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NASA NTRS1984

A Wide Latitude CO Survey of Molecular Clouds in the Northern Milky Way

It is now well established that molecular clouds are an important part of the interstellar medium, containing much or most of the dense, cold component of the gas, and producing the massive stars and supernovae responsible for the diffuse, hot component. It would therefore appear essential in formulating a complete picture of the local interstellar medium to have some knowledge of the distribution and properties of nearly molecular clouds. The Goddard-Columbia 1.2 meter telescope was used to carry out a wide latitude, low angular resolution survey of CO along most of the first galactic quadrant and a small part of the second. A plane-of-the-sky map, which resulted from numerically integrating the survey over radial velocity, is presented. The Great Rift and the Aquila Rift molecular clouds of the Milky Way are discussed.

Dame, T. M.↗

NASA NTRS1984

High altitude chemically reacting gas particle mixtures. Volume 1: A theoretical analysis and development of the numerical solution

The overall contractual effort and the theory and numerical solution for the Reacting and Multi-Phase (RAMP2) computer code are described. The code can be used to model the dominant phenomena which affect the prediction of liquid and solid rocket nozzle and orbital plume flow fields. Fundamental equations for steady flow of reacting gas-particle mixtures, method of characteristics, mesh point construction, and numerical integration of the conservation equations are considered herein.

Smith, S. D.↗

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

Capture of Planetesimals into a Circumterrestrial Swarm

The lunar origin model considered in this report involves processing of protolunar material through a circumterrestrial swarm of particles. Once such a swarm has formed, it can gain mass by capturing infalling planetesimals and ejecta from giant impacts on the Earth, although the angular momentum supply from these sources remains a problem. The first stage of formation of a geocentric swarm by capture of planetesimals from initially heliocentric orbits is examined. The only plausible capture mechanism that is not dependent on very low approach velocities is the mutual collision of planetesimals passing within Earth's sphere of influence. The dissipation of energy in inelastic collisions or accretion events changes the value of the Jacobi parameter, allowing capture into bound geocentric orbits. This capture scenario was tested directly by many body numerical integration of planetesimal orbits in near Earth space.

Weidenschilling, S. J.↗

NASA NTRS1985

A 4-node Bilinear Isoparametric Element in Rockwell NASTRAN

The development and evaluation of the Rockwell NASTRAN four node quadrilateral (QUAD4) element is presented. The element derivation utilizes bilinear isoparametric techniques both for membrane and bending characteristics. The QUAD4 element coordinate system, membrane properties, lumped mass matrix, and treatment of warping are based upon the COSMIC/NASTRAN QDMEMI element while the bending characteristics are based on a paper by T. J. R. Hughes. The effects of warping on the bending stiffness, consistent mass, and geometric stiffness are based upon a paper by R. H. MacNeal. Numerical integration is accomplished by Gaussian quadrature on a 2 x 2 grid. Practical user support features include variable element thickness, thermal analysis and layered composite material definitions.

Liao, C.↗

NASA NTRS1985

Vortex studies relating to boundary layer turbulence and noise

The present study considers the two-dimensional case of an array of N rectilinear, like-sign vortices above an infinite flat boundary. The method of images can be employed with this configuration to reduce the problem to that of 2N vortices in free space, constrained by 2N symmetry relations. This system is Hamiltonian and therefore certain invariants of the motion are known. Futher, from the Hamiltonian constant, the equations of motion are readily derived and may be integrated numerically to determine the vortex trajectories. This knowledge of the time-dependent vortex motion then allows the resulting noise radiation to be computed by standard aeroacoustic techniques.

Adelman, J. L.↗

NASA NTRS1985

Preliminary Results from Numerical Experiments on the Summer 1980 Heat Wave and Drought

During the summer of 1980, a prolonged heat wave and drought affected the United States. A preliminary set of experiments has been conducted to study the effect of varying boundary conditions on the GLA model simulation of the heat wave. Five 10-day numerical integrations with three different specifications of boundary conditions were carried out: a control experiment which utilized climatological boundary conditions, an SST experiment which utilized summer 1980 sea-surface temperatures in the North Pacific, but climatological values elsewhere, and a Soil Moisture experiment which utilized the values of Mintz-Serafini for the summer, 1980. The starting dates for the five forecasts were 11 June, 7 July, 21 July, 22 August, and 6 September of 1980. These dates were specifically chosen as days when a heat wave was already established in order to investigate the effect of soil moistures or North Pacific sea-surface temperatures on the model's ability to maintain the heat wave pattern. The experiments were evaluated in terms of the heat wave index for the South Plains, North Plains, Great Plains and the entire U.S. In addition a subjective comparison of map patterns has been performed.

Wolfson, N.↗

NASA NTRS1985

On Fofonoff's Mode

The classical barotropic ocean model of Veronis (1966) is reexamined to verify the possible existence of Fofonoff's (1954) steady free inertial mode by considering the balance where J is the Jacobian, eta is the streamfunction of the horizontal velocity, and R is a parameter of nonlinearity. A linear functional relationship between the potential vorticity and the streamfunction and inertial boundary layers along the ocean basin was suggested by Fofonoff. However, the numerical integration showed that the system is barotropically unstable. The typical instantaneous field is given. The statistical equilibrium state eta is also given. Although it resembles Fofonoff's solution, it is maintained by the Reynolds stress field induced by the eddies in addition to the wind stress and dissipation. The plot of eta versus R delta sq +y is given. It is shown that the Fofonoff's linear relation between the potential vorticity and the streamfunction does not hold uniformly over the entire basin. The above results show that the Fofonoff's solution can not be realized physically.

Merkine, L. O.↗

NASA NTRS1985

SPAR improved structural-fluid dynamic analysis capability

The results of a study whose objective was to improve the operation of the SPAR computer code by improving efficiency, user features, and documentation is presented. Additional capability was added to the SPAR arithmetic utility system, including trigonometric functions, numerical integration, interpolation, and matrix combinations. Improvements were made in the EIG processor. A processor was created to compute and store principal stresses in table-format data sets. An additional capability was developed and incorporated into the plot processor which permits plotting directly from table-format data sets. Documentation of all these features is provided in the form of updates to the SPAR users manual.

Pearson, M. L.↗

NASA NTRS1985

Application of closed-form solutions to a mesh point field in silicon solar cells

A computer simulation method is discussed that provides for equivalent simulation accuracy, but that exhibits significantly lower CPU running time per bias point compared to other techniques. This new method is applied to a mesh point field as is customary in numerical integration (NI) techniques. The assumption of a linear approximation for the dependent variable, which is typically used in the finite difference and finite element NI methods, is not required. Instead, the set of device transport equations is applied to, and the closed-form solutions obtained for, each mesh point. The mesh point field is generated so that the coefficients in the set of transport equations exhibit small changes between adjacent mesh points. Application of this method to high-efficiency silicon solar cells is described; and the method by which Auger recombination, ambipolar considerations, built-in and induced electric fields, bandgap narrowing, carrier confinement, and carrier diffusivities are treated. Bandgap narrowing has been investigated using Fermi-Dirac statistics, and these results show that bandgap narrowing is more pronounced and that it is temperature-dependent in contrast to the results based on Boltzmann statistics.

Lamorte, M. F.↗

NASA NTRS1985

Electrophoretic mobility of cells in a vertical Ficoll gradiant

The upward migration of living cells and test particles under the influence of a constant electric field in a low conductivity Ficoll gradient occurs at nearly constant velocity. Viscosity and neutral polymer concentration affect migration rate. Decreasing viscosity speeds up the particle migration, decreasing neutral polymer (Ficoll) concentration, slows particle migration, since electrophoretic mobility increases approximately linearly with neutral polymer concentration. Neutral polymers interact with the cell surface to effectively raise its zeta potential. An analytic function was developed from the known dependence of these physical variables on migration distance; the analysis expresses migration velocity as an explicit function of position in the density gradient. It predicts an almost linear increase in velocity of about 12 to 16% over the working region of the gradient. It was numerically integrated and correctly predicts cell migration distance vs time curves without the use of any fitted parameters. The resulting migration curves follow the expected slowly varying exponential form that closely resembles a straight line. The ability to determine standard electrophoretic mobilities from such curves depends on knowledge of the effect of Ficoll on the zeta potential of the cell type that is separated.

Plank, L. D.↗

NASA NTRS1985

Pulsars as cosmic ray particle accelerators: Proton orbits

Proton orbits are calculated in the electromagnetic vacuum field of a magnetic point dipole rotating with its angular velocity omega perpendicular to its dipole moment mu by numerical integration of the Lorentz-Dirac equation. Trajectories are shown and discussed for various initial conditions. A critical surface is shown separating initial positions of protons which finally hit the pulsar in the polar region from those which finally recede to infinity.

Thielheim, K. O.↗

NASA NTRS1985

Pulsars as cosmic ray accelerators: Energy development of protons

Results of numerical integrations of the Lorentz-Dirac-equation with Landau approximation for protons in the electromagnetic vacuum field of a magnetic dipole rotating with its angular velocity omega perpendicular to its magnetic moment mu will be discussed with special attention to the energy development of protons.

Thielheim, K. O.↗

NASA NTRS1985

A new world survey expression for cosmic ray vertical intensity vs. depth in standard rock

The cosmic ray data on vertical intensity versus depth below 10 to the 5th power g sq cm is fitted to a 5 parameter empirical formula to give an analytical expression for interpretation of muon fluxes in underground measurements. This expression updates earlier published results and complements the more precise curves obtained by numerical integration or Monte Carlo techniques in which the fit is made to an energy spectrum at the top of the atmosphere. The expression is valid in the transitional region where neutrino induced muons begin to be important, as well as at great depths where this component becomes dominant.

Crouch, M.↗

NASA NTRS1984

Final stages of transition to turbulence in plane channel flow

This paper involves a numerical simulation of the final stages of transition to turbulence in plane channel flow at a Reynolds number of 1500. Three-dimensional incompressible Navier-Stokes equations are numerically integrated to obtain the time evolution of two- and three-dimensional finite-amplitude disturbances. Computations are performed on the CYBER-203 vector processor for a 32 x 51 x 32 grid. Solutions indicate the existence of structures similar to those observed in the laboratory and characteristics of the various stages of transition that lead to final breakdown. In particular, evidence points to the formation of a upside-down-V-shaped vortex and the subsequent system of horseshoe vortices inclined to the main flow direction as the primary elements of transition. Details of the resulting flow field after breakdown indicate the evolution of streaklike formations found in turbulent flows. Although the flow field does approach a steady state (turbulent channel flow), the introduction of subgrid-scale terms seems necessary to obtain fully developed turbulence statistics.

Biringen, S.↗

NASA NTRS1985

Bounds and approximations for rapid evaluation of coherent MPSK error probabilities

The error probability for MPSK detection is expressed here as a sum of a familiar upper-bound approximation and a correction term which is well suited for numerical integration. An asymptotic expansion of the correction term is derived, from which simple and extremely tight upper and lower bounds are obtained. Relative errors in using these bounds and approximations of them are graphed for cases of practical interest.

Chie, C. M.↗

NASA NTRS1985

A comparison of observed and forecast energetics over North America

The observed kinetic energy balance is calculated over North America and compared with that computed from forecast fields for the 13-15 January 1979 cyclone. The FGGE upper-air rawinsonde network serves as the observational database while the forecast energetics are derived from a numerical integration with the GLAS fourth-order general circulation model initialized at 00 GMT 13 January. Maps of the observed and predicted kinetic energy and eddy conversion are in good qualitative agreement, although the model eddy conversion tends to be 2 to 3 times stronger than the observed values. Both the forecast and observations exhibit the lower and upper tropospheric maxima in vertical profiles of kinetic energy generation and dissipation typically found in cyclonic disturbances. An interesting time lag is noted in the observational analysis with the maximum observed kinetic energy occurring 12 h later than the maximum eddy conversion over the same region.

Baker, W. E.↗

NASA NTRS1985

Transition probabilities of the B-prime 1Sigma(u)(+) to X 1Sigma(g)(+) system of molecular hydrogen

From published potential energy curves and transition dipole moments, there are obtained by numerical integration of the equations of nuclear motion the vibrational eigenfunctions of the X 1Sigma(g)(+) and B-prime 1Sigma(u)(+) states of H2. The probabilities of radiative transitions from the discrete vibrational levels of the excited B-prime 1Sigma(u)(+) electronic state of H2 to the discrete and continuum vibrational levels of the ground X 1Sigma(g)(+) electronic state are calculated. The Franck-Condon factors are also presented.

Kwok, T. L.↗