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NASA NTRS1973

Divergence and Necessary Conditions for Extremums

The problem is considered of finding a dimension reducing transformation matrix B that maximizes the divergence in the reduced dimension for multi-class cases. A comparitively simple expression for the gradient of the average divergence with respect to B is developed. The developed expression for the gradient contains no eigenvectors or eigenvalues; also, all matrix inversions necessary to evaluate the gradient are available from computing the average divergence.

Quirein, J. A.↗

NASA NTRS1977

Mass drivers. 2: Structural dynamics

Various structural and dynamical problems related to both small-scale forces between the drive coils and within the bucket structure as well as the overall combined large-scale dynamical interaction of the bucket stream and MDRE (Mass Drive Reaction Engine) structure are examined. The large-scale dynamics appear weakly stable. Finally, MDRE operation in an inverse-square-law gravitational field is discussed and the required curved shape of the guideway is computed.

William H. Arnold↗

NASA NTRS1981

On regulators with a prescribed degree of stability

Several important aspects of the Regulator with a Prescribed Degree of Stability (RPDS) methodology and its applications are considered. The solution of the time varying RPDS problem as well as the characterization of RPDS closed loop eigenstructure properties are obtained. Based on the asymptotic behavior of RPDS root loci, a one step algorithm for designing Regulators with Prescribed Damping Ratio (RPDR) is developed. The robustness properties of RPDS are characterized in terms of the properties of the return difference and the inverse return difference matrices for the RPDS state feedback loop. This class of regulators is found to possess excellent multiloop margins with respect to stability and degree of stability properties. The ability of RPDS design to tolerate changing operating conditions and unmodelled dynamics are illustrated with a multiterminal dc/ac power system example. The output feedback realization of RPDS requires the use of Linear Quadratic Gaussian (LQG) methodology.

Ng, P. T. P.↗

NASA NTRS1988

A noise source identification technique using an inverse Helmholtz integral equation method

A technique is developed which utilizes numerical models and field pressure information to characterize acoustic fields and identify acoustic sources. The numerical models are based on boundary element numerical procedures. Either pressure, velocity, or passive boundary conditions, in the form of impedance boundary conditions, may be imposed on the numerical model. Alternatively, if no boundary information is known, a boundary condition can be left unspecified. Field pressure data may be specified to overdetermine the numerical problem. The problem is solved numerically for the complete sound field from which the acoustic sources may be determined. The model can then be used to idenfify acoustic intensity paths in the field. The solution can be modified and the model used to evaluate design alternatives. In this investigation the method is tested analytically and verified. In addition, the sensitivity of the method to random and bias error in the input data is demonstrated.

Gardner, B. K.↗

NASA NTRS1993

The soliton transform and a possible application to nonlinear Alfven waves in space

The inverse scattering transform (IST) based on the derivative nonlinear Schroedinger (DNLS) equation is applied to a complex time series of nonlinear Alfven wave data generated by numerical simulation. The IST describes the long-time evolution of quasi-parallel Alfven waves more efficiently than the Fourier transform, which is adapted to linear rather than nonlinear problems. When dissipation is added, so the conditions for the validity of the DNLS are not strictly satisfied, the IST continues to provide a compact description of the wavefield in terms of a small number of decaying envelope solitons.

Hada, T.↗

NASA NTRS1975

Radiation of cylindrical duct acoustic modes with flow mismatch

Motivated by the problem of Mach number and temperature discontinuity mismatch between the tailpipe and the surrounding medium, and the effect of this flow mismatch on aircraft engine noise, the radiation of spinning turbo-acoustic modes from a round duct is investigated. The model, based on a plug flow exhaust jet, solves the convected wave equations using Fourier transforms, inversion being accomplished via a coupled Wiener-Hopf and Carrier-Koiter technique. It is concluded that the Mach number discontinuity results in a conflict between convection and refraction effects, while the temperature mismatch results in a sharp beaming of sound off to the side.

Savkar, S. D.↗

NASA NTRS1977

Low Reynolds number flow past a blunt axisymmetric body at angle of attack

Low Reynolds number flow of an ideal gas over a blunt axisymmetric body of large half-angle at small angles of attack is investigated, for the case of laminar hypersonic flow. Time-varying viscous shock layer equations describing the flowfield are obtained from the full Navier-Stokes system by keeping terms to second order in the inverse square root of Re in both viscous and inviscid regions; the equations are valid for moderate to high Re. Drag, skin friction, and heating rates were obtained at small (or zero) angles of attack. Conditions experienced by planetary entry probes during the high-altitude (early) legs of an atmospheric entry trajectory are pertinent to the problem.

Kumar, A.↗

NASA NTRS1989

A spatial operator algebra for manipulator modeling and control

A spatial operator algebra for modeling the control and trajectory design of manipulation is discussed, with emphasis on its analytical formulation and implementation in the Ada programming language. The elements of this algebra are linear operators whose domain and range spaces consist of forces, moments, velocities, and accelerations. The effect of these operators is equivalent to a spatial recursion along the span of the manipulator. Inversion is obtained using techniques of recursive filtering and smoothing. The operator alegbra provides a high-level framework for describing the dynamic and kinematic behavior of a manipulator and control and trajectory design algorithms. Implementable recursive algorithms can be immediately derived from the abstract operator expressions by inspection, thus greatly simplifying the transition from an abstract problem formulation and solution to the detailed mechanization of a specific algorithm.

Rodriguez, G.↗

NASA NTRS1945

Bending and shear stresses developed by the instantaneous arrest of the root of a cantilever beam rotating with constant angular velocity about a transverse axis through the root

A theoretical investigation was made of the behavior of a cantilever beam in rotational motion about a transverse axis through the root determining the stresses, the deflections, and the accelerations that occur in the beam as a result of the arrest of motion. The equations for bending and shear stress reveal that, at a given percentage of the distance from root to tip and at a given trip velocity, the bending stresses for a particular mode are independent of the length of the beam and the shear stresses vary inversely with the length. When examined with respect to a given angular velocity instead of a given tip velocity, the equations reveal that the bending stress is proportional to the length of the beam whereas the shear stress is independent of the length. Sufficient experimental verification of the theory has previously been given in connection with another problem of the same type.

BEAMS - VIBRATION↗

NASA NTRS1996

High Performance Parallel Multigrid Algorithms for Unstructured Grids

We describe a high performance parallel multigrid algorithm for a rather general class of unstructured grid problems in two and three dimensions. The algorithm PUMG, for parallel unstructured multigrid, is related in structure to the parallel multigrid algorithm PSMG introduced by McBryan and Frederickson, for they both obtain a higher convergence rate through the use of multiple coarse grids. Another reason for the high convergence rate of PUMG is its smoother, an approximate inverse developed by Baumgardner and Frederickson.

Frederickson, Paul O.↗

NASA NTRS2003

Thermocapillary Convection Due to a Stationary Bubble - A Paradox

We analyze the velocity and temperature fields at steady state due to thermocapillary convection around a gas bubble that is stationary in a liquid. A linear temperature field is imposed in the undisturbed liquid. Our interest is in investigating the effect of convective transport of momentum and energy on the velocity and temperature fields. We assume the pertinent physical properties to be constant, and that buoyant convection is negligible. Suitably defined Reynolds and Marangoni numbers are assumed to be small compared with unity. When both the Reynolds and Marangoni numbers are set equal to zero, a solution can be found. In this solution, far from the bubble, the velocity field decays as the inverse of the distance from the bubble, and the disturbance temperature field decays as the inverse of the square of this distance. We now attempt to obtain a solution when the Reynolds number is zero, but the Marangoni number is small, but non-zero, by a perturbation expansion in the Marangoni number. When the temperature field is expanded in a regular perturbation series in the Marangoni number, we show that the problem for the first correction field is ill-posed. The governing equation for this perturbation field contains an inhomogeneity, and the corresponding particular solution neither decays far from the bubble, nor can be canceled by a homogeneous solution. Additional information is included in the original extended abstract.

Balasubramaniam, R.↗

NASA NTRS2023

Future Atmospheric Rivers and Impacts on Precipitation: Overview of the ARTMIP Tier2 High-Resolution Global Warming Experiment

Atmospheric rivers (ARs) are long, narrow synoptic scale weather features important for Earth’s hydrological cycle typically transporting water vapor poleward, delivering precipitation important for local climates. Understanding ARs in a warming climate is problematic because the AR response to climate change is tied to how the feature is defined. The Atmospheric River Tracking Method Intercomparison Project (ARTMIP) provides insights into this problem by comparing 16 atmospheric river detection tools (ARDTs) to a common dataset consisting of high resolution climate change simulations from a global atmospheric general circulation model. ARDTs mostly show increases in frequency and intensity, but the scale of the response is largely dependent on algorithmic criteria. Across ARDTs, bulk characteristics suggest intensity and spatial footprint are inversely correlated, and most focus regions experience increases in precipitation volume coming from extreme ARs. The spread of the AR precipitation response under climate change is large and dependent on ARDT selection.

Atmospheric Rivers↗

NASA NTRS1977

A numerical study of the unsteady leading edge separation bubble on an oscillating airfoil

A preliminary study of the unsteady viscous flow in the region of an airfoil leading edge was performed, in which the interaction between the viscous and inviscid flow fields is neglected. The solution method uses the finite difference form of the governing equations throughout the separated flow field and incorporates a transition model based on the integral turbulence kinetic energy equation. The validity of the numerical procedure is verified by making comparisons with analytical solutions to several test problems, including unsteady flow over a plate oscillating in its own plane. The method was then applied to the problem of unsteady viscous flow over a NACA 0012 airfoil oscillating sinusoidally in pitch. The flow field characteristics were in qualitative agreement with experimental results. The bubble moved forward on the airfoil and decreased in size as incidence was increased. Viscous flow in the leading edge region was found to be quasi-steady, while bubble height varied inversely with Reynolds number.

Kreskovsky, J. P.↗

NASA NTRS1984

Applications of spectral methods to turbulent magnetofluids in space and fusion research

Recent and potential applications of spectral method computation to incompressible, dissipative magnetohydrodynamics are surveyed. Linear stability problems for one dimensional, quasi-equilibria are approachable through a close analogue of the Orr-Sommerfeld equation. It is likely that for Reynolds-like numbers above certain as-yet-undetermined thresholds, all magnetofluids are turbulent. Four recent effects in MHD turbulence are remarked upon, as they have displayed themselves in spectral method computations: (1) inverse cascades; (2) small-scale intermittent dissipative structures; (3) selective decays of ideal global invariants relative to each other; and (4) anisotropy induced by a mean dc magnetic field. Two more conjectured applications are suggested. All the turbulent processes discussed are sometimes involved in current carrying confined fusion magnetoplasmas and in space plasmas.

Montgomery, D.↗

NASA NTRS1986

Inversion of limb radiance measurements - An operational algorithm

The limb radiance inversion radiometer (LRIR) and limb infrared monitor of the stratosphere (LIMS) experiments aboard the Nimbus 6 and 7 spacecraft have made observations of infrared emission by CO2, O3, H2O, HNO3, and NO2 at the earth's limb. This paper describes a method by which such measurements can be inverted to give vertical distributions of temperature and mixing ratios as functions of pressure. The simple and efficient approach was successfully applied to the LRIR data and subsequently in the initial assessment of the LIMS data. Inversion of synthetic data indicates the size of the errors to be expected as a result of the assumptions and instrumental errors. Retrievals of measured LIMS radiances are shown as examples and compared to in situ observations. The differences are comparable to those obtained with the more complex retrieval scheme used to process the LIMS archival products. Some problems are noted.

Bailey, P. L.↗

NASA NTRS1993

On the cross-stream spectral method for the Orr-Sommerfeld equation

Cross-stream models are defined as solutions to the Orr-Sommerfeld equation which are propagating normal to the flow direction. These models are utilized as a basis for a Hilbert space to approximate the spectrum of the Orr-Sommerfeld equation with plane Poiseuille flow. The cross-stream basis leads to a standard eigenvalue problem for the frequencies of Poiseuille flow instability waves. The coefficient matrix in the eigenvalue problem is shown to be the sum of a real matrix and a negative-imaginary diagonal matrix which represents the frequencies of the cross-stream modes. The real coefficient matrix is shown to approach a Toeplitz matrix when the row and column indices are large. The Toeplitz matrix is diagonally dominant, and the diagonal elements vary inversely in magnitude with diagonal position. The Poiseuille flow eigenvalues are shown to lie within Gersgorin disks with radii bounded by the product of the average flow speed and the axial wavenumber. It is shown that the eigenvalues approach the Gersgorin disk centers when the mode index is large, so that the method may be used to compute spectra with an essentially unlimited number of elements. When the mode index is large, the real part of the eigenvalue is the product of the axial wavenumber and the average flow speed, and the imaginary part of the eigen value is identical to the corresponding cross-stream mode frequency. The cross-stream method is numerically well-conditioned in comparison to Chebyshev based methods, providing equivalent accuracy for small mode indices and superior accuracy for large indices.

Zorumski, William E.↗

NASA NTRS2010

Fast Solution in Sparse LDA for Binary Classification

An algorithm that performs sparse linear discriminant analysis (Sparse-LDA) finds near-optimal solutions in far less time than the prior art when specialized to binary classification (of 2 classes). Sparse-LDA is a type of feature- or variable- selection problem with numerous applications in statistics, machine learning, computer vision, computational finance, operations research, and bio-informatics. Because of its combinatorial nature, feature- or variable-selection problems are NP-hard or computationally intractable in cases involving more than 30 variables or features. Therefore, one typically seeks approximate solutions by means of greedy search algorithms. The prior Sparse-LDA algorithm was a greedy algorithm that considered the best variable or feature to add/ delete to/ from its subsets in order to maximally discriminate between multiple classes of data. The present algorithm is designed for the special but prevalent case of 2-class or binary classification (e.g. 1 vs. 0, functioning vs. malfunctioning, or change versus no change). The present algorithm provides near-optimal solutions on large real-world datasets having hundreds or even thousands of variables or features (e.g. selecting the fewest wavelength bands in a hyperspectral sensor to do terrain classification) and does so in typical computation times of minutes as compared to days or weeks as taken by the prior art. Sparse LDA requires solving generalized eigenvalue problems for a large number of variable subsets (represented by the submatrices of the input within-class and between-class covariance matrices). In the general (fullrank) case, the amount of computation scales at least cubically with the number of variables and thus the size of the problems that can be solved is limited accordingly. However, in binary classification, the principal eigenvalues can be found using a special analytic formula, without resorting to costly iterative techniques. The present algorithm exploits this analytic form along with the inherent sequential nature of greedy search itself. Together this enables the use of highly-efficient partitioned-matrix-inverse techniques that result in large speedups of computation in both the forward-selection and backward-elimination stages of greedy algorithms in general.

Moghaddam, Baback↗

NASA NTRS1984

Problems in simulating the stratocumulus-topped boundary layer with a third-order closure model

The Andre et al. (1976, 1978) third-order closure model, in which the time rate of change terms, the relaxation and rapid effects for pressure-related terms, and the clipping approximation are used along with the quasi-normal closure, is invoked in the study of turbulence in a cloudy layer that is radiatively cooled from above. A spurious oscillation whose greatest amplitude lies near the inversion is shown by analysis to arise from the mean gradient and buoyancy terms of the triple-moment equations. An attempt is made to damp the oscillation through the introduction of diffusion terms into the triple-moment equations. The results obtained are noted to be sensitive to the ad hoc eddy coefficient applied in the third-moment equations.

Moeng, C.-H.↗