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NASA NTRS1972

Optimal control of first order distributed systems

The problem of characterizing optimal controls for a class of distributed-parameter systems is considered. The system dynamics are characterized mathematically by a finite number of coupled partial differential equations involving first-order time and space derivatives of the state variables, which are constrained at the boundary by a finite number of algebraic relations. Multiple control inputs, extending over the entire spatial region occupied by the system ("distributed controls') are to be designed so that the response of the system is optimal. A major example involving boundary control of an unstable low-density plasma is developed from physical laws.

Johnson, T. L.↗

NASA NTRS1973

Redistribution of resonance radiation. II - The effect of magnetic fields.

Previously obtained results for scattering of radiation in the presence of collisions are restated in a density matrix formalism which employs an irreducible-tensor description of the radiation field. This formalism is particularly useful for problems associated with radiative transfer theory. The redistribution is then extended to include the effect of a weak magnetic field. By averaging over a finite bandwidth which is on the order of the Doppler width, simplified expressions of physical significance for the scattering in the Doppler core and the Lorentz wings are obtained. Expressions are also obtained for the corresponding source function of radiative transfer theory.

Omont, A.↗

NASA NTRS1976

Ion temperatures in HIP-1 and SUMMA from charge-exchange neutral optical emission spectra

Ion temperatures were obtained from observations of the H sub alpha, D sub alpha, and He 587.6 nm lines emitted from hydrogen, deuterium, and helium plasmas in the SUMMA and HIP-1 mirror devices at Lewis Research Center. Steady state discharges were formed by applying a radially inward dc electric field between cylindrical or annular anodes and hollow cathodes located at the peaks of the mirrors. The ion temperatures were found from the Doppler broadening of the charge-exchange components of spectral lines. A statistical method was developed for obtaining scaling relations of ion temperature as a function of current, voltage, and magnetic flux density. Derivations are given that take into account triangular monochromator slit functions, loss cones, and superimposed charge-exchange processes. In addition, the Doppler broadening was found to be sensitive to the influence of drift on charge-exchange cross section. The effects of finite ion-cyclotron radius, cascading, and delayed emission are reviewed.

Patch, R. W.↗

NASA NTRS1984

Influence of damage on the thermal response of graphite-epoxy laminates

A constrained-displacement finite-element approach for studying the influence of transverse cracks and delaminations on the thermal response of laminated composites is presented. Typical results are given in the form of percent-retention curves for the coefficient of thermal expansion as a function of crack density. Cross-ply and quasi-isotropic T300/5208 graphite-epoxy laminates are considered. It is shown that transverse cracks can have a significant influence on the coefficient of thermal expansion, but delaminations located symmetrically about the laminate midplane have no influence on thermal expansion.

Adams, D. S.↗

NASA NTRS1996

Design of a Long-Stroke Noncontact Electromagnetic Actuator for Active Vibration Isolation

A long-stroke moving coil Lorentz Actuator was designed for use in a microgravity vibration isolation experiment. The final design had a stroke of 5.08 cm (2 in) and enough force capability to isolate a mass of the order of 22.7-45.4 kg. A simple dynamic magnetic circuit analysis, using an electrical analog, was developed for the initial design of the actuator. A neodymium-iron-boron material with energy density of 278 T-kA/m (35 MGOe) was selected to supply the magnetic field. The effect of changes in the design parameters of core diameter, shell outer diameter, pole face length, and coil wire layers were investigated. An extensive three-dimensional finite element analysis was carried out to accurately determine linearity with regard to axial position of the coil and coil current levels. The actuator was constructed and tested on a universal testing machine. Example plots are shown, indicating good linearity over the stroke of approximately 5.08 cm (2 in) and a range of coil currents from -1.5 A to +1.5 A. The actuator was then used for the microgravity vibration isolation experiments, described elsewhere.

Banerjee, Bibhuti↗

NASA NTRS2001

Retrieval of Polar Stratospheric Cloud Microphysical Properties From Lidar Measurements: Dependence on Particle Shape Assumptions

Knowledge of particle sizes and number densities of polar stratospheric clouds (PSCs) is highly important, because they are critical parameters for the modeling of the ozone chemistry of the stratosphere. In situ measurements of PSC particles are rare. the main instrument for the accumulation of PSC data are lidar systems. Therefore the derivation of some microphysical properties of PSCS from the optical parameters measured by lidars would be highly beneficial for ozone research. Inversion of lidar data obtained in the presence of PSCs formed from crystalline particles type 11 and the various nitric acid tri Ydrrate (NAT) types cannot be easily accomplished, because a suitable scattering theory for small faceted crystals has not been readily available tip to now. As a consequence, the T-matrix method is commonly used for the interpretation of these PSC lidar data. Here the assumption is made that the optical properties of an ensemble of spheroids resemble those of crystalline PSCs, and microphysical properties of the PSC are inferred from the optical signatures of the PSC at two or more wavelengths. The problem with the T-matrix approach is that the assumption of spheroidal instead of faceted particles can lead to dramatically wrong results: Usually cloud particle properties are deduced from analysis of lidar profiles of backscatter ratio and depolarization ratio. The particle contribution to the backscatter ratio is given by the product of the particle number density and the backscattering cross section. The latter is proportional to the value of the particle's scattering phase function at 180 degrees scattering angle. At 180 degrees however, the phase functions of rough, faceted crystals and of spheroids with same maximum dimension differ by a factor of 6. From this it follows that for a PSC consisting of faceted crystals, the particle number density is underestimated by roughly the same factor if spheroidal particles are unrealistically assumed. We are currently developing a retrieval technique for determining the microphysical parameters of crystalline PSCs that takes into account the faceted shape of the PSC particles. This approach utilizes finite-difference time-domain (FDTD) calculations of particle optical properties. The accuracy and the free choice of the shape of the scattering particle make the FDTD technique a promising tool for the inversion of PSC lidar data. A first comparison of FDTD and T-matrix calculations will be presented.

Reichardt, Susanne↗

NASA NTRS2010

Broken Ergodicity in Two-Dimensional Homogeneous Magnetohydrodynamic Turbulence

Two-dimensional (2-D) homogeneous magnetohydrodynamic (MHD) turbulence has many of the same qualitative features as three-dimensional (3-D) homogeneous MHD turbulence.The se features include several ideal invariants, along with the phenomenon of broken ergodicity. Broken ergodicity appears when certain modes act like random variables with mean values that are large compared to their standard deviations, indicating a coherent structure or dynamo.Recently, the origin of broken ergodicity in 3-D MHD turbulence that is manifest in the lowest wavenumbers was explained. Here, a detailed description of the origins of broken ergodicity in 2-D MHD turbulence is presented. It will be seen that broken ergodicity in ideal 2-D MHD turbulence can be manifest in the lowest wavenumbers of a finite numerical model for certain initial conditions or in the highest wavenumbers for another set of initial conditions.T he origins of broken ergodicity in ideal 2-D homogeneous MHD turbulence are found through an eigen analysis of the covariance matrices of the modal probability density functions.It will also be shown that when the lowest wavenumber magnetic field becomes quasi-stationary, the higher wavenumber modes can propagate as Alfven waves on these almost static large-scale magnetic structures

Shebalin, John V.↗

NASA NTRS1972

Pioneer 7 observations of the August 29, 1966, interplanetary shock-wave ensemble.

The detailed plasma (except for electrons) and magnetic field data from Pioneer 7 are presented for a proposed double-shock ensemble. The Ames Research Center plasma probe data are compared with that of the MIT probe. These data are compared with MHD theory to show that the discontinuities themselves satisfy the magnetic Hugoniot equations. The data are also compared with the theoretical predictions for the double-shock structure. The theory requires as input only the forward shock velocity, the original ambient solar wind conditions, and a reasonable assumption regarding the density and azimuthal magnetic field in the 'new' solar wind which is detected after passage of the reverse shock. A unique solution is then obtained for the theoretical piston and reverse shock positions as well as for the temporal plasma behavior for both infinite and finite electrical conductivities.

Dryer, M.↗

NASA NTRS1974

The diffusive idealization of charged particle transport in random magnetic fields

The transport of charged particles diffusing in a random magnetic field parallel to a relatively large guiding field is presented. The same coefficient of diffusion is obtained by three methods. Two corrections must be added to the expression in which the diffusive flux is proportional to the gradient of the density. Explicit expressions are given for a characteristic time and a characteristic length which describe the corrections. The well known divergence of the coefficient of diffusion, which is implied by the quasilinear analysis of pitch angle scattering, does not occur if the scattering rate is finite at 90 deg pitch angle. This effect is illustrated by formulas which give the coefficient of diffusion when the quasilinear expression is perturbed by a variable amount of isotropic scattering.

Earl, J. A.↗

NASA NTRS1979

Rigid-drift magnetohydrodynamic equilibria for cylindrical screw pinches

The rigid-drift equations of MHD equilibria in cylindrical geometry are solved analytically in terms of an infinite series of hypergeometric functions for the case where the pressure is proportional to the square of number density and the current density is arbitrarily pitched. Solutions are obtained for a pure Z pinch, a pure theta pinch, and a general screw pinch. It is found that the shapes of the pressure and magnetic-field profiles are completely determined by the model once two parameters are specified: the local plasma beta on the axis and a quantity related to the pitch of the current density. A set of profiles that resemble those observed experimentally in reversed-field pinches is presented. The results also indicate that hollow pressure profiles and reversed Bz profiles can occur either simultaneously or independently and that the pressure always falls to zero at a finite value of the radius.

Turner, L.↗

NASA NTRS1982

Queueing analysis of synchronous time division multiplexing with individual source buffering

Synchronous time division multiplexing is analyzed. Packets of information arrive at the system as a compound Poisson process, and are transmitted only during individual periodic intervals. Packet arrivals are blocked (lost) if the system has a finite capacity and is congested. Using the theory of semiregenerative processes, the distribution of the number of packets in the system (system size) is found. This nonstationary distribution is used to determine the complete system behavior, including the delay distributions, the blocking probability, and the density of the system size at arrival instants. Numerical examples illustrate applications of the results given.

Clare, L.↗

NASA NTRS1987

Cosmic string wakes

Accretion of matter onto wakes left behind by horizon-sized pieces of cosmic string is investigated, and the effects of wakes on the large-scale structure of the universe are determined. Accretion of cold matter onto wakes, the effects of a long string on fluids with finite velocity dispersion or sound speeds, the interactions between loops and wakes, and the conditions for wakes to survive disruption by loops are discussed. It is concluded that the most important wakes are those which were formed at the time of equal matter and radiation density. This leads to sheetlike overdense regions of galaxies with a mean separation in agreement with the scale of the bubbles of de Lapparent, Geller, and Huchra (1986). However, for the value of G(mu) favored from galaxy formation considerations in a universe with cold dark matter, a wake accretes matter from a distance of only about 1.5 Mpc, which is much less than the distance between the wakes.

Stebbins, Albert↗

NASA NTRS1990

Nonlinear viscoelastic response of highly filled elastomers under multiaxial finite deformation

A biaxial tester was used to obtain precise biaxial stress responses of highly filled, high strain capability elastomers. Stress-relaxation experiments show that the time-dependent part of the relaxation response can be reasonably approximated by a function which is strain and biaxiality independent. Thus, isochronal data from the stress-relaxation curves can be used to determine the stored energy density function. The complex behavior of the elastomers under biaxial deformation may be caused by dewetting.

Peng, Steven T. J.↗

NASA NTRS1994

Nonlinear calculations of the time evolution of black hole accretion disks

Based on previous works on black hole accretion disks, I continue to explore the disk dynamics using the finite difference method to solve the highly nonlinear problem of time-dependent alpha disk equations. Here a radially zoned model is used to develop a computational scheme in order to accommodate functional dependence of the viscosity parameter alpha on the disk scale height and/or surface density. This work is based on the author's previous work on the steady disk structure and the linear analysis of disk dynamics to try to apply to x-ray emissions from black candidates (i.e., multiple-state spectra, instabilities, QPO's, etc.).

Luo, C.↗

NASA NTRS2001

Response of the Alliance 1 Proof-of-Concept Airplane Under Gust Loads

This report presents the work performed by Lockheed Martin's Langley Program Office in support of NASA's Environmental Research Aircraft and Sensor Technology (ERAST) program. The primary purpose of this work was to develop and demonstrate a gust analysis method which accounts for the span-wise variation of gust velocity. This is important because these unmanned aircraft having high aspect ratios and low wing loading are very flexible, and fly at low speeds. The main focus of the work was therefore to perform a two-dimensional Power Spectrum Density (PSD) analysis of the Alliance 1 Proof-of-Concept Unmanned Aircraft, As of this writing, none of the aircraft described in this report have been constructed. They are concepts represented by analytical models. The process first involved the development of suitable structural and aeroelastic Finite Element Models (FEM). This was followed by development of a one-dimensional PSD gust analysis, and then the two-dimensional (PSD) analysis of the Alliance 1. For further validation and comparison, two additional analyses were performed. A two-dimensional PSD gust analysis was performed on a simplet MSC/NASTRAN example problem. Finally a one-dimensional discrete gust analysis was performed on Alliance 1. This report describes this process, shows the relevant comparisons between analytical methods, and discusses the physical meanings of the results.

Naser, A. S.↗

NASA NTRS1972

Hydrodynamic water impact

The hydrodynamic impact of a falling body upon a viscous incompressible fluid was investigated by numerically solving the equations of motion. Initially the mathematical model simulated the axisymmetric impact of a rigid right circular cylinder upon the initially quiescent free surface of a fluid. A compressible air layer exists between the falling cylinder and the liquid free surface. The mathematical model was developed by applying the Navier-Stokes equations to the incompressible air layer and the incompressible fluid. Assuming the flow to be one dimensional within the air layer, the average velocity, pressure and density distributions were calculated. The liquid free surface was allowed to deform as the air pressure acting on it increases. For the liquid the normalized equations were expressed in two-dimensional cylindrical coordinates. The governing equations for the air layer and the liquid were expressed in finite difference form and solved numerically. For the liquid a modified version of the Marker-and-Cell method was used. The mathematical model has been reexamined and a new approach has recently been initiated. Essentially this consists of examining the impact of an inclined plate onto a quiesent water surface with the equations now formulated in cartesian coordinates.

Kettleborough, C. F.↗

NASA NTRS1982

Electromagnetic radiation from beam-plasma instabilities

The mechanism by which unstable electrostatic waves of an electron-beam plasma system are converted into observed electromagnetic waves is of great current interest in space plasma physics. Electromagnetic radiation arises from both natural beam-plasma systems, e.g., type III solar bursts and kilometric radiation, and from man-made electron beams injected from rockets and spacecraft. In the present investigation the diagnostic difficulties encountered in space plasmas are overcome by using a large laboratory plasma. A finite diameter (d approximately equal to 0.8 cm) electron beam is injected into a uniform quiescent magnetized afterglow plasma of dimensions large compared with electromagnetic wavelength. Electrostatic waves grow, saturate and decay within the uniform central region of the plasma volume so that linear mode conversion on density gradients can be excluded as a possible generation mechanism for electromagnetic waves.

Stenzel, R. L.↗

NASA NTRS1984

A two-point difference scheme for computing steady-state solutions to the conservative one-dimensional Euler equations

An implicit finite-difference method is presented for obtaining steady-state solutions to the time-dependent, conservative Euler equations for flows containing shocks. The method uses a two-point central-difference scheme for the flux derivatives with dissipation added at supersonic points via the retarded density concept. Application of the method to 1-dimensional nozzle flow equations for various combinations of subsonic and supersonic boundary conditions show the method to be very efficient. Residuals are typically reduced to machine zero in approximately 35 time steps for 50 mesh points. For 1-dimensional Euler calculations, it is shown that the scheme offers two advantages over the more widely-used three-point schemes. The first is in regard to application of boundary conditions, and the second relates to the fact that the two-point algorithm is well-conditioned for large time steps.

Wornom, S. F.↗