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At least 811 records · Page 45
All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Nonlinear photorefractive response at high modulation depths

The response of photorefractive materials to sinusoidal intensity patterns of high modulation depths is considered. It is shown that the induced refractive-index response in this regime is highly nonlinear. Concise analytic expressions for the various nonlinear harmonics of the photorefractive response field are developed and compared with exact numerical solutions of the underlying charge-transport equations as well as with the results of previous theoretical models over a broad range of physical parameters. We show that the nonlinear response characteristics are strongly dependent on both the magnitude of applied electric fields and the relative concentrations of charge donor and acceptor sites in the material. For drift dominated recording, in particular, we determine analytically that in the limit of a minimal acceptor/donor ratio, the amplitudes of higher spatial harmonics of the response reach a maximum and eventually decay as functions of increasing applied field, whereas these amplitudes reach a nonzero limit in the case of a near-unity acceptor/donor ratio. Finally, we generalize our results to account for diffusion effects in an appended derivation.

Vachss, Frederick↗
NASA NTRS1988

Geodetic altitude to a triaxial ellipsoidal planet

An efficient theoretical model for determining geodetic altitudes with better than millimeter accuracy is proposed, with application to the TOPEX/Poseidon project. The triaxial ellipsoidal subsurface point of a satellite is used as the initial trial solution to achieve an efficient and simple iterative solution. It is found that the second-iteration solution is exact to an accuracy of at least 10 to the -9th km.

Tang, Charles C. H.↗
NASA NTRS1990

A numerical study of the separation wavenumber in the two-scale scattering approximation

The choice of the separation wavenumber Kd for the two-scale scattering approximation is examined by the comparison of two-scale calculations with exact numerical solutions using the moment method. It was found that the optimal choice of Kd is near k/2 when attempting to optimize for all incidence angles. When optimizing for specific incidence angles, Kd varied from k/5 at low incidence angles to just below k at higher incidence angles. These numerical results are in rough agreement with previous theoretical derivations of the separation wavenumber.

Durden, Stephen L.↗
NASA NTRS1990

Resonance absorption of propagating fast waves in a cold plasma

Absorption of propagating waves impinging on a surface in which the plasma and magnetic field may change is investigated by examining in depth the problem of a combination of cold plasma, uniform magnetic field and a surface density which varies linearly from zero at the left end to some finite value at the right end, beyond which the density is constant. Two cases are considered: one in which the plasma is a vacuum everywhere to the left of the surface (which may correspond to coronal conditions) and one in which the plasma density jumps to a very large value to the left of the surface (which may mimic the magnetosphere with the dense region at the left corresponding to the plasmasphere). A complete discussion of the resonance absorption of propagating fast waves for the case considered by Kiveloson and Southwood (1986) is presented, emphasizing approximate analytical results whenever possible; these results are then compared with exact numerical solutions.

Hollweg, Joseph V.↗
NASA NTRS1990

Injection efficiency of bound modes

Previous work on efficiency of light injection into the core of a fiber from a thin film and a bulk distribution of sources in the cladding have used the fields of a weakly guiding fiber. This approximation simplifies the analysis of the power efficiency by introducing universal values for the eigenvalues of different fibers with the same V-number, but cannot predict accurately the behavior of the injected light into a fiber with arbitrary differences in indices of refraction. The exact field solution was used in the expressions of the power efficiency, p sub eff, and its behavior as a function of the fiber parameter was analyzed. Weakly guiding results obtained previously are confirmed. However, P sub eff does not always increase with the V-number but with the difference in the indices of refraction, eta sub core-eta sub clad. For the bulk distribution it was found that P sub eff increases with the wavelength, lambda, and decreases with the fiber core radius, a, i.e., it decreases with the V-number. However, for the thin film, the P sub eff remains almost constant with lambda and the fiber core radius.

Egalon, Claudio Oliveira↗
NASA NTRS1990

Low-frequency ionization-driven instability of a discrete auroral arc model

The low-frequency (time scales of tens of seconds) dynamics of the auroral ionosphere differs from that of the nonauroral ionosphere by the presence of strong, unstable space- and time-dependent ionospheric ionization produced by precipitating auroral electrons. If recombination is relatively unimportant (as at high ionospheric heights), it is shown that, in general, transport processes cannot remove this ionization as fast as it is created, and no equilibrium is possible. These nonequilibrium phenomena are investigated in the context of a nonlinear adiabatic auroral model, which has previously been studied in static situations. A linearized local perturbation analysis is given of what amounts to a current-driven E x B gradient-drift instability with an ionization source, as well as some exact nonlinear solutions valid in a finite but limited spatial region. These solutions show continuing motion of auroral potential and plasma density, as the aurora tries to shift its ionization problems from one place to another. The analysis gives clues to the possibility of generation of chaos and of fine-scale spatial structure.

Cornwall, John M.↗
NASA NTRS1991

Modified ICED-ALE method for astrogeophysical plasma flows

The Implicit-Continuous-Eulerian-Difference Mesh-Arbitrary-Lagrangian-Eulerian (ICED-ALE) algorithm of Brackbill and Pracht (1973) is modified for the study of astrophysical plasma flows in which dynamical effects are important. In the present study the general-energy-conservation law is directly applied to the iteration process, with the total (kinetic-, specific-internal-, and magnetic-) energy density being obtained implicitly at the end of the process. An example is computed in which the convergence speed of the latter method is substantially faster than that of the former. The initializing calculation, or explicit phase, in which the electric current density, magnetic diffusion of field, energy augmentation, and zero-order approximation of the flow velocity are given, is described. Consideration is given to the iteration process, or implicit phase, from which the exact Lagrangian solution for energy density, velocity, and a magnetic field is obtained.

Wu, S. T.↗
NASA NTRS1991

A critical comparison of second order closures with direct numerical simulation of homogeneous turbulence

Recently, several second order closure models have been proposed for closing the second moment equations, in which the velocity-pressure gradient (and scalar-pressure gradient) tensor and the dissipation rate tensor are two of the most important terms. In the literature, these correlation tensors are usually decomposed into a so called rapid term and a return-to-isotropy term. Models of these terms have been used in global flow calculations together with other modeled terms. However, their individual behavior in different flows have not been fully examined because they are un-measurable in the laboratory. Recently, the development of direct numerical simulation (DNS) of turbulence has given us the opportunity to do this kind of study. With the direct numerical simulation, we may use the solution to exactly calculate the values of these correlation terms and then directly compare them with the values from their modeled formulations (models). Here, we make direct comparisons of five representative rapid models and eight return-to-isotropy models using the DNS data of forty five homogeneous flows which were done by Rogers et al. (1986) and Lee et al. (1985). The purpose of these direct comparisons is to explore the performance of these models in different flows and identify the ones which give the best performance. The modeling procedure, model constraints, and the various evaluated models are described. The detailed results of the direct comparisons are discussed, and a few concluding remarks on turbulence models are given.

Shih, Tsan-Hsing↗
NASA NTRS1991

A two-dimensional Euler solution for an unbladed jet engine configuration

A two dimensional nonaxisymmetric Euler solution in a geometric representation of a jet engine configuration without blades is presented. The domain, including internal and external flow, is covered with a multiblock grid. To construct the grid, a domain decomposition technique is used to subdivide the domain and smooth grids are dimensioned and placed in each block. The grid contains 44 blocks which cover the external field, the inlet, bypass duct, core duct and nozzle of the nonaxisymmetric engine configuration. The geometry is symmetric about the meanline of the hub, but the grid is not since there is no symmetry condition applied to the grid between the two halves. With a symmetric grid at zero angle of attack, the measures of the solution would cancel exactly. With an asymmetric grid, the solution will not necessarily be symmetric and the lift coefficient will not necessarily be zero. Thus, grid asymmetry can be exploited to verify the resolution of the solution. The solution may be verified on the basis of five theoretical quantities: conservation of mass and energy, deviation of the lift coefficient from zero, deviation of the drag coefficient from zero, deviations from constant entropy, and deviations in the pressure distributions over the symmetric surfaces of the components. This technique is suitable for obtaining numerical solutions in complex geometries and provides a foundation for complete engine throughflow calculations.

Stewart, Mark E. M.↗
NASA NTRS1992

Excitation efficiency of an optical fiber core source

The exact field solution of a step-index profile fiber is used to determine the excitation efficiency of a distribution of sources in the core of an optical fiber. Previous results of a thin-film cladding source distribution to its core source counterpart are used for comparison. The behavior of power efficiency with the fiber parameters is examined and found to be similar to the behavior exhibited by cladding sources. It is also found that a core-source fiber is two orders of magnitude more efficient than a fiber with a bulk distribution of cladding sources. This result agrees qualitatively with previous ones obtained experimentally.

Egalon, Claudio O.↗
NASA NTRS1991

Model of a thin film optical fiber fluorosensor

The efficiency of core-light injection from sources in the cladding of an optical fiber is modeled analytically by means of the exact field solution of a step-profile fiber. The analysis is based on the techniques by Marcuse (1988) in which the sources are treated as infinitesimal electric currents with random phase and orientation that excite radiation fields and bound modes. Expressions are developed based on an infinite cladding approximation which yield the power efficiency for a fiber coated with fluorescent sources in the core/cladding interface. Marcuse's results are confirmed for the case of a weakly guiding cylindrical fiber with fluorescent sources uniformly distributed in the cladding, and the power efficiency is shown to be practically constant for variable wavelengths and core radii. The most efficient fibers have the thin film located at the core/cladding boundary, and fibers with larger differences in the indices of refraction are shown to be the most efficient.

Egalon, Claudio O.↗
NASA NTRS1992

Electromagnetic scattering from an inhomogeneous object by ray tracing

A 'shooting and bouncing ray' (SBR) formulation is presented for treating the electromagnetic scattering from electrically large, inhomogeneous objects. A dense grid of rays representing the incident plane wave is shot toward the inhomogeneous object. At the scatterer boundary, reflected rays and refracted rays are generated due to discontinuity of the medium parameters. The trajectory, amplitude, phase and polarization of the rays inside the inhomogeneous object are traced based on geometrical optics. Whenever the rays cross the scatterer surface, additional reflected/refracted rays are generated and are tracked. This process is repeated until the intensities of the refracted/reflected rays become negligible. The contributions of the exiting rays to the total scattered field are calculated by using the equivalence principle in conjunction with a ray-tube integration scheme. The ray formulation is applied to calculate the backscattering from cylinders and spheres and good agreement with the exact series solutions is observed in the high frequency range. In addition, the backscattering mechanisms in penetrable objects are interpreted in terms of simple ray pictures.

Kim, Hyeongdong↗
NASA NTRS1992

Interpreting asteroid photometry and polarimetry using a model of shadowing and coherent backscattering

The shadow-hiding models for the opposition effect and negative polarization of atmosphereless solar system bodies do not explain some experimental findings, such as the enhancing opposition effect and negative polarization with decreasing particle size down to wavelength scales. The enhancement for laboratory photometric and polarimetric data on artificial glass samples with different particle size is shown. These results are in agreement with the so-called coherent backscattering or interference mechanism proposed for the interpretation of the opposition effect and negative polarization. Two different approaches for describing the opposition effect and negative polarization produced by the shadow-interference mechanism were developed. One is based on exact electromagnetic solutions for simple scattering systems that include dipole-dipole and dipole-surface coupling; The other is based on a point-scatterer approximation characterized by model photometric and polarimetric phase functions, and the mutual shadowing effect is derived using virtual volumes associated with the point-scatterers. Both approaches yield qualitatively similar results, although neither is entirely satisfactory. We regard them as prototypes for a future unified model of shadowing and coherent backscattering. The sharp opposition effect of 44 Nysa and the asteroid albedo-polarization rule are here explained using the point-scatterer approach.

Shkuratov, Y. G.↗
NASA NTRS1992

Source polarization effects in an optical fiber fluorosensor

The exact field solution of a step-index profile fiber was used to determine the injection efficiency of a thin-film distribution of polarized sources located in the cladding of an optical fiber. Previous results for random source orientation were confirmed. The behavior of the power efficiency, P(eff), of a polarized distribution of sources was found to be similar to the behavior of a fiber with sources with random orientation. However, for sources polarized in either the x or y direction, P(eff) was found to be more efficient.

Egalon, Claudio O.↗
NASA NTRS1991

Stochastic inflation lattice simulations - Ultra-large scale structure of the universe

Non-Gaussian fluctuations for structure formation may arise in inflation from the nonlinear interaction of long wavelength gravitational and scalar fields. Long wavelength fields have spatial gradients, a (exp -1), small compared to the Hubble radius, and they are described in terms of classical random fields that are fed by short wavelength quantum noise. Lattice Langevin calculations are given for a toy model with a scalar field interacting with an exponential potential where one can obtain exact analytic solutions of the Fokker-Planck equation. For single scalar field models that are consistent with current microwave background fluctuations, the fluctuations are Gaussian. However, for scales much larger than our observable Universe, one expects large metric fluctuations that are non-Gaussian. This example illuminates non-Gaussian models involving multiple scalar fields which are consistent with current microwave background limits.

Salopek, D. S.↗
NASA NTRS1994

Second-order reconstruction of the inflationary potential

To first order in the deviation from scale invariance the inflationary potential and its first two derivatives can be expressed in terms of the spectral indices of the scalar and tensor perturbations, n and n(sub T), and their contributions to the variance of the quadrupole CBR temperature anisotropy, S and T. In addition, there is a 'consistency relation' between these quantities: n(sub T) = (-1/ 7)(T/S). We derive the second-order expressions for the inflationary potential and its first two derivatives and the first-order expression for its third derivative, in terms, of n, n(sub T), S, T, and dn/d ln gamma. We also obtain the second-order consistency relation, n(sub T) = (-1/7)(T/S)(1 + 0.11(T/S) + 0.15(n-1)). As an example we consider the exponential potential, the only known case where exact analytic solutions for the perturbation spectra exist. We reconstruct the potential via Taylor expansion (with coefficients calculated at both first and second order), and introduce the Pade approximate as a greatly improved alternative.

Liddle, Andrew R.↗
NASA NTRS1994

Mass and radius of cosmic balloons

Cosmic balloons are spherical domain walls with relativistic particles trapped inside. We derive the exact mass and radius relations for a static cosmic balloon using Gauss-Codazzi equations. The cosmic balloon mass as a function of its radius, M(R), is found to have a functional form similar to that of fermion soliton stars, with a fixed point at 2GM(R)/R approximately or equal to 0.486 which corresponds to the limit of infinite central density. We derive a simple analytical approximation for the mass density of a spherically symmetric relativistic gas star. When applied to the computation of the mass and radius of a cosmic balloon, the analytical approximation yields fairly good agreement with the exact numerical solutions.

Wang, Yun↗