Radial distributions of ions for a primitive model of an electrolyte solution.
Ion radial distribution functions for primitive model of electrolyte solution using Percus- Yevick and convolution-hypernetted-chain integral equations
ION DISTRIBUTION↗
SEARCH · Engineering Papers
Results for “Distribution function”
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.
Atomic oscillations in the statistical approximation.
Atomic dipolar spectral distribution function in statistical approximation derived from dynamic equations, describing atom density fluctuations induced by external field
INTEGRAL EQUATION↗
Damping of initial perturbation and steady fluctuations in a collisionless plasma
Distribution function perturbation expression for establishing fluctuation mechanism of steady plasma fluctuations
PLASMA OSCILLATION↗
Applications of Sunphotometry to Aerosol Extinction and Surface Anisotropy
Support cost-sharing of a newly developed sunphotometer in field deployment for aerosol studies. This is a cost-sharing research to deploy a newly developed sun-sky-surface photometer for studying aerosol extinction and surface anisotropy at the ARM SGP, TWP, and NSA-AAO CART sites and in many field campaigns. Atmospheric aerosols affect the radiative energy balance of the Earth, both directly by perturbing the incoming/outgoing radiation fields and indirectly by influencing the properties/processes of clouds and reactive greenhouse gases. The surface bidirectional reflectance distribution function (BRDF) also plays a crucial role in the radiative energy balance, since the BRDF is required to determine (1) the spectral and spectrally-averaged surface albedo, and (2) the top-of-the-atmosphere (TOA) angular distribution of radiance field. Therefore, the CART sites provide an excellent, albeit unique, opportunity to collect long-term climatic data in characterizing aerosol properties and various types of surface anisotropy.
Aerosols↗
RUSHMAPS: Real-Time Uploadable Spherical Harmonic Moment Analysis for Particle Spectrometers
RUSHMAPS is a new onboard data reduction scheme that gives real-time access to key science parameters (e.g. moments) of a class of heliophysics science and/or solar system exploration investigation that includes plasma particle spectrometers (PPS), but requires moments reporting (density, bulk-velocity, temperature, pressure, etc.) of higher-level quality, and tolerates a lowpass (variable quality) spectral representation of the corresponding particle velocity distributions, such that telemetry use is minimized. The proposed methodology trades access to the full-resolution velocity distribution data, saving on telemetry, for real-time access to both the moments and an adjustable-quality (increasing quality increases volume) spectral representation of distribution functions. Traditional onboard data storage and downlink bandwidth constraints severely limit PPS system functionality and drive cost, which, as a consequence, drives a limited data collection and lower angular energy and time resolution. This prototypical system exploit, using high-performance processing technology at GSFC (Goddard Space Flight Center), uses a SpaceCube and/or Maestro-type platform for processing. These processing platforms are currently being used on the International Space Station as a technology demonstration, and work is currently ongoing in a new onboard computation system for the Earth Science missions, but they have never been implemented in heliospheric science or solar system exploration missions. Preliminary analysis confirms that the targeted processor platforms possess the processing resources required for realtime application of these algorithms to the spectrometer data. SpaceCube platforms demonstrate that the target architecture possesses the sort of compact, low-mass/power, radiation-tolerant characteristics needed for flight. These high-performing hybrid systems embed unprecedented amounts of onboard processing power in the CPU (central processing unit), FPGAs (field programmable gate arrays), and DSP (digital signal processing) elements. The fundamental computational algorithm de constructs 3D velocity distributions in terms of spherical harmonic spectral coefficients (which are analogous to a Fourier sine-cosine decomposition), but uses instead spherical harmonics Legendre polynomial orthogonal functions as a basis for the expansion, portraying each 2D angular distribution at every energy or, geometrically, spherical speed-shell swept by the particle spectrometer. Optionally, these spherical harmonic spectral coefficients may be telemetered to the ground. These will provide a smoothed description of the velocity distribution function whose quality will depend on the number of coefficients determined. Successfully implemented on the GSFC-developed processor, the capability to integrate the proposed methodology with both heritage and anticipated future plasma particle spectrometer designs is demonstrated (with sufficiently detailed design analysis to advance TRL) to show specific science relevancy with future HSD (Heliophysics Science Division) solar-interplanetary, planetary missions, sounding rockets and/or CubeSat missions.
Figueroa-Vinas, Adolfo↗
The acoustic response of rooms with open windows to airborne sounds.
The objective of the work described in this and the companion paper was to establish a theory for predicting the sound field generated in a room by a sonic boom incident on an open window. In this paper, some basic theoretical results are presented. First, the case of a normally incident harmonic wave was considered. Expressions for the pressure field were obtained by viewing the room as a terminated duct and by using a Green function method. The concept of mode excitation distribution functions was formulated and used to match the boundary conditions. This concept has been extended for oblique incidence. A modified form of Laplace transform technique was used to obtain expressions in the time domain for transient signals.
Vaidya, P. G.↗
Mathematical model of the current density for the 30-cm engineering model thruster
Mathematical models are presented for both the singly and doubly charged ion current densities downstream of the 30-cm engineering model thruster with 0.5% compensated dished grids. These models are based on the experimental measurements of Vahrenkamp at a 2-amp ion beam operating condition. The cylindrically symmetric beam of constant velocity ions is modeled with continuous radial source and focusing functions across 'plane' grids with similar angular distribution functions. A computer program is used to evaluate the double integral for current densities in the near field and to obtain a far field approximation beyond 10 grid radii. The utility of the model is demonstrated for (1) calculating the directed thrust and (2) determining the impingement levels on various spacecraft surfaces from a two-axis gimballed, 2 x 3 thruster array.
Cuffel, R. F.↗
Computations and applications of linear hypergeometric transformations
Linear transformations are well-known in the theory of hypergeometric functions. In this note, it is indicated, both by analyses and by supporting numerical experiments, how these transformations can be applied to the computation of Legendre's functions, the incomplete Beta function, and the variance-ratio probability distribution function. It is shown that a simple transformation can in many cases cause dramatic improvement in computation.
Ng, E. W.↗
Mean-spherical model for soft potentials - The hard core revealed as a perturbation
The mean-spherical approximation for fluids is extended to treat the case of dense systems interacting via soft potentials. The extension takes the form of a generalized statement concerning the behavior of the direct-correlation function c(r) and the radial-distribution function g(r). From a detailed analysis that views the hard-core portion of a potential as a perturbation on the whole, a specific model is proposed which possesses analytic solutions for both Coulomb and Yukawa potentials, in addition to certain other remarkable properties. A variational principle for the model leads to a relatively simple method for obtaining numerical solutions.
Rosenfeld, Y.↗
A performance analysis study of a complex G field experiment
A performance analysis on data from an experiment which illustrates the degradation of tracking performance as the human is subjected to an environmental stressor is presented. The performance changes are defined and the statistical properties of human tracking with and without the stress effects examined. Performance is evaluated using an extension of a phase plane technique. A quantiative determination of stress effects on performance is defined explicitly in terms of parameters of a density function identified from the empirical data. The distribution functions which characterize tracking in a phase plane representation of the closed loop error signal are determined.
Repperger, D. W.↗
Space station internal propagation
The Space Station Freedom (SSF) is planned with a wireless communication system in place for the transmission of information between crew members on board. The clarity of transmission is paramount to an effective system of communication. A short overview is presented of the system including the requirements of interest, and a statement of the problem. The theory used to solve the problem is explored. The results given are for the experiments performed on a mockup of the proposed structure at NASA-Marshall. The requirements on the signal level are that there is a 45 dB signal to noise ratio from end to end, and that coverage over 99 pct. of the volume be maintained. The Rice probability distribution function, a simple extension of the Rayleigh distribution, is used to estimate the field strength inside a volume, where a significant line of sight from the transmitter to the receiver exists. For the SSF, this distribution will correspond to the summation of a coherent line of sight path between the transmitter and the receiver and an incoherent portion. The incoherent portion is the sum of reflections from the walls and the equipment inside the SSF. The Rice distribution was found to be the optimal distribution from the results.
Richie, J. E.↗
Accounting for the Effects of Surface BRDF on Satellite Cloud and Trace-Gas Retrievals: A New Approach Based on Geometry-Dependent Lambertian-Equivalent Reflectivity Applied to OMI Algorithms
Most satellite nadir ultraviolet and visible cloud, aerosol, and trace-gas algorithms make use of climatological surface reflectivity databases. For example, cloud and NO2 retrievals for the Ozone Monitoring Instrument (OMI) use monthly gridded surface reflectivity climatologies that do not depend upon the observation geometry. In reality, reflection of incoming direct and diffuse solar light from land or ocean surfaces is sensitive to the sun-sensor geometry. This dependence is described by the bidirectional reflectance distribution function (BRDF). To account for the BRDF, we propose to use a new concept of geometry-dependent Lambertian equivalent reflectivity (LER). Implementation within the existing OMI cloud and NO2 retrieval infrastructure requires changes only to the input surface reflectivity database. The geometry-dependent LER is calculated using a vector radiative transfer model with high spatial resolution BRDF information from the Moderate Resolution Imaging Spectroradiometer (MODIS) over land and the Cox-Munk slope distribution over ocean with a contribution from water-leaving radiance. We compare the geometry-dependent and climatological LERs for two wavelengths, 354 and 466 nm, that are used in OMI cloud algorithms to derive cloud fractions. A detailed comparison of the cloud fractions and pressures derived with climatological and geometry-dependent LERs is carried out. Geometry-dependent LER and corresponding retrieved cloud products are then used as inputs to our OMI NO2 algorithm. We find that replacing the climatological OMI-based LERs with geometry-dependent LERs can increase NO2 vertical columns by up to 50% in highly polluted areas; the differences include both BRDF effects and biases between the MODIS and OMI-based surface reflectance data sets. Only minor changes to NO2 columns (within 5 %) are found over unpolluted and overcast areas.
Lambert-equivalent reflectivity↗
CLARREO Pathfinder Solar Diffuser Calibration Progress
Climate Absolute Radiance and Refractivity Observatory (CLARREO) Pathfinder (CPF) mission’s Hyperspectral Imager for Climate Science (HySICS) instrument’s transmissive flight diffuser calibration is presented. The absolute Bidirectional Transmittance Distribution Function (BTDF) measurement of the transmissive diffuser is needed to calculate the instrument’s absolute efficiency. Along with a known solar irradiance source such as Total Solar Irradiance Sensor (TSIS), it can provide an absolute irradiance measurement path on orbit, with NIST traceability. This provides an additional path for CPF to cross compare with other on orbit sensors’ measurement such as Visible-Infrared Imaging Radiometer Suite (VIIRS), Clouds and the Earth’s Radiant Energy System (CERES). The flight diffuser was calibrated at NASA’s Goddard Space Flight Center (GSFC) using the Facility’s Optical Scatterometer.
Bidirectional Transmittance Distribution Function↗
Optical Studies of Low Reflectance Materials at Solar Reflective Wavelengths in Support of Remote Sensing Instrument Development and Calibration
We report the Bidirectional Reflection Distribution Function (BRDF) and Total Hemispheric Reflectance (THR) results of several low reflectance materials using a Table-top Goniometer (TTG) and a commercial UV-VIS-NIR spectrophotometer in support of the NASA GSFC PACE project. The newly developed TTG was utilized to perform the BRDF measurements for several black candidate samples in in-plane and out-of-plane configurations from 300 nm to 2000 nm. These measurements demonstrated the BRDF capability of the TTG to calibrate the dim calibration target with a reflectance of approximately 2 % for the OCI of the PACE project. The spectral THR of the black samples from 200 nm to 2500 nm was determined using a 10 % reflectance diffuse black standard and a monochromator-based light source equipped with a 150 mm diameter integrating sphere. The THR measurement is used to compliment and validate the BRDF measurements acquired from these samples. In this presentation, we also show examples of UV induced BRDF and THR changes on two black coatings. We will discuss validation of the BRDF scale, source stability, measurement repeatability, instrument signature, and uncertainty components.
Bidirectional Reflection Distribution Function (BR↗
Nonparametric discrimination using tolerance regions.
Nonparametric discrimination among distributions on Euclidean space with continuous distribution functions by tolerance regions method, emphasizing errors probability distribution control
Gessaman, M. P.↗
Some spatially homogeneous gas motions
A functional equation is derived for a spatially homogeneous distribution function and examples of spatially homogeneous gas motions are considered. Numerical calculation was conducted for one such motion with the use of a model equation.
Rykov, V. A.↗
Effect of the size distribution on the thermal emission from cometary dust
The IR thermal emission from cometary dust is analyzed by two size distribution functions, Sekanina A and a modified Sekanina Miller distribution. The resulting thermal emission spectra are illustrated for heliocentric distances 0.15 to 1.6 AU. The Sekania A distribution does not predict the observed heliocentric variation in the flux ratio I (4.8 micron) I (3.5 micron) for bright comets. A size distribution intermediate between the two presented is a better representation of the dust in recently observed comets.
Hanner, M. S.↗
Correlation of hard X-ray and type 3 bursts in solar flares
Correlations between X-ray and type 3 radio emission of solar bursts are described through a bivariate distribution function. Procedures for determining the form of this distribution are described. A model is constructed to explain the correlation between the X-ray spectral index and the ratio of X-ray to radio intensities. Implications of the model are discussed.
Petrosian, V.↗