Search NASA⌕ Search

SEARCH · Search NASA

Results for “Approximation methods”

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 1,153 records · Page 64
All sourcesNASA NTRSDOE OSTI
NASA NTRS1997

Wave Number Selection for Incompressible Parallel Jet Flows Periodic in Space

The temporal instability of a spatially periodic parallel flow of an incompressible inviscid fluid for various jet velocity profiles is studied numerically using Floquet Analysis. The transition matrix at the end of a period is evaluated by direct numerical integration. For verification, a method based on approximating a continuous function by a series of step functions was used. Unstable solutions were found only over a limited range of wave numbers and have a band type structure. The results obtained are analogous to the behavior observed in systems exhibiting complexity at the edge of order and chaos.

Miles, Jeffrey Hilton↗
NASA NTRS1997

Ocean Observations with EOS/MODIS: Algorithm Development and Post Launch Studies

Significant accomplishments made during the present reporting period are as follows: (1) We developed a new method for identifying the presence of absorbing aerosols and, simultaneously, performing atmospheric correction. The algorithm consists of optimizing the match between the top-of-atmosphere radiance spectrum and the result of models of both the ocean and aerosol optical properties; (2) We developed an algorithm for providing an accurate computation of the diffuse transmittance of the atmosphere given an aerosol model. A module for inclusion into the MODIS atmospheric-correction algorithm was completed; (3) We acquired reflectance data for oceanic whitecaps during a cruise on the RV Ka'imimoana in the Tropical Pacific (Manzanillo, Mexico to Honolulu, Hawaii). The reflectance spectrum of whitecaps was found to be similar to that for breaking waves in the surf zone measured by Frouin, Schwindling and Deschamps, however, the drop in augmented reflectance from 670 to 860 nm was not as great, and the magnitude of the augmented reflectance was significantly less than expected; and (4) We developed a method for the approximate correction for the effects of the MODIS polarization sensitivity. The correction, however, requires adequate characterization of the polarization sensitivity of MODIS prior to launch.

Gordon, Howard R.↗
NASA NTRS1999

Phenomenological Theory of the Translational Relaxation Times in Gases

The exact solution to the classical equations governing the translational dispersion and absorption of sound in a gas obscures its relaxational character because of its mathematical complexity. The approach taken here is to solve the secular equation by the method of Pade approximants, which even to the relatively low order R(sub 11) yields a remarkably close approximation to the exact solution over a wide range of frequency/pressure (f/P) ratios. As a result, translational relaxation can be formulated in terms of a conventional relaxation process with well-defined relaxation times, relaxation strength, collision numbers, additivity relations, etc. To extend the theory to high values of f/P ratio, a model is proposed to account for the noncontinuum behavior of the transport coefficients (viscosity and thermal conductivity) as the molecular mean free path approaches the acoustical enclosure dimensions. The theoretical dispersion and absorption show good agreement with measurements in argon over the classical and transition regions of f/P, but a discrepancy appears at higher values of f/P, where collective propagating modes, assumed in the theory, give way to single-particle modes, prevailing in the experiments.

Zuckerwar, Allan J.↗
NASA NTRS1944

The Wall Interference of a Wind Tunnel of Elliptic Cross Section

The wall interference is obtained for a wind tunnel of elliptic section for the two cases of closed and open working sections. The approximate and exact methods used gave results in practically good agreement. Corresponding to the result given by Glauert for the case of the closed rectangular section, the interference is found to be a minimum for a ratio of minor to major axis of 1:square root of 6 This, however, is true only for the case where the span of the airfoil is small in comparison with the width of the tunnel. For a longer airfoil the favorable ellipse is flatter. In the case of the open working section the circular shape gives the minimum interference.

Tani, Itiro↗
NASA NTRS2007

Lunar Return Reentry Thermal Analysis of a Generic Crew Exploration Vehicle Wall Structures

Thermostructural analysis was performed on generic crew exploration vehicle (GCEV) heat shielded wall structures subjected to reentry heating rates based on five potential lunar return reentry trajectories. The GCEV windward outer wall is fabricated with a graphite/epoxy composite honeycomb sandwich panel and the inner wall with an aluminum honeycomb sandwich panel. The outer wall is protected with an ablative Avcoat-5026-39H/CG thermal protection system (TPS). A virtual ablation method (a graphical approximation) developed earlier was further extended, and was used to estimate the ablation periods, ablation heat loads, and the TPS recession layer depths. It was found that up to 83 95 percent of the total reentry heat load was dissipated in the TPS ablation process, leaving a small amount (3-15 percent) of the remaining total reentry heat load to heat the virgin TPS and maintain the TPS surface at the ablation temperature, 1,200 F. The GCEV stagnation point TPS recession layer depths were estimated to be in the range of 0.280-0.910 in, and the allowable minimum stagnation point TPS thicknesses that could maintain the substructural composite sandwich wall at the limit temperature of 300 F were found to be in the range of 0.767-1.538 in. Based on results from the present analyses, the lunar return abort ballistic reentry was found to be quite attractive because it required less TPS weight than the lunar return direct, the lunar return skipping, or the low Earth orbit guided reentry, and only 11.6 percent more TPS weight than the low Earth orbit ballistic reentry that will encounter a considerable weight penalty to obtain the Earth orbit. The analysis also showed that the TPS weight required for the lunar return skipping reentry was much more than the TPS weight necessary for any of the other reentry trajectories considered.

Ko, William L.↗
NASA NTRS2005

Design and Optimization of Low-thrust Orbit Transfers Using Q-law and Evolutionary Algorithms

Future space missions will depend more on low-thrust propulsion (such as ion engines) thanks to its high specific impulse. Yet, the design of low-thrust trajectories is complex and challenging. Third-body perturbations often dominate the thrust, and a significant change to the orbit requires a long duration of thrust. In order to guide the early design phases, we have developed an efficient and efficacious method to obtain approximate propellant and flight-time requirements (i.e., the Pareto front) for orbit transfers. A search for the Pareto-optimal trajectories is done in two levels: optimal thrust angles and locations are determined by Q-law, while the Q-law is optimized with two evolutionary algorithms: a genetic algorithm and a simulated-annealing-related algorithm. The examples considered are several types of orbit transfers around the Earth and the asteroid Vesta.

low-thrust orbit transfer↗
NASA NTRS2009

Highly Scalable Matching Pursuit Signal Decomposition Algorithm

Matching Pursuit Decomposition (MPD) is a powerful iterative algorithm for signal decomposition and feature extraction. MPD decomposes any signal into linear combinations of its dictionary elements or atoms . A best fit atom from an arbitrarily defined dictionary is determined through cross-correlation. The selected atom is subtracted from the signal and this procedure is repeated on the residual in the subsequent iterations until a stopping criterion is met. The reconstructed signal reveals the waveform structure of the original signal. However, a sufficiently large dictionary is required for an accurate reconstruction; this in return increases the computational burden of the algorithm, thus limiting its applicability and level of adoption. The purpose of this research is to improve the scalability and performance of the classical MPD algorithm. Correlation thresholds were defined to prune insignificant atoms from the dictionary. The Coarse-Fine Grids and Multiple Atom Extraction techniques were proposed to decrease the computational burden of the algorithm. The Coarse-Fine Grids method enabled the approximation and refinement of the parameters for the best fit atom. The ability to extract multiple atoms within a single iteration enhanced the effectiveness and efficiency of each iteration. These improvements were implemented to produce an improved Matching Pursuit Decomposition algorithm entitled MPD++. Disparate signal decomposition applications may require a particular emphasis of accuracy or computational efficiency. The prominence of the key signal features required for the proper signal classification dictates the level of accuracy necessary in the decomposition. The MPD++ algorithm may be easily adapted to accommodate the imposed requirements. Certain feature extraction applications may require rapid signal decomposition. The full potential of MPD++ may be utilized to produce incredible performance gains while extracting only slightly less energy than the standard algorithm. When the utmost accuracy must be achieved, the modified algorithm extracts atoms more conservatively but still exhibits computational gains over classical MPD. The MPD++ algorithm was demonstrated using an over-complete dictionary on real life data. Computational times were reduced by factors of 1.9 and 44 for the emphases of accuracy and performance, respectively. The modified algorithm extracted similar amounts of energy compared to classical MPD. The degree of the improvement in computational time depends on the complexity of the data, the initialization parameters, and the breadth of the dictionary. The results of the research confirm that the three modifications successfully improved the scalability and computational efficiency of the MPD algorithm. Correlation Thresholding decreased the time complexity by reducing the dictionary size. Multiple Atom Extraction also reduced the time complexity by decreasing the number of iterations required for a stopping criterion to be reached. The Course-Fine Grids technique enabled complicated atoms with numerous variable parameters to be effectively represented in the dictionary. Due to the nature of the three proposed modifications, they are capable of being stacked and have cumulative effects on the reduction of the time complexity.

Christensen, Daniel↗
NASA NTRS2009

Automatic Determination of the Conic Coronal Mass Ejection Model Parameters

Characterization of the three-dimensional structure of solar transients using incomplete plane of sky data is a difficult problem whose solutions have potential for societal benefit in terms of space weather applications. In this paper transients are characterized in three dimensions by means of conic coronal mass ejection (CME) approximation. A novel method for the automatic determination of cone model parameters from observed halo CMEs is introduced. The method uses both standard image processing techniques to extract the CME mass from white-light coronagraph images and a novel inversion routine providing the final cone parameters. A bootstrap technique is used to provide model parameter distributions. When combined with heliospheric modeling, the cone model parameter distributions will provide direct means for ensemble predictions of transient propagation in the heliosphere. An initial validation of the automatic method is carried by comparison to manually determined cone model parameters. It is shown using 14 halo CME events that there is reasonable agreement, especially between the heliocentric locations of the cones derived with the two methods. It is argued that both the heliocentric locations and the opening half-angles of the automatically determined cones may be more realistic than those obtained from the manual analysis

Pulkkinen, A.↗
NASA NTRS2016

Comparison of Areas in Shadow from Imaging and Altimetry in the North Polar Region of Mercury and Implications for Polar Ice Deposits

Earth-based radar observations and results from the MESSENGER mission have provided strong evidence that permanently shadowed regions near Mercury's poles host deposits of water ice. MESSENGER's complete orbital image and topographic datasets enable Mercury's surface to be observed and modeled under an extensive range of illumination conditions. The shadowed regions of Mercury's north polar region from 65 deg N to 90 deg N were mapped by analyzing Mercury Dual Imaging System (MDIS) images and by modeling illumination with Mercury Laser Altimeter (MLA) topographic data. The two independent methods produced strong agreement in identifying shadowed areas. All large radar-bright deposits, those hosted within impact craters greater than or equal to 6 km in diameter, collocate with regions of shadow identified by both methods. However, only approximately 46% of the persistently shadowed areas determined from images and approximately 43% of the permanently shadowed areas derived from altimetry host radar-bright materials. Some sizable regions of shadow that do not host radar-bright deposits experience thermal conditions similar to those that do. The shadowed craters that lack radar-bright materials show a relation with longitude that is not related to the thermal environment, suggesting that the Earth-based radar observations of these locations may have been limited by viewing geometry, but it is also possible that water ice in these locations is insulated by anomalously thick lag deposits or that these shadowed regions do not host water ice.

MESSENGER↗
NASA NTRS2016

Deposition, Accumulation, and Alteration of Cl(-), NO3(-), ClO4(-) and ClO3(-) Salts in a Hyper-Arid Polar Environment: Mass Balance and Isotopic Constraints

The salt fraction in permafrost soils/sediments of the McMurdo Dry Valleys (MDV) of Antarctica can be used as a proxy for cold desert geochemical processes and paleoclimate reconstruction. Previous analyses of the salt fraction in MDV permafrost soils have largely been conducted in coastal regions where permafrost soils are variably affected by aqueous processes and mixed inputs from marine and stratospheric sources. We expand upon this work by evaluating permafrost soil/sediments in University Valley, located in the ultraxerous zone where both liquid water transport and marine influences are minimal. We determined the abundances of Cl(-), NO3(-, ClO4(-)and ClO3(-)in dry and ice-cemented soil/sediments, snow and glacier ice, and also characterized Cl(-) and NO3(-) isotopically. The data are not consistent with salt deposition in a sublimation till, nor with nuclear weapon testing fall-out, and instead point to a dominantly stratospheric source and to varying degrees of post depositional transformation depending on the substrate, from minimal alteration in bare soils to significant alteration (photodegradation and/or volatilization) in snow and glacier ice. Ionic abundances in the dry permafrost layer indicate limited vertical transport under the current climate conditions, likely due to percolation of snowmelt. Subtle changes in ClO4(-)/NO3(-) ratios and NO3(-) isotopic composition with depth and location may reflect both transport related fractionation and depositional history. Low molar ratios of ClO3(-)/ClO4(-) in surface soils compared to deposition and other arid systems suggest significant post depositional loss of ClO3(-), possibly due to reduction by iron minerals, which may have important implications for oxy-chlorine species on Mars. Salt accumulation varies with distance along the valley and apparent accumulation times based on multiple methods range from approximately 10 to 30 kyr near the glacier to 70-200 kyr near the valley mouth. The relatively young age of the salts and relatively low and homogeneous anion concentrations in the ice-cemented sediments point to either a mechanism of recent salt removal, or to relatively modern permafrost soils (less than 1 million years). Together, our results show that near surface salts in University Valley serve as an end-member of stratospheric sources not subject to biological processes or extensive remobilization.

cold desert geochemical processes↗
NASA NTRS2017

Testing the Accuracy of Data-Driven MHD Simulations of Active Region Evolution

Models for the evolution of the solar coronal magnetic field are vital for understanding solar activity, yet the best measurements of the magnetic field lie at the photosphere, necessitating the development of coronal models which are "data-driven" at the photosphere. We present an investigation to determine the feasibility and accuracy of such methods. Our validation framework uses a simulation of active region (AR) formation, modeling the emergence of magnetic flux from the convection zone to the corona, as a ground-truth data set, to supply both the photospheric information and to perform the validation of the data-driven method. We focus our investigation on how the accuracy of the data-driven model depends on the temporal frequency of the driving data. The Helioseismic and Magnetic Imager on NASA's Solar Dynamics Observatory produces full-disk vector magnetic field measurements at a 12-minute cadence. Using our framework we show that ARs that emerge over 25 hours can be modeled by the data-driving method with only approximately 1 percent error in the free magnetic energy, assuming the photospheric information is specified every 12 minutes. However, for rapidly evolving features, under-sampling of the dynamics at this cadence leads to a strobe effect, generating large electric currents and incorrect coronal morphology and energies. We derive a sampling condition for the driving cadence based on the evolution of these small-scale features, and show that higher-cadence driving can lead to acceptable errors. Future work will investigate the source of errors associated with deriving plasma variables from the photospheric magnetograms as well as other sources of errors, such as reduced resolution, instrument bias, and noise.

Leake, James E.↗
NASA NTRS2003

UCLA parallel PIC framework

The UCLA Parallel PIC Framework (UPIC) has been developed to provide trusted components for the rapid construction of new, parallel Particle-in-Cell (PIC) codes. The Framework uses object-based ideas in Fortran95, and is designed to provide support for various kinds of PIC codes on various kinds of hardware. The focus is on student programmers. The Framework supports multiple numerical methods, different physics approximations, different numerical optimizations and implementations for different hardware. It is designed with "defensive" programming in mind, meaning that it contains many error checks and debugging helps. Above all, it is designed to hide the complexity of parallel processing. It is currently being used in a number of new Parallel PIC codes.

Norton, Charles D.↗
NASA NTRS2022

Comparison of Likelihood Methods for Generalized Linear Mixed Models with Application to Quiet Supersonic Flights 2018 Data

Repeated measurement will be a feature of the survey data collected during the Quesst missionX-59 community response tests (CRT). Since each participant will report his or her categorical level of annoyance in response to multiple events, the responses from any single individual may be correlated with one another. Several models within the class of generalized linear mixed models (GLMM) are pertinent to the analysis of correlated categorical outcomes; the random intercept logistic regression model is one example. Both Bayesian and frequentist methods for fitting these models are available, with frequentist methods relying on some form of approximation (of either an integral or the integrand) that appears in the marginal likelihood function. Given several anticipated similarities of the X-59 CRT data to data collected during a past risk reduction, Quiet Supersonic Flights 2018 (QSF18), this short note is intended to create awareness. It documents an instance in which a reported population average dose-response relationship derived from QSF18 single event data was distorted by the integral approximation applied in likelihood-based methods. We review some of the available literature on the topic, compare the outputs of several different computational approaches implemented in available statistical software, and present simple corrective actions that may be useful during the Quesst mission.

dose-response model↗
NASA NTRS2018

Variability Timescale and Spectral Index of Sgr A* in the Near Infrared: Approximate Bayesian Computation Analysis of the Variability of the Closest Supermassive Black Hole

Sagittarius A* (Sgr A* ) is the variable radio, near-infrared (NIR), and X-ray source associated with accretion onto the Galactic center black hole. We present an analysis of the most comprehensive NIR variability data set of Sgr A* to date: eight 24 hr epochs of continuous monitoring of Sgr A* at 4.5 μm with the IRAC instrument on the Spitzer Space Telescope, 93 epochs of 2.18 μm data from Naos Conica at the Very Large Telescope, and 30 epochs of 2.12 μm data from the NIRC2 camera at the Keck Observatory, in total 94,929 measurements. A new approximate Bayesian computation method for fitting the first-order structure function extracts information beyond current fast Fourier transformation (FFT) methods of power spectral density (PSD) estimation. With a combined fit of the data of all three observatories, the characteristic coherence timescale of Sgr A* is b 243 57 82 t = - + minutes (90% credible interval). The PSD has no detectable features on timescales down to 8.5 minutes (95% credible level), which is the ISCO orbital frequency for a dimensionless spin parameter a = 0.92. One light curve measured simultaneously at 2.12 and 4.5 μm during a low flux-density phase gave a spectral index αs = 1.6 ± 0.1 (F µ n s n -a ). This value implies that the Sgr A* NIR color becomes bluer during higher flux-density phases. The probability densities of flux densities of the combined data sets are best fit by log-normal distributions. Based on these distributions, the Sgr A* spectral energy distribution is consistent with synchrotron radiation from a nonthermal electron population from below 20 GHz through the NIR.

accretion↗
NASA NTRS2022

Observational Signatures of Coronal Heating in Magnetohydrodynamic Simulations without Radiation or a Lower Atmosphere

It is extremely difficult to simulate the details of coronal heating and also make meaningful predictions of the emitted radiation. Thus, testing realistic models with observations is a major challenge. Observational signatures of coronal heating depend crucially on radiation, thermal conduction, and the exchange of mass and energy with the transition region and chromosphere below. Many magnetohydrodynamic simulation studies do not include these effects, opting instead to devote computational resources to the magnetic aspects of the problem. We have developed a simple method of accounting approximately for the missing effects. It is applied to the simulation output ex post facto and therefore may be a valuable tool for many studies. We have used it to predict the emission from a model corona that is driven by vortical boundary motions meant to represent photospheric convection. We find that individual magnetic strands experience short-term brightenings, both scattered throughout the computational volume and in localized clusters. The former may explain the diffuse component of the observed corona, while the latter may explain bright coronal loops. Several observed properties of loops are reproduced reasonably well: width, lifetime, and quasi-circular cross section (aspect ratio not high). Our results lend support to the idea that loops are multistranded structures heated by "storms" of nanoflares.

James A. Klimchuk↗
NASA NTRS1993

Microwave Scattering Model for Grass Blade Structures

In this paper, the electromagnetic scattering solution for a grass blade with complex cross-section geometry is considered. It is assumed that the blade cross section is electrically small, but its length is large compared to the incident wavelength. In a recent study it has been shown that the scattering solution for such problems, in the form of a polarizability tensor, can be obtained using the low-frequency approximation in conjunction with the method of moments. In addition, the study shows that the relationship between the polarizability tensor of a dielectric cylinder and its dielectric constant can be approximated by a simple algebraic expression. The results of this study are used to show that this algebraic approximation is valid also for cylinders with cross sections the shape of grass blades, providing that proper values am selected for each of three constants appearing in the expression. These constants are dependent on cylinder shape, and if the relationship between the constants and the three parameters describing a grass blade shape can be determined, an algebraic approximation relating polarizability tensor to blade shape, as well as dielectric constant, can be formed. Since the elements of the polarizability tensor are dependent on only these parameters, this algebraic approximation can replace the cumbersome method of moments model. A conjugate gradient method is then implemented to correctly determine the three constants of the algebraic approximation for each blade shape. A third-order polynomial fit to the data is then determined for each constant, thus providing a complete analytic replacement to the numerical (moment method) scattering model. Comparisons of this approximation to the numerical model show an average error of less than 3%.

Stiles, James M.↗
NASA NTRS1984

Extensions of the Ritz-Galerkin method for the forced, damped vibrations of structural elements

The Ritz-Galerkin methods were used to obtain approximate solutions for free undamped, vibration problems. It is demonstrated that these same methods may be used straightforwardly to analyze forced vibrations with damping without requiring the free vibration eigenfunctions. It was shown that the Galerkin method is an effective technique for these types of problems. The Ritz method has the advantage that it does not need to satisfy the force-type boundary conditions, which is particularly important for plates and shells. Proper functionals representing the forcing and damping terms were developed. Two types of damping--viscous and material (hysteretic) are discussed. Distributed and concentrated exciting forces are treated. Numerical results are obtained for cantilevered beams and rectangular plates. The rates of convergence of the solutions are shown. Approximate solutions from the present methods are compared with the exact solutions for the cantilever beam.

Leissa, A. W.↗