, and S-N curve parameters. The damage is computed by the following methods: (a) traditional method using Miner s rule with stress cycles determined from a Rayleigh distribution up to 3*sigma; and (b) classical fatigue damage formula involving the Gamma function, which is derived from the integral version of Miner's rule. The integration is carried out over all stress amplitudes. This software solves the problem of probabilistic fatigue damage using the integral form of the Palmgren-Miner rule. The software computes fatigue life using an approach involving all stress amplitudes, up to N*sigma, as specified by the user. It can be used in the design of structural components subjected to random dynamic loading, or by any stress analyst with minimal training for fatigue life estimates of structural components.
The variability of cirrus ice microphysical properties is investigated using observations obtained during the Small Particles in Cirrus (SPARTICUS) campaign. An existing approach that represents a size distribution (SD) as a single gamma function using an ellipsoid of equally realizable solutions in (N(sub 0), lambda, mu) phase space is modified to automatically identify multiple modes in SDs and characterize each mode by such an ellipsoid. The modified approach is applied to ice crystals with maximum dimension D greater than15 micrometers collected by the 2-D stereo and 2-D precipitation probes on the Stratton Park Engineering Company Learjet. The dependencies of N(sub 0), mu, and lambda from each mode, total number concentration, bulk extinction, ice water content (IWC), and mass median maximum dimension D(sub mm) as a function of temperature T and cirrus type are then analyzed. The changes in the observed codependencies between N(sub 0), mu, and lambda, bulk extinction, IWC, and D(sub mm) with environmental conditions indicate that particles were larger at higher T during SPARTICUS. At most two modes were observed in any SD during SPARTICUS, with the average boundary between them at 115 micrometers, similar to past studies not using probes with shatter mitigating tips and artifact removal algorithms. The bimodality of the SDs increased with T. This and the differences in N(sub 0), mu, and lambda between the modes suggest that particles with smaller D nucleated more recently than particles with larger D, which grew via vapor deposition and aggregation. Because smaller crystals, whose concentrations are uncertain, make marginal contributions to higher order moments, the use of higher moments for evaluating model fields is suggested.
GPM DSD retrievals exhibit inconsistencies between GV, DPR and Combined algorithm retrievals. Development of positive bias in convective Dm rain DSD noted, and strongest in KuPR retrieval. Associated epsilons are too low and result in markedly reduced convective rain rates (a current issue in the retrievals). Source may be NUBF. Issues with the large end of the DSD not withstanding, on the small end of the DSD, combined MPS and 2DVD measurements fit with generalized gamma functions exhibit strong potential for representing the entire spectrum of the DSD and subsequently the whole rain rate spectrum.
In this study, we evaluate a decadal ozone profile record derived from Suomi NPP Ozone Mapping and Profiler Suite (OMPS) Limb Profiler (LP). The data from OMPS LP were re-processed with the new retrieval algorithm from 2012 to present. The new reprocessing includes adjustments in both Level 1 and Level 2 algorithms. The sensor’s altitude registration, updates in radiometric calibrations, under-sampling and stray light corrections were addressed in Level 1 processing. The new retrieval algorithm (version 2.7) combines measurements from UV and VIS parts of the spectra to retrieve a single vertical ozone profile between 12.5 km (or cloud tops) and 57.5 km, unlike to previous version 2.5 where ozone profiles were retrieved independently from UV and VIS. To improve ozone retrievals in the Upper Troposphere Lower Stratosphere (UTLS) region, we implemented a new aerosol correction that assumes a gamma-function particle size distribution. In addition, ozone and nitrogen dioxide cross sections and climatologies were updated. We discuss sensitivity of the ozone retrievals to implemented changes in Level 1 and Level 2 algorithms. We focus our analysis on evaluation of the stability of the 10-year record from OMPS LP. We show results from the internal methods for characterizing the stability of the LP altitude registration and compare the LP reflectivity and ozone with the similar quantities measured by OMPS nadir sensors. Finally, we will show results from comparisons with independent satellite (MLS and SAGE III) and ozone sonde measurements.
In this presentation we evaluate ozone profile retrievals from Ozone Mapping and Profiling Suite Limb Profiler (OMPS-LP) launched in October 2011 on Suomi NPP satellite. The data from OMPS-LP were re-processed with the new retrieval algorithm that combines measurements from UV and VIS parts of the spectra to retrieve a single ozone profile between 12.5 km (or cloud tops) and 57.5 km. To improve ozone retrievals in the Upper Troposphere Lower Stratosphere (UTLS) region, a new aerosol correction with a gamma-function particle size distribution was implemented. The OMPS-LP altitude registration was also adjusted in the new version to ensure the stability of the ozone record. The continuous ozone profile observations with Suomi NPP OMPS LP exceeds 10 years. We will compare OMPS-LP ozone profiles with coincident stratospheric ozone measurements from NASA Aura MLS, ISS SAGE III, and OMPS NP and with the observations in UTLS and middle stratosphere from a ground-based network of ozone sonde stations to evaluate accuracy and precision of OMPS-LP retrievals and overall stability of the record. We will also investigate the quality of stratospheric ozone columns obtained from OMPS-LP and estimate the contribution of various errors to integrated stratospheric columns from OMPS-LP.
We evaluate a decadal ozone profile record derived from the Suomi National Polar-orbiting Partnership (SNPP) Ozone Mapping and Profiler Suite (OMPS) Limb Profiler (LP) satellite instrument. In 2023, the OMPS LP data were re-processed with the new version 2.6 retrieval algorithm that combines measurements from the ultraviolet (UV) and visible (VIS) parts of the spectra and employs the second order Tikhonov regularization to retrieve a single vertical ozone profile between 12.5 km (or cloud tops) and 57.5 km with the vertical resolution of about 1.9 - 2.5 km between 20-55 km. The algorithm uses radiances measured at six UV ozone-sensitive wavelengths (295, 302, 306, 312, 317 and 322 nm) paired with 353 nm, and one VIS wavelength at 606 nm combined with 510 nm and 675 nm to form a triplet. Each wavelength pair or triplet is used over a limited range of tangent altitudes where the sensitivity to ozone changes are strongest. A new implemented aerosol correction scheme is based on a gamma-function particle size distribution. Numerous calibration changes that affected ozone retrievals were also applied to measured LP radiances, including updates in altitude registration, radiometric calibration, stray light, and spectral registration. The key version 2.6 improvement is the reduction in relative drifts between LP ozone and correlative measurements, linked previously to a drift in the version 2.5 LP altitude registration. We compare LP ozone profiles with those from Aura Microwave Limb Sensor (MLS) to quantify ozone changes in version 2.6.
We have utilized the integral moment analysis technique of Horack & Emslie to extract information on the allowable form of the luminosity function for gamma-ray bursts observed by Burst and Transient Source Experiment (BATSE). Using the general properties of moments, we are able to derive constraints on the range of luminosity from which the gamma-ray bursts must be sampled. These constraints are independent of the form of the radial distribution of the gamma-ray bursts, and depend only on the assumptions that space is Euclidean and that the luminosity function phi(L) is distance independent. For power-law luminosity functions of the form phi(L) = A(sub 0)L(exp -alpha), we find that the range of luminosity from which 80% of the gamma-ray bursts must be sampled cannot exceed approximately 6.5, with a 3 sigma upper limit of 12-15, regardless of the value of alpha.
A model of the largest gust amplitude and gust length is presented which uses the properties of the bivariate gamma distribution. The gust amplitude and length are strongly dependent on the filter function; the amplitude increases with altitude and is larger in winter than in summer.