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NASA NTRS1983

Uniform asymptotic approximations for duct eigenfunctions in a thin boundary layer flow

Analytical approximations for the acoustic modes in a duct carrying a uniform core flow with a thin shear layer at the walls are developed using the Method of Matched Asymptotic Expansions. Both two-dimensional and cylindrical duct propagation are considered. Numerical results for eigenvalues calculated using the theory are presented for the two dimensional problem and compared with results from earlier analyses. It is found that the new approximations yield a significant increase in accuracy.

Myers, M. K.↗

NASA NTRS1982

Spanwise mass transfer variations on a cylinder in 'nominally' uniform crossflow

Mass transfer experiments on a circular cylinder in a 'nominally' uniform crossflow are described. Experiments were conducted at the tunnel's turbulence level and with a woven-wire turbulence screen. In both cases spanwise and circumferential mass transfer measurements were made. Without the turbulence screen, the results were found to be spanwise independent and agreed quite well with both theory and the result of others. In addition to the mass transfer measurements, spanwise traverse measurements of the mean velocity and turbulence quantities in the incident flow were made and showed that the screen produced a small-amplitude spanwise periodic perturbation in the incident flow. Although this perturbation was only one quarter of a percent in the mean velocity and buried in the stream's turbulence, disproportionately large spanwise variations of 15 percent were found in the mass transfer rate.

Mayle, R. E.↗

NASA NTRS1983

The Gravitational Potential Due to Uniform Disks and Rings

The gravitational potential of bodies possessing axial symmetry can be expressed as a power series in distance, with the Legendre polynomials as coefficients. Such series, however, converge so slowly in the neighborhood of thin, uniform disks and rings that too many series terms must be summed in order to obtain an accurate field measure. A gravitational potential expression is presently obtained in closed form, in terms of complete elliptic integrals.

Lass, H.↗

NASA NTRS1984

Orbital stability in combined uniform axial and three-dimensional wiggler magnetic fields for free-electron lasers

Zachary Phys. Rev. A 29 (6), 3224 (1984) recently analyzed the instability of relativistic-electron helical trajectories in combined uniform axial and helical wiggler magnetic fields when the radial variation of the wiggler field is taken into account. It is shown here that the type 2 instability comprised of secular terms growing linearly in time, identified by Zachary and earlier by Diament Phys. Rev. A 23 (5), 2537 (1981), is an artifact of simple perturbation theory. A multiple-time-scale perturbation analysis reveals a nonsecular evolution on a slower time scale which accommodates an arbitrary initial perturbation. It is shown that, in the absence of exponential instability, the electron seeks a modified helical orbit more appropriate to its perturbed state and oscillates stably about it. Thus, the perturbed motion is oscillatory but nonsecular, and hence the helical orbits are stable.

Johnston, S.↗

NASA NTRS1982

TDM/FM/FDMA - A modulation technique for multiple-beam satellites which precludes cochannel interference and allows non-uniform geographic distribution of user channels

The technique outlined in this paper is intended to eliminate the problems of cochannel interference and uniform geographic distribution of user channels which arise in conventional designs for a multiple spot beam communication satellite to serve mobile telephony users across the CONUS. By time multiplexing FM/FDMA signal ensembles so that only those beams operating on distinct frequency subbands are allowed to transmit concurrently, cochannel interference arising from simultaneous frequency subband reuse is precluded. Thus, time disjoint frequency reuse is accomplished over a repetitive sequence of fixed time slots. By assigning different size subbands to each time slot, a market of nonuniform users can be accommodated. The technique results in a greatly simplified antenna feed system design for the satellite, at a cost of imposing the need for time slot synchronization on the mobile FM receivers whose ability for rejecting adjacent channel interference is somewhat diminished.

Springett, J. C.↗

NASA NTRS1984

Gamma-ray imaging with a rotating hexagonal uniformly redundant array

Laboratory experiments have been performed to demonstrate the capabilities of a gamma-ray imaging system employing a NaI Anger camera and a rotating coded aperture mask. The mask incorporates in its design a new type of hexagonal uniformly redundant array (HURA) which is essentially antisymmetric under 60 deg rotation. The image formation techniques are described and results are presented that demonstrate the imaging capability of the system for individual and multiple point sources of gamma-ray emission. The results are compared to analytical predictions for the imaging and point source localization capabilities of coded aperture systems using continuous detectors.

Cook, W. R.↗

NASA NTRS1984

The uniform asymptotic swallowtail approximation - Practical methods for oscillating integrals with four coalescing saddle points

Methods that can be used in the numerical implementation of the uniform swallowtail approximation are described. An explicit expression for that approximation is presented to the lowest order, showing that there are three problems which must be overcome in practice before the approximation can be applied to any given problem. It is shown that a recently developed quadrature method can be used for the accurate numerical evaluation of the swallowtail canonical integral and its partial derivatives. Isometric plots of these are presented to illustrate some of their properties. The problem of obtaining the arguments of the swallowtail integral from an analytical function of its argument is considered, describing two methods of solving this problem. The asymptotic evaluation of the butterfly canonical integral is addressed.

Connor, J. N. L.↗

NASA NTRS1984

Legendre-Tau approximation for functional differential equations. Part 3: Eigenvalue approximations and uniform stability

The stability and convergence properties of the Legendre-tau approximation for hereditary differential systems are analyzed. A charactristic equation is derived for the eigenvalues of the resulting approximate system. As a result of this derivation the uniform exponential stability of the solution semigroup is preserved under approximation. It is the key to obtaining the convergence of approximate solutions of the algebraic Riccati equation in trace norm.

Ito, K.↗

NASA NTRS1983

Planar dynamics of a uniform beam with rigid bodies affixed to the ends

The planar dynamics of a uniform elastic beam subject to a variety of geometric and natural boundary conditions and external excitations were analyzed. The beams are inextensible and capable of small transverse bending deformations only. Classical beam vibration eigenvalue problems for a cantilever with tip mass, a cantilever with tip body and an unconstrained beam with rigid bodies at each are examined. The characteristic equations, eigenfunctions and orthogonality relations for each are derived. The forced vibration of a cantilever with tip body subject to base acceleration is analyzed. The exact solution of the governing nonhomogeneous partial differential equation with time dependent boundary conditions is presented and compared with a Rayleigh-Ritz approximate solution. The arbitrary planar motion of an elastic beam with rigid bodies at the ends is addressed. Equations of motion are derived for two modal expansions of the beam deflection. The motion equations are cast in a first order form suitable for numerical integration. Selected FORTRAN programs are provided.

Storch, J.↗

NASA NTRS1985

Forced MHD turbulence in a uniform external magnetic field

Two-dimensional dissipative MHD turbulence is randomly driven at small spatial scales and is studied by numerical simulation in the presence of a strong uniform external magnetic field. A behavior is observed which is apparently distinct from the inverse cascade which prevails in the absence of an external magnetic field. The magnetic spectrum becomes dominated by the three longest wavelength Alfven waves in the system allowed by the boundary conditions: those which, in a box size of edge 2 pi, have wave numbers (kx' ky) = (1, 1), and (1, -1), where the external magnetic field is in the x direction. At any given instant, one of these three modes dominates the vector potential spectrum, but they do not constitute a resonantly coupled triad. Rather, they are apparently coupled by the smaller-scale turbulence.

Hossain, M.↗

NASA NTRS1985

Uniformly high-order accurate non-oscillatory schemes, 1

The construction and the analysis of nonoscillatory shock capturing methods for the approximation of hyperbolic conservation laws was begun. These schemes share many desirable properties with total variation diminishing schemes (TVD), but TVD schemes have at most first order accuracy, in the sense of truncation error, at extreme of the solution. A uniformly second order approximation was constucted, which is nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time. This is achieved via a nonoscillatory piecewise linear reconstruction of the solution from its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell.

Harten, A.↗

NASA NTRS1983

GaAs MESFET with lateral non-uniform doping

An analytical model of the GaAs MESFET with arbitrary non-uniform doping is presented. Numerical results for linear lateral doping profile are given as a special case. Theoretical considerations predict that better device linearity and improved F(T) can be obtained by using linear lateral doping when doping density increases from source to drain.

Wang, Y. C.↗

NASA NTRS1985

Hexagonal uniformly redundant arrays for coded-aperture imaging

Uniformly redundant arrays are used in coded-aperture imaging, a technique for forming images without mirrors or lenses. This technique is especially important for the high energy X-ray and gamma-ray region above 20 kev. In this technique, a mask consisting of opaque (closed) and trasparent (open) areas is placed between the photon sources to be imaged and a position sensitive detector or a detector array. Each source casts a shadow pattern of the mask or aperture onto the detector. This shadow pattern may be viewed as an encoded signal for that source direction. If each possible source code is unique, the detected composite of overlapping shadow patterns may be decoded to produce an image of the source distribution.

Finger, M. H.↗

NASA NTRS1985

Stresses and deformations in cross-ply composite tubes subjected to a uniform temperature change: Elasticity and Approximate Solutions

The effects of a uniform temperature change on the stresses and deformations of composite tubes are investigated. The accuracy of an approximate solution based on the principle of complementary virtual work is determined. Interest centers on tube response away from the ends and so a planar elasticity approach is used. For the approximate solution a piecewise linear variation of stresses with the radial coordinate is assumed. The results from the approximate solution are compared with the elasticity solution. The stress predictions agree well, particularly peak interlaminar stresses. Surprisingly, the axial deformations also agree well. This, despite the fact that the deformations predicted by the approximate solution do not satisfy the interface displacement continuity conditions required by the elasticity solution. The study shows that the axial thermal expansion coefficient of tubes with a specific number of axial and circumferential layers depends on the stacking sequence. This is in contrast to classical lamination theory which predicts the expansion to be independent of the stacking arrangement. As expected, the sign and magnitude of the peak interlaminar stresses depends on stacking sequence.

Hyer, M. W.↗

NASA NTRS1984

Uniformly spaced field-aligned ionization ducts

A number of interesting cases of combination mode ducted echoes for mid- and low-latitude regions are presented that show nearly uniformly spaced multiple combination mode traces on the ionograms in the frequency range above 1 MHz. These traces suggest that a parallel system of field-aligned ducts is present. Ray tracing studies are made to determine the structure that would explain the observations using the electron density profile derivable from the vertical trace and assuming field-aligned ducts. Spacing perpendicular to the ducts is found to be as much as 70 km. Some of these parallel duct structures are found to extend to the conjugate hemisphere, possibly to the F peak.

Gross, S. H.↗

NASA NTRS1984

Thermal expansion uniformity of materials for large telescope mirrors

Uniformity of thermal expansion has been measured for fused quartz and borosilicate glass. The variation of expansion coefficient for three melts of TO8E was 5 x 10 to the -9th/K over a temperature range of 300 to 100 K and was found to vary linearly with position in the melt. This spatial gradient averaged 3.5 x 10 to the -11th/K-cm. The room-temperature thermal expansivity variation of Duran (Tempax) glass was about 27 x 10 to the -9th/K, while that of E6 glass was about 52 x 10 to the -9th/K.

Jacobs, S. F.↗

NASA NTRS1985

On the evolution of accretion disc flow in cataclysmic variables. III - Outburst properties of constant and uniform-alpha model discs

Attention is given to the stability and evolution of some simple accretion disk models in which the viscosity is prescribed by an ad hoc, uniform-alpha model. Emphasis is placed on systems in which the mass input rate from the secondary to the disk around the primary is assumed to be constant, although initial calculations with variable mass input rates are also performed. Time-dependent visual magnitude light curves constructed for cataclysmic binaries with a range of disk size, primary mass and mass input rate, and viscosity magnitude, are compared with the observed properties of various cataclysmic variable subclasses. The results obtained indicate that the observational differences between novae and dwarf novae may be due to mass input rate differences. The present models can reproduce the gross observational features of U-Gem-type dwarf nova outbursts.

Lin, D. N. C.↗

NASA NTRS1985

Dynamic compensation and decoupling for systems of uniform index 2

A procedure for the design of n-dimensional dynamic compensators for systems of dimension 2n and uniform controllability and observability indexes two was developed. The design in state space and in frequency domain is presented. The design and a minimal dimension dynamic compensator and Luenberger observer are applied to a two-link nonlinear biped (n=2) model in the vicinity of the vertical stance to test the effectiveness of their regulating actions, and the results are presented.

Bavarian, B.↗