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NASA NTRS1983

An interval logic for higher-level temporal reasoning

Prior work explored temporal logics, based on classical modal logics, as a framework for specifying and reasoning about concurrent programs, distributed systems, and communications protocols, and reported on efforts using temporal reasoning primitives to express very high level abstract requirements that a program or system is to satisfy. Based on experience with those primitives, this report describes an Interval Logic that is more suitable for expressing such higher level temporal properties. The report provides a formal semantics for the Interval Logic, and several examples of its use. A description of decision procedures for the logic is also included.

Schwartz, R. L.↗

NASA NTRS1983

Sound velocity anisotropy in cubic crystals

Simple analytical expressions may be derived for sound velocities in cubic crystals by using lattice harmonics or functions which are invariant under the crystal symmetry operations. These expressions are in good agreement with the exact results for typical crystals such as metallic iron and potassium fluoride.

Tsang, T.↗

NASA NTRS1984

Pea amyloplast DNA is qualitatively similar to pea chloroplast DNA

Amyloplast DNA (apDNA), when subjected to digestion with restriction endonucleases, yields patterns nearly identical to that of DNA from mature pea chloroplasts (ctDNA). Southern transfers of apDNA and ctDNA, probed with the large subunit (LS) gene of ribulose-1,5-bisphosphate carboxylase (Rubisco), shows hybridization to the expected restriction fragments for both apDNA and ctDNA. However, Northern transfers of total RNA from chloroplasts and amyloplasts, probed again with the LS gene of Rubisco, shows that no detectable LS meggage is found in amyloplasts although LS expression in mature chloroplasts is high. Likewise, two dimensional polyacrylamide gel electrophoresis of etiolated gravisensitive pea tissue shows that both large and small subunits of Rubisco are conspicuously absent; however, in greening tissue these two constitute the major soluble proteins. These findings suggest that although the informational content of these two organelle types is equivalent, gene expression is quite different and is presumably under nuclear control.

Gaynor, J. J.↗

NASA NTRS1984

Creep-rupture reliability analysis

A probabilistic approach to the correlation and extrapolation of creep-rupture data is presented. Time temperature parameters (TTP) are used to correlate the data, and an analytical expression for the master curve is developed. The expression provides a simple model for the statistical distribution of strength and fits neatly into a probabilistic design format. The analysis focuses on the Larson-Miller and on the Manson-Haferd parameters, but it can be applied to any of the TTP's. A method is developed for evaluating material dependent constants for TTP's. It is shown that optimized constants can provide a significant improvement in the correlation of the data, thereby reducing modelling error. Attempts were made to quantify the performance of the proposed method in predicting long term behavior. Uncertainty in predicting long term behavior from short term tests was derived for several sets of data. Examples are presented which illustrate the theory and demonstrate the application of state of the art reliability methods to the design of components under creep.

Peralta-Duran, A.↗

NASA NTRS1984

Investigation and appreciation of optimal output feedback. Volume 1: A convergent algorithm for the stochastic infinite-time discrete optimal output feedback problem

The stochastic, infinite time, discrete output feedback problem for time invariant linear systems is examined. Two sets of sufficient conditions for the existence of a stable, globally optimal solution are presented. An expression for the total change in the cost function due to a change in the feedback gain is obtained. This expression is used to show that a sequence of gains can be obtained by an algorithm, so that the corresponding cost sequence is monotonically decreasing and the corresponding sequence of the cost gradient converges to zero. The algorithm is guaranteed to obtain a critical point of the cost function. The computational steps necessary to implement the algorithm on a computer are presented. The results are applied to a digital outer loop flight control problem. The numerical results for this 13th order problem indicate a rate of convergence considerably faster than two other algorithms used for comparison.

Halyo, N.↗

NASA NTRS1984

Variational objective analyses for cyclone studies

The basic analysis equations, i.e., the two horizontal momentum equations, the hydrostatic equation, and the integrated continuity equation were derived for the nonlinear vertical coordinate, nondimensionalized, and expressed in finite differences on a staggered grid. Special care was taken to transform the hydrostatic equation and the pressure gradient terms of the horizontal momentum equations to nearly eliminate truncation error over steeply sloping terrain. This formulation also eliminated explicit reference to orographically induced variations in the thermodynamic variables so that the variational adjustments are on the scale of the meteorological perturbations. The analysis equations were subjected to the Euler-Lagrange operations as expressed for finite differences and an additional set of five partial differential equations was derived, bringing to nine the number of equations in Model I. Higher order terms, terms containing observed quantities, and terms containing none of the variables to be adjusted were grouped into forcing functions and the equations were solved for the zero order terms. Zero order variables were eliminated between these equations and there resulted two diagnostic equations which take the form of general linear second order partial differential equations with nonconstant coefficients.

Achtemeier, G. L.↗

NASA NTRS1983

AIDDE the Ames Interactive Dynamic Display Editor

This paper describes the design and development of the Ames Interactive Dynamic Display Editor language (AIDDE). AIDDE and its associated tools are a software system that facilitates the interactive creation and use of real-time displays. For the present purposes, real-time displays are pictures on a CRT that change over time to reflect the state of a system. A graphics tree describes a display. Display dynamics are specified by attaching expressions to the tree. Offline, AIDDE is used to draw displays, define display dynamics, and generate host computer source code and a representation of the tree convenient for use in a graphics device. At run time, the compiled host code passes the results of the expressions to a graphics device to modify the tree. The graphics processor repeatedly traverses the tree to draw a changing display on the CRT. Several real-time displays have been implemented using AIDDE with good results.

Globus, A.↗

NASA NTRS1983

Emission, absorption, and polarization of gyrosynchrotron radiation of mildly relativistic particles

Approximate analytic expressions for the emissivity and absorption coefficient of synchrotron radiation of mildly relativistic particles with an arbitrary energy spectrum and pitch angle distribution are given. From these, an expression for the degree of polarization is derived. To accomplish this, previously developed methods of integration are used. The analytic results are compared with numerical results for both thermal and nonthermal (power law) distributions of particles. Previously announced in STAR as N82-34197

Petrosian, V.↗

NASA NTRS1983

Pair production in superstrong magnetic fields

The production of electron-positron pairs by single photons in magnetic fields of not less than about 10 to the 12th gauss has been investigated in detail for photon energy. The exact attenuation coefficient, which is derived and then evaluated numerically, is strongly influenced by the discrete energy states of the electron and positron. Near threshold, it exhibits a 'sawtooth' pattern as a function of photon energy and its value is significantly below that predicted by the asymptotic expression for the attenuation coefficient. The energy distributions of the created pair are computed numerically near threshold, and analytic expressions are derived in the asymptotic limit. These results indicate that as field strength and photon energy increase, it becomes increasingly probable for the pair to divide strength energy unequally. This effect, as well as the threshold behavior of the attenuation coefficient, could have important consequences to pulsar models.

Daugherty, J. K.↗

NASA NTRS1983

The extreme nearfield of an acoustic diffraction grating

An expression for the transmitted sound field near (within a fraction of a wavelength) an array of slits is derived under the assumption that the normal component of the particle velocity is the same, in the slits, as if no grating were present and zero everywhere else in the plane of the grating. The expression is in the form of an inverse Fourier transform and can be evaluated quickly using a standard fast-Fourier-transform (FFT) algorithm. Using this technique, the sound pressure on the axis of symmetry normal to the grating was evaluated for a plane-wave incident at various angles with respect to the normal to the grating, and the results were found to provide an excellent qualitative (and to a significant degree quantitative) description of some experimental measurements. Extensions of the method to oscillating pistons of arbitrary (but planar) configuration in a rigid baffle are indicated.

Ochs, R. L., Jr.↗

NASA NTRS1983

Transient nucleation in condensed systems

Using classical nucleation theory we consider transient nucleation occurring in a one-component, condensed system under isothermal conditions. We obtain an exact closed-form expression for the time dependent cluster populations. In addition, a more versatile approach is developed: a numerical simulation technique which models directly the reactions by which clusters are produced. This simulation demonstrates the evolution of cluster populations and nucleation rate in the transient regime. Results from the simulation are verified by comparison with exact analytical solutions for the steady state. Experimental methods for measuring transient nucleation are assessed, and it is demonstrated that the observed behavior depends on the method used. The effect of preexisting cluster distributions is studied. Previous analytical and numerical treatments of transient nucleation are compared to the solutions obtained from the simulation. The simple expressions of Kashchiev are shown to give good descriptions of the nucleation behavior.

Kelton, K. F.↗

NASA NTRS1984

An invariant derivation of flame stretch

The flame stretch factor is derived using an invariant formulation in a consistent manner. The derived generalized expression has two terms and completely describes the flame area evolution with its movement. One term represents the stretch due to the nonuniform tangential velocity field and the other represents the effect of the curvature of the propagating flame. The effect of curvature for stationary flames is implicitly included in the former term through variations of the tangential velocity. The flame sheet assumption, and thereby the stretch factor, are uniquely defined. Another expression is derived under the assumption that the tangential velocity of the flame equals the tangential component of the fluid velocity.

Chung, S. H.↗

NASA NTRS1983

Sound velocity anisotropy in cubic crystals

Tsang, T.↗

NASA NTRS1984

Testing the strong equivalence principle by radio ranging

Planetary range data offer the most promising means to test the validity of the Strong Equivalence Principle (SEP). Analytical expressions for the perturbation in the 'range' expected from an SEP violation predicted by the 'variation-of-G' method and by the 'two-times' approach are derived and compared. The dominant term in both expressions is quadratic in time. Analysis of existing range data should allow a determination of the coefficient of this term with a one-standard-deviation uncertainty of about 1 part in 100 billion/yr.

Canuto, V. M.↗

NASA NTRS1984

Assessment of the contribution of differential polarization to improved rainfall measurements

A measurement technique employing the differential reflectivity factor Z(DR) and the horizontal polarization reflectivity factor Z(H) is the basis of the present study of the effects of variations in the shape or breadth of the drop size distribution (DSD) on rainfall parameters. Theoretical expressions are derived for rainfall rate, liquid water content W, and median volume diameter D(O) in terms of Z(DR), Z(H), and size distribution-dependent factors. The latter calculations assume backscattering cross sections for oblate, nonoscillating raindrops falling in still air with equilibrium shapes. These expressions are used to quantitatively assess the effects of changes in DSD breadth on values of R, W, and D(O) deduced from Z(DR) and Z(H).

Ulbrich, C. W.↗

NASA NTRS1983

Relationships between mineralization and silicic volcanism in the central Andes

Existing models for the genesis of porphyry copper deposits indicate that they formed in granodioritic stocks located in the infrastructure of andesitic stratovolcanoes. It is noted that sites of porphyry-type subvolcanic tin mineralization in the Eastern Cordillera of Bolivia are distinguished by the absence of such andesitic structures. The surface expression of a typical subvolcanic porphyry tin deposit is thought to be an extrusive dome of quartz latite porphyry, sometimes related to a larger caldera structure. Evidence from the El Salvador porphyry copper deposit in the Eocene magmatic belt in Chile indicates that it too may be more closely related to a silicic volcanic structure than to an andesitic stratovolcano. The dome of La Soufriere, Guadeloupe is offered as a modern analog for the surface expression of subvolcanic mineralization processes, with the phreatic eruptions there indicating the formation of hydrothermal breccia bodies in depths. It is pointed out that the occurrence of mineralized porphyries, millions of years after caldera formation, does not necessarily indicate that tin intrusions and mineralization are not genetically related to the subcaldera pluton, but may be a consequence of the long thermal histories (1-10 million years) of the lowermost parts of large plutons.

Francis, P. W.↗

NASA NTRS1984

Wave-particle transport from density drift instabilities - A comparison of local and nonlocal theories

Second-order Vlasov theory is used to compute the dissipation rates of plasma irregularities with a variety of shapes. A derivation of the nonlocal dispersion equation using linearized Vlasov theory is presented. Expressions for the normalized amplitudes of the first-order plasma density and electrostatic potential fluctuations are derived. Expressions are given for the saturation amplitudes of the electrostatic eigenmodes. The wave-particle transport and irregularity dissipation rate are computed by using formulas whose derivation is presented. Computational results for specific density variations are shown, and conclusions on the validity of the local theory as opposed to the nonlocal theory are given.

Bernhardt, P. A.↗

NASA NTRS1984

Basic governing equations for the flight regimes of aeroassisted orbital transfer vehicles

The basic governing equations for the low-density, high-enthalpy flow regimes expected in the shock layers over the heat shields of the proposed aeroassisted orbital transfer vehicles are derived by combining and extending existing theories. The conservation equations are derived from gas kinetic principles for a four-component ionized gas consisting of neutral molecules, neutral atoms, singly ionized ions, and electrons, assuming a continuum flow. The differences among translational-rotational, vibrational, and electron temperatures are accounted for, as well as chemical nonequilibrium and electric-charge separation. Expressions for convective and viscous fluxes, transport properties, and the terms representing interactions among various energy modes are given explicitly. The expressions for the rate of electron-vibration energy transfer, which violates the Landau-Teller conditions, is derived by solving the system of master equations accounting for the multiple-level transitions.

Lee, J.-H.↗