Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “generalized functions”

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 505 records · Page 28

Potential flow about arbitrary biplane wing sections

A rigorous treatment is given of the problem of determining the two-dimensional potential flow around arbitrary biplane cellules. The analysis involves the use of elliptic functions and is sufficiently general to include the effects of such elements as the section shapes, the chord ratio, gap, stagger, and decalage, which elements may be specified arbitrarily. The flow problem is resolved by making use of the methods of conformal representation. Thus the solution of the problem of transforming conformally two arbitrary contours into two circles is expressed by a pair of simultaneous integral equations, for which a method of numerical solution is outlined. As an example of the numerical process, the pressure distribution over certain arrangements of the NACA 4412 airfoil in biplane combinations is presented and compared with the monoplane pressure distribution.

Garrick, I E↗

Fracture mechanics life analytical methods verification testing

Verification and validation of the basic information capabilities in NASCRAC has been completed. The basic information includes computation of K versus a, J versus a, and crack opening area versus a. These quantities represent building blocks which NASCRAC uses in its other computations such as fatigue crack life and tearing instability. Several methods were used to verify and validate the basic information capabilities. The simple configurations such as the compact tension specimen and a crack in a finite plate were verified and validated versus handbook solutions for simple loads. For general loads using weight functions, offline integration using standard FORTRAN routines was performed. For more complicated configurations such as corner cracks and semielliptical cracks, NASCRAC solutions were verified and validated versus published results and finite element analyses. A few minor problems were identified in the basic information capabilities of the simple configurations. In the more complicated configurations, significant differences between NASCRAC and reference solutions were observed because NASCRAC calculates its solutions as averaged values across the entire crack front whereas the reference solutions were computed for a single point.

Favenesi, J. A.↗

ASIC For Complex Fixed-Point Arithmetic

Application-specific integrated circuit (ASIC) performs 24-bit, fixed-point arithmetic operations on arrays of complex-valued input data. High-performance, wide-band arithmetic logic unit (ALU) designed for use in computing fast Fourier transforms (FFTs) and for performing ditigal filtering functions. Other applications include general computations involved in analysis of spectra and digital signal processing.

Petilli, Stephen G.↗

OVERGRID: A Unified Overset Grid Generation Graphical Interface

This paper presents a unified graphical interface and gridding strategy for performing overset grid generation. The interface called OVERGRID has been specifically designed to follow an efficient overset gridding strategy, and contains general grid manipulation capabilities as well as modules that are specifically suited for overset grids. General grid utilities include functions for grid redistribution, smoothing, concatenation, extraction, extrapolation, projection, and many others. Modules specially tailored for overset grids include a seam curve extractor, hyperbolic and algebraic surface grid generators, a hyperbolic volume grid generator, and a Cartesian box grid generator, Grid visualization is achieved using OpenGL while widgets are constructed with Tcl/Tk. The software is portable between various platforms from UNIX workstations to personal computers.

Chan, William M.↗

Tactical Defenses Against Systematic Variation in Wind Tunnel Testing

This paper examines the role of unexplained systematic variation on the reproducibility of wind tunnel test results. Sample means and variances estimated in the presence of systematic variations are shown to be susceptible to bias errors that are generally non-reproducible functions of those variations. Unless certain precautions are taken to defend against the effects of systematic variation, it is shown that experimental results can be difficult to duplicate and of dubious value for predicting system response with the highest precision or accuracy that could otherwise be achieved. Results are reported from an experiment designed to estimate how frequently systematic variations are in play in a representative wind tunnel experiment. These results suggest that significant systematic variation occurs frequently enough to cast doubts on the common assumption that sample observations can be reliably assumed to be independent. The consequences of ignoring correlation among observations induced by systematic variation are considered in some detail. Experimental tactics are described that defend against systematic variation. The effectiveness of these tactics is illustrated through computational experiments and real wind tunnel experimental results. Some tutorial information describes how to analyze experimental results that have been obtained using such quality assurance tactics.

DeLoach, Richard↗

Non-invasive neuroimaging using near-infrared light

This article reviews diffuse optical brain imaging, a technique that employs near-infrared light to non-invasively probe the brain for changes in parameters relating to brain function. We describe the general methodology, including types of measurements and instrumentation (including the tradeoffs inherent in the various instrument components), and the basic theory required to interpret the recorded data. A brief review of diffuse optical applications is included, with an emphasis on research that has been done with psychiatric populations. Finally, we discuss some practical issues and limitations that are relevant when conducting diffuse optical experiments. We find that, while diffuse optics can provide substantial advantages to the psychiatric researcher relative to the alternative brain imaging methods, the method remains substantially underutilized in this field.

Non-NASA Center↗

Nonlinear Dynamics of Cantilever-Sample Interactions in Atomic Force Microscopy

The interaction of the cantilever tip of an atomic force microscope (AFM) with the sample surface is obtained by treating the cantilever and sample as independent systems coupled by a nonlinear force acting between the cantilever tip and a volume element of the sample surface. The volume element is subjected to a restoring force from the remainder of the sample that provides dynamical equilibrium for the combined systems. The model accounts for the positions on the cantilever of the cantilever tip, laser probe, and excitation force (if any) via a basis set of set of orthogonal functions that may be generalized to account for arbitrary cantilever shapes. The basis set is extended to include nonlinear cantilever modes. The model leads to a pair of coupled nonlinear differential equations that are solved analytically using a matrix iteration procedure. The effects of oscillatory excitation forces applied either to the cantilever or to the sample surface (or to both) are obtained from the solution set and applied to the to the assessment of phase and amplitude signals generated by various acoustic-atomic force microscope (A-AFM) modalities. The influence of bistable cantilever modes of on AFM signal generation is discussed. The effects on the cantilever-sample surface dynamics of subsurface features embedded in the sample that are perturbed by surface-generated oscillatory excitation forces and carried to the cantilever via wave propagation are accounted by the Bolef-Miller propagating wave model. Expressions pertaining to signal generation and image contrast in A-AFM are obtained and applied to amplitude modulation (intermittent contact) atomic force microscopy and resonant difference-frequency atomic force ultrasonic microscopy (RDF-AFUM). The influence of phase accumulation in A-AFM on image contrast is discussed, as is the effect of hard contact and maximum nonlinearity regimes of A-AFM operation.

Cantrell, John H.↗

Effects of Bed Rest on Conduction Velocity of the Triceps Surae Stretch Reflex and Postural Control

Despite rigorous exercise and nutritional management during space missions, astronauts returning from microgravity exhibit neuromuscular deficits and a significant loss in muscle mass in the postural muscles of the lower leg. Similar changes in the postural muscles occur in subjects participating in long-duration bed rest studies. These adaptive muscle changes manifest as a reduction in reflex conduction velocity during head-down bed rest. Because the stretch reflex encompasses both the peripheral (muscle spindle and nerve axon) and central (spinal synapse) components involved in adaptation to calf muscle unloading, it may be used to provide feedback on the general condition of neuromuscular function, and might be used to evaluate the effectiveness of countermeasures aimed at preserving muscle mass and function during periods of unloading. Stretch reflexes were measured on 18 control subjects who spent 60 to 90 days in continuous 6 deg head-down bed rest. Using a motorized system capable of rotating the foot around the ankle joint (dorsiflexion) through an angle of 10 degrees at a peak velocity of about 250 deg/sec, a stretch reflex was recorded from the subject's left triceps surae muscle group. Using surface electromyography, about 300 reflex responses were obtained and ensemble-averaged on 3 separate days before bed rest, 3 to 4 times in bed, and 3 times after bed rest. The averaged responses for each test day were examined for reflex latency and conduction velocity (CV) across gender. Computerized posturography was also conducted on these same subjects before and after bed rest as part of the standard measures. Peak-to-peak sway was measured during Sensory Organization Tests (SOTs) to evaluate changes in the ability to effectively use or suppress visual, vestibular, and proprioceptive information for postural control. Although no gender differences were found, a significant increase in reflex latency and a significant decrease in CV were observed during the bed rest period, with a return to baseline 3 to 5 days after bed rest, depending on the duration of bed rest. In addition, a relationship between CV and loss of muscle strength in the lower leg was observed post bed rest for most subjects. Immediately post-bed rest, most subjects showed decreased performance on SOTs, with the greater decrements on sway-referenced support and head movement conditions. Post-bed rest decrements were less than typically observed following spaceflight. Decrements in postural control and the stretch reflex can be primarily attributed to the unloading mechanisms this ground-based analog provides. The stretch reflex is a concise test measurement that can be obtained during the head-down phase of bed rest, as it does not interfere with the bed rest paradigm. This makes it an ideal tool that can detect, early on, whether a countermeasure is successful in preserving muscle function.

Reschke, M. F.↗

Leveraging the Cloud for Robust and Efficient Lunar Image Processing

The Lunar Mapping and Modeling Project (LMMP) is tasked to aggregate lunar data, from the Apollo era to the latest instruments on the LRO spacecraft, into a central repository accessible by scientists and the general public. A critical function of this task is to provide users with the best solution for browsing the vast amounts of imagery available. The image files LMMP manages range from a few gigabytes to hundreds of gigabytes in size with new data arriving every day. Despite this ever-increasing amount of data, LMMP must make the data readily available in a timely manner for users to view and analyze. This is accomplished by tiling large images into smaller images using Hadoop, a distributed computing software platform implementation of the MapReduce framework, running on a small cluster of machines locally. Additionally, the software is implemented to use Amazon's Elastic Compute Cloud (EC2) facility. We also developed a hybrid solution to serve images to users by leveraging cloud storage using Amazon's Simple Storage Service (S3) for public data while keeping private information on our own data servers. By using Cloud Computing, we improve upon our local solution by reducing the need to manage our own hardware and computing infrastructure, thereby reducing costs. Further, by using a hybrid of local and cloud storage, we are able to provide data to our users more efficiently and securely. 12 This paper examines the use of a distributed approach with Hadoop to tile images, an approach that provides significant improvements in image processing time, from hours to minutes. This paper describes the constraints imposed on the solution and the resulting techniques developed for the hybrid solution of a customized Hadoop infrastructure over local and cloud resources in managing this ever-growing data set. It examines the performance trade-offs of using the more plentiful resources of the cloud, such as those provided by S3, against the bandwidth limitations such use encounters with remote resources. As part of this discussion this paper will outline some of the technologies employed, the reasons for their selection, the resulting performance metrics and the direction the project is headed based upon the demonstrated capabilities thus far.

Cloud Computing↗

On the Composition of Young, Directly Imaged Giant Planets

The past decade has seen significant progress on the direct detection and characterization of young, self-luminous giant planets at wide orbital separations from their host stars. Some of these planets show evidence for disequilibrium processes like transport-induced quenching in their atmospheres; photochemistry may also be important, despite the typically large orbital distances. Disequilibrium chemical processes such as these can alter the expected composition, spectral behavior, thermal structure, and cooling history of the planets, and can potentially confuse determinations of bulk elemental ratios, which provide important insights into planet-formation mechanisms. Using a thermo/photochemical kinetics and transport model, we investigate the extent to which disequilibrium chemical processes affect the composition and spectra of directly imaged giant exoplanets. Results for specific "young Jupiters" such as HR 8799 b and c and 51 Eri b are presented, as are general trends as a function of planetary effective temperature, surface gravity, incident ultraviolet flux, and strength of deep atmospheric convection. We find that quenching is very important on young Jupiters, leading to CO/CH4 and N2/NH3 ratios much greater than; and H2O mixing ratios a factor of a few less than chemical equilibrium predictions. Photochemistry can also be important on such planets, with CO2 and HCN being key photochemical products. Carbon dioxide becomes a particularly major constituent when stratospheric temperatures are low and recycling of water following H2O photolysis becomes stifled. Young Jupiters with effective temperatures less than 700 degrees Kelvin are in a particularly interesting photochemical regime that differs from both transiting hot Jupiters and our own solar-system giant planets.

photochemistry↗

Modulation-transfer-function analysis for sampled image systems

Sampling generally causes the response of a digital imaging system to be locally shift-variant and not directly amenable to Modulation Transfer Function (MTF) analysis. However, this paper demonstrates that a meaningful system response can be calculated by averaging over an ensemble of point-source system inputs to yield an MTF which accounts for the combined effects of image formation, sampling, and image reconstruction. As an illustration, the MTF of the Landsat MSS system is analyzed to reveal an average effective instantaneous field of view which is significantly larger than the commonly accepted value, particularly in the along-track direction where undersampling contributes markedly to an MTF reduction and resultant increase in image blur.

Park, S. K.↗

Development of a winter wheat adjustable crop calendar model

The author has identified the following significant results. Least squares techniques were applied for parameter estimation of functions to predict winter wheat phenological stage with daily maximum temperature, minimum temperature, daylength, and precipitation as independent variables. After parameter estimation, tests were conducted using independent data. It may generally be concluded that exponential functions have little advantage over polynomials. Precipitation was not found to significantly affect the fits. The Robertson triquadratic form, in general use for spring wheat, yielded good results, but special techniques and care are required. In most instances, equations with nonlinear effects were found to yield erratic results when utilized with averaged daily environmental values as independent variables.

Baker, J. R.↗

Equilibrium models of self-gravitating inviscid disks resulting from the collapse of rotating clouds

A method is presented for the construction of velocity and surface density profiles of infinitely thin, self-gravitating disks formed from the collapse of spherical clouds, under the condition that the angular momentum of each material parcel is conserved. Results are presented for initially uniformly rotating clouds with density distributions varying as R exp -n and n = 0, 1, 2. The resulting disk surface density distributions are well represented by power laws in the cylindrical radius over most of their extent. The form of the zeroth-order approximation provides a useful representation of the final surface density function near the center for all three cases, and for n = 2 this result holds throughout the disk. This result is not generally true for the velocity functions, however.

Stemwedel, Sally W.↗

Extension of the quasistatic far-wing line shape theory to multicomponent anisotropic potentials

The formalism developed previously for the calculation of the far-wing line shape function and the corresponding absorption coefficient using a single-component anisotropic interaction term and the binary collision and quasistatic approximations is generalized to multicomponent anisotropic potential functions. Explicit expressions are presented for several common cases, including the long-range dipole-dipole plus dipole-quadrupole interaction and a linear molecule interacting with a perturber atom. After determining the multicomponent functional representation for the interaction between the CO2 and Ar from previously published data, we calculate the theoretical line shape function and the corresponding absorption due to the nu(sub 3) band of CO2 in the frequency range 2400-2580 cm(exp -1) and compare our results with previous calculations carried out using a single-component anisotropic interaction, and with the results obtained assuming Lorentzian line shapes. The principal uncertainties in the present results, possible refinements of the theoretical formalism, and the applicability to other systems are discussed briefly.

Ma, Q.↗

Overview of the fatigue/fracture/life working group program at the Lewis Research Center

Constitutive and life prediction models are developed and verified for materials typically used in hot gas path components of reusable space propulsion systems over the range of relevant operating environments. The efforts were centered on the development of crack initiation life prediction methods, while the efforts of a counterpart group were centered on the development of cyclic crack propagation life prediction methods. The complexion of the active tasks are presented. A significant new task started this year will incorporate the various material constitutive and life prediction models developed in this program into a comprehensive creep-fatigue damage analysis and life assessment computer code. The program will function as a postprocessor to general structural analysis programs (such as finite element or boundary element codes) using the output of such analyses (stress, strain, and temperature fields as functions of time) as the input to the damage analysis and life assessment code. The code will be designed to execute on engineering/scientific workstations and will feature a windowing, mouse-driven user interface. Current plans call for the code to be finished and made available for use in mid 1991.

Mcgaw, Michael A.↗

Polynomial approximation of functions of matrices and its application to the solution of a general system of linear equations

During the process of solving a mathematical model numerically, there is often a need to operate on a vector v by an operator which can be expressed as f(A) while A is NxN matrix (ex: exp(A), sin(A), A sup -1). Except for very simple matrices, it is impractical to construct the matrix f(A) explicitly. Usually an approximation to it is used. In the present research, an algorithm is developed which uses a polynomial approximation to f(A). It is reduced to a problem of approximating f(z) by a polynomial in z while z belongs to the domain D in the complex plane which includes all the eigenvalues of A. This problem of approximation is approached by interpolating the function f(z) in a certain set of points which is known to have some maximal properties. The approximation thus achieved is almost best. Implementing the algorithm to some practical problem is described. Since a solution to a linear system Ax = b is x= A sup -1 b, an iterative solution to it can be regarded as a polynomial approximation to f(A) = A sup -1. Implementing the algorithm in this case is also described.

Tal-Ezer, Hillel↗