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At least 937 records · Page 52

Quotient-difference type generalizations of the power method and their analysis

The recursion relations that were proposed by W. F. Ford and A. Sidi (Appl. Numer. Math, 4 (1988), pp. 477-489) for implementing vector extrapolation methods are used for devising generalizations of the power method for linear operators. These generalizations are shown to produce approximations to largest eigenvalues of a linear operator under certain conditions. They are similar in form to the quotient-difference algorithm and share similar convergence properties with the latter. These convergence properties also resemble those obtained for the basic LR and QR algorithms. Finally, it is shown that the convergence rate produced by one fo these generalizations is twice as fast for normal operators as it is for nonnormal operators.

Sidi, Avram↗

Analytical study of the liquid phase transient behavior of a high temperature heat pipe

The transient operation of the liquid phase of a high temperature heat pipe is studied. The study was conducted in support of advanced heat pipe applications that require reliable transport of high temperature drops and significant distances under a broad spectrum of operating conditions. The heat pipe configuration studied consists of a sealed cylindrical enclosure containing a capillary wick structure and sodium working fluid. The wick is an annular flow channel configuration formed between the enclosure interior wall and a concentric cylindrical tube of fine pore screen. The study approach is analytical through the solution of the governing equations. The energy equation is solved over the pipe wall and liquid region using the finite difference Peaceman-Rachford alternating direction implicit numerical method. The continuity and momentum equations are solved over the liquid region by the integral method. The energy equation and liquid dynamics equation are tightly coupled due to the phase change process at the liquid-vapor interface. A kinetic theory model is used to define the phase change process in terms of the temperature jump between the liquid-vapor surface and the bulk vapor. Extensive auxiliary relations, including sodium properties as functions of temperature, are used to close the analytical system. The solution procedure is implemented in a FORTRAN algorithm with some optimization features to take advantage of the IBM System/370 Model 3090 vectorization facility. The code was intended for coupling to a vapor phase algorithm so that the entire heat pipe problem could be solved. As a test of code capabilities, the vapor phase was approximated in a simple manner.

Roche, Gregory Lawrence↗

An iterative implicit diagonally-dominant factorization algorithm for solving the Navier-Stokes equations

Presented here is an algorithm for solving the multidimensional unsteady Navier-Stokes equations for compressible flows. It is based on a diagonally-dominant approximate factorization procedure. The factorization error and the timewise linearization error associated with this procedure are reduced by performing Newton-type inner iterations at each time step. The inviscid fluxes are evaluated by the fourth-order central differencing scheme amended with a numerical dissipation directly proportional to the entire dissipative part of the truncation error intrinsic to the third order biased upwind scheme. The important features of the proposed solution are elucidated by the numerical results of the convection of a vortex and the backward-facing step flows.

Chen, Shu-Cheng↗

Hysteresis effects in instantaneous frequency scaling of attenuation on 20 and 30 GHz satellite links

It has been observed with 20/30 GHz satellite beacon measurements that the ratio of 30 GHz to 20 GHz attenuation changes during some fade events. This ratio displays a hysteresis effect. This effect can be explained by a change in the drop size distribution (DSD) during the event. However, it appears only above approximately 6-8 dB of attenuation at 20 GHz. Instantaneous frequency scaling of attenuation is being proposed as part of an algorithm for uplink power control (ULPC) and the dynamic range of such an algorithm must be appropriately limited to avoid the hysteresis.

Sweeney, D. G.↗

A signal preprocessing algorithm applicable to both DTF and SSME spectral diagnostics

An account is given of research conducted by NASA-Stennis' Diagnostic Test Facility (DTF), which is designed to obtain spectra approximating those of the SSME while allowing full control of dopant and thruster conditions. A simple preprocessing technique which emphasizes the essential spectral components of plume spectra that are indicative of dopant levels has been used and found to remain sensitive to wavelength shift even for high-resolution spectra. Mathematical analyses of the problem are presented which are based on the Taylor's series linearization procedure.

Nail, Bert↗

Improving the reconstruction of the velocity potential and primordial density fluctuations by choice of smoothing windows

Recently considerable attention has been focused on improving algorithms for restoring primordial density fluctuations in the universe or investigating large-scale velocity fields by going to higher order approximations relating nonlinear states to their initial conditions. An alternative approach is to investigate the use of alternative smoothing windows within the context of first-order approximations. I present evidence that the universally used Gaussian smoothing window is far from optimal. A sharp truncation P(k) = 0 for k greater than k(c) leads to a much more direct connection to initial conditions for either 'Gaussianization' methods or use of the Zel'dovich approximation, as discussed in the text.

Melott, Adrian L.↗

Chemistry and transport in a multi-dimensional model

The focus of our research program is the achievement of a quantitative understanding of the spatial distribution and temporal variation of chemical species in the terrestrial middle atmosphere, with emphasis on ozone. Although not directed at assessments of anthropogenic impacts, our activities contribute to a refinement of model descriptions of chemical and dynamical processes that are needed for assessment tasks. A unique feature of our research effort is a close interaction with the chemical kinetics group at JPL and the field measurement groups at JPL. The principal tools used in our investigations are l-D and 2-D photochemical models. The advective component of the meridional transport in these models is approximated by the diabatic circulation, which is derived diagnostically from the net radiative heating rates. We are developing accurate radiative transfer algorithms to find the net heating rates and the diabatic circulation for use in the 2-D model.

Yung, Yuk L.↗

Automated Coronal Loop Identification Using Digital Image Processing Techniques

The results of a master thesis project on a study of computer algorithms for automatic identification of optical-thin, 3-dimensional solar coronal loop centers from extreme ultraviolet and X-ray 2-dimensional images will be presented. These center splines are proxies of associated magnetic field lines. The project is pattern recognition problems in which there are no unique shapes or edges and in which photon and detector noise heavily influence the images. The study explores extraction techniques using: (1) linear feature recognition of local patterns (related to the inertia-tensor concept), (2) parametric space via the Hough transform, and (3) topological adaptive contours (snakes) that constrains curvature and continuity as possible candidates for digital loop detection schemes. We have developed synthesized images for the coronal loops to test the various loop identification algorithms. Since the topology of these solar features is dominated by the magnetic field structure, a first-order magnetic field approximation using multiple dipoles provides a priori information in the identification process. Results from both synthesized and solar images will be presented.

Lee, Jong K.↗

A Most Probable Point-Based Method for Reliability Analysis, Sensitivity Analysis and Design Optimization

A major step in a most probable point (MPP)-based method for reliability analysis is to determine the MPP. This is usually accomplished by using an optimization search algorithm. The optimal solutions associated with the MPP provide measurements related to safety probability. This study focuses on two commonly used approximate probability integration methods; i.e., the Reliability Index Approach (RIA) and the Performance Measurement Approach (PMA). Their reliability sensitivity equations are first derived in this paper, based on the derivatives of their respective optimal solutions. Examples are then provided to demonstrate the use of these derivatives for better reliability analysis and Reliability-Based Design Optimization (RBDO).

Hou, Gene J.-W.↗

Validation of Atmospheric Correction of Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) Radiance Data Based on Radiative Transfer Modeling

An evaluation of atmospheric correction of AVIRIS data using radiative transfer codes LOWTRAN7 and MODTRAN is presented. The algorithm employed is based on a simple model of radiance L at each wavelength at the sensor that can be written approximately LAV=Lp+Tp, where subscript AV referes to AVIRIS, Lp is the path radiance and Tp is the diffuse + direct transmitted radiance of the atmosphere at AVIRIS.

Infrared Mapping↗

Exploring Quantum State Preparation Using Tensor Networks and Sparse Wavefunction Simulations

The variational quantum eigenvalue solver is a powerful hybrid quantum-classical approach that has been suggested as a candidate method to run on near-term quantum hardware for computing ground state electronic energies of molecular systems. However, even for small molecules, the number of variational parameters and qubits required to minimize the electronic energy is beyond the reach of current quantum computers except for small basis sets. We explore a new paradigm for state preparation where we test how much of the optimization can be approximately prepared with classical computers to reduce the number of optimization steps performed using a quantum device. By adapting a recent algorithm for the factorized form of the UCC ansatz, we can study molecular electronic structure problems with up to 64 qubits. In addition, we also test a related approach of using tensor networks to optimize quantum circuits in order to benchmark various lattice models. We present results using these approaches and discuss strategies for incorporating these ideas into variational algorithms involving near-term quantum computers. Our results help demonstrate the strength of the UCC ansatz and address pressing questions about optimal initial parameterizations and circuit construction.

quantum computing↗

Cloud parameters from GOES visible and infrared radiances during the FIRE Cirrus IFO, October 1986

Visible (VIS, 0.65 micron) and infrared (IR, 10.5 microns) channels on geostationary satellites are the key elements of the International Satellite Cloud Climatology Project (ISCCP). All daytime ISCCP cloud parameters are derived from a combination of VIS and IR data. Validation and improvement of the ISCCP and other cloud retrieval algorithms are important components of the First ISCCP Regional Experiment (FIRE) Intensive Field Observations (IFO). Data from the Cirrus IFO (October 19 to November 2, 1986) over Wisconsin are available for validating cirrus cloud retrievals from satellites. The Geostationary Operational Environmental Satellite (GOES) located over the Equator at approximately 100 deg W provided nearly continuous measurements of VIS and IR radiances over the IFO areas. The preliminary results of cloud parameters derived from the IFO GOES data are presented. Cloud attitudes are first derived using an algorithms without corrections for cloud emissivity. These same parameters will then be computed from the same data relying on an emissivity correction algorithm based on correlative data taken during the Cirrus IFO.

Heck, Patrick W.↗

Using Approximations to Accelerate Engineering Design Optimization

Optimization problems that arise in engineering design are often characterized by several features that hinder the use of standard nonlinear optimization techniques. Foremost among these features is that the functions used to define the engineering optimization problem often are computationally intensive. Within a standard nonlinear optimization algorithm, the computational expense of evaluating the functions that define the problem would necessarily be incurred for each iteration of the optimization algorithm. Faced with such prohibitive computational costs, an attractive alternative is to make use of surrogates within an optimization context since surrogates can be chosen or constructed so that they are typically much less expensive to compute. For the purposes of this paper, we will focus on the use of algebraic approximations as surrogates for the objective. In this paper we introduce the use of so-called merit functions that explicitly recognize the desirability of improving the current approximation to the objective during the course of the optimization. We define and experiment with the use of merit functions chosen to simultaneously improve both the solution to the optimization problem (the objective) and the quality of the approximation. Our goal is to further improve the effectiveness of our general approach without sacrificing any of its rigor.

Torczon, Virginia↗

Atmospheric Ascent Guidance for Rocket-Powered Launch Vehicles

An advanced ascent guidance algorithm for rocket- powered launch vehicles is developed. This algorithm cyclically solves the calculus-of-variations two-point boundary-value problem starting at vertical rise completion through main engine cutoff. This is different from traditional ascent guidance algorithms which operate in a simple open-loop mode until high dynamic pressure (including the critical max-Q) portion of the trajectory is over, at which time guidance operates under the assumption of negligible aerodynamic acceleration (i.e., vacuum dynamics). The initial costate guess is corrected based on errors in the terminal state constraints and the transversality conditions. Judicious approximations are made to reduce the order and complexity of the state/costate system. Results comparing guided launch vehicle trajectories with POST open-loop trajectories are given verifying the basic formulation of the algorithm. Multiple shooting is shown to be a very effective numerical technique for this application. In particular, just one intermediate shooting point, in addition to the initial shooting point, is sufficient to significantly reduce sensitivity to the guessed initial costates. Simulation results from a high-fidelity trajectory simulation are given for the case of launch to sub-orbital cutoff conditions as well as launch to orbit conditions. An abort to downrange landing site formulation of the algorithm is presented.

Dukeman, Greg A.↗

Global Discrete Artificial Boundary Conditions for Time-Dependent Wave Propagation

We construct global artificial boundary conditions (ABCs) for the numerical simulation of wave processes on unbounded domains using a special non-deteriorating algorithm that has been developed previously for the long-term computation of wave-radiation solutions. The ABCs are obtained directly for the discrete formulation of the problem; in so doing, neither a rational approximation of 'non-reflecting kernels,' nor discretization of the continuous boundary conditions is required. The extent of temporal nonlocality of the new ABCs appears fixed and limited; in addition, the ABCs can handle artificial boundaries of irregular shape on regular grids with no fitting/adaptation needed and no accuracy loss induced. The non-deteriorating algorithm, which is the core of the new ABCs is inherently three-dimensional, it guarantees temporally uniform grid convergence of the solution driven by a continuously operating source on arbitrarily long time intervals, and provides unimprovable linear computational complexity with respect to the grid dimension. The algorithm is based on the presence of lacunae, i.e., aft fronts of the waves, in wave-type solutions in odd-dimension spaces, It can, in fact, be built as a modification on top of any consistent and stable finite-difference scheme, making its grid convergence uniform in time and at the same time keeping the rate of convergence the same as that of the non-modified scheme. In the paper, we delineate the construction of the global lacunae-based ABCs in the framework of a discretized wave equation. The ABCs are obtained for the most general formulation of the problem that involves radiation of waves by moving sources (e.g., radiation of acoustic waves by a maneuvering aircraft). We also present systematic numerical results that corroborate the theoretical design properties of the ABCs' algorithm.

Ryabenkii, V. S.↗

The star identification, pointing and tracking system of UVSTAR, an attached payload instrument system for the Shuttle Hitchhiker-M platform

We describe an algorithm for star identification and pointing/tracking of a spaceborne electro-optical system and simulation analyses to test the algorithm. The algorithm will be implemented in the guiding system of UVSTAR, a spectrographic telescope for observations of astronomical and planetary sources operating in the 500-1250 A waveband at approximately 1 A resolution. The experiment is an attached payload and will fly as a Hitchhiker-M payload on the Shuttle. UVSTAR includes capabilities for independent target acquisition and tracking. The spectrograph package has internal gimbals that allow angular movement of plus or minus 3 deg from the central position. Rotation about the azimuth axis (parallel to the Shuttle z axis) and elevation axis (parallel to the Shuttle x axis) will actively position the field of view to center the target of interest in the fields of the spectrographs. The algorithm is based on an on-board catalog of stars. To identify star fields, the algorithm compares the positions of stars recorded by the guiding imager to positions computed from the on-board catalog. When the field has been identified, its position within the guiding imager field of view can be used to compute the pointing corrections necessary to point to a target of interest. In tracking mode, the software uses the past history to predict the quasi-periodic attitude control motions of the shuttle and sends pointing commands to cancel the motion and stabilize UVSTAR on the target. The guiding imager (guider) will have an 80-mm focal length and f/1.4 optics giving a field of view of 6 deg x 4.5 deg using a 385 x 288 pixel intensified CCD. It will be capable of providing high accuracy (better than 2 arc-sec) attitude determination from coarse (6 deg x 4.5 deg) initial knowledge of the pointing direction; and of pointing toward the target. It will also be capable of tracking at the same high accuracy with a processing time of less than a few hundredths of a second.

Decarlo, Francesco↗

Entropy Stable Nonconforming Discretizations with the Summation-By-Parts Property for Curvilinear Coordinates

The entropy conservative/stable algorithm of Friedrichet al.(2018) for hyperbolic conservation laws on nonconforming p-refined/coarsened Cartesian grids, is extended to curvilinear grids for the compressible Euler equations. The primary focus is on constructing appropriate coupling procedures across the curvilinear nonconforming interfaces. A simple and flexible approach is proposed that uses interpolation operators from one element to the other. On the element faces,the analytic metrics are used to construct coupling terms, while metric terms in the volume are approximated to satisfy a discretization of the geometric conservation laws. The resulting scheme is entropy conservative/stable, elementwise conservative, and freestream preserving. The accuracy and stability properties of the resulting numerical algorithm are shown to be comparable to those ofthe original conforming scheme (∼p+ 1 convergence) in the context of the isentropic Euler vortex and the inviscid Taylor–Green vortex problems on manufactured high order grids.

David Del Rey Fernandez↗

Use of multiple gauges and microwave attenuation of precipitation for satellite verification

In this paper both a microwave attenuation measurement along a horizontal line and multiple point gauge measurements are analyzed as possible ground-truth designs to validate satellite precipitation retrieval algorithms at the field of view spatial level (typically about 20 km). The design consists of comparing a sequence of pairs of contemporaneous measurements taken from the ground and from space. The authors examine theoretically the variance of expected differences between the two systems. The line average measurement leads to a smaller mean-square error compared to the case of a single point gauge, since some of the small-scale variability of the rain field is smoothed away by the line integration. The multiple point gauge measurements also give smaller mean-square error than that of a single point gauge. The centroid of the line and point gauge configurations are considered to be located randomly inside the field of view for different overpasses. A space-time spectral formalism is used with a noise-forced diffusive rain field to find the mean-square error. By considering instantaneous ground and satellite measurement pairs over about 50 visits when raining, we can reduce the expected error to approximately 10% of the standard deviation of climatological variability. This is considered to be a useful level of tolerance for identifying biases in the retrieval algorithms. It is found that the multiple point gauges (especially two gauges) are the economical ground-truth design compared to the microwave attenuation based on the mean-square error comparison. The major finding of this study is that a significant improvement over the point gauge is obtained by adding a single additional piece of information; adding more gauges or extending the line of attenuation is not an important improvement.

Ha, Eunho↗