Search NASA⌕ Search

SEARCH · Search NASA

Results for “Gaussian Approximation”

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.

At least 253 records · Page 14

Proton-deuteron double scattering

A simple but accurate form for the proton-deuteron elastic double scattering amplitude, which includes both projectile and target recoil motion and is applicable at all momentum transfer, is derived by taking advantage of the restricted range of Fermi momentum allowed by the deuteron wave function. This amplitude can be directly compared to approximations which have neglected target recoil or are limited to small momentum transfer; the target recoil and large momentum transfer effects are evaluated explicitly within the context of a Gaussian model.

Wilson, J. W.↗

Losses introduced by tilting intracavity etalons

An approximate analytical expression and numerical results for the on-resonance losses caused by tilting an intracavity etalon are given, when the laser operates in the zero-order Gaussian mode.

Leeb, W. R.↗

Validity of the Relation Between Spontaneous and Stimulated Emissions in Semiconductors

The Einstein relation between spontaneous emission and absorption was originally derived for a system consists of a two-state subsystem representing matter and harmonic fields representing radiation. The derivation is based on the detailed balance between these two subsystems under thermal equilibrium. The relationship was later investigated in connection with the interactions between radiation field and solids or semiconductors. The simple derivation dose not hold for semiconductors in general. In certain limiting cases, simple relation was obtained. The validity of this relation is important not only because of its fundamental role connecting two of the most fundamental optical processes in semiconductors, but mostly also because of its wide use as a practical method to measure the optical gain of a semiconductor. The validity of this relation for semiconductors has been an issue of controversial for some time. In this paper we numerically examine the validity of this relationship for several different lineshapes including Lorentzian, Gaussian, Sech, and a convoluted double Lorentzians (CDL). We find out that at relatively low density above transparency level, all first three lineshapes violate the Einstein relation. The relation is approximately valid at high density. At very high density, the validity of the Einstein relation holds well for all three lineshapes. The reason behind this observation is explained. The CDL lineshape has been shown analytically to obey the Einstein relationship previously. We show that for a 2D semiconductor with parabolic bands, the CDL lineshape can be integrated analytically. This analytic lineshape is compared with a simple Lorentzian lineshape.

Ning, Cun-Zheng↗

Preliminary Results of a Microgravity Investigation to Measure Net Charge on Granular Materials

Accurate characterization of the electrostatic charge on granular materials has typically been limited to materials with diameters on the order of 10 microns and below due to high settling velocities of larger particles. High settling velocities limit both the time and the acceptable uncertainty with which a measurement can be made. A prototype device has been developed at NASA Glenn Research Center (GRC) to measure coulombic charge on individual particles of granular materials that are 50 to 500 microns in diameter. This device, a novel extension of Millikan's classic oil drop experiment, utilizes the NASA GRC 2.2 second drop tower to extend the range of electrostatic charge measurements to accommodate moderate size granular materials. A dielectric material with a nominal grain diameter between 1.06 and 250 microns was tribocharged using a dry gas jet, suspended in a 5x10x10 cm enclosure during a 2.2 second period of microgravity and exposed to a known electric field. The response was recorded on video and post processed to allow tracking of individual particles. By determining the particle trajectory and velocity, estimates of the coulombic charge were made. Over 30 drops were performed using this technique and the analysis showed that first order approximations of coulombic charge could successfully be obtained, with the mean charge of 3.4E-14 coulombs measured for F-75 Ottawa quartz sand. Additionally, the measured charge showed a near-Gaussian distribution, with a standard deviation of 2.14E -14 coulombs.

Green, Robert D.↗

Coupling between the nickel-carbon and carbon-oxygen stretch motion in NiCO

Linear-combination-of-Gaussian-type-orbital (LCGTO) X-alpha calculations are performed on NiCO for various linear Ni-CO and NiC-O bond distances. The basis sets used are moderately large, approximately double zeta, and thus are fairly accurate within the X-alpha approximation. The electronic structure and equilibrium bond distances are consistent with recent CI calculations, indicating a much stronger Ni-CO bond than occurs in Ni(CO)4. The calculations agree to within 100/cm with the experimentally observed NiC-O stretch frequency. The Ni-CO stretch is predicted to occur at 656/cm, although at an intensity that is 640 times less. Compared with experimental results for CO adsorbed on single crystal Ni(100), the computed vibrational frequencies and intensities are less appropriate than the relevant experimental values for Ni(CO)4. This is interpreted to mean that an accurate description of the electronic structure of the nickel atom participating directly in the surface bond requires proper accounting of the bonds to its other nearest neighbors.

Dunlap, B. I.↗

Reduced electrical bandwidth receivers for direct detection 4-ary PPM optical communication intersatellite links

This interim progress report consists of copies of three reports written for NASA's Flight System Development and Demonstration (FSDD) project on optical intersatellite links. The first report, 'Test results of the PlessCor avalanche photodiode (APD) preamplifier for use in the 50 Mbps quaternary pulse position modulator (QPPM) receiver,' was prepared for NASA Goddard Space Flight Center. The second, 'Performance of Q-ary PPM receiver under additive white Gaussian noise,' was prepared at the request of NASA Lewis Research Center for testing the electronic systems for the FSDD project. The third, 'Use of a Bessel lowpass filter as an approximate raised cosine filter,' was written for raised cosine filter implementation in the FSDD QPPM receiver.

Davidson, Frederic M.↗

Coherent laser radar performance for general atmospheric refractive turbulence

A general theory for the signal-to-noise ratio (SNR) of a coherent detection laser radar is developed using the path-integral formulation (Fresnel approximation), which is valid for any typical path-integrated atmospheric refractive turbulence. The principal effects of refractive turbulence are discussed, and analytical expressions are presented for the case of untruncated Gaussians for the transmitted field, local oscillator field, and transmitter/receiver optics. The physical mechanisms that reduce heterodyne efficiency are identified.

Frehlich, Rod G.↗

Application of neural network to remote sensing of soil moisture using theoretical polarimetric backscattering coefficients

This paper investigates the potential application of neural network to inversion of soil moisture using polarimetric remote sensing data. The neural network used for the inversion of soil parameters is multi-layer perceptron trained with the back-propagation algorithm. The training data include the polarimetric backscattering coefficients obtained from theoretical surface scattering models together with an assumed nominal range of soil parameters which are comprised of the soil permittivity and surface roughness parameters. Soil permittivity is calculated from the soil moisture and the assumed soil texture based on an empirical formula at C-, L-, and P-bands. The rough surface parameters for the soil surface, which is described by the Gaussian random process, are the root-mean-square (rms) height and correlation length. For the rough surface scattering, small perturbation method is used for the L-band frequency, and Kirchhoff approximation is used for the C-band frequency to obtain the corresponding backscattering coefficients. During the training, the backscattering coefficients are the inputs to the neural net and the output from the net are compared with the desired soil parameters to adjust the interconnecting weights. The process is repeated for each input-output data entry and then for the entire training data until convergence is reached. After training, the backscattering coefficients are applied to the trained neural net to retrieve the soil parameters which are compared with the desired soil parameters to verify the effectiveness of this technique. Several cases are examined. First, for simplicity, the correlation length and rms height of the soil surface are fixed while soil moisture is varied. Soil moisture obtained using the neural networks with either L-band or C-band backscattering coefficients for the HH and VV polarizations as inputs is in good agreement with the desired soil moisture. The neural net output matches the desired output for the soil moisture range of 16 to 60 percent for the C-band case. The next case investigated is to vary both soil moisture and rms height while keeping the correlation length fixed. For this case, C-band backscattering coefficients are not sufficient for retrieving two parameters because the Kirchhoff approximation gives the same HH and VV backscattering coefficients. Therefore, the backscattering coefficients at two different frequency bands are necessary to find both the soil moisture and rms height. Finally, the neural nets are also applied to simultaneously invert soil moisture, rms height, and correlation length. Overall, the soil moisture retrieved from the neural network agrees very well with the desired soil moisture. This suggests that the neural network shows potential for retrieval of soil parameters from remote sensing data.

Wang, L.↗

Atacama Cosmology Telescope: Component-separated maps of CMB temperature and the thermal Sunyaev-Zel'dovich effect

Optimal analyses of many signals in the cosmic microwave background (CMB) require map-level extraction of individual components in the microwave sky, rather than measurements at the power spectrum level alone. To date, nearly all map-level component separation in CMB analyses has been performed exclusively using satellite data. In this paper, we implement a component separation method based on the internal linear combination (ILC) approach which we have designed to optimally account for the anisotropic noise (in the 2D Fourier domain) often found in ground-based CMB experiments. Using this method, we combine multi-frequency data from the Planck satellite and the Atacama Cosmology Telescope Polarimeter (ACTPol) to construct the first wide area (≈2100 sq. deg.), arcminute-resolution component-separated maps of the CMB temperature anisotropy and the thermal Sunyaev-Zel'dovich (tSZ) effect sourced by the inverse-Compton scattering of CMB photons off hot, ionized gas. Our ILC pipeline allows for explicit deprojection of various contaminating signals, including a modified blackbody approximation of the cosmic infrared background (CIB) spectral energy distribution. The cleaned CMB maps will be a useful resource for CMB lensing reconstruction, kinematic SZ cross-correlations, and primordial non-Gaussianity studies. The tSZ maps will be used to study the pressure pro les of galaxies, groups, and clusters through cross-correlations with halo catalogs, with dust contamination controlled via CIB deprojection. The data products described in this paper are available on LAMBDA.

Mathew S. Madhavacheril↗

Equilibrium wave spectrum and sea state bias in satellite altimetry

For a well-developed sea at equilibrium with a constant wind, the energy-containing range of the wavenumber spectrum for wind-generated gravity waves is approximated by a generalized power law involving the angular spread function and mu, interpreted as a fractal codimension of a small surface patch. Dependence of mu on the wave age is estimated, and the 'Phillips constant', beta, along with the low-wavenumber boundary, k0, of the inertial subrange are analyzed on the basis of the wave action and energy conservation principles. The resulting expressions are employed to evaluate various non-Gaussian statistics of a weakly nonlinear sea surface, which determine the sea state bias in satellite altimetry. The locally accelerated decay of the spectral density function in a high-wavenumber dissipation subrange is pointed out as an important factor of wave dynamics and the geometrical optics treatment of the sea state bias. The analysis is carried out in the approximation of a unidirectional wave field and confined to the case of a well-developed sea.

Glazman, Roman E.↗

Nonlinear estimation theory applied to orbit determination

The development of an approximate nonlinear filter using the Martingale theory and appropriate smoothing properties is considered. Both the first order and the second order moments were estimated. The filter developed can be classified as a modified Gaussian second order filter. Its performance was evaluated in a simulated study of the problem of estimating the state of an interplanetary space vehicle during both a simulated Jupiter flyby and a simulated Jupiter orbiter mission. In addition to the modified Gaussian second order filter, the modified truncated second order filter was also evaluated in the simulated study. Results obtained with each of these filters were compared with numerical results obtained with the extended Kalman filter and the performance of each filter is determined by comparison with the actual estimation errors. The simulations were designed to determine the effects of the second order terms in the dynamic state relations, the observation state relations, and the Kalman gain compensation term. It is shown that the Kalman gain-compensated filter which includes only the Kalman gain compensation term is superior to all of the other filters.

Choe, C. Y.↗

ORACLS: A system for linear-quadratic-Gaussian control law design

A modern control theory design package (ORACLS) for constructing controllers and optimal filters for systems modeled by linear time-invariant differential or difference equations is described. Numerical linear-algebra procedures are used to implement the linear-quadratic-Gaussian (LQG) methodology of modern control theory. Algorithms are included for computing eigensystems of real matrices, the relative stability of a matrix, factored forms for nonnegative definite matrices, the solutions and least squares approximations to the solutions of certain linear matrix algebraic equations, the controllability properties of a linear time-invariant system, and the steady state covariance matrix of an open-loop stable system forced by white noise. Subroutines are provided for solving both the continuous and discrete optimal linear regulator problems with noise free measurements and the sampled-data optimal linear regulator problem. For measurement noise, duality theory and the optimal regulator algorithms are used to solve the continuous and discrete Kalman-Bucy filter problems. Subroutines are also included which give control laws causing the output of a system to track the output of a prescribed model.

Armstrong, E. S.↗

Molecular collisions in a laser field - Effect of the laser linewidth

The effect of the laser linewidth on molecular collision processes taking place in a laser field is studied, using an approximation scheme that replaces the actual frequency distribution of the field by a finite number of frequencies and weights. The choice of the frequencies and weights is conveniently accomplished by the method of Gaussian quadrature. Close-coupling calculations are performed on model systems, and the results indicate that the neglect of the laser linewidth may be justified in most collision processes in a laser field.

Lee, H. W.↗

Particle Filtering for Model-Based Anomaly Detection in Sensor Networks

A novel technique has been developed for anomaly detection of rocket engine test stand (RETS) data. The objective was to develop a system that postprocesses a csv file containing the sensor readings and activities (time-series) from a rocket engine test, and detects any anomalies that might have occurred during the test. The output consists of the names of the sensors that show anomalous behavior, and the start and end time of each anomaly. In order to reduce the involvement of domain experts significantly, several data-driven approaches have been proposed where models are automatically acquired from the data, thus bypassing the cost and effort of building system models. Many supervised learning methods can efficiently learn operational and fault models, given large amounts of both nominal and fault data. However, for domains such as RETS data, the amount of anomalous data that is actually available is relatively small, making most supervised learning methods rather ineffective, and in general met with limited success in anomaly detection. The fundamental problem with existing approaches is that they assume that the data are iid, i.e., independent and identically distributed, which is violated in typical RETS data. None of these techniques naturally exploit the temporal information inherent in time series data from the sensor networks. There are correlations among the sensor readings, not only at the same time, but also across time. However, these approaches have not explicitly identified and exploited such correlations. Given these limitations of model-free methods, there has been renewed interest in model-based methods, specifically graphical methods that explicitly reason temporally. The Gaussian Mixture Model (GMM) in a Linear Dynamic System approach assumes that the multi-dimensional test data is a mixture of multi-variate Gaussians, and fits a given number of Gaussian clusters with the help of the wellknown Expectation Maximization (EM) algorithm. The parameters thus learned are used for calculating the joint distribution of the observations. However, this GMM assumption is essentially an approximation and signals the potential viability of non-parametric density estimators. This is the key idea underlying the new approach.

Solano, Wanda↗

High-Resolution N-Band Observations of the Nova Rs Ophiuchi: First Science with the Keck Interferometer Nuller

We report new observations of the nova RS Ophiuchi using the Keck Interferometer Nulling Instrument (KIN), approximately 3.8 days following the most recent outburst that occurred on 2006 February 12. These observations represent the first scientific results from the KIN, which operates in N-band from 8 to 12.5 microns. The nulling technique is the sparse aperture equivalent of the conventional coronagraphic technique used in filled aperture telescopes. By fitting the unique KIN inner and outer spatial regime data, we have obtained an angular size of the mid-infrared continuum of 6.2,4.0, or 5.4 mas for a disk profile, Gaussian profile, and shell profile respectively. The data show evidence of enhanced neutral atomic hydrogen emission and atomic metals including silicon located in the inner spatial regime near the white dwarf relative to the outer regime. There are also nebular emission lines and evidence of hot silicate dust in the outer spatial region, centered at approximately 2.5E14 cm from the WD, that are not found in the inner regime. The nova flash in the outer spatial regime evidently excited these features before the blast wave reached these regions. These identifications support the following interpretation. The dust appears to be present between outbursts and was not created during the outburst event. We further discuss the present results in terms of a unifying model of the system that includes an increase in density in the plane of the orbit of the two stars created by a spiral shock wave caused by the motion of the stars through the cool wind of the red giant star. These data show the power and potential of the nulling technique which has been developed for the detection of Earthlike planets around nearby stars for the Terrestrial Planet Finder Mission and Darwin missions.

Danchi, William↗

Steady and Oscillatory, Subsonic and Supersonic, Aerodynamic Pressure and Generalized Forces for Complex Aircraft Configurations and Applications to Flutter

A general method for analyzing aerodynamic flows around complex configurations is presented. By applying the Green function method, a linear integral equation relating the unknown, small perturbation potential on the surface of the body, to the known downwash is obtained. The surfaces of the aircraft, wake and diaphragm (if necessary) are divided into small quadrilateral elements which are approximated with hyperboloidal surfaces. The potential and its normal derivative are assumed to be constant within each element. This yields a set of linear algebraic equations and the coefficients are evaluated analytically. By using Gaussian elimination method, equations are solved for the potentials at the centroids of elements. The pressure coefficient is evaluated by the finite different method; the lift and moment coefficients are evaluated by numerical integration. Numerical results are presented, and applications to flutter are also included.

Chen, L. T.↗

Estimating unsteady aerodynamic forces on a cascade in a three-dimensional turbulence field

An analytical method has been developed to estimate the unsteady aerodynamic forces caused by flow field turbulence on a wind tunnel turning vane cascade system (vane set). This method approximates dynamic lift and drag by linearly perturbing the appropriate steady state force equations, assuming that the dynamic loads are due only to free stream turbulence and that this turbulence is homogeneous, isotropic, and Gaussian. Correlation and unsteady aerodynamic effects are also incorporated into the analytical model. Using these assumptions, equations relating dynamic lift and drag to flow turbulence, mean velocity, and vane set geometry are derived. From these equations, estimates for the power spectra and rms (root mean squared value, delta) loading of both lift and drag can be determined.

Norman, T.↗

Estimating unsteady aerodynamic forces on a cascade in a three-dimensional turbulence field

An analytical method has been developed to estimate tne unsteady aerodynamic forces caused by flow field turbulence on a wind tunnel turning vane cascade system (vane set). This method approximates dynamic lift and drag by linearly perturbing the appropriate steady state force equations, assuming that the dynamic loads are due only to free stream turbulence and that this turbulence is homogeneous, isotropic, and Gaussian. Correlation and unsteady aerodynamic effects are also incorporated into the analytical model. Using these assumptions, equations relating dynamic lift and drag to flow turbulence, mean velocity, and vane set geometry are derived. From these equations, estimates for the power spectra and rms (root mean squared value, delta) loading of both lift and drag can be determined.

Norman, T. R.↗