Approximate calculation of cumulative probability from a moment-generating function.
Cumulative probability distribution of positive random variable from moment generating function, exemplifying exponential and Poisson functions
Helstrom, C. W.↗
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A kinetic study of solar wind electrons in the transition region from collision dominated to collisionless flow
We have studied the evolution of the velocity distribution function of a test population of electrons in the solar corona and inner solar wind region, using a recently developed kinetic model. The model solves the time dependent, linear transport equation, with a Fokker-Planck collision operator to describe Coulomb collisions between the 'test population' and a thermal background of charged particles, using a finite differencing scheme. The model provides information on how non-Maxwellian features develop in the distribution function in the transition region from collision dominated to collisionless flow. By taking moments of the distribution the evolution of higher order moments, such as the heat flow, can be studied.
Lie-Svendsen, O.↗
A Search Model for Imperfectly Detected Targets
Under the assumptions that 1) the search region can be divided up into N non-overlapping sub-regions that are searched sequentially, 2) the probability of detection is unity if a sub-region is selected, and 3) no information is available to guide the search, there are two extreme case models. The search can be done perfectly, leading to a uniform distribution over the number of searches required, or the search can be done with no memory, leading to a geometric distribution for the number of searches required with a success probability of 1/N. If the probability of detection P is less than unity, but the search is done otherwise perfectly, the searcher will have to search the N regions repeatedly until detection occurs. The number of searches is thus the sum two random variables. One is N times the number of full searches (a geometric distribution with success probability P) and the other is the uniform distribution over the integers 1 to N. The first three moments of this distribution were computed, giving the mean, standard deviation, and the kurtosis of the distribution as a function of the two parameters. The model was fit to the data presented last year (Ahumada, Billington, & Kaiwi, 2 required to find a single pixel target on a simulated horizon. The model gave a good fit to the three moments for all three observers.
Ahumada, Albert↗
The mosaic structure of plasma bulk flows in the Earth's magnetotail
Moments of plasma distributions observed in the magnetotail vary with different time scales. In this paper we attempt to explain the observed variability on intermediate timescales of approximately 10-20 min that result from the simultaneous energization and spatial structuring of solar wind plasma in the distant magnetotail. These processes stimulate the formation of a system of spatially disjointed. highly accelerated filaments (beamlets) in the tail. We use the results from large-scale kinetic modeling of magnetotail formation from a plasma mantle source to calculate moments of ion distribution functions throughout the tail. Statistical restrictions related to the limited number of particles in our system naturally reduce the spatial resolution of our results, but we show that our model is valid on intermediate spatial scales Delta(x) x Delta(z) equal to approximately 1 R(sub E) x 1000 km. For these spatial scales the resulting pattern, which resembles a mosaic, appears to be quite variable. The complexity of the pattern is related to the spatial interference between beamlets accelerated at various locations within the distant tail which mirror in the strong near-Earth magnetic field. Global motion of the magnetotail results in the displacement of spacecraft with respect to this mosaic pattern and can produce variations in all of the moments (especially the x-component of the bulk velocity) on intermediate timescales. The results obtained enable us to view the magnetotail plasma as consisting of two different populations: a tailward-Earthward system of highly accelerated beamlets interfering with each other, and an energized quasithermal population which gradually builds as the Earth is approached. In the near-Earth tail, these populations merge into a hot quasi-isotropic ion population typical of the near-Earth plasma sheet. The transformation of plasma sheet boundary layer (PSBL) beam energy into central plasma sheet (CPS) quasi-thermal energy occurs in the absence of collisions or noise. This paper also clarifies the relationship between the global scale where an MHD description might be appropriate and the lower intermediate scales where MHD fails and large-scale kinetic theory should be used.
Ashour-Abdalla, M.↗
Investigation of the Distribution of Lift, Drag, and Pitching Moment Between the Wing and Fuselage of a 1/30-scale Semispan Model of the Bell X-5 Airplane at a Mach Number of 1.24 by the Naca Wing-flow Method
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Morris, Garland J↗
Airfoil section characteristics as applied to the prediction of air forces and their distribution on wings
The results of previous reports dealing with airfoil section characteristics and span load distribution data are coordinated into a method for determining the air forces and their distribution on airplane wings. Formulas are given from which the resultant force distribution may be combined to find the wing aerodynamic center and pitching moment. The force distribution may also be resolved to determine the distribution of chord and beam components. The forces are resolved in such a manner that it is unnecessary to take the induced drag into account. An illustration of the method is given for a monoplane and a biplane for the conditions of steady flight and a sharp-edge gust. The force determination is completed by outlining a procedure for finding the distribution of load along the chord of airfoil sections.
Jacobs, Eastman N↗
Multi-beam energy moments of measured compound ion velocity distributions
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M. V. Goldman↗
An evaluation of a parabolized Navier-Stokes (PNS) code for cone-cylinder-flared configurations
A PNS code's capability to predict the onset of laminar and turbulent boundary layer separation, forces, moments, and pressure distributions was investigated. Predictions of incipient separation show good agreement with experimental results. Force and moment calculations were found to agree favorably with experimental data for a wide range of geometries for Mach numbers from 2 to 4 with turbulent boundary layers. Limited comparison of pressure distribution data also showed good agreement. Skin friction and Stanton number calculations are presented to indicate the code's capability to calculate this information and hence, provide a complete data base for attached flow conditions. The sensitivity of these calculations to smoothing and marching parameter variations was examined and found to be acceptable for most design work. The code was found to be suitable to complement or reduce wind tunnel experimentation for the design of this class of configuration with regard to accuracy, cost and usability.
Cottrell, C. J.↗
Analyses of convective flows and spatial gradients in energetic ion observations
Based on the measured anisotropy of three-dimensional energetic ion distributions obtained from the Medium Energy Particle Instrument experiment of the ISEE 1 spacecraft, bulk flow, epsilon x B convection, and pressure gradients in magnetospheric plasmas are measured with two techniques. In the first technique, using a Compton-Getting transform into the appropriate rest frame in an iterative fashion and converging to the unique velocity that removes the first-order anisotropy from the flux angular distribution, the actual measured angular distribution, and spectrum at each angle, are employed. The second technique uses a first moment of the distribution function in which the shift in velocity space of the distribution function is obtained at two phase space density values. The convection contribution to the velocity shift is assumed to be perpendicular to the pressure gradient contribution if an MHD generator condition is assumed, rendering the two shifts separable, and a gradient scale and a lower limit to the convection electric field are derived in one calculation.
Mitchell, D. G.↗
Exploratory experimental aerodynamic investi- gation of tension shell shapes at mach 7
Aerodynamic force and moment measurements, pressure distribution, and heating rates of tension shell shapes at Mach 7
MOMENT↗
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.↗
Is coverage a factor in non-Gaussianity of IMF parameters?
Recently, Feynman and Ruzmaikin (1994) showed that IMF parameters for the 1973 to 1990 period are not log-normally distributed as previously suggested by Burlaga and King (1979) for the data obtained over a shorter time period (1963-75). They studied the first four moments, namely: mean, variance, skewness, and kurtosis. For a Gaussian distribution, moments higher than the variance should vanish. In particular, Feynman and Ruzmaikin obtained very high values of kurtosis during some periods of their analysis. We note that the coverage for IMF parameters is very uneven for the period analyzed by them, ranging from less than 40% to greater than 80%. So a question arises as to whether the amount of coverage is a factor in their analysis. We decided to test this for the B(sub z) component of IMF, since it is an effective geoactive parameter for short term disturbances. Like them, we used 1-hour averaged data available on the Omnitape. We studied the scatter plots of the annual mean values of B(sub z)(nT) and its kurtosis versus the percent coverage for the year. We obtain a correlation coefficient of 0.48 and 0.42 respectively for the 1973-90 period. The probability for a chance occurrence of these correlation coefficients for 18 pair of points is less than 8%. As a rough measure of skewness, we determined the percent asymmetry between the areas of the histograms representing the distributions of the positive and the negative values of B(sub z) and studied its correlation with the coverage for the year. This analysis yields a correlation coefficient of 0.41 When we extended the analysis for the whole period for which IMF data are available (1963-93) the corresponding correlation coefficients are 0.59, 0.14, and 0.42. Our findings will be presented and discussed
Ahluwalia, H. S.↗
Particle Size Distributions in Atmospheric Clouds
In this note, we derive a transport equation for a spatially integrated distribution function of particles size that is suitable for sparse particle systems, such as in atmospheric clouds. This is done by integrating a Boltzmann equation for a (local) distribution function over an arbitrary but finite volume. A methodology for evolving the moments of the integrated distribution is presented. These moments can be either tracked for a finite number of discrete populations ('clusters') or treated as continuum variables.
Paoli, Roberto↗
Angular momentum desaturation for Skylab using gravity gradient torques
An angular momentum desaturation method for momentum exchange devices of orbiting spacecraft is described. The specific application of the method is to the Skylab which contains three double-gimbaled control moment gyros for precise attitude control and maneuvering. It is assumed that the attitude reference is inertially fixed and that two of the vehicle principal moments of inertia are much larger than the third. Gravity gradient torques and resultant angular momentum accumulation are developed for small deviations from the reference. The assumed moment-of-inertia distribution allows desaturation about all axes with only two attitude angles each for the two axes with large moments of inertia. The necessary desaturation maneuvers can be decoupled for a special set of orbital coordinates. All maneuvers are made during the night portion of the orbit, and the percentage utilized for desaturation is selectable. Expressions for the attitude angle commands are developed assuming infinite vehicle rates. The effect of finite rates introduces an efficiency into the desaturation. Expressions for this efficiency are developed and means for compensation are treated. Arbitrary misalignments between geometric vehicle axes and principal moment-of-inertia axes are permissible. An angle bias about the sun line minimizes the angular momentum accumulation about the sun line projection into the orbital plane. Adaptive desaturation maneuver limiting consistent with the available maneuver momentum is included.
Kennel, H. F.↗
Experimental and Computational Induced Aerodynamics from Missile Jet Reaction Controls at Angles of Attack to 75 Degrees
An investigation was conducted in the Langley 16-Foot Transonic Tunnel to determine induced aerodynamic effects from jet reaction controls of an advanced air-to-air missile concept. The 75-percent scale model featured independently controlled reaction jets located near the nose and tail of the model. Aerodynamic control was provided by four fins located near the tail of the model. This investigation was conducted at Mach numbers of 0.35 and 0.60, at angles of attack up to 75 deg and at nozzle pressure ratios up to 90. Jet-reaction thrust forces were not measured by the force balance but jet-induced forces were. In addition, a multiblock three-dimensional Navier-Stokes method was used to calculate the flowfield of the missile at angles of attack up to 40 deg. Results indicate that large interference effects on pitching moment were induced from operating the nose jets with the the off. Excellent correlation between experimental and computational pressure distributions and pitching moment were obtained a a Mach number of 0.35 and at angles of attack up to 40 deg.
Capone, Francis J.↗
Pressures, forces, moments and shock shapes for a geometrically matched sphere-cone and hyperboloid at Mach 20.3 in helium
An investigation was conducted to compare measured and predicted pressure distributions, forces and moments, and shock shapes on a geometrically matched sphere-cone and hyperboloid. A hyperboloid with a nose radius of 0.5276 in. and an asymptotic angle of 39.9871 deg was matched to a sphere-cone with a nose radius of 0.750 in. and a cone half-angle of 45 deg. Experimental results in helium at a free-stream Mach number of 20.3 and a free-stream unit Reynolds number of 6.83 x 10 to the 6th power per foot were combined with predicted results from a theoretical method to compare the two shapes. Comparisons of experimental results showed small differences in the two shapes, but the prediction method provided better results for the hyperboloid than for the sphere-cone.
Calloway, R. L.↗
Theoretical Calculations of the Pressures, Forces, and Moments Due to Various Lateral Motions Acting on Tapered Sweptback Vertical Tails with Supersonic Leading and Trailing Edges
Based on expressions for the linearized velocity potentials and pressure distributions given in NACA Technical Report 1268, formulas for the span load distribution, forces, and moments are derived for families of thin isolated vertical tails with arbitrary aspect ratio, taper ratio, and sweepback performing the motions constant sideslip, steady rolling, steady yawing, and constant lateral acceleration. The range of Mach number considered corresponds, in general, to the condition that the tail leading and trailing edges are supersonic. To supplement the analytical results, design-type charts are presented which enable rapid estimation of the forces and moments (expressed as stability derivatives) for given combinations of geometry parameters and Mach number.
Margolis, Kenneth↗
A statistical study of high coronal densities from X-ray line-ratios of Mg XI
An X-ray line-ratio density diagnostic was applied to 50 Mg XI spectra of flaring active regions on the sun recorded by the Flat Crystal Spectrometer on the SMM. The plasma density is derived from R, the flux ratio of the forbidden to intercombination lines of the He-like ion, Mg XI. The R ratio for Mg XI is only density sensitive when the electron density exceeds a critical value (about 10 to the 12th/cu cm), the low-density limit (LDL). This theoretical value of the low-density limit is uncertain as it depends on complex atomic theory. Reported coronal densities above 10 to the 12th/cu cm are uncommon. In this study, the distribution of R ratio values about the LDL is estimated and the empirical values are derived for the 1st and 2nd moments of this distribution from 50 Mg XI spectra. From these derived parameters, the percentage of observations is derived which indicated densities above this limit.
Linford, G. A.↗