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NASA NTRS1992

Transition operators in electromagnetic-wave diffraction theory - General theory

A formal theory is developed for the scattering of time-harmonic electromagnetic waves from impenetrable immobile obstacles with given linear, homogeneous, and generally nonlocal boundary conditions of Leontovich (impedance) type for the wave of the obstacle's surface. The theory is modeled on the complete Green's function and the transition (T) operator in time-independent formal scattering theory of nonrelativistic quantum mechanics. An expression for the differential scattering cross section for plane electromagnetic waves is derived in terms of certain matrix elements of the T operator for the obstacle.

Hahne, G. E.↗

NASA NTRS1982

The effect of solute on the homogeneous crystal nucleation frequency in metallic melts

A complete calculation that extends the classical theory for crystal nucleation in pure melts to binary alloys has been made. Using a regular solution model, approximate expressions have been developed for the free energy change upon crystallization as a function of solute concentration. They are used, together with model-based estimates of the interfacial tension, to calculate the nucleation frequency. The predictions of the theory for the maximum attainable undercooling are compared with existing experimental results for non-glass forming alloys. The theory is also applied to several easy glass-forming alloys (Pd-Si, Au-Si, Fe-B) for qualitative comparison with the present experimental experience on the ease of glass formation, and for assessment of the potential for formation of the glass in bulk.

Thompson, C. V.↗

NASA NTRS1992

Vibration of thick composite laminates - Analytic theory and finite element approximations

Two versions of a (1,2) higher-order laminate plate theory are extended to elastodynamics, and their performance on free vibration problems for homogeneous and laminated plates is examined. Both versions are based on continuously varying through-the-thickness linear and parabolic distributions for the inplane and transverse displacements, respectively. They also use continuous parabolic distributions for the transverse shear strains. The theory is capable of providing an improved accuracy as compared to other approximate theories and accurately predicting the lowest thickness-stretch frequencies which cannot be obtained with shear-deformable theories. The theory is considered to be particularly well-suited for generating simple and efficient variationally-based displacement finite elements leading to C sup 0 elements with only five degrees of freedom per node.

Tessler, A.↗

NASA NTRS1973

The Fokker-Planck coefficient for pitch-angle scattering of cosmic rays

For the case of homogeneous, isotropic magnetic field fluctuations, it is shown that most theories which are based on the quasi-linear and adiabatic approximation yield the same integral for the Fokker-Planck coefficient for the pitch angle scattering of cosmic rays. For example, despite apparent differences, the theories due to Jokipii and to Klimas and Sandri yield the same integral. It is also shown, however, that this integral in most cases has been evaluated incorrectly in the past. For large pitch angles these errors become significant, and for pitch angles of 90 deg the actual Fokker-Planck coefficient contains a delta function. The implications for these corrections relating cosmic ray diffusion coefficients to observed properties of the interplanetary magnetic field are discussed.

Fisk, L. A.↗

NASA NTRS1974

Aeroelastic stability of coupled flap-lag motion of hingeless helicopter blades at arbitrary advance ratios

Equations for large amplitude coupled flap-lag motion of a hingeless elastic helicopter blade in forward flight are derived. Only a torsionally rigid blade excited by quasi-steady aerodynamic loads is considered. The effects of reversed flow together with some new terms due to radial flow are included. Using Galerkin's method the spatial dependence is eliminated and the equations are linearized about a suitable equilibrium position. The resulting system of homogeneous periodic equations is solved using multivariable Floquet-Liapunov theory, and the transition matrix at the end of the period is evaluated by two separate methods. Computational efficiency of the two numerical methods is compared. Results illustrating the effects of forward flight and various important blade parameters on the stability boundaries are presented.

Friedmann, P.↗

NASA NTRS1974

The Fokker-Planck coefficient for pitch-angle scattering of cosmic rays

For the case of homogeneous, isotropic magnetic field fluctuations, it is shown that most theories which are based on the quasi-linear and adiabatic approximations yield the same integral for the Fokker-Planck coefficient for the pitch-angle scattering of cosmic rays. For example, despite apparent differences, the theories due to Jokipii and to Klimas and Sandri yield the same integral. It is also shown, however, that this integral in most cases has been evaluated incorrectly in the past. For small pitch angles, the errors in previous evaluations are fortuitously of minor importance. For large pitch angles, however, these errors become more significant; and for pitch angles of 90 deg, the actual Fokker-Planck coefficient contains a delta function which has been overlooked in the past. The implications of these corrections on the possibility of relating cosmic-ray diffusion coefficients to observed properties of the interplanetary magnetic field are discussed.

Fisk, L. A.↗

NASA NTRS1987

A spectral view of nonlinear fluxes and stationary-transient interaction in the atmosphere

Nonlinear spectral transfers of kinetic energy and enstrophy, and stationary-transient interaction, are studied using global FGGE data for January 1979. The spectral transfers are found to be dominated by two dynamically distinct components, one due to nonlinear self-interactions within the transient flow and the other arising from coupled interactions between the stationary and transient parts of the flow. The former seems to be attributable to two-dimensional homogeneous turbulence, while the second cannot be understood within that theory. It is argued that the mixed stationary-transient interactions can be understood physically as a process of shear-induced spectral transfer of transient enstrophy along lines of constant zonal wavenumber. The transients act mainly to strengthen the stationary flow, and this 'forcing' operates on a timescale comparable to presumed viscous timescales.

Shepherd, Theodore G.↗

NASA NTRS1994

Pondermotive versus mirror force in creation of the filamentary cavities in auroral plasma

Recently rocket observations on spikelets of lower-hybrid waves along with strong density cavities and transversely heated ions were reported. The observed thin filamentary cavities oriented along the magnetic field in the auroral plasma have density depletions up to several tens of percent. These observations have been interpreted in terms of a theory for lower-hybrid wave condensation and collapse. The modulational instability leading to the wave consensation of the lower-hybrid waves yields only weak density perturbations, which cannot explain the above strong density depletions. The wave collapse theory is based on the nonlinear pondermotive force in a homogeneous ambient plasma and the density depletion is determined by the balance between the wave pressure (pondermotive force) and the plasma pressure. In the auroral plasma, the balance is achieved in a time tau(sub wc) equal to or less than 1 ms. It is shown here that the mirror force, acting on the transversely heated ions at a relatively long time scale, is an effective mechanism for creating the strong plasma cavities. We suggest that the process of wave condensation, through the pondermotive force causing generation of short wavelength waves from relatively long wavelength waves, is a dominant process until the former waves evolve and become effective in the transverse heating of ions. As soon as this happens, mirror force on ions becomes an important factor in the creation of the density cavities, which may further trap and enhance the waves. Results from a model of cavity formation by transverse ion heating show that the observed depletions in the density cavities can be produced by the heating rates determined by the observed wave amplitudes near the lower-hybrid frequency. It is found that the creation of a strong density cavity takes a few minutes.

Singh, Nagendra↗

NASA NTRS2012

Aerosol Remote Sensing

This book gives a much needed explanation of the basic physical principles of radia5tive transfer and remote sensing, and presents all the instruments and retrieval algorithms in a homogenous manner. For the first time, an easy path from theory to practical algorithms is available in one easily accessible volume, making the connection between theoretical radiative transfer and individual practical solutions to retrieve aerosol information from remote sensing. In addition, the specifics and intercomparison of all current and historical methods are explained and clarified.

Lenoble, Jacqueline↗

NASA NTRS2011

CUDA Simulation of Homogeneous, Incompressible Turbulence

We discuss very fast Compute Unified Device Architecture (CUDA) simulations of ideal homogeneous incompressible turbulence based on Fourier models. These models have associated statistical theories that predict that Fourier coefficients of fluid velocity and magnetic fields (if present) are zero-mean random variables. Prior numerical simulations have shown that certain coefficients have a non-zero mean value that can be very large compared to the associated standard deviation. We review the theoretical basis of this "broken ergodicity" as applied to 2-D and 3-D fluid and magnetohydrodynamic simulations of homogeneous turbulence. Our new simulations examine the phenomenon of broken ergodicity through very long time and large grid size runs performed on a state-of-the-art CUDA platform. Results comparing various CUDA hardware configurations and grid sizes are discussed. NS and MHD results are compared.

Morin, Lee↗

NASA NTRS1973

Backscattering from a two-scale rough surface with application to radar sea return

A two-scale composite surface scattering theory was developed without using the noncoherent assumption. The surface is assumed electrically homogeneous and finitely conducting; the surface roughness may be nonuniform geometrically. The special forms of the terms for excluding the non-coherent assumption and the meanings of these terms are discussed. To gain insight into the mechanisms of backscattering, the results are compared with those obtained by previous theories. The comparison with NRL data shows satisfactory agreement for both horizontal and vertical polarization, especially for incident angles larger than 30 deg. For smaller incident angles, NASA/JSC data have been chosen for comparison and close agreement is again observed.

Chan, H. L.↗

NASA NTRS1990

Some aeroacoustic and aerodynamic applications of the theory of nonequilibrium thermodynamics

An exact equation is derived for the dissipation function of a homogeneous, isotropic, Newtonian fluid, with terms associated with irreversible compression or expansion, wave radiation, and the square of the vorticity. This and other forms of the dissipation function are used to identify simple flows, such as incompressible channel flow, the potential vortex with rotational core, and incompressible, irrotational flow as minimally dissipative distributions. A comparison of the hydrodynamic and thermodynamic stability characteristics of a parallel shear flow suggests that an association exists between flow stability and the variation of net dissipation with disturbance amplitude, and that nonlinear effects, such as bounded disturbance amplitude, may be examined from a thermodynamic basis.

Horne, W. Clifton↗

NASA NTRS1997

Validation of a Pseudo-Sound Theory for the Pressure-Dilatation in DNS of Compressible Turbulence

The results of an asymptotic theory for statistical closures for compressible turbulence are explored and validated with the direct numerical simulation of the isotropic decay and the homogeneous shear. An excellent collapse of the data is seen. The slow portion is found to scale, as predicted by the theory, with the quantity M(sub t)(sup 2) and epsilon(sub s). The rapid portion has an unambiguous scaling with alpha(sup 2)M(sub t)(sup s)epsilon(sub s)[P(sub k)/epsilon - l](Sk/epsilon)(sup 2). Implicit in the scaling is a dependence, as has been noted by others, on the gradient Mach number. A new feature of the effects of compressibility, that of the Kolmogorov scaling coefficient, alpha, is discussed. It is suggested that alpha may contain flow specific physics associated with large scales that might provide further insight into the structural effects of compressibility.

Ristorcelli, J. R.↗

NASA NTRS2002

Applicability of the Continuum-Shell Theories to the Mechanics of Carbon Nanotubes

Validity of the assumptions relating the applicability of continuum shell theories to the global mechanical behavior of carbon nanotubes is examined. The present study focuses on providing a basis that can be used to qualitatively assess the appropriateness of continuum-shell models for nanotubes. To address the effect of nanotube structure on their deformation, all nanotube geometries are divided into four major classes that require distinct models. Criteria for the applicability of continuum models are presented. The key parameters that control the buckling strains and deformation modes of these classes of nanotubes are determined. In an analogy with continuum mechanics, mechanical laws of geometric similitude are presented. A parametric map is constructed for a variety of nanotube geometries as a guide for the applicability of different models. The continuum assumptions made in representing a nanotube as a homogeneous thin shell are analyzed to identify possible limitations of applying shell theories and using their bifurcation-buckling equations at the nano-scale.

Harik, V. M.↗

NASA NTRS1973

Phase matrix induced symmetrics for multiple scattering using the matrix operator method

Entirely rigorous proofs of the symmetries induced by the phase matrix into the reflection and transmission operators used in the matrix operator theory are given. Results are obtained for multiple scattering in both homogeneous and inhomogeneous atmospheres. These results will be useful to researchers using the method since large savings in computer time and storage are obtainable.

Hitzfelder, S. J.↗

NASA NTRS1977

Two phase choke flow in tubes with very large L/D

Data were obtained for two phase and gaseous choked flow nitrogen in a long constant area duct of 16200 L/D with a diverging diffuser attached to the exit. Flow rate data were taken along five isotherms (reduced temperature of 0.81, 0.96, 1.06, 1.12, and 2.34) for reduced pressures to 3. The flow rate data were mapped in the usual manner using stagnation conditions at the inlet mixing chamber upstream of the entrance length. The results are predictable by a two phase homogeneous equilibrium choking flow model which includes wall friction. A simplified theory which in essence decouples the long tube region from the high acceleration choking region also appears to predict the data resonably well, but about 15 percent low.

Hendricks, R. C.↗

NASA NTRS1977

Two phase choke flow in tubes with very large L/D

Two phase and gaseous choked flow data for fluid nitrogen were obtained for a test section which was a long constant area duct of 16 200 L/D with a diverging diffuser attached to the exit. Flow rate data were taken along five isotherms (reduced temperature of 0.81, 0.96, 1.06, 1.12, and 2.34) for reduced pressures to 3. The flow rate data were mapped in the usual manner using stagnation conditions at the inlet mixing chamber upstream of the entrance length. The results are predictable by a two-phase homogeneous equilibrium choking flow model which includes wall fraction. A simplified theory which in essence decouples the long tube region from the high acceleration choking region also appears to predict the data reasonably well, but about 15 percent low.

Hendricks, R. C.↗

NASA NTRS1983

Psuedospectral calculation of shock turbulence interactions

A Chebyshev-Fourier discretization with shock fitting is used to solve the unsteady Euler equations. The method is applied to shock interactions with plane waves and with a simple model of homogeneous isotropic turbulence. The plane wave solutions are compared to linear theory.

Zang, T. A.↗