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NASA NTRS1987

Numerical analysis of discrete fractional integrodifferential structural dampers

This paper develops solution algorithms enabling the handling of the dynamic response of nonlinear structures contained discretely attached dampers modeled by fractional integrodifferential operators of the Grunwald-Liouville-Riemann type. The development consists of two levels of formulation, namely: (1) numerical approximations of fractional operators and, (2) the establishment of global level implicit schemes enabling the solution to nonlinear structural formulations. To generalize the overall results, error estimates are derived for the fractional operator approximation algorithm. These enable an ongoing optimization of solution efficiency for a given error tolerance. To benchmark the scheme, the results of several numerical experiments are presented. These illustrate the numerical characteristics of the overall formulation.

Padovan, Joseph↗

NASA NTRS1988

Electro-impulse de-icing electrodynamic solution by discrete elements

This paper describes a technique for analyzing the electrodynamic phenomena associated with electro-impulse deicing. The analysis is done in the time domain and utilizes a discrete element formulation concept expressed in state variable form. Calculated results include coil current, eddy currents in the target (aircraft leading edge skin), pressure distribution on the target, and total force and impulse on the target. Typical results are presented and described. Some comparisons are made between calculated and experimental results, and also between calculated values from other theoretical approaches. Application to the problem of a nonrigid target is treated briefly.

Bernhart, W. D.↗

NASA NTRS1988

Numerical approximation for the infinite-dimensional discrete-time optimal linear-quadratic regulator problem

An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.

Gibson, J. S.↗

NASA NTRS1987

Adaptive proximate time optimal servomechanisms: Discrete time case

Following a review of the continuous time proximate time-optimal servomechanism (PTOS), a discrete-time PTOS is developed, along with conditions for its stability. An algorithm is proposed for adapting PTOS when the plant parameters are not known yielding APTOS (adaptive PTOS). Under ideal conditions APTOs is shown to be uniformly asymptotically stable. Simulation results demonstrate the predicted performance, and experimental results validate the practically of APTOS.

Workman, M. L.↗

NASA NTRS1988

Parallel discrete event simulation using shared memory

With traditional event-list techniques, evaluating a detailed discrete-event simulation-model can often require hours or even days of computation time. By eliminating the event list and maintaining only sufficient synchronization to ensure causality, parallel simulation can potentially provide speedups that are linear in the numbers of processors. A set of shared-memory experiments, using the Chandy-Misra distributed-simulation algorithm, to simulate networks of queues is presented. Parameters of the study include queueing network topology and routing probabilities, number of processors, and assignment of network nodes to processors. These experiments show that Chandy-Misra distributed simulation is a questionable alternative to sequential-simulation of most queueing network models.

Reed, Daniel A.↗

NASA NTRS1988

Finite element discrete ordinates method for radiative transfer in non-rotationally invariant scattering media - Application to the leaf canopy problem

A finite element discrete ordinates method for solving the radiative transfer equation in nonrotationally invariant scattering media has been applied to the lead-canopy problem, and results are presented on the cross sections and the reflection functions. The method is based on a unique implementation of the Galerkin integral law formulation of the transport equation. For both near-normal and grazing incidences, the transfer functions of leaf canopies are found to be strongly anisotropic, with relatively more scattered flux in the vertical directions. It is suggested that the assumption of isotropic scattering in leaf canopies is not valid.

Myneni, Ranga B.↗

NASA NTRS1988

An automatic frequency control loop using overlapping DFTs (Discrete Fourier Transforms)

An automatic frequency control (AFC) loop is introduced and analyzed in detail. The new scheme is a generalization of the well known Cross Product AFC loop that uses running overlapping discrete Fourier transforms (DFTs) to create a discriminator curve. Linear analysis is included and supported with computer simulations. The algorithm is tested in a low carrier to noise ratio (CNR) dynamic environment, and the probability of loss of lock is estimated via computer simulations. The algorithm discussed is a suboptimum tracking scheme with a larger frequency error variance compared to an optimum strategy, but offers simplicity of implementation and a very low operating threshold CNR. This technique can be applied during the carrier acquisition and re-acquisition process in the Advanced Receiver.

Aguirre, S.↗

NASA NTRS1988

Cosmology of biased discrete symmetry breaking

The cosmological consequences of spontaneous breaking of an approximate discrete symmetry are studied. The breaking leads to formation of proto-domains of false and true vacuum separated by domain walls of thickness determined by the mass scale of the model. The cosmological evolution of the walls is extremely sensitive to the magnitude of the biasing; several scenarios are possible, depending on the interplay between the surface tension on the walls and the volume pressure from the biasing. Walls may disappear almost immediately after they form, or may live long enough to dominate the energy density of the Universe and cause power-law inflation. Limits are obtained on the biasing that characterizes each possible scenario.

Gelmini, Graciela B.↗

NASA NTRS1988

The discrete correlation function: A new method for analyzing unevenly sampled variability data

A method of measuring correlation functions without interpolating in the temporal domain, the discrete correlation function, is introduced. It provides an assumption-free representation of the correlation measured in the data, and allows meaningful error estimates. This method does not produce spurious correlations at zero lag due to correlated errors. It is shown that physical interpretation of active galactic nuclei cross-correlation functions requires knowledge of the input function's fluctuation power spectrum, involves model-dependence in the form of symmetry assumptions, and must take into account intrinsic scale bias. This technique was used to find a correlation in published IUE data for NGC 4151, which indicates that the broad C IV feature emanates from a shell 15 to 75 light-days in radius, assuming spherical symmetry.

Edelson, R. A.↗

NASA NTRS1988

U-Pb ages and Sr, Pb and Nd isotope data for gneisses near the Kolar Schist Belt: Evidence for the juxtaposition of discrete Archean terranes

Uranium-lead ages and Sr, Pb, and Nd isotopic data for gneisses near the Kolar Schist Belt and their interpretation as evidence for the juxtaposition of discrete Archean terranes were presented. The granodioritic Kambha gneiss east of the schist belt has a zircon age of 2532 + or - 3 Ma and mantle-like initial Sr, Pb, and Nd isotopic ratios. Therefore these gneisses are thought to represent new crust added to the craton in the latest Archean. By contrast, more mafic Dod gneisses and leucocratic Dosa gneisses west of the schist belt (2632 + or - 7 and 2610 + or - 10 Ma) show evidence for contamination of their magmatic precursors (LREE-enriched mantle-derived for the Dod gneisses) by older (greater than 3.2 Ga) continental crust. Fragments of this older crust may be present as granitic and tonalitic inclusions in the 2.6-Ga gneisses and in shear zones. The antiquity of these fragments is supported by their Nd, Sr, and Pb isotopic compositions and by 2.8 to greater than 3.2 Ga zircon cores.

Krogstad, E. J.↗

NASA NTRS1989

An Investigation of the Overlap Between the Statistical Discrete Gust and the Power Spectral Density Analysis Methods

The results of a NASA investigation of a claimed Overlap between two gust response analysis methods: the Statistical Discrete Gust (SDG) Method and the Power Spectral Density (PSD) Method are presented. The claim is that the ratio of an SDG response to the corresponding PSD response is 10.4. Analytical results presented for several different airplanes at several different flight conditions indicate that such an Overlap does appear to exist. However, the claim was not met precisely: a scatter of up to about 10 percent about the 10.4 factor can be expected.

Perry, Boyd, III↗

NASA NTRS1988

Effect of aerodynamic detuning on supersonic rotor discrete frequency noise generation

A mathematical model was developed to predict the effect of alternate blade circumferential aerodynamic detuning on the discrete frequency noise generation of a supersonic rotor. Aerodynamic detuning was shown to have a small beneficial effect on the noise generation for reduced frequencies less than 3. For reduced frequencies greater than 3, however, the aerodynamic detuning either increased or decreased the noise generated, depending on the value of the reduced frequency.

Hoyniak, D.↗

NASA NTRS1988

Singular perturbation and time scale approaches in discrete control systems

After considering a singularly perturbed discrete control system, a singular perturbation approach is used to obtain outer and correction subsystems. A time scale approach is then applied via block diagonalization transformations to decouple the system into slow and fast subsystems. To a zeroth-order approximation, the singular perturbation and time-scale approaches are found to yield equivalent results.

Naidu, D. S.↗

NASA NTRS1989

An investigation of the 'Overlap' between the Statistical-Discrete-Gust and the Power-Spectral-Density analysis methods

This paper presents the results of a NASA investigation of a claimed 'Overlap' between two gust response analysis methods: the Statistical Discrete Gust (SDG) method and the Power Spectral Density (PSD) method. The claim is that the ratio of an SDG response to the corresponding PSD response is 10.4. Analytical results presented in this paper for several different airplanes at several different flight conditions indicate that such an 'Overlap' does appear to exist. However, the claim was not met precisely: a scatter of up to about 10 percent about the 10.4 factor can be expected.

Perry, Boyd, III↗

NASA NTRS1988

Stability of semi-discrete approximations for hyperbolic initial-boundary-value problems. II - Asymptotic estimates

The stability of semi-discrete approximations for hyperbolic initial-boundary-value problems is considered. Asymptotic estimates of the eigenvalues of the finite-domain problem are given. These estimates are used to examine questions relating the normal mode analysis of the finite-domain problem and the normal mode quarter-plane analysis of the Gustafsson, Kreiss, and Sundstroem theory.

Warming, Robert F.↗

NASA NTRS1989

Discrete wave packets upstream from the earth and comets

Discrete wave packets are nearly monochromatic waves lasting several wave cycles which are frequently found on the leading edge of steepened low-frequency waves or shocklets upstream from the earth's bow shock. Similarly appearing waves are present at comet Giacobini-Zinner. To determine if these waves are the same as those observed at earth a detailed comparison of the properties of the two sets of waves is presented. The waves have very similar amplitudes, durations, and directions of propagation. Thus it is concluded that the source mechanism for the two phenomena must be the same, i.e., wave steepening.

Le, G.↗

NASA NTRS1989

Sequential design of discrete linear quadratic regulators via optimal root-locus techniques

A sequential method employing classical root-locus techniques has been developed in order to determine the quadratic weighting matrices and discrete linear quadratic regulators of multivariable control systems. At each recursive step, an intermediate unity rank state-weighting matrix that contains some invariant eigenvectors of that open-loop matrix is assigned, and an intermediate characteristic equation of the closed-loop system containing the invariant eigenvalues is created.

Shieh, Leang S.↗

NASA NTRS1989

Galerkin/Runge-Kutta discretizations for parabolic equations with time-dependent coefficients

A new class of fully discrete Galerkin/Runge-Kutta methods is constructed and analyzed for linear parabolic initial boundary value problems with time dependent coefficients. Unlike any classical counterpart, this class offers arbitrarily high order convergence while significantly avoiding what has been called order reduction. In support of this claim, error estimates are proved, and computational results are presented. Additionally, since the time stepping equations involve coefficient matrices changing at each time step, a preconditioned iterative technique is used to solve the linear systems only approximately. Nevertheless, the resulting algorithm is shown to preserve the original convergence rate while using only the order of work required by the base scheme applied to a linear parabolic problem with time independent coefficients. Furthermore, it is noted that special Runge-Kutta methods allow computations to be performed in parallel so that the final execution time can be reduced to that of a low order method.

Keeling, Stephen L.↗