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Calculating integral generation multiplicity factor for neutron detector and ionization chamber to determine solar cosmic ray spectrum in high energy region
The thermal equilibrium coefficient of spatial diffusion transverse to a strong uniform dc magnetic field is calculated for a fully ionized plasma. The particles are assumed to move transverse to the field only as a consequence of the E x B drift, but to move freely parallel to it. The particles interact only electrostatically. The calculation is done at large, but fixed and finite, plasma volume. It is shown that, as magnetic field density approaches infinity, the leading term of the coefficient of transverse spatial diffusion falls off in a prescribed manner, but contains a multiplicative factor which goes to zero as the plasma volume becomes infinite. The method of calculation fails for unbounded plasmas.
In order to validate methods and cross sections used in the neutronic design of compact fast-spectrum reactors for generating electric power in space, an analysis of a boron-carbide-drum-controlled critical reactor was made. For this reactor the transport analysis gave generally satisfactory results. The calculated multiplication factor for the most detailed calculation was only 0.7-percent Delta k too high. Calculated reactivity worth of the control drums was $11.61 compared to measurements of $11.58 by the inverse kinetics methods and $11.98 by the inverse counting method. Calculated radial and axial power distributions were in good agreement with experiment.
The Thermionic Reactor Critical Experiments (TRCE) consisted of fast spectrum highly enriched U-235 cores reflected by different thicknesses of beryllium or beryllium oxide with a transition zone of stainless steel between the core and reflector. The mixed fast-thermal spectrum at the core reflector interface region poses a difficult neutron transport calculation. Calculations of TRCE using ENDF/B fast spectrum data and GATHER library thermal spectrum data agreed within about 1 percent for the multiplication factor and within 6 to 8 percent for the power peaks. Use of GAM library fast spectrum data yielded larger deviations. The results were obtained from DOT R Theta calculations with leakage cross sections, by region and by group, extracted from DOT RZ calculations. Delineation of the power peaks required extraordinarily fine mesh size at the core reflector interface.
Computer code is used to determine heat transfer multiplication factors, special flow field simulation techniques, different heat transfer methods, different transition criteria, crossflow simulation, and more efficient thin skin thickness optimization procedure.
When incorporating formulations of instantaneous solar heating or photolytic rates as functions of altitude and sun angle into long range forecasting models, it may be desirable to replace the time integrals by daily average rates that are simple functions of latitude and season. This replacement is accomplished by approximating the integral over the solar day by a pure exponential. This gives a daily average rate as a multiplication factor times the instantaneous rate evaluated at an appropriate sun angle. The accuracy of the exponential approximation is investigated by a sample calculation using an instantaneous ozone heating formulation available in the literature.
Degree of signal phase shift determines desired multiplication factor.
Flight data from an F-8 Corsair and a Cessna 172 was analyzed to demonstrate specific improvements in the LRC parameter extraction computer program. The Cramer-Rao bounds were shown to provide a satisfactory relative measure of goodness of parameter estimates. It was not used as an absolute measure due to an inherent uncertainty within a multiplicative factor, traced in turn to the uncertainty in the noise bandwidth in the statistical theory of parameter estimation. The measure was also derived on an entirely nonstatistical basis, yielding thereby also an interpretation of the significance of off-diagonal terms in the dispersion matrix. The distinction between coefficients as linear and non-linear was shown to be important in its implication to a recommended order of parameter iteration. Techniques of improving convergence generally, were developed, and tested out on flight data. In particular, an easily implemented modification incorporating a gradient search was shown to improve initial estimates and thus remove a common cause for lack of convergence.
The problem of comparing laboratory spectra of sulfur-containing binary mixtures with the spectrum of Io is discussed. For the satellite, the observable is the geometric albedo as a function of wavelength, whereas in the laboratory one often measures some other type of albedo. A previous paper demonstrated that for pure sulfur the multiplicative factor which converts the laboratory albedos to geometric albedos can be strongly wavelength dependent. The present paper demonstrates that this is also true for binary sulfur-containing mixtures. Furthermore, there is no universal conversion factor applicable to all binary mixtures, nor can the factor be interpolated for a particular mixture from the conversion factors of the two end members. The conversion factor is a function not only of the specific composition of a binary mixture but also of the relative particle size distributions of the two components, and must be measured specifically for each individual sample if a quantitative comparison between a laboratory sample and Io's surface is desired.
A class of receivers called conditionally nulling receivers is defined for quantum noise limited optical communications. These receivers have the ability to decide at each moment in time whether or not to coherently combine a predetermined local oscillator field with the received optical field, prior to performing an energy measurement (photodetection) on the combined field. Conditionally nulling receivers are applicable to pulse position modulation and related modulation schemes, which have the property that, at each moment in time, the transmitted signal is in one of only two states, on or off. The local oscillator field which may or may not be added by the receiver is an exact replica of the negative of the received on field; hence, the receiver can exactly null the on signal if the on signal is present and the receiver chooses to use the local field. An ideal conditionally nulling receiver achieves very nearly the same error probability (within a multiplicative factor varying froom 1 to 2.15) as the optimum quantum measurement for quantum noise limited detection of M-ary PPM signals. In contrast, other known receiving methods, such as direct, heterodyne, and homodyne detection, are exponentially suboptimum.
Progress during ERIM's tenth quarter of effort under the LANDSAT-4 and 5 Image Data Quality Assessment program for the Thematic Mapper is described. Coincident LANDSAT-4 and 5 fully corrected (CCT-PT) TM data are analyzed in more detail and revised band-by-band relationships between the two sensors derived. An analysis technique employing the matching of cumulative distributions is developed and used and is believed to offer advantages over the histogram matching procedure currently used to produce LANDSAT data. Multiplicative factors ranging from 0.987 to 1.145 and offsets ranging from -2.7 to -6.2 video quantum levels are required to cause LANDSAT-5 data to match LANDSAT-4 data values. Evidence of low level clipping is found in TM Bands 5 and 7 of LANDSAT-5 but not LANDSAT-4. Analysis of the information content of LANDSAT TM and MSS data is continued. Components of information loss are identified and quantified and the effects of coarsened quantization are explored.
The validity of the modified equation stability analysis introduced by Warming and Hyett was investigated. It is shown that the procedure used in the derivation of the modified equation is flawed and generally leads to invalid results. Moreover, the interpretation of the modified equation as the exact partial differential equation solved by a finite-difference method generally cannot be justified even if spatial periodicity is assumed. For a two-level scheme, due to a series of mathematical quirks, the connection between the modified equation approach and the von Neuman method established by Warming and Hyett turns out to be correct despite its questionable original derivation. However, this connection is only partially valid for a scheme involving more than two time levels. In the von Neumann analysis, the complex error multiplication factor associated with a wave number generally has (L-1) roots for an L-level scheme. It is shown that the modified equation provides information about only one of these roots.
A Monte Carlo technique is used to investigate the effects of a hot electron scattering cloud surrounding a time-dependent X-ray source. Results are presented for the time-averaged emergent energy spectra and the mean residence time in the cloud as a function of energy. Moreover, after Fourier transforming the scattering Green's function, it is shown how the cloud affects both the observed power spectrum of a time-dependent source and the cross spectrum (Fourier transform of a cross correlation between energy bands). It is found that the power spectra intrinsic to the source are related to those observed by a relatively simple frequency-dependent multiplicative factor (a transmission function). The cloud can severely attenuate high frequencies in the power spectra, depending on optical depth, and, at lower frequencies, the transmission function has roughly a Lorentzian shape. It is also found that if the intrinsic energy spectrum is constant in time, the phase of the cross spectrum is determined entirely by scattering. Finally, the implications of the results for studies of the X-ray quasi-periodic oscillators are discussed.
The determinants of effective or ineffective cockpit resurce management and the difficulties these multiple factors pose for validation of the effectiveness of cockpit resource management (CRM) training are discussed. A model of an evaluation design that may be applied to this type of training is presented. Concept validation is discussed as well as criteria for judging crew proficiency. Attention is given to accidents and proficiency checks, incidents and repeated maneuvers, attitude measuremet, and self-report evauation of training.
Liquid nitrogen mass flow rate, pressure drop, and temperature drop data were obtained for a series of multiple orifice Joule-Thomson devices, known as Visco Jets, over a wide range of flow resistance. The test rig used to acquire the data was designed to minimize heat transfer so that fluid expansion through the Visco Jets would be isenthalpic. The data include a range of fluid inlet pressures from 30 to 60 psia, fluid inlet temperatures from 118 to 164 R, outlet pressures from 2.8 to 55.8 psia, outlet temperatures from 117 to 162 R and flow rate from 0.04 to 4.0 lbm/hr of nitrogen. A flow rate equation supplied by the manufacturer was found to accurately predict single-phase (noncavitating) liquid nitrogen flow through the Visco Jets. For cavitating flow, the manufacturer's equation was found to be inaccurate. Greatly improved results were achieved with a modified version of the single-phase equation. The modification consists of a multiplication factor to the manufacturer's equation equal to one minus the downstream quality on an isenthalpic expansion of the fluid across the Visco Jet. For a range of flow resistances represented by Visco Jet Lohm ratings between 17,600 and 80,000, 100 percent of the single-phase data and 85 percent of the two-phase data fall within + or - 10 percent of predicted values.
The modified equation technique of Warming and Hyett (1974), which evaluates the behavior of a difference scheme by means of the coefficients of a certain modified equation, established a link between such coefficients and the multiplication factor obtained from the von Neumann analysis. It follows from this pioneering work that modified equations should be derived from the difference scheme, rather than from the original differential equation; a rigorous investigation is presently made of this link without resort to their original interpretation. Only partial validity is establishable for the case of multilevel schemes.
A method is presented for calculating the binomial SF (cumulative binomial distribution), binfc(k;p,n), especially for a large n, beyond the range of existing tables, where conventional computer programs fail because of underflow and overflow, and Gaussian or Poisson approximations yield insufficient accuracy for the purpose at hand. This method is used to calculate and sum the individual binomial terms while using multiplication factors to avoid underflow; the factors are then divided out of the partial sum whenever it has the potential to overflow. A computer program uses this technique to calculate the binomial SF for arbitrary inputs of k, p, and n. Two other algorithms are presented to determine the value of p needed to yield a specified SF for given values of k and n and calculate the value where p = SF for a given k and n. Reliability applications of each algorithm/program are given, e.g., the value of p needed to achieve a stated k-out-of-n:G system reliability and the value of p for which k-out-of-n:G system reliability equals p.
In a previous paper, a time domain transformation useful for extrapolating 3-D near zone finite difference time domain (FDTD) results to the far zone was presented. In this paper, the corresponding 2-D transform is outlined. While the 3-D transformation produced a physically observable far zone time domain field, this is not convenient to do directly in 2-D, since a convolution would be required. However, a representative 2-D far zone time domain result can be obtained directly. This result can then be transformed to the frequency domain using a Fast Fourier Transform, corrected with a simple multiplicative factor, and used, for example, to calculate the complex wideband scattering width of a target. If an actual time domain far zone result is required it can be obtained by inverse Fourier transform of the final frequency domain result.