Use of transformations in multiparameter data sorting.
Multiparameter data sorting technique for one- parameter information represented by simple distribution described by appropriate transformation coefficients
TRANSFORMATION TENSOR↗
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Fourier transform methods for analyzing nonuniform arrays.
Radiation pattern of nonuniformly spaced array, using transform method
RADIATION DISTRIBUTION↗
Plane-wave spectrum representation of a field in a magnetoionic medium due to a plane distribution of source currents.
Plane wave spectrum representation of field in magnetoionic medium due to source current plane distribution, using Fourier transform
FOURIER TRANSFORM↗
Application of queueing models to multiprogrammed computer systems operating in a time-critical environment
A model of a central processor (CPU) which services background applications in the presence of time critical activity is presented. The CPU is viewed as an M/M/1 queueing system subject to periodic interrupts by deterministic, time critical process. The Laplace transform of the distribution of service times for the background applications is developed. The use of state of the art queueing models for studying the background processing capability of time critical computer systems is discussed and the results of a model validation study which support this application of queueing models are presented.
Eckhardt, D. E., Jr.↗
Flight-Stability Extremes Calculated From the Uncertainty Ellipse
Tangents and normals to ellipse derived for situations with two correlated aerodynamic force or moment variables having normally (Gaussian) distributed uncertainty. Although transformations and vector calculations tedious when done by hand, equations in closed form and give rapid results when performed by computers or programable desk calculators. Probability extremes of ratios and magnitude obtained directly, without repeated table lookup or other complication.
Dominik, D. F.↗
Secondary pattern computation of an offset reflector antenna
Reflector antennas are widely used in communications satellite systems because they provide high gain at low cost. In analyzing reflector antennas the computation of the secondary pattern is the main concern. A computer program for calculating the secondary pattern of an offset reflector has been developed and implemented at the NASA Lewis Research Center. The theoretical foundation for this program is based on the use of geometrical optics to describe the fields from the feed to the reflector surface and to the aperture plane. The resulting aperture field distribution is then transformed to the far-field zone by the fast Fourier transform algorithm. Comparing this technique with other well-known techniques (the geometrical theory of diffraction, physical optics (Jacobi-Bessel), etc.) shows good agreement for large (diameter of 100 lambda or greater) reflector antennas.
Acosta, R. J.↗
Analysis of exhaustive limited service for token ring networks
Token ring operation is well-understood in the cases of exhaustive, gated, gated limited, and ordinary cyclic service. There is no current data, however, on queueing models for the exhaustive limited service type. This service type differs from the others in that there is a preset maximum (omega) on the number of packets which may be transmitted per token reception, and packets which arrive after token reception may still be transmitted if the preset packet limit has not been reached. Exhaustive limited service is important since it closely approximates a timed token service discipline (the approximation becomes exact if packet lengths are constant). A method for deriving the z-transforms of the distributions of the number of packets present at both token departure and token arrival for a system using exhaustive limited service is presented. This allows for the derivation of a formula for mean queueing delay and queue lengths. The method is theoretically applicable to any omega. Fortunately, as the value of omega becomes large (typically values on the order of omega = 8 are considered large), the exhaustive limited service discipline closely approximates an exhaustive service discipline.
Peden, Jeffery H.↗
Transform methods for precision continuum and control models of flexible space structures
An open loop optimal control algorithm is developed for general flexible structures, based on Laplace transform methods. A distributed parameter model of the structure is first presented, followed by a derivation of the optimal control algorithm. The control inputs are expressed in terms of their Fourier series expansions, so that a numerical solution can be easily obtained. The algorithm deals directly with the transcendental transfer functions from control inputs to outputs of interest, and structural deformation penalties, as well as penalties on control effort, are included in the formulation. The algorithm is applied to several structures of increasing complexity to show its generality.
Lupi, Victor D.↗
Dynamics of the atmospheres of the outer planets
Current knowledge about dynamics and the thermal structure of the outer planets is reviewed with the aim of identifying important measurements which should be made in the post-Voyager era. The existence of jets and cloud bands is the puzzle that underlies all others. The discussion focuses on the particular case of Jupiter because the documentation is the most complete. It is argued that the gross dynamical parameters of the outer planetary atmospheres are the keys to their behaviors, rather than the particular specifics of radiative forcing, cloud distributions, or thermodynamic transformations. Voyager data has shown that the jet systems decay with height in the region above the visible clouds. Therefore, the highest priority must be given to establishing dynamical parameters that characterize levels within and beneath the clouds. These require the determination of the deep structure of the jets, of the density stratification, and of the horizontal density contrasts. The deep regions are not easily accessible and these measurements present challenging opportunities. Indirect inferences about the controlling processes may sometimes be possible by observing waves and other activity in the more easily accessible stratosphere.
Gierasch, Peter J.↗
On the Application of Hilbert Spectral Analysis for Climate Studies
The Hilbert spectral analysis (Huang et al, 1998, Proceedings of the Royal Society of London, A 454, pp 903-995) consisted of two steps: First, the data has to be reduced into a finite number of Intrinsic Mode Function by the Empirical Mode Decomposition method, then the resulting Intrinsic Mode Functions are converted to time-frequency-energy distribution through Hilbert transform. In this approach, the Empirical Mode Functions served as the basis functions with which the data is expanded. This basis function is adaptive, and the decomposition is nonlinear. Furthermore, as the Hilbert transform is a singular transform, it retains a high degree of local information. The instantaneous frequency is determined by differentiation of the phase function; therefore, there is no restriction of the 'uncertainty principle' for all the time-frequency analysis resulting from a priori basis approach. With the adaptive basis and the instantaneous frequency, the Hilbert Spectral analysis can represent data from nonlinear and nonstationary processes without resorting to the harmonics. Another advantage of using instantaneous frequency is the ability to find out frequency from limited length of data, which is a critical problem in climate studies. As the processes driving the climate changes could be both nonlinear and nonstationary, the Hilbert Spectral Analysis could be of great use in examining the underlying mechanisms. A preliminary study based on the length of day data will be presented as example for the application of the Hilbert Spectral Analysis for climate study.
Huang, Norden E.↗
Boundary-Layer Receptivity and Integrated Transition Prediction
The adjoint parabold stability equations (PSE) formulation is used to calculate the boundary layer receptivity to localized surface roughness and suction for compressible boundary layers. Receptivity efficiency functions predicted by the adjoint PSE approach agree well with results based on other nonparallel methods including linearized Navier-Stokes equations for both Tollmien-Schlichting waves and crossflow instability in swept wing boundary layers. The receptivity efficiency function can be regarded as the Green's function to the disturbance amplitude evolution in a nonparallel (growing) boundary layer. Given the Fourier transformed geometry factor distribution along the chordwise direction, the linear disturbance amplitude evolution for a finite size, distributed nonuniformity can be computed by evaluating the integral effects of both disturbance generation and linear amplification. The synergistic approach via the linear adjoint PSE for receptivity and nonlinear PSE for disturbance evolution downstream of the leading edge forms the basis for an integrated transition prediction tool. Eventually, such physics-based, high fidelity prediction methods could simulate the transition process from the disturbance generation through the nonlinear breakdown in a holistic manner.
Chang, Chau-Lyan↗
Satellite Image Mosaic Engine
A computer program automatically builds large, full-resolution mosaics of multispectral images of Earth landmasses from images acquired by Landsat 7, complete with matching of colors and blending between adjacent scenes. While the code has been used extensively for Landsat, it could also be used for other data sources. A single mosaic of as many as 8,000 scenes, represented by more than 5 terabytes of data and the largest set produced in this work, demonstrated what the code could do to provide global coverage. The program first statistically analyzes input images to determine areas of coverage and data-value distributions. It then transforms the input images from their original universal transverse Mercator coordinates to other geographical coordinates, with scaling. It applies a first-order polynomial brightness correction to each band in each scene. It uses a data-mask image for selecting data and blending of input scenes. Under control by a user, the program can be made to operate on small parts of the output image space, with check-point and restart capabilities. The program runs on SGI IRIX computers. It is capable of parallel processing using shared-memory code, large memories, and tens of central processing units. It can retrieve input data and store output data at locations remote from the processors on which it is executed.
Plesea, Lucian↗
Generalized probability model for calculation of interference to the Deep Space Network due to circularly Earth-orbiting satellites
The probability of exceeding interference power levels and the duration of interference at the Deep Space Network (DSN) antenna is calculated parametrically when the state vector of an Earth-orbiting satellite over the DSN station view area is not known. A conditional probability distribution function is derived, transformed, and then convolved with the interference signal uncertainties to yield the probability distribution of interference at any given instant during the orbiter's mission period. The analysis is applicable to orbiting satellites having circular orbits with known altitude and inclination angle.
Ruggier, C. J.↗
A body-fitted conformal mapping method with grid-spacing control
It is demonstrated by analyses and by numerical illustrations that any arbitrarily prescribed contour, open or closed, can be mapped conformally onto a simple contour, such as a unit circle, using any arbitrarily prescribed distribution of scale factor of transformation. This flexibility of selecting a scale factor distribution on the contour is not in violation of the well-known Riemann's uniqueness theory for conformal mapping.
Wu, J. C.↗
Liquid Water Cloud Properties During the Polarimeter Definition Experiment (PODEX)
We present retrievals of water cloud properties from the measurements made by the Research Scanning Polarimeter (RSP) during the Polarimeter Definition Experiment (PODEX) held between January 14 and February 6, 2013. The RSP was onboard the high-altitude NASA ER-2 aircraft based at NASA Dryden Aircraft Operation Facility in Palmdale, California. The retrieved cloud characteristics include cloud optical thickness, effective radius and variance of cloud droplet size distribution derived using a parameter-fitting technique, as well as the complete droplet size distribution function obtained by means of Rainbow Fourier Transform. Multi-modal size distributions are decomposed into several modes and the respective effective radii and variances are computed. The methodology used to produce the retrieval dataset is illustrated on the examples of a marine stratocumulus deck off California coast and stratus/fog over California's Central Valley. In the latter case the observed bimodal droplet size distributions were attributed to two-layer cloud structure. All retrieval data are available online from NASA GISS website.
Electromagnetic scattering↗
Low-energy ion distribution functions on a magnetically quiet day at geostationary altitude /L = 7/
Ion energy and pitch angle distribution functions are examined for a magnetically quiet day using averaged data from ATS 6. For both field-aligned and perpendicular fluxes, the populations have a mixture of characteristic energies, and the distribution functions can be fairly well approximated by Maxwellian distributions over three different energy bands in the range 3-600 eV. Pitch angle distributions varying with local time, and energy distributions are used to compute total ion density. Pitch angle scattering mechanisms responsible for the observed transformation of pitch angle distribution are examined, and it is found that a magnetic noise of a certain power spectral density belonging to the electromagnetic ion cyclotron mode near the ion cyclotron frequency can be effective in trapping the field aligned fluxes by pitch angle scattering.
Singh, N.↗
Good Practices in Free-energy Calculations
As access to computational resources continues to increase, free-energy calculations have emerged as a powerful tool that can play a predictive role in drug design. Yet, in a number of instances, the reliability of these calculations can be improved significantly if a number of precepts, or good practices are followed. For the most part, the theory upon which these good practices rely has been known for many years, but often overlooked, or simply ignored. In other cases, the theoretical developments are too recent for their potential to be fully grasped and merged into popular platforms for the computation of free-energy differences. The current best practices for carrying out free-energy calculations will be reviewed demonstrating that, at little to no additional cost, free-energy estimates could be markedly improved and bounded by meaningful error estimates. In energy perturbation and nonequilibrium work methods, monitoring the probability distributions that underlie the transformation between the states of interest, performing the calculation bidirectionally, stratifying the reaction pathway and choosing the most appropriate paradigms and algorithms for transforming between states offer significant gains in both accuracy and precision. In thermodynamic integration and probability distribution (histogramming) methods, properly designed adaptive techniques yield nearly uniform sampling of the relevant degrees of freedom and, by doing so, could markedly improve efficiency and accuracy of free energy calculations without incurring any additional computational expense.
Pohorille, Andrew↗
The Application of Time-Frequency Methods to HUMS
This paper reports the study of four time-frequency transforms applied to vibration signals and presents a new metric for comparing them for fault detection. The four methods to be described and compared are the Short Time Frequency Transform (STFT), the Choi-Williams Distribution (WV-CW), the Continuous Wavelet Transform (CWT) and the Discrete Wavelet Transform (DWT). Vibration data of bevel gear tooth fatigue cracks, under a variety of operating load levels, are analyzed using these methods. The new metric for automatic fault detection is developed and can be produced from any systematic numerical representation of the vibration signals. This new metric reveals indications of gear damage with all of the methods on this data set. Analysis with the CWT detects mechanical problems with the test rig not found with the other transforms. The WV-CW and CWT use considerably more resources than the STFT and the DWT. More testing of the new metric is needed to determine its value for automatic fault detection and to develop methods of setting the threshold for the metric.
Pryor, Anna H.↗