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Approximate variation principle for calculating energies and wave functions in electron impact experiments
In order to understand the origin of differing ilmenite/armalcolite textural relationships, bulk rock composition, oxygen fugacity and cooling rate have been experimentally investigated. Results show that armalcolite and ilmenite compositions are dependent upon the liquid composition and temperature at the time of crystallization. Furthermore, the different armalcolite/ilmenite textures rely to a greater extent on f sub O2 than on cooling rate or bulk rock composition, and the Ti(3+) content of armalcolite can be used as an indicator of the approximate f sub O2 prevailing at the time of crystallization.
Observations of the Venus atmosphere with the infrared radiometer on Mariner 10 have been analyzed by Taylor (1975) in terms of the vertical distribution of opacity at wavelengths near 11 microns and 45 microns in the thermal infrared. In this paper, we discuss models of the Venus atmosphere which are consistent with the inferred opacity structure. Either a two-layer cloud structure, or a single cloud deck overlaid by a layer containing approximately 40 precipitable microns of water vapor, would have the required limb-darkening characteristics at the wavelengths of observation.
A finite element CFD algorithm is developed for Euler and Navier-Stokes aerodynamic applications. For the linear basis, the resultant approximation is at least second-order-accurate in time and space for synergistic use of three procedures: (1) a Taylor weak statement, which provides for derivation of companion conservation law systems with embedded dispersion-error control mechanisms; (2) a stiffly stable second-order-accurate implicit Rosenbrock-Runge-Kutta temporal algorithm; and (3) a matrix tensor product factorization that permits efficient numerical linear algebra handling of the terminal large-matrix statement. Thorough analyses are presented regarding well-posed boundary conditions for inviscid and viscous flow specifications. Numerical solutions are generated and compared for critical evaluation of quasi-one- and two-dimensional Euler and Navier-Stokes benchmark test problems.
Previous studies in one spatial dimension showed that the precursors of cosmic-ray-dominated shocks are unstable against traveling acoustic disturbances. Here we report that a secondary, Rayleigh-Taylor type instability can exist in cosmic-ray-dominated media influenced by the acoustic instability. Using the local WKB approximation, the growth rate of the secondary instability is shown to be comparable to that of the one-dimensional acoustic instability itself in the cases we have considered. The nonlinear development has been followed numerically with a two-dimensional PPM hydrodynamics code that also incorporates the two-fluid cosmic-ray energy equation. We show that the secondary instability may cause the precursor and postshock flows to become highly turbulent.
Ground-based infrared observations of SN 1987A on day 612 after the explosion have yielded resolved line profiles of Co II, Ni I, Fe II at 10.52, 11.31, and 17.94 micron, respectively. The spectra were taken at a resolving power of about 1000 with an array grating spectrometer on the 4 m telescope of Cerro Tololo Inter-American Observatory. Based on the observed line intensities we have estimated the minimum mass of each ion: M(Co II) = (6.0 +/- 1.8) x 10 exp -5 solar mass; M(Ni I) = (1.1 +/- 0.1) x 10 exp -3 solar mass; and M(Fe II) = (8.0 +/- 1.5) x 10 exp -3 solar mass. From these we infer total masses for cobalt, nickel, and iron in the ejecta. The nickel and iron line profiles are markedly asymmetric. We interpret these as arising from two components, one centered on the stellar rest velocity with an approximately 3250 km/s full width, and the second at about +1200 km/s with an approximately 1100 km/s full width. The asymmetry may represent a large-scale fracturing of the ejecta by Rayleigh-Taylor instabilities.
A new method for propagating the solution of the radial Schroedinger equation is derived from a Taylor series expansion of the wavefunction and partial re-summation of the infinite series. Truncation of the series yields an approximation to the exact propagator which is applied to a model calculation and found to be highly convergent.
A development status evaluation is presented for applications of main approximation concepts in nonlinear programming for structural optimization requiring local, midrange, and global approximations. It is noted that there is not yet a sufficient basis for a comprehensive evaluation of relative effectiveness among approximation concepts. Attention is presently given to the careful selection of intermediate-variable and response quantity, and improvements in the traditional Taylor-series expansion by inclusion of either some higher-order terms or information at various points in the design space.
Data obtained by the Pioneer Venus Orbiter Infrared Radiometer in late 1978 and early 1979 are presented in tabular form, including, in particular, the mean temperature structure, with complete latitudinal and longitudinal coverage, and zonal-mean cloud properties. The mean thermal and cloud structures can be interpreted in terms of general circulation of the middle atmosphere. The interim results indicate that (1) the zonal winds on Venus fall to very low values above 90 km, (2) there is a strong midlatitude jet which circles the planet approximately every two days, and (3) the observed solar tides are dominated by the semidiurnal component.
Calculations are presented of the turbulent Prandtl number Pr(T) in the near-wall region of a turbulent channel flow. It is shown that only the first-order terms in the Taylor series expansions for the eddy diffusivity and the Pr(T) are independent of the molecular Prandtl number Pr, at least to a first approximation. Also presented are calculations of the near-wall behavior of the correlations between temperature fluctuations and velocity fluctuations, as well as for their dependence on Pr.
This research addresses turbulent gas flows laden with fine solid particles at sufficiently large mass loading that strong two-way coupling occurs. By two-way coupling we mean that the particle motion is governed largely by the flow, while the particles affect the gas-phase mean flow and the turbulence properties. Our main interest is in understanding how the particles affect the turbulence. Computational techniques have been developed which can accurately predict flows carrying particles that are much smaller than the smallest scales of turbulence. Also, advanced computational techniques and burgeoning computer resources make it feasible to fully resolve very large particles moving through turbulent flows. However, flows with particle diameters of the same order as the Kolmogorov scale of the turbulence are notoriously difficult to predict. Some simple flows show strong turbulence attenuation with reductions in the turbulent kinetic energy by up to a factor of five. On the other hand, some seemingly similar flows show almost no modification. No model has been proposed that allows prediction of when the strong attenuation will occur. Unfortunately, many technological and natural two-phase flows fall into this regime, so there is a strong need for new physical understanding and modeling capability. Our objective is to study the simplest possible turbulent particle-laden flow, namely homogeneous, isotropic turbulence with a uniform dispersion of monodisperse particles. We chose such a simple flow for two reasons. First, the simplicity allows us to probe the interaction in more detail and offers analytical simplicity in interpreting the results. Secondly, this flow can be addressed by numerical simulation, and many research groups are already working on calculating the flow. Our detailed data can help guide some of these efforts. By using microgravity, we can further simplify the flow to the case of no mean velocity for either the turbulence or the particles. In fact the addition of gravity as a variable parameter may help us to better understand the physics of turbulence attenuation. The experiments are conducted in a turbulence chamber capable of producing stationary or decaying isotropic turbulence with nearly zero mean flow and Taylor microscale Reynolds numbers up to nearly 500. The chamber is a 410 mm cubic box with the corners cut off to make it approximately spherical. Synthetic jet turbulence generators are mounted in each of the eight corners of the box. Each generator consists of a loudspeaker forcing a plenum and producing a pulsed jet through a 20 mm diameter orifice. These synthetic jets are directed into ejector tubes pointing towards the chamber center. The ejector tubes increase the jet mass flow and decrease the velocity. The jets then pass through a turbulence grid. Each of the eight loudspeakers is forced with a random phase and frequency. The resulting turbulence is highly Isotropic and matches typical behavior of grid turbulence. Measurements of both phases are acquired using particle image velocimetry (PIV). The gas is seeded with approximately 1 micron diameter seeding particles while the solid phase is typically 150 micron diameter spherical glass particles. A double-pulsed YAG laser and a Kodak ES-1.0 10-bit PIV camera provide the PIV images. Custom software is used to separate the images into individual images containing either gas-phase tracers or large particles. Modern high-resolution PIV algorithms are then used to calculate the velocity field. A large set of image pairs are acquired for each case, then the results are averaged both spatially and over the ensemble of acquired images. The entire apparatus is mounted in two racks which are carried aboard NASA's KC-135 Flying Microgravity Laboratory. The rack containing the turbulence chamber, the laser head, and the camera floats freely in the airplane cabin (constrained by competent NASA personnel) to minimize g-jitter.
A new test chamber and precision hydraulic actuation system were incorporated into an active clearance control (ACC) test rig at NASA Glenn Research Center. Using the improved system, a fast-acting, mechanically-actuated, ACC concept was evaluated at engine simulated temperatures and pressure differentials up to 1140 F and 120 psig, on the basis of secondary seal leakage and kinematic controllability. During testing, the ACC concept tracked a simulated flight clearance transient profile at 1140 F, 120 psig, with a maximum error of only 0.0012 in. Comparison of average dynamic leakage of the system with average static leakage did not show significant differences between the two operating conditions. Calculated effective clearance values for the rig were approximately 0.0002 in. at 120 psig, well below the industry specified effective clearance threshold of 0.001 in.
The goal of this project is to approximate how many government-sourced code repositories are being reused by other federal agencies.
The theoretical problem posed by the buoyant escape of a magnetic field from the interior of a stably stratified body bears directly on the question of the present existence of primordial magnetic fields in stars. This paper treats the onset of the Rayleigh-Taylor instability of the upper boundary of a uniform horizontal magnetic field in a stably stratified atmosphere. The calculations are carried out in the Boussinesq approximation and show the rapid growth of the initial infinitesimal perturbation of the boundary. This result is in contrast to the extremely slow buoyant rise of a separate flux tube in the same atmosphere. Thus for instance, at a depth of 1/3 of a solar radius beneath the surface of the sun, a field of 100 G develops ripples over a scale of 1000 km in a characteristic time of 50 years, whereas the characteristic rise time of the same field in separate flux tubes with the same dimensions is 10 billion years. Thus, the development of irregularities proceeds quickly, soon slowing, however, to a very slow pace when the amplitude of the irregularities becomes significant. Altogether, the calculations show the complexity of the question of the existence of remnant primordial magnetic fields in stellar interiors.
Full CI calculations are presented for the 1A1, 3B1, and 1B1 states of SiH2 at their respective equilibrium geometries and at geometries with the SiH bonds stretched. These results are compared with those obtained from single-reference and multireference CI calculations. The computed Te values agree well with the full CI results, provided that the effects of higher-than-double excitations are accounted for either by the Davidson correction or by a multireference approach. When the SiH bonds are stretched, the single-reference methods are not sufficiently flexible, and only CASSCF/MRCI achieves chemical accuracy (i.e., agrees with the full CI to 1 kcal/mol). Overall, the accuracy of the various approximate methods is very similar to that found for H2O, NH2, and CH2.
We present a series of gasdynamical simulations of the interaction of a dense, cool interstellar cloud with a high-speed, supersonic wind that confines and accelerates the embedded cloud. Our goal is to attempt to determine if such clouds can survive various potentially disruptive instabilities, that occur at their peripheries, long enough to be accelerated to speeds which are comparable to the wind velocity. These simulations are performed using two-dimensional, Eulerian gas dynamics on both an axisymmetric (about the cloud axis) and 'slab' geometric grid. The spatial and temporal resolutions of the simulations are varied over a wide range to investigate the effects of small-scale instabilities on the overall acceleration of clouds and the development of large-scale, disruptive instabilities. Also, we study the effects of wind/cloud Mach number variations by changing the wind speed constant at about 12 km/s (which corresponds to a cloud temperature of 10,000 K). The current simulations track the evolution of clouds as they are accelerated to speeds approximately 4-5 times greater than their internal sound speeds. Furthermore, the models with the highest resolution were extended far beyond quasi-linear Rayleigh-Taylor growth times reaching 6-7 Rayleigh-Taylor growth times for the largest scale instabilities before being terminated because of the accumulation of errors at the rear grid boundary.
The conical flow solution for axisymmetric supersonic flow past cones has been found to be virtually independent of the ratio of specific heats when normalized in a certain way. A simple rational approximation to this flow is derived. The important singularities and the limiting behavior of the solution are also discussed.
The integration is discussed of the vector differential equation X = F(x, t) from time t sub i to t sub (i = 1) where only the values of x sub i are available for the the integration. No previous values of x or x prime are used. Using an orbit integration problem, comparisons are made between Taylor series integrators and various types and orders of Runge-Kutta integrators. A fourth order Runge-Kutta type integrator for orbital work is presented, and approximate (there may be no exact) fifth order Runge-Kutta integrators are discussed. Also discussed and compared is a self starting integrator ising delta f/delta x. A numerical method for controlling the accuracy of integration is given, and the special equations for accurately integrating accelerometer data are shown.