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NASA NTRS1982

An approximation theory for nonlinear partial differential equations with applications to identification and control

Approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations. These ideas are used to establish theoretical convergence results for parameter identification using modal (eigenfunction) approximation techniques. Results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given.

Banks, H. T.↗
NASA NTRS1983

Flow in a differentially rotated cylindrical drop at low Reynolds number

A liquid drop held captive between parallel disks that are differentially rotated is a model for the swirling flows induced by crystal rotation in the floating-zone process for growing semiconductor materials. An asymptotic analysis for a cylindrical drop is presented that elucidates the structure of the axisymmetric cellular motions caused by disk rotation at low Reynolds number. Variations of meniscus shape induced by these flows are described in the limit of small capillary number. Most cellular flow fields break the bifurcation point that corresponds to the Plateau-Rayleigh limit for the length of a static drop into two disjoint shape families and lower the maximum stable drop length. This effect is studied by a singular bifurcation analysis.

Harriott, G. M.↗
NASA NTRS1983

Experimental comparison of heterodyne and direct detection for pulsed differential absorption CO2 lidar

A pulsed dual-wavelength dual-CO2-laser differential-absorption lidar (DIAL) system has been developed which permits simultaneous heterodyne and direct detection of the same lidar returns. This system has been used to make an experimental comparison of the SNRs and statistical and temporal characteristics of the DIAL returns from several topographic targets. These results were found to be in general agreement with theory and were used to quantify the relative merits of the two detection techniques. The measured parameter values were applied to an analytical treatment to predict system trade-offs for the remote sensing of atmospheric species, with application to both path-averaged and range-resolved measurements.

Killinger, D. K.↗
NASA NTRS1982

Electron impact excitation of SO2 - Differential, integral, and momentum transfer cross sections

Electron impact excitation of the electronic states of SO2 was investigated. Differential, integral, and inelastic momentum transfer cross sections were obtained by normalizing the relative measurements to the elastic cross sections. The cross sections are given for seven spectral ranges of the energy-loss spectra extending from the lowest electronic state to near the first ionization limit. Most of the regions represent the overlap of several electronic transitions. No measurements for these cross sections have been reported previously.

Vuskovic, L.↗
NASA NTRS1982

Differential imaging using charge-coupled device (CCD) imagers with on-chip charge storage

A CCD technique is described which allows long integration periods between readouts together with moderate chopping rates. During each phase of a differential chopping cycle, one set of charge images is shifted to the center of the chip, which is light sensitive. At the same time, the other set of charge images is shifted under one of two masked areas which serve as charge-storage sites. Since the vertical shifting between phases can be accomplished in much less time than the typical exposure per phase, there is negligible image smearing. For a given light level and chopping rate the performance of this technique is limited primarily by the readout noise and the vertical charge transfer inefficiency. If many transfer cycles are required between readouts, the charge transfer inefficiency will diffuse the accumulated charge images along the vertical columns. Laboratory and astronomical data obtained with this technique using a CCD camera and the 2.3 m telescope on Kitt Peak are presented.

Stockman, H. S.↗
NASA NTRS1983

Period doubling and chaos in partial differential equations for thermosolutal convection

Numerical experiments on two-dimensional thermosolutal convection reveal a transition from periodic oscillations to chaos through a sequence of period-doubling bifurcations. Within the chaotic region there are narrow periodic windows. This is the first example of period-doubling in solutions of partial differential equations. A truncated model indicates that this behavior is associated with heteroclinic explosions.

Moore, D. R.↗
NASA NTRS1982

The use of solution adaptive grids in solving partial differential equations

The grid point distribution used in solving a partial differential equation using a numerical method has a substantial influence on the quality of the solution. An adaptive grid which adjusts as the solution changes provides the best results when the number of grid points available for use during the calculation is fixed. Basic concepts used in generating and applying adaptive grids are reviewed in this paper, and examples illustrating applications of these concepts are presented.

Anderson, D. A.↗
NASA NTRS1982

Grid generation by elliptic partial differential equations for a tri-element Augmentor-Wing airfoil

Two efforts to numerically simulate the flow about the Augmentor-Wing airfoil in the cruise configuration using the GRAPE elliptic partial differential equation grid generator algorithm are discussed. The Augmentor-Wing consists of a main airfoil with a slotted trailing edge for blowing and two smaller airfoils shrouding the blowing jet. The airfoil and the algorithm are described, and the application of GRAPE to an unsteady viscous flow simulation and a transonic full-potential approach is considered. The procedure involves dividing a complicated flow region into an arbitrary number of zones and ensuring continuity of grid lines, their slopes, and their point distributions across the zonal boundaries. The method for distributing the body-surface grid points is discussed.

Sorenson, R. L.↗
NASA NTRS1982

Marching grid generation using parabolic partial differential equations

The feasibility of using parabolic partial differential equations for grid generation is examined. Source terms in the form of a linear interpolation between the current grid and the outer boundary are used in generating a grid for a two-dimensional airfoil flow. Grid generation equations are derived by assuming that grid spacings are locally nonuniform on the computational domain. The grid spacing control method is described in detail, and the local orthogonality of the grid lines is discussed. An O-mesh and an H-mesh generated by the described method are shown.

Nakamura, S.↗
NASA NTRS1983

Explicit finite difference predictor and convex corrector with applications to hyperbolic partial differential equations

An explicit finite difference scheme consisting of a predictor and a corrector has been developed and applied to solve some hyperbolic partial differential equations (PDEs). The corrector is a convex-type function which is applied at each time level and at each mesh point. It consists of a parameter which may be estimated such that for larger time steps the algorithm should remain stable and generate a fast speed of convergence to the steady-state solution. Some examples have been given.

Dey, C.↗
NASA NTRS1983

Atmospheric pressure and temperature profiling using near IR differential absorption lidar

The present investigation is concerned with differential absorption lidar techniques for remotely measuring the atmospheric temperature and pressure profile, surface pressure, and cloud top pressure-height. The procedure used in determining the pressure is based on the conduction of high-resolution measurements of absorption in the wings of lines in the oxygen A band. Absorption with respect to these areas is highly pressure sensitive in connection with the mechanism of collisional line broadening. The method of temperature measurement utilizes a determination of the absorption at the center of a selected line in the oxygen A band which originates from a quantum state with high ground state energy.

Korb, C. L.↗
NASA NTRS1985

Differential-Coil Eddy-Current Material Sorter

Small metal or other electrically conductive parts of same shape but different composition quickly sorted with differential-coil eddy-current sorter. Developed to distinguish between turbine blades of different alloys, hardnesses, and residual stress, sorter generally applicable to parts of simple and complex shape.

Nummelin, J.↗
NASA NTRS1985

Differential Pressure Helps Seal Ball Valve

Leakage suppressed despite O-ring wear. New design eliminates leakage in vacuum selector valve on Space Shuttle waste-control subsystem. Applied to improve sealing in laboratory and industrial vacuum systems and other plumbing involving switching among lines with pressure differentials of order of 1 atmosphere (0.1 MPa).

Mangialardi, J. K.↗
NASA NTRS1983

Spectral methods for time dependent partial differential equations

The theory of spectral methods for time dependent partial differential equations is reviewed. When the domain is periodic Fourier methods are presented while for nonperiodic problems both Chebyshev and Legendre methods are discussed. The theory is presented for both hyperbolic and parabolic systems using both Galerkin and collocation procedures. While most of the review considers problems with constant coefficients the extension to nonlinear problems is also discussed. Some results for problems with shocks are presented.

Gottlieb, D.↗
NASA NTRS1984

Growth and differentiation of mammalian embryonic tissues exposed to hypergravity in vivo and in vitro

In about 10 years or so, men and women from Earth will be long-term inhabitants of a space station aboard which plants and animals will be growing and developing in gravities other than that of Earth. The effect of gravitational changes on development was examined. It is indicated that differentiation is speeded up under excess G and slowed in low or null G. The effects of exposure to excess gravity on fusion of the embryonic mouse secondary palate were studied. During fusion, the palatal shelves first adhere by means of glycoproteins appearing along the medial epithelial edge (MEE). The contacting epithelia then reorganize and undergo programmed cell death, allowing the underlying mesenchymes to come in contact. The process of cell death occurs in vitro at about the same rate that it occurs in vivo.

Duke, P. J.↗
NASA NTRS1984

Isolation and characterization of beta-glucan synthase: A potential biochemical regulator of gravistimulated differential cell wall loosening

In plants, gravity stimulates differential growth in the upper and lower halves of horizontally oriented organs. Auxin regulation of cell wall loosening and elongation is the basis for most models of this phenomenon. Auxin treatment of pea stem tissue rapidly increases the activity of Golgi-localized Beta-1,4-glucan synthase, an enzyme involved in biosynthesis of wall xyloglucan which apparently constitutes the substrate for the wall loosening process. The primary objective is to determine if auxin induces de novo formation of Golgi glucan synthase and increases the level of this glucan synthase mRNA. This shall be accomplished by (a) preparation of a monoclonal antibody to the synthase, (b) isolation, and characterization of the glucan synthase, and (c) examination for cross reactivity between the antibody and translation products of auxin induced mRNAs in pea tissue. The antibody will also be used to localize the glucan synthase in upper and lower halves of pea stem tissue before, during and after the response to gravity.

Kuzmanoff, K. M.↗
NASA NTRS1984

Legendre-tau approximation for functional differential equations. Part 2: The linear quadratic optimal control problem

The numerical scheme based on the Legendre-tau approximation is proposed to approximate the feedback solution to the linear quadratic optimal control problem for hereditary differential systems. The convergence property is established using Trotter ideas. The method yields very good approximations at low orders and provides an approximation technique for computing closed-loop eigenvalues of the feedback system. A comparison with existing methods (based on averaging and spline approximations) is made.

Ito, K.↗