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Results for “variational distribution approximations”

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.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

Modelling atmospheric aerosol backscatter at CO2 laser wavelengths. I - Aerosol properties, modeling techniques, and associated problems. II - Modeled values in the atmosphere. III - Effects of changes in wavelength and ambient conditions

The various methods of calculating the atmospheric aerosol backscattering function, beta(CO2), both from measured aerosol characteristics and from optical measurements made at other wavelengths, are discussed in detail, with limits placed on their accuracy. The most significant factor in determining beta(CO2) is found to be the aerosol size distribution and concentration; this should be known accurately for particle radii up to at least 1 micron for stratospheric particles and 5 microns for tropospheric particles. Results are then presented from the modeling of the aerosol backscattering function at a wavelength of 10.6 microns in the lowest 20 km of the atmosphere. It is found that beta(CO2) varies from 10 to the -6th per m per sr in the planetary boundary layer to less than 10 to the -11th per m per sr in the stratosphere. It is next shown that, with the exception of (NH4)2SO4-containing aerosols, whose size distributions have relatively large numbers of small particles, the variation of backscattering with CO2 wavelength is less than a factor of approximately 3. For such (NH4)2SO4 aerosol distributions, however, the variation of backscatter function with CO2 wavelengths between 9.1 and 11.1 microns may reach one order of magnitude.

Kent, G.S.↗
NASA NTRS1971

Dynamics of plane stellar systems.

The evolution of initially balanced rotating disks of stars is investigated with a computer model for isolated disks of stars. An isolated, initially cold balanced disk is found to be violently unstable. Adding a sufficient amount of velocity dispersion will stabilize all small-scale disturbances. However, the disks are still unstable against slowly growing long wave-length modes and after about two rotations most disks tend to assume a bar-shaped structure. It is found that the final mass distribution over most of the disk can be closely approximated by an exponential variation, irrespective of the initial mass distribution. The gravitational two-stream instability is investigated by means of a modified computer model for infinite doubly periodic stellar systems.

Hohl, F.↗
NASA NTRS1972

Dynamics of plane stellar systems.

The evolution of initially balanced rotating disks of stars is investigated with a computer model for isolated disks of stars. An isolated, initially cold balanced disk is found to be violently unstable. Adding a sufficient amount of velocity dispersion will stabilize all small-scale disturbances. However, the disks are still unstable against slowly growing long wave-length modes and after about two rotations most disks tend to assume a bar-shaped structure. It is found that the final mass distribution over most of the disk can be closely approximated by an exponential variation, irrespective of the initial mass distribution. The gravitational two-stream instability is investigated by means of a modified computer model for infinite doubly periodic stellar systems.

Hohl, F.↗
NASA NTRS1990

Fuselage design for a specified Mach-sliced area distribution

A procedure for designing a fuselage having a prescribed effective area distribution computed from -90 deg Mach slices is described. This type of calculation is an essential tool in designing a complete configuration with an effective area distribution that corresponds to a desired sonic boom signature shape. Sample calculations are given for M=2 and M=3 designs. The examples include fuselages constrained to have circular cross sections and fuselages having cross sections of arbitrary shape. It is found that, for a prescribed effective area distribution having sharp variations, the iterative procedure converges to a smoothed approximation to the prescribed distribution. For a smooth prescribed area distribution, the solution is not unique.

Barger, Raymond L.↗
NASA NTRS1978

Cumulative slant path rain attenuation associated with COMSTAR beacon at 28.56 GHz for Wallops Island, Virginia

Yearly, monthly, and time of day fade statistics are presented and characterized. A 19.04 GHz yearly fade distribution, corresponding to a second COMSTAR beacon frequency, is predicted using the concept of effective path length, disdrometer, and rain rate results. The yearly attenuation and rain rate distributions follow with good approximation log normal variations for most fade and rain rate levels. Attenuations were exceeded for the longest and shortest periods of times for all fades in August and February, respectively. The eight hour time period showing the maximum and minimum number of minutes over the year for which fades exceeded 12 db were approximately between 1600 to 2400, and 0400 to 1200 hours, respectively. In employing the predictive method for obtaining the 19.04 GHz fade distribution, it is demonstrated theoretically that the ratio of attenuations at two frequencies is minimally dependent of raindrop size distribution providing these frequencies are not widely separated.

Goldhirsh, J.↗
NASA NTRS1928

The Effect of a Flap and Ailerons on the N.A.C.A. M-6 Airfoil Section

This report contains the results obtained at the Langley Memorial Aeronautical Laboratory on an N. A. C. A. M-6 airfoil, fitted with a flap and ailerons, and tested in the variable density wind tunnel at a density of 20 atmospheres. Airfoil characteristics are given for the model up to 48 degree angle of attack with the flap set at various angles, and also with the ailerons set at similar angles. The approximate lift distribution and the center of pressure variation along the span are determined with the model at 18 degree angle of attack and with the ailerons displaced at 20 degrees. Approximate rolling moment and yawing moment coefficients are determined for the various aileron settings. A comparison of the calculated angles of zero lift and the calculated lift and moment coefficiencies with those observed is given in the appendix.

Higgins, George J↗
NASA NTRS1995

The luminosity structure and objective classification of galaxies

The luminosity structure of spiral galaxies is studied using the technique of principal component analysis. It is found that approximately 94% of the variation in the luminosity distribution of galaxies can be accounted for by just two principal components. The principal luminosity components may contain valuable information about star formation history or whatever luminosity-regulating process occurs in galaxies. Practically, these principal components provide a new approach for the investigation of the luminosity structures of galaxies and their dependence on other properties. They also serve as an excellent objective classification system for galaxies. We introduce in this paper such a classification scheme and explore its various properties. The new system shows a number of very impressive characteristics. Most important, it can well segregate virtually all the important galactic properties we tested and does so much better than the conventional morphological classification systems. Of particular interest is that some distance-dependent parameters can also be determined to a surprisingly good accuracy; for example, absolute magnitude may be determined to an accuracy of approximately 0.6 mag (yet further improvement is believed to be highly possible). Second, the system is objective, and the classification procedure can be automated to a large degree; also the new system can apply to much smaller and fainter images than do eye-based clasification systems. These properties make the new system suitable for practical application, especially on very large (and deeper) digital image catalogs. Third, the classification is expressed in dimensionless numbers, yet the simple notation bears significant and easily understandable meaning, making it easy and convenient to use. Finally, the new system has another extremely useful feature: it provides a very powerful and convenient platform not only for classification, but also for easily recording, examining, and studying the variations and correlations of galaxy properties-all these may be carried out graphically by using the C-vectors and the C-diagrams introduced in the paper. We wil also give an example to demonstrate the use of the classification system for the study of the internal extinction problem in spiral galaxies.

Han, Mingshen↗
NASA NTRS2023

A New View of the Lunar South Pole from the Lunar Orbiter Laser Altimeter (LOLA)

Upcoming missions to the lunar south pole require detailed maps over large areas to fully characterize landing sites locally and regionally and to place their data into proper geologic context. To that end, we enhanced the Lunar Orbiter Laser Altimeter (LOLA) altimetry dataset for the south polar region, from which we produced new maps of topography, topographic roughness, and permanently shadowed regions (PSRs). The roughness maps reveal a diversity of terrains characterized by hectometer-scale roughness which is controlled in this region primarily by cratering and downslope mass transport. The south polar region is littered with linear roughness features of order ~1 – 10 km wide and ~10s – 100s of km long hypothesized to be secondary impacts within extended ejecta rays. Non uniformities in these features could reflect variations in secondary impactor properties and/or target terrain properties. Poleward of 80° S, the PSR cumulative size-frequency distribution (CSFD) shows an approximately power-law behavior whose exponent has a spatial variation of ~10%. PSRs with areas < 1 km2 contain 15 ± 5% of the total PSR area. Finally, we studied the effect of false positives and false negatives on the accuracy of the measured PSR cumulative size-frequency distribution (CSFD) and on the area for any individual PSR. The new maps presented here have many applications in the science and exploration of the lunar south polar region, such as geologic mapping and traverse planning.

Michael K. Barker↗
NASA NTRS1978

Distribution of atmospheric ozone and how it is measured

The total amount of ozone in a vertical column has been measured spectroscopically at near ultraviolet and visible wavelengths, using ground- and satellite-based instruments. The vertical distribution of ozone from the surface up to approximately 100 km has been measured by a variety of techniques - chemical and optical - and from a number of observing platforms, including balloon, rocket, and satellite platforms. The various methods presently used for determining the atmospheric ozone distribution are reviewed, along with a discussion of their advantages and disadvantages. The observed average distribution of total ozone for the period 1958-1975 shows the expected geographic and seasonal variations. The variations of total ozone, including hemispheric differences, are clearly associated with large-scale circulation processes in the lower stratosphere. Approximately ten years of observations of the vertical ozone distribution, up through the ozone maximum, also show geographic and seasonal variations strongly related to the lower stratosphere circulation. The distribution above the maximum, however, results from the interaction of photochemistry and stratospheric motions.

London, J.↗
NASA NTRS2018

Computational Icing Risk Analysis of the D8 "Double Bubble" Aircraft

A computational icing risk analysis utilizing LEWICE3D was performed for the D8 Double Bubble aircraft. A variety of discrete drop sizes spanning the Appendix C and O regimes were simulated. For computational efficiency a 50-bin global discretization was produced and projected onto the distributions of interest, eliminating redundant simulations. The trajectory and impingement characteristics for discrete drop diameters were analyzed to help understand the behavior of the water drops in the presence of a complex flow field. The collection efficiency results for the discrete drop diameters were then weighted by their contributions to the total water content of six different continuous distributions and subsequently superposed to approximate these curves. Results indicate that significant variation in impingement exists as a function of drop diameter for complex wing body geometries, and that current discretization practices may be insufficient to accurately predict water collection on certain regions of the aircraft. Results also indicate that the Appendix O distributions, specifically those with considerable water content at large drops, generates water collection patterns that are markedly different from distributions representative of Appendix C.

icing↗
NASA NTRS2018

Computational Icing Risk Analysis of the D8 "Double Bubble" Aircraft

A computational icing risk analysis utilizing LEWICE3D was performed for the D8 Double Bubble aircraft. A variety of discrete drop sizes spanning the Appendix C and O regimes were simulated. For computational efficiency a 50-bin global discretization was produced and projected onto the distributions of interest, eliminating redundant simulations. The trajectory and impingement characteristics for discrete drop diameters were analyzed to help understand the behavior of the water drops in the presence of a complex flow field. The collection efficiency results for the discrete drop diameters were then weighted by their contributions to the total water content of six different continuous distributions and subsequently superposed to approximate these curves. Results indicate that significant variation in impingement exists as a function of drop diameter for complex wing body geometries, and that current discretization practices may be insufficient to accurately predict water collection on certain regions of the aircraft. Results also indicate that the Appendix O distributions, specifically those with considerable water content at large drops, generates water collection patterns that are markedly different from distributions representative of Appendix C.

Porter, Christopher E.↗
NASA NTRS1984

A variational formulation for time-dependent climate models

A variational principle for time dependent diffusion problems is presented and is demonstrated by applying it to simple seasonal climate models. Two cases are treated. The first, a North-Coakley-type model with constant properties, is used as a tutorial example for the application of the technique. For the second case, heat capacity and thermal conductivity are considered to be latitude dependent in order to treat the effects of land/ocean distribution on the seasonal temperature distribution over the earth. The variational equations are derived and approximate analytical solutions are developed which delineate the influences of the physical asymmetries of the hemispheres in producing an asymmetric annual cycle.

Smith, G. L.↗
NASA NTRS1994

Vertical velocity in oceanic convection off tropical Australia

Time series of 1-Hz vertical velocity data collected during aircraft penetrations of oceanic cumulonimbus clouds over the western Pacific warm pool as part of the Equatorial Mesoscale Experiment (EMEX) are analyzed for updraft and downdraft events called cores. An updraft core is defined as occurring whenever the vertical velocity exceeds 1 m/sec for at least 500 m. A downdraft core is defined analogously. Over 19,000 km of straight and level flight legs are used in the analysis. Five hundred eleven updraft cores and 253 downdraft cores are included in the dataset. Core properties are summarized as distributions of average and maximum vertical velocity, diameter, and mass flux in four altitude intervals between 0.2 and 5.8 km. Distributions are approximately lognormal at all levels. Examination of the variation of the statistics with height suggests a maximum in vertical velocity between 2 and 3 km; slightly lower or equal vertical velocity is indicated at 5 km. Near the freezing level, virtual temperature deviations are found to be slightly positive for both updraft and downdraft cores. The excess in updraft cores is much smaller than that predicted by parcel theory. Comparisons with other studies that use the same analysis technique reveal that EMEX cores have approximately the same strength as cores of other oceanic areas, despite warmer sea surface temperatures. Diameter and mass flux are greater than those in the Global Atmospheric Research Program (GATE) but smaller than those in hurricane rainbands. Oceanic cores are much weaker and appear to be slightly smaller than those observed over land during the Thunderstorm Project. The markedly weaker oceanic vertical velocities below 5.8 km (compared to the continental cores) cannot be attributed to smaller total convective available potential energy or to very high water loading. Rather, it is suggested that water loading, although less than adiabatic, is more effective in reducing buoyancy of oceanic cores because of the smaller potential buoyancy below 5.8 km. Entrainment appears to be more effective in reducing buoyancy to well below adiabatic values in oceanic cores, a result consistent with the smaller oceanic core diameters in the lower cloud layer. It is speculated further that core diameters are related to boundary layer depth, which is clearly smaller over the oceans.

Lucas, Christopher↗
NASA NTRS1993

Detection of traveling ionospheric disturbances induced by atmospheric gravity waves using the global positioning system

Natural and man-made events like earthquakes and nuclear explosions launch atmospheric gravity waves (AGW) into the atmosphere. Since the particle density decreases exponentially with height, the gravity waves increase exponentially in amplitude as they propagate toward the upper atmosphere and ionosphere. As atmospheric gravity waves approach the ionospheric heights, the neutral particles carried by gravity waves collide with electrons and ions, setting these particles in motion. This motion of charged particles manifests itself by wave-like fluctuations and disturbances that are known as traveling ionospheric disturbances (TID). The perturbation in the total electron content due to TID's is derived analytically from first principles. Using the tilted dipole magnetic field approximation and a Chapman layer distribution for the electron density, the variations of the total electron content versus the line-of-sight direction are numerically analyzed. The temporal variation associated with the total electron content measurements due to AGW's can be used as a means of detecting characteristics of the gravity waves. As an example, detection of tsunami generated earthquakes from their associated atmospheric gravity waves using the Global Positioning System is simulated.

Bassiri, Sassan↗
NASA NTRS1938

The variation with Reynolds number of pressure distribution over an airfoil section

Pressures were simultaneously measured at 54 orifices distributed over the midspan section of a 5 by 30-inch rectangular model of the NACA 4412 airfoil in the variable-density tunnel. These measurements were made at 17 angles of attack from -20 degrees to 30 degrees for eight values of the effective Reynolds number form approximately 100,000 to 8,200,000. Accurate data were thus obtained for studying the variation of pressure distribution with Reynolds number. These results on the NACA 4412 section indicated that the pressure distribution is practically unaffected by changes in Reynolds number except where separation is involved.

Pinkerton, Robert M↗
NASA NTRS1993

Microwave emission from a sunspot. I - Implications for the sunspot magnetic structure

The magnetic field strength of a sunspot can be determined from the gyroresonance brightness temperature spectrum by using the property that microwave brightness is limited above a frequency given by an integer-multiple of the gyrofrequency. This concept is used to find the radial distribution of the magnetic field at the coronal base of a sunspot in the active region NOAA 4741. It is shown that the o-mode emission must arise primarily from the second harmonic of the gyrofrequency, and that the third harmonic is responsible for the x-mode emission. An expression is given to describe the radial distribution of magnetic fields at the coronal base of a sunspot. Coronal magnetic fields are found to originate mainly in the photospheric umbral region. Finally, while it is possible to approximate roughly the derived vertical variation of magnetic fields by means of a dipole model, the radial field distribution at coronal heights is determined to be more confined than predicted by this model.

Lee, Jeongwoo W.↗
NASA NTRS1995

Chemical studies of H chondrites. 4: New data and comparison of Antarctic suites

We report data for the trace elements Au, Co, Sb, Ga, Rb, Ag, Se, Cs, Te, Zn, Cd, Bi, Ti, and In (ordered by putative volatility during nebular condensation and accretion) determined by neutron activation analysis in 13 H5 chondrites from Victoria Land and 20 H4-6 chondrites from Queen Maud Land, Antarctica. These and earlier results provide Antarctic sample suites of 34 chondrites from Victoria Land and 25 from Queen Maud Land. Treatment of data for the most volatile 10 elements (Rb to In) in these studies by multivariate statistical techniques more robust, as well as more conservative, than conventional linear discriminant analysis and logistic regression demonstrates that compositions differ at marginally significant levels. This difference cannot be explained by trivial (terrestrial) causes and becomes more significant, despite the smaller size of the database, when comparisons are limited to data from a single analyst and when all upper limits are eliminated from consideration. The Victoria Land and Queen Maud Land suites have different mean terrestrial ages (approximately 300 kyr and approximately 100 kyr, respectively) and age distributions, suggesting that a time-dependent variation of chondritic sources with different thermal histories is responsible. As a result, these two Antarctic suites are, on average, chemically distinguishable from each other. Since H chondrites serve as a paradigm for other meteorite classes, these results indicate that the near-Earth populations of planetary materials varied with time on the 10(exp 5)-year timescale.

Wolf, Stephen F.↗
NASA NTRS1996

Fossil preservation and the stratigraphic ranges of taxa

The incompleteness of the fossil record hinders the inference of evolutionary rates and patterns. Here, we derive relationships among true taxonomic durations, preservation probability, and observed taxonomic ranges. We use these relationships to estimate original distributions of taxonomic durations, preservation probability, and completeness (proportion of taxa preserved), given only the observed ranges. No data on occurrences within the ranges of taxa are required. When preservation is random and the original distribution of durations is exponential, the inference of durations, preservability, and completeness is exact. However, reasonable approximations are possible given non-exponential duration distributions and temporal and taxonomic variation in preservability. Thus, the approaches we describe have great potential in studies of taphonomy, evolutionary rates and patterns, and genealogy. Analyses of Upper Cambrian-Lower Ordovician trilobite species, Paleozoic crinoid genera, Jurassic bivalve species, and Cenozoic mammal species yield the following results: (1) The preservation probability inferred from stratigraphic ranges alone agrees with that inferred from the analysis of stratigraphic gaps when data on the latter are available. (2) Whereas median durations based on simple tabulations of observed ranges are biased by stratigraphic resolution, our estimates of median duration, extinction rate, and completeness are not biased.(3) The shorter geologic ranges of mammalian species relative to those of bivalves cannot be attributed to a difference in preservation potential. However, we cannot rule out the contribution of taxonomic practice to this difference. (4) In the groups studied, completeness (proportion of species [trilobites, bivalves, mammals] or genera [crinoids] preserved) ranges from 60% to 90%. The higher estimates of completeness at smaller geographic scales support previous suggestions that the incompleteness of the fossil record reflects loss of fossiliferous rock more than failure of species to enter the fossil record in the first place.

NASA Program Exobiology↗