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At least 1,423 records · Page 79

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NASA NTRS1987

On the stochastic dissemination of faults in an admissible network

The dynamic distribution of faults in a general type network is discussed. The starting point is a uniquely branched network in which each pair of nodes is connected by a single branch. Mathematical expressions for the uniquely branched network transition matrix are derived to show that sufficient stationarity exists to ensure the validity of the use of the Markov Chain model to analyze networks. In addition the conditions for the use of Semi-Markov models are discussed. General mathematical expressions are derived in an examination of branch redundancy techniques commonly used to increase reliability.

Kyrala, A.↗

NASA NTRS1987

Plates and shells containing a surface crack under general loading conditions

Various through and part-through crack problems in plates and shells are considered. The line-spring model of Rice and Levy is generalized to the skew-symmetric case to solve surface crack problems involving mixed-mode, coplanar crack growth. Compliance functions are introduced which are valid for crack depth to thickness ratios at least up to .95. This includes expressions for tension and bending as well as expressions for in-plane shear, out-of-plane shear, and twisting. Transverse shear deformation is taken into account in the plate and shell theories and this effect is shown to be important in comparing stress intensity factors obtained from the plate theory with three-dimensional solutions. Stress intensity factors for cylinders obtained by the line-spring model also compare well with three-dimensional solution. By using the line-spring approach, stress intensity factors can be obtained for the through crack and for part-through crack of any crack front shape, without recalculation integrals that take up the bulk of the computer time. Therefore, parameter studies involving crack length, crack depth, shell type, and shell curvature are made in some detail. The results will be useful in brittle fracture and in fatigue crack propagation studies. All problems considered are of the mixed boundary value type and are reducted to strongly singular integral equations which make use of the finite-part integrals of Hadamard. The equations are solved numerically in a manner that is very efficient.

Joseph, Paul F.↗

NASA NTRS1985

Surface-slip equations for multicomponent, nonequilibrium air flow

Equations are presented for the surface slip (or jump) values of species concentration, pressure, velocity, and temperature in the low-Reynolds-number, high-altitude flight regime of a space vehicle. These are obtained from closed-form solutions of the mass, momentum, and energy flux equations using the Chapman-Enskog velocity distribution function. This function represents a solution of the Boltzmann equation in the Navier-Stokes approximation. The analysis, obtained for nonequilibrium multicomponent air flow, includes the finite-rate surface catalytic recombination and changes in the internal energy during reflection from the surface. Expressions for the various slip quantities have been obtained in a form which can readily be employed in flow-field computations. A consistent set of equations is provided for multicomponent, binary, and single species mixtures. Expression is also provided for the finite-rate species-concentration boundary condition for a multicomponent mixture in absence of slip.

Gupta, Roop N.↗

NASA NTRS1986

On the symbolic manipulation and code generation for elasto-plastic material matrices

A computerized procedure for symbolic manipulations and FORTRAN code generation of elastoplastic material matrix for finite element applications is presented. Special emphasis is placed on expression simplifications during intermediate derivations, optimal code generation, and interface with the main program. A systematic procedure is outlined to avoid redundant algebraic manipulations. Symbolic expressions of the derived material stiffness matrix are automatically converted to RATFOR code which is then translated into FORTRAN statements through a preprocessor. To minimize the interface problem with the main program, a template file is prepared so that the translated FORTRAN statements can be merged into the file to form a subroutine (or a submodule). Three constitutive models; namely, von Mises plasticity, the Drucker-Prager model, and a concrete plasticity model, are used as illustrative examples.

Chang, T. Y.↗

NASA NTRS1986

Comparison of exact and approximate formulas for the Mott correction to energy loss of relativistic heavy ions

A comparison is conducted between an exact numerical calculation and two approximate analytic expressions for the Mott correction to energy loss of heavy ions. A complete tabulation of the Mott correction is presented together with a comparison of some of the approximate expressions for the Mott correction due to Ahlen (1978) and Morgan and Eby (1973). Comparison is made with results of an experimental calibration of the HEAO-3 Heavy Cosmic Ray experimental chambers at the Bevalac.

Eby, P. B.↗

NASA NTRS1986

Three-wave coupling coefficient in a drifting bi-Maxwellian plasma

A general electrostatic coupling coefficient which satisfies the Manley-Rowe relations is used to derive an explicit expression for the resonant three-wave coupling coefficient between electrostatic normal modes of a uniformly magnetized, infinite, homogeneous plasma with species described by drifting bi-Maxwellian distribution functions. The limit of this expression is taken when the phase velocities of the three waves are much larger than a species thermal speed, and also when the phase velocities are much smaller than the thermal speed. These are fluid limits and are applicable to the three-wave interaction between some low-frequency electrostatic waves, such as ion acoustic and ion cyclotron modes, in a plasma where T(e) is much greater than T(i).

Bergmann, Rachelle↗

NASA NTRS1987

Pressure-coupled combustion response model for solid propellants based on Zeldovich-Novozhilov approach

An exact analytical solution is given to the problem of long-time propellant thermal response to a specified pressure oscillation. Coupling to the gas phase is made using the quasisteady Zeldovich-Novozhilov approximation. Explicit linear and lowest order (quadratic) nonlinear expressions for propellant response are obtained from the implicit nonlinear solutions. Using these expressions, response curves are presented for an ammonium perchlorate composite propellant and HMX monopropellant.

Harstad, K. G.↗

NASA NTRS1986

Kinetic study of polymerization/curing of filament-wound composite epoxy resin systems with aromatic diamines

The kinetics of polymerization/curing of a filament-wound composite epoxy resin consisting of an 80/20 DGEBA/DGEBD blend and an MDA/m-PDA blend (Tonox 60/40) was studied at various temperatures and at amine epoxy ratios between 1.1 and 4.4 by means of Fourier-transform (FT) IR and bulk viscosity measurements. The activation energy for the polymerization/curing reaction using an amine/epoxy ratio of 1.1 was 11.9 kcal/mole, in agreement with a previous value. The FT-IR conversion-time plots were fitted to a kinetic expression containing two rate constants with activation energies of 13.7 and 10.0 kcal/mole. The bulk viscosity followed the Williams et al. (1955) equation, with a Di Benedetto (1965) expression for the glass transition temperature.

Golub, M. A.↗

NASA NTRS1986

Concurrent Cholesky factorization of positive definite banded Hermitian matrices

First, the Cholesky factorization is extended to cover uniformly partitioned banded positive definite matrices of rank n which may be real symmetric or Hermitian. Then, two stratagems are given for the use of the algorithm in concurrent machines where the number of processing elements is less than required to factor the matrix in as few serial steps as possible, and where uniformly high efficiency is expected from all processing elements. Expressions are given for the efficiency factor e appearing in the speed-up expression q = eN, and these are specialized for the N node hypercube machine as a function of partition size s, the number N of processing elements of the hypercube machine, and the cost mu of interelement transmission relative to computation. It is shown that the efficiency factor e is inversely proportional to mu/s, and that e is almost independent of N when N is large and mu/s = 0. The task is completed in n/s serial steps with no limit on n. The half bandwidth b of the matrix is 2 Ns.

Utku, S.↗

NASA NTRS1986

Topographic effect on tilt, strain, and displacement measurements

An approximate analytical method is used to give simple expressions for the effect of arbitrarily shaped topography on vertical, horizontal and surface tilt measurements. Corrections to tilt fields are found to be directly proportional to the local slope of the topography. Comparison is made between expressions for tilt and those for strain and displacement. Although the topographic effects on secular tilt, strain, and vertical displacement are not yet measurable, the topographic effect on precision tidal tilt and strain measurements can be significant.

Meertens, Charles M.↗

NASA NTRS1986

On the free vibrations of spinning paraboloids

The dynamic behavior of a spinning linear-elastic paraboloid subject to nonaxisymmetric deformation is investigated analytically, applying the Rayleigh-Ritz procedure described by Utku et al. (1983). Energy-density, strain-displacement, and velocity-displacement expressions are generated; expressions for the generalized strain and position vector are derived; and the discretized dynamic equations are obtained. Numerical results obtained with a computer-program implementation of the method are presented in extensive tables and graphs. The effects of spin rate and bending rigidity and results for the special case of a spinning disk are included.

Shoemaker, W. L.↗

NASA NTRS1986

Parallel solution of closely coupled systems

The odd-even permutation and associated unitary transformations for reordering the matrix coefficient A are employed as means of breaking the strong seriality which is characteristic of closely coupled systems. The nested dissection technique is also reviewed, and the equivalence between reordering A and dissecting its network is established. The effect of transforming A with odd-even permutation on its topology and the topology of its Cholesky factors is discussed. This leads to the construction of directed graphs showing the computational steps required for factoring A, their precedence relationships and their sequential and concurrent assignment to the available processors. Expressions for the speed-up and efficiency of using N processors in parallel relative to the sequential use of a single processor are derived from the directed graph. Similar expressions are also derived when the number of available processors is fewer than required.

Utku, S.↗

NASA NTRS1987

Evolution of interstellar pickup ions in the solar wind

A model is constructed for the evolution of an interstellar pickup ion distribution in the solar wind. The model assumes that the ions are immediately isotropized at ionization and follows the subsequent development of the distribution function as the particles are convected with the solar wind. The effects of energy diffusion in an ambient wave field with a power law spectrum, adiabatic deceleration in the expanding solar wind, and continual addition of newly ionized particles are all included in the model. An analytical expression describing the evolution of the distribution function in phase space velocity and heliocentric radius is obtained. The distribution quickly approaches an asymptotic shape in phase space which depends on the relative efficiency of the energy diffusion process compared to that of adiabatic deceleration. At large distances from the sun the density of pickup ions falls as 1/r in this model. An expression for the distribution function at large distances and for large particle speed is presented. The asymptotic shape should describe the distribution of pickup ions in the outer heliosphere and could be used as an input distribution for a model of the anomalous component of heliosphere and could be used as an input distribution for a model of the anomalous component of cosmic rays. Comparison of this work with the recent observation of He(+) at 1 AU implies that the energy diffusion process is very weak inside 1 AU.

Isenberg, Philip A.↗

NASA NTRS1986

Wavelength dependence of aerosol extinction coefficient for stratospheric aerosols

A simple empirical formula for the wavelength dependence of the aerosol extinction coefficient is proposed. The relationship between the constants in the formula and the variable parameter in the aerosol size distribution is explicitly expressed. Good agreement is found between the extinction coefficients calculated from the proposed formula and that calculated from Mie theory. The proposed expression is shown to be better than the Angstroem formula commonly used by atmospheric scientists.

Yue, Glenn K.↗

NASA NTRS1987

Inferring spectral reflectances of plant elements by simple inversion of bidirectional reflectance measurements

Inverting previously developed explicit expressions for a vertical architecture, bidirectional reflectances measured over corn viewing from the solar quadrant at azimuths near the principal plane are used to determine the spectral reflectances of plant elements. The leaf reflectance values extracted in three visible bands at viewing zenith angles of 70 deg, 60 deg, and 45 deg agree closely with laboratory-measured reflectances of corn leaves. At viewing zenith angle of 30 deg, the inversion breaks down, inasmuch as the inferred plant element reflectances are too high. Satisfactory results are also achieved when the same approach is applied to bidirectional reflectances measured over potted balsam firs, but when applied to soybeans reflectances, the procedure yields unreasonably high leaf reflectances. The failure in this case is attributed to the nonvertical architecture of the soybean canopy; however, for this canopy, inversion based on horizontal architecture is possible. The bidirectional reflectances measured from the solar quadrant, at viewing angles appreciably far from 'hot spot' viewing, approximately equal in magnitude half of the leaf reflectance. The 0.5 ratio is predicted by a previous analysis of opaque horizontal Lambertian facets, as the asymptotic value for a dense canopy at any viewing angle. For soybeans, this ratio applies very closely at 15 deg viewing zenith angle. The results suggest that inversion based on simple architecture, applying explicit expressions, might be of value, either in itself or as a preliminary step before inversion applying complex models.

Otterman, J.↗

NASA NTRS1987

Cutoff wavenumbers and modes for annular-cross-section waveguide with eccentric inner conductor of small radius

Analytical expressions are derived for the cutoff wavenumbers and the corresponding modes in annular-cross-section waveguides having inner conductors of small radius. Waveguides with circular and rectangular outer boundary are considered. In the case of the circular eccentric annular waveguide, comparison is made between the values of cutoff wavenumbers computed from the expressions derived in this paper and data obtained by a more rigorous numerical technique.

Davidovitz, Marat↗

NASA NTRS1987

Near-symmetric instability for general Prandtl number

An analysis of the stability of a simple baroclinic flow to perturbations whose horizontal wave vector lies in and near the vertical plane containing the density gradient has been performed. The Ekman number (E) and 'azimuthal' wavenumber (alpha) were both assumed much less than 1, and expansions about these quantities were performed for the eigenmodes and Richardson number (R). Agreement with the previous analysis of Busse and Chen (1981) that the correction to the critical R was O(alpha) for Prandtl number (P) away from unity was obtained. An expression for the correction to the critical R for arbitrary P, and an approximate expression for P = 1 were obtained as new results. The correction for P = 1 has the same sign as that for P less than 1, and is O(alpha E exp 2/3). This result compares well with the numerical results of Miller and Antar (1986) for small E.

Reynolds, Nathaniel D.↗

NASA NTRS1987

Acoustic radiation force on a particle in a temperature gradient

After deriving a general expression for the acoustic radiation force on a small spherical particle of radius R in a standing wave field in a temperature gradient, attention is given to the case of a particle in a long tube chamber having a temperature gradient along the axis of symmetry. A simplification of the analysis is obtained through the introduction of the mass flux density potential. A general expression is presented for the time-averaged acoustic force; results of the new sample positions and restoring forces for a plane-wave mode are compared to the homogeneous case.

Collas, P.↗