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A nonlinear theory for sound propagation in nearly sonic flows in variable area ducts is outlined. The theory is based on a quasi-one-dimensional model and the use of matched asymptotic expansions. The problem of an acoustic source located in the throat region of a duct with a converging section is treated. It is shown that the near-sonic region has a marked nonlinear effect on sound propagation in the duct.
A Fourier phase-difference technique for cloud motion estimation from pairs of pictures is described, and results obtained using this technique are compared with the results of a Fourier-domain cross-correlation scheme. The phase-difference technique makes use of the phase of the cross-spectral density and allows motion estimates to be made for individual spatial frequencies, which are related to cloud pattern dimensions. When objects being tracked do not change their shape, size, and orientation to more than a limited degree, both techniques are effective. The phase difference technique is relatively sensitive to the presence of mixtures of motions, changes in cloud shape, and edge effects; in these circumstances, the cross-correlation scheme is preferable. It is suggested that the Fourier transform phase difference estimation methods can be applied in problems such as landmark matching.
The philosophy and data encoding possible in systolic array optical processor (SAOP) were reviewed. The multitude of linear algebraic operations achievable on this architecture is examined. These operations include such linear algebraic algorithms as: matrix-decomposition, direct and indirect solutions, implicit and explicit methods for partial differential equations, eigenvalue and eigenvector calculations, and singular value decomposition. This architecture can be utilized to realize general techniques for solving matrix linear and nonlinear algebraic equations, least mean square error solutions, FIR filters, and nested-loop algorithms for control engineering applications. The data flow and pipelining of operations, design of parallel algorithms and flexible architectures, application of these architectures to computationally intensive physical problems, error source modeling of optical processors, and matching of the computational needs of practical engineering problems to the capabilities of optical processors are emphasized.
Viewgraphs on a stochastic approach to robust broadband structural control are presented. Topics covered include: travelling wave model; dereverberated mobility model; computation of dereverberated mobility; power flow; impedance matching; stochastic systems; control problem; control of stochastic systems; using cost functional; Bernoulli-Euler beam example; compensator design; 'power' dual variables; dereverberation of complex structure; and dereverberated transfer function.
The heliospheric termination shock must exhibit asymmetry in its shape, due in part to internal latitude variations in the solar wind, and in part to the special directions defined by the external interstellar flow and/or the galactic magnetic field. This asymmetry shows up naturally in numerical simulations of the interaction between the heliosphere and local interstellar medium. However, to date only one analytical treatment of the theory has appeared, which discussed the modification of the shock shape due to solar wind latitude variations in the presence of spherically symmetric outer boundary conditions. In the present report, we discuss an extension and generalization of this theory to an axially symmetric gasdynamic system, in which departure from spherical symmetry may be due either to internal solar wind variations or to the directional properties of the external interstellar medium. It is shown that for steady flow the post-shock region is characterized by an infinite set of quantities that are conserved along streamlines; among these invariants are the stagnation pressure and a quantity closely related to vorticity. Moreover, for a given latitude profile of the (supersonic) solar wind, the geometry of the termination shock uniquely determines the valued of these invariants at the points where the streamlines emerge from the shock. A self-consistent solution of the problem thus requires a match between the shock geometry and distant boundary conditions. The theory is applied to give estimates of termination-shock asymmetry for various internal and external conditions.
NASA's Short-term Prediction Research and Transition (SPoRT) program is a contributing partner with the GOES-R Proving Ground (PG) preparing forecasters to understand and utilize the unique products that will be available in the GOES-R era. This presentation emphasizes SPoRT s actions to prepare the end user community for the Geostationary Lightning Mapper (GLM). This preparation is a collaborative effort with SPoRT's National Weather Service partners, the National Severe Storms Laboratory (NSSL), and the Hazardous Weather Testbed s Spring Program. SPoRT continues to use its effective paradigm of matching capabilities to forecast problems through collaborations with our end users and working with the developers at NSSL to create effective evaluations and visualizations. Furthermore, SPoRT continues to develop software plug-ins so that these products will be available to forecasters in their own decision support system, AWIPS and eventually AWIPS II. In 2009, the SPoRT program developed the original pseudo geostationary lightning mapper (PGLM) flash extent product to demonstrate what forecasters may see with GLM. The PGLM replaced the previous GLM product and serves as a stepping-stone until the AWG s official GLM proxy is ready. The PGLM algorithm is simple and can be applied to any ground-based total lightning network. For 2011, the PGLM used observations from four ground-based networks (North Alabama, Kennedy Space Center, Oklahoma, and Washington D.C.). While the PGLM is not a true proxy product, it is intended as a tool to train forecasters about total lightning as well as foster discussions on product visualizations and incorporating GLM-resolution data into forecast operations. The PGLM has been used in 2010 and 2011 and is likely to remain the primary lightning training tool for the GOES-R program for the near future. This presentation will emphasize the feedback received during the 2011 Spring Program. This will discuss several topics. Based on feedback from the 2010 Spring Program, SPoRT created two variant PGLM products, which NSSL produced locally and provided in real-time within AWIPS for 2011. The first is the flash initiation density (FID) product, which creates a gridded display showing the number of flashes that originated in each 8 8 km grid box. The second product is the maximum flash density (MFD). This shows the highest PGLM value for each grid point over a specific period of time, ranging from 30 to 120 minutes. In addition to the evaluation of these two new products, the evaluation of the PGLM itself will be covered. The presentation will conclude with forecaster feedback for additional improvements requested for future evaluations, such as within the 2012 Spring Program.
This talk is an introduction to the knowledge discovery process, beginning with: identifying the problem, choosing data sources, matching the appropriate machine learning tools, and reviewing the results. The overview will be given in the context of an ongoing study that is assessing RNAV adherence of commercial aircraft in the national airspace.
Advanced aircraft designs such as the hybrid wing body, in conjunction with open rotor engines, may allow for significant improvements in the environmental impact of aviation. System noise assessments allow for the prediction of the aircraft noise of such designs while they are still in the conceptual phase. Due to significant requirements of computational methods, these predictions still rely on experimental data to account for the interaction of the open rotor tones with the hybrid wing body airframe. Recently, multiple aircraft system noise assessments have been conducted for hybrid wing body designs with open rotor engines. These assessments utilized measured benchmark data from a Propulsion Airframe Aeroacoustic interaction effects test. The measured data demonstrated airframe shielding of open rotor tonal and broadband noise with legacy F7/A7 open rotor blades. Two methods are proposed for improving the use of these data on general open rotor designs in a system noise assessment. The first, direct difference, is a simple octave band subtraction which does not account for tone distribution within the rotor acoustic signal. The second, tone matching, is a higher-fidelity process incorporating additional physical aspects of the problem, where isolated rotor tones are matched by their directivity to determine tone-by-tone shielding. A case study is conducted with the two methods to assess how well each reproduces the measured data and identify the merits of each. Both methods perform similarly for system level results and successfully approach the experimental data for the case study. The tone matching method provides additional tools for assessing the quality of the match to the data set. Additionally, a potential path to improve the tone matching method is provided.
A detailed evaluation is performed of a guidance algorithm for aeroassisted orbit transfer that was developed earlier based on the method of matched asymptotic expansions. It is shown that, by exploiting the structure of the matched asymptotic expansion solution procedure, the original problem which requires the solution of a set of 20 implicit algebraic equations can be reduced to a problem of six implicit equations in six unknowns. The main contribution here is that it was possible to obtain a solution that is near optimal, requires a minimum of computation, and thus can be implemented in real time and on-board the vehicle. Guidance law implementation entails treating the current state as a new initial state and repetitively solving the matched asymptotic expansion problem to obtain the feedback controls.
A novel computational framework was developed of a 2D affine invariant matching exploiting a parameter space. Named as affine invariant parameter space (AIPS), the technique can be applied to many image-processing and computer-vision problems, including image registration, template matching, and object tracking from image sequence. The AIPS is formed by the parameters in an affine combination of a set of feature points in the image plane. In cases where the entire image can be assumed to have undergone a single affine transformation, the new AIPS match metric and matching framework becomes very effective (compared with the state-of-the-art methods at the time of this reporting). No knowledge about scaling or any other transformation parameters need to be known a priori to apply the AIPS framework. An automated suite of software tools has been created to provide accurate image segmentation (for data cleaning) and high-quality 2D image and 3D surface registration (for fusing multi-resolution terrain, image, and map data). These tools are capable of supporting existing GIS toolkits already in the marketplace, and will also be usable in a stand-alone fashion. The toolkit applies novel algorithmic approaches for image segmentation, feature extraction, and registration of 2D imagery and 3D surface data, which supports first-pass, batched, fully automatic feature extraction (for segmentation), and registration. A hierarchical and adaptive approach is taken for achieving automatic feature extraction, segmentation, and registration. Surface registration is the process of aligning two (or more) data sets to a common coordinate system, during which the transformation between their different coordinate systems is determined. Also developed here are a novel, volumetric surface modeling and compression technique that provide both quality-guaranteed mesh surface approximations and compaction of the model sizes by efficiently coding the geometry and connectivity/topology components of the generated models. The highly efficient triangular mesh compression compacts the connectivity information at the rate of 1.5-4 bits per vertex (on average for triangle meshes), while reducing the 3D geometry by 40-50 percent. Finally, taking into consideration the characteristics of 3D terrain data, and using the innovative, regularized binary decomposition mesh modeling, a multistage, pattern-drive modeling, and compression technique has been developed to provide an effective framework for compressing digital elevation model (DEM) surfaces, high-resolution aerial imagery, and other types of NASA data.
Lifting line theory is applied to describe the flow about a lifting wing at transonic speeds. The method extends that of Van Dyke (1975), in which lifting line theory is viewed as a singular perturbation problem, to transonic flows. Inner and outer expansions as the aspect ratio approaches infinity of the transonic small disturbance equations are found. It is shown that the solutions match asymptotically. A boundary value problem is formulated which describes the first aspect ratio correction to the two dimensional cross sectional transonic flow. The theory is especially applicable to wings of similar cross-sections.
Unsteady lifting-line theory is developed for a wing of large aspect ratio oscillating at low frequency in inviscid incompressible flow. The wing is assumed to have a rigid chord but a flexible span. Use of the method of matched asymptotic expansions reduces the problem from a singular integral equation to quadrature. The pressure field and airloads, for a prescribed wing shape and motion, are obtained in closed form as expansions in inverse aspect ratio. A rigorous definition of unsteady induced downwash is also obtained. Numerical calculations are presented for an elliptic wing in pitch and heave; compared with numerical lifting-surface theory, computation time is reduced significantly. The present work also identifies and resolves errors in the unsteady lifting line theory of James (1975), and points out a limitation in that of Van Holten (1975, 1976, 1977).
The organization and functions of an interdisciplinary team for the application of aerospace generated technology to the solution of discrete technological problems within the public sector are presented. The interdisciplinary group formed at Stanford Research Institute, California is discussed. The functions of the group are to develop and conduct a program not only optimizing the match between public sector technological problems in criminalistics, transportation, and the postal services and potential solutions found in the aerospace data base, but ensuring that appropriate solutions are acutally utilized. The work accomplished during the period from July 1, 1970 to June 30, 1971 is reported.
Point matching method, solving boundary value problem in uniform cylindrical waveguide with inserted conductor within conducting tube
The process by which raw astronomical data acquisition is transformed into scientifically meaningful results and interpretation typically involves many statistical steps. Traditional astronomy limits itself to a narrow range of old and familiar statistical methods: means and standard deviations; least-squares methods like chi(sup 2) minimization; and simple nonparametric procedures such as the Kolmogorov-Smirnov tests. These tools are often inadequate for the complex problems and datasets under investigations, and recent years have witnessed an increased usage of maximum-likelihood, survival analysis, multivariate analysis, wavelet and advanced time-series methods. The Statistical Consulting Center for Astronomy (SCCA) assisted astronomers with the use of sophisticated tools, and to match these tools with specific problems. The SCCA operated with two professors of statistics and a professor of astronomy working together. Questions were received by e-mail, and were discussed in detail with the questioner. Summaries of those questions and answers leading to new approaches were posted on the Web (www.state.psu.edu/ mga/SCCA). In addition to serving individual astronomers, the SCCA established a Web site for general use that provides hypertext links to selected on-line public-domain statistical software and services. The StatCodes site (www.astro.psu.edu/statcodes) provides over 200 links in the areas of: Bayesian statistics; censored and truncated data; correlation and regression, density estimation and smoothing, general statistics packages and information; image analysis; interactive Web tools; multivariate analysis; multivariate clustering and classification; nonparametric analysis; software written by astronomers; spatial statistics; statistical distributions; time series analysis; and visualization tools. StatCodes has received a remarkable high and constant hit rate of 250 hits/week (over 10,000/year) since its inception in mid-1997. It is of interest to scientists both within and outside of astronomy. The most popular sections are multivariate techniques, image analysis, and time series analysis. Hundreds of copies of the ASURV, SLOPES and CENS-TAU codes developed by SCCA scientists were also downloaded from the StatCodes site. In addition to formal SCCA duties, SCCA scientists continued a variety of related activities in astrostatistics, including refereeing of statistically oriented papers submitted to the Astrophysical Journal, talks in meetings including Feigelson's talk to science journalists entitled "The reemergence of astrostatistics" at the American Association for the Advancement of Science meeting, and published papers of astrostatistical content.
The Monte Carlo method (MCM) is applied to analyze radiative heat transfer in nongray gases. The nongray model employed is based on the statistical narrow band model with an exponential-tailed inverse intensity distribution. The amount and transfer of the emitted radiative energy in a finite volume element within a medium are considered in an exact manner. The spectral correlation between transmittances of two different segments of the same path in a medium makes the statistical relationship different from the conventional relationship, which only provides the non-correlated results for nongray methods is discussed. Validation of the Monte Carlo formulations is conducted by comparing results of this method of other solutions. In order to further establish the validity of the MCM, a relatively simple problem of radiative interactions in laminar parallel plate flows is considered. One-dimensional correlated Monte Carlo formulations are applied to investigate radiative heat transfer. The nongray Monte Carlo solutions are also obtained for the same problem and they also essentially match the available analytical solutions. the exact correlated and non-correlated Monte Carlo formulations are very complicated for multi-dimensional systems. However, by introducing the assumption of an infinitesimal volume element, the approximate correlated and non-correlated formulations are obtained which are much simpler than the exact formulations. Consideration of different problems and comparison of different solutions reveal that the approximate and exact correlated solutions agree very well, and so do the approximate and exact non-correlated solutions. However, the two non-correlated solutions have no physical meaning because they significantly differ from the correlated solutions. An accurate prediction of radiative heat transfer in any nongray and multi-dimensional system is possible by using the approximate correlated formulations. Radiative interactions are investigated in chemically reacting compressible flows of premixed hydrogen and air in an expanding nozzle. The governing equations are based on the fully elliptic Navier-Stokes equations. Chemical reaction mechanisms were described by a finite rate chemistry model. The correlated Monte Carlo method developed earlier was employed to simulate multi-dimensional radiative heat transfer. Results obtained demonstrate that radiative effects on the flowfield are minimal but radiative effects on the wall heat transfer are significant. Extensive parametric studies are conducted to investigate the effects of equivalence ratio, wall temperature, inlet flow temperature, and nozzle size on the radiative and conductive wall fluxes.
A closed-form mathematical solution to the classical photogrammetric problem is presented. Although quite general, the solution is more applicable to problems in which the image-space conjugates are very difficult to match but one of the elements of the pair is not. Additionally, observations are made that should make the solution to the general problem of automatic matching less computationally intensive. This approach was used to analyze flow visualization data for the F-18 High Alpha Research Vehicle. The conditions for this analysis were less than ideal for image-to-object-space transformation.
The structure modification problem, where the computer model of a structure is to be upgraded on the basis of experimental measurements of normal mode frequencies, is approached by the modal energy concept. The modes for correlation with test data are selected on the basis of relative strain energy participation. The resulting procedure can be viewed as an extension of White's (1972) method. Its advantage lies in that both the number and choice of structural parameters to be varied in the modification are arbitrary.