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NASA NTRS1989

Qualitative simulation for process modeling and control

A qualitative model is developed for a first-order system with a proportional-integral controller without precise knowledge of the process or controller parameters. Simulation of the qualitative model yields all of the solutions to the system equations. In developing the qualitative model, a necessary condition for the occurrence of oscillatory behavior is identified. Initializations that cannot exhibit oscillatory behavior produce a finite set of behaviors. When the phase-space behavior of the oscillatory behavior is properly constrained, these initializations produce an infinite but comprehensible set of asymptotically stable behaviors. While the predictions include all possible behaviors of the real system, a class of spurious behaviors has been identified. When limited numerical information is included in the model, the number of predictions is significantly reduced.

Dalle Molle, D. T.↗

NASA NTRS1989

Energetic charged particles in the magnetosphere of Neptune

The Voyager 2 cosmic ray system (CRS) measured significant fluxes of energetic greater than or equal to about 1 megaelectron volt (MeV) trapped electrons and protons in the magnetosphere of Neptune. The intensities are maximum near a magnetic L shell of 7, decreasing closer to the planet because of absorption by satellites and rings. In the region of the inner satellites of Neptune, the radiation belts have a complicated structure, which provides some constraints on the magnetic field geometry of the inner magnetosphere. Electron phase-space densities have a positive radial gradient, indicating that they diffuse inward from a source in the outer magnetosphere. Electron spectra from 1 to 5 MeV are generally well represented by power laws with indices near 6, which harden in the region of peak flux to power law indices of 4 to 5. Protons have significantly lower fluxes than electrons throughout the magnetosphere, with large anisotropies due to radial intensity gradients. The radiation belts resemble those of Uranus to the extent allowed by the different locations of the satellites, which limit the flux at each planet.

Stone, E. C.↗

NASA NTRS1989

Experimental study of the dynamics of a ruby laser pumped by a CW argon-ion laser

A study of the dynamics of a ruby laser pumped by a CW argon-ion laser is presented. The ruby laser is predominantly stable but has two accessible unstable states. One state exhibits chaotic output, while the other results in regular self-pulsing. The conditions needed for instability are discussed and homodyne spectra and temporal maps of the phase-space attractors are obtained. In addition, a numerical simulation of nonlinear beam propagation in ruby is presented that shows that strong deviations from plane-wave behavior exist, and that transverse effects must be incorporated into theoretical models of the instability.

Afzal, R. S.↗

NASA NTRS1989

Inhibition of quantum transport due to 'scars' of unstable periodic orbits

A new quantum mechanism for the suppression of chaotic ionization of highly excited hydrogen atoms explains the appearance of anomalously stable states in the microwave ionization experiments of Koch et al. A novel phase-space representation of the perturbed wave functions reveals that the inhibition of quantum transport is due to the selective excitation of wave functions that are highly localized near unstable periodic orbits in the chaotic classical phase space. The 'scarred' wave functions provide a new basis for the quantum description of a variety of classically chaotic systems.

Jensen, R. V.↗

NASA NTRS1990

Trapping saturation of the bump-on-tail instability and electrostatic harmonic excitation in earth's foreshock

The Vlasov simulation is used to examine the trapping saturation of the bump-on-tail instability both with and without mode-mode coupling and subsequent harmonic excitation. It is found that adding the pumped harmonic modes leads to a significant difference in the behavior of the phase-space distribution function near the unstable bump at the saturation time of the instability. The pumped modes permit rapid plateau formation on the space-averaged velocity distribution, in effect preventing the onset of the quasi-linear velocity-diffusion saturation mechanism.

Klimas, Alexander J.↗

NASA NTRS1990

Low-dimensional chaos in magnetospheric activity from AE time series

The magnetospheric response to the solar-wind input, as represented by the time-series measurements of the auroral electrojet (AE) index, has been examined using phase-space reconstruction techniques. The system was found to behave as a low-dimensional chaotic system with a fractal dimension of 3.6 and has Kolmogorov entropy less than 0.2/min. These indicate that the dynamics of the system can be adequately described by four independent variables, and that the corresponding intrinsic time scale is of the order of 5 min. The relevance of the results to magnetospheric modeling is discussed.

Vassiliadis, D. V.↗

NASA NTRS1990

Viscosity and mass transport in nonuniform Keplerian disks

A quantitative formalism for Keplerian particulate disk dynamics having its basis in a heuristic description of viscous transport is presently applied to the case of a ring with optical thickness radial gradient. A steady-state velocity distribution solution directly yields both the radial mass transport and the viscosity. The analytical method employed involves the solution of a novel form of the Krook equation through the separation of the phase-space collisional-products distribution into a symmetrical component and a delta function-approachable remainder. While this model is simplified for the case treated, its general approach may be extended to less artificially restricted cases.

Ojakangas, G. W.↗

NASA NTRS1990

Computational technology for flight vehicles; Proceedings of the Symposium on Computational Technology on Flight Vehicles, Washington, DC, Nov. 5-7, 1990

The present conference on computational methods for aeronautics applications discusses topics in the fields of parallel computing, multidisciplinary computational methods, grid generation, visualization methods for CFD, probabilistic modeling, numerical simulations and methodologies for different flow regimes, computational strategies and adaptive methods in CFD, and computational strategies and dynamics and control. Attention is given to the MACH system-software kernel, a multidisciplinary approach to aeroelastic analysis, interactive grid generation with control points, interactive flow visualization using stream surfaces, numerical simulations of dynamic/aerodynamic interactions, implicit mathods for the Navier-Stokes equations, and the automatic phase-space analysis of dynamical systems.

Noor, Ahmed K.↗

NASA NTRS1992

The origin of non-classical effects in a one-dimensional superposition of coherent states

We investigate the nature of the quantum fluctuations in a light field created by the superposition of coherent fields. We give a physical explanation (in terms of Wigner functions and phase-space interference) why the 1-D superposition of coherent states in the direction of the x-quadrature leads to the squeezing of fluctuations in the y-direction, and show that such a superposition can generate the squeezed vacuum and squeezed coherent states.

Buzek, V.↗

NASA NTRS1992

Squeezed states and path integrals

The continuous-time regularization scheme for defining phase-space path integrals is briefly reviewed as a method to define a quantization procedure that is completely covariant under all smooth canonical coordinate transformations. As an illustration of this method, a limited set of transformations is discussed that have an image in the set of the usual squeezed states. It is noteworthy that even this limited set of transformations offers new possibilities for stationary phase approximations to quantum mechanical propagators.

Daubechies, Ingrid↗

NASA NTRS1991

Energetic particles at Uranus

The energetic particle measurements by the low-energy charged-particle and cosmic-ray instruments on the Voyager 2 spacecraft in the magnetosphere of Uranus are reviewed. Upstream events were observed outside the Uranian bow shock, probably produced by ion escape from the magnetosphere. Evidence of earthlike substorm activity was discovered within the Uranian magnetosphere. A proton injection event was observed within the orbit of Umbriel and proton events were observed in the magnetotail plasma-sheet boundary layer that are diagnostic of earthlike substorms. The magnetospheric composition is totally dominated by protons, with only a trace abundance of H(2+) and no evidence for He or heavy ions; the Uranian atmophere is argued to be the principal plasma source. Phase-space densities of medium energy protons show inward radial diffusion and are quantitatively similar to those observed at the earth, Jupiter, and Saturn. These findings and plasma wave data suggest the existence of structures analogous to the earth's plasmasphere and plasmapause.

Cheng, Andrew F.↗

NASA NTRS1992

Interaction of photons in a canopy of finite-dimensional leaves

Neutral particle interaction for photons traveling in media consisting of finite-dimensional scattering centers is investigated. A leaf canopy, a typical example of such media, is idealized as a binary medium consisting of gaps (voids) and regions with phytoelements (turbid phytomedium). The leaf canopy is represented by a combination of all possible open oriented spheres. The extinction coefficient at any phase-space location in a leaf canopy is the product of the extinction coefficient in the turbid phytomedium and the probability of absence gaps at that location. An expression for the differential scattering coefficient is derived using the same approach. The effect of canopy parameters and direction of photon travel on the extinction coefficient is illustrated by numerical examples.

Knyazikhin, Yuri V.↗

NASA NTRS1991

Interaction between photons and leaf canopies

The physics of neutral particle interaction for photons traveling in media consisting of finite-dimensional scattering centers that cross-shade mutually is investigated. A leaf canopy is a typical example of such media. The leaf canopy is idealized as a binary medium consisting of randomly distributed gaps (voids) and regions with phytoelements (turbid phytomedium). In this approach, the leaf canopy is represented by a combination of all possible open oriented spheres. The mathematical approach for characterizing the structure of the host medium is considered. The extinction coefficient at any phase-space location in a leaf canopy is the product of the extinction coefficient in the turbid phytomedium and the probability of absence gaps at that location. Using a similar approach, an expression for the differential scattering coefficient is derived.

Knyazikhin, Yuri V.↗

NASA NTRS1992

Polynomial approximation of Poincare maps for Hamiltonian system

Different methods are proposed and tested for transforming a non-linear differential system, and more particularly a Hamiltonian one, into a map without integrating the whole orbit as in the well-known Poincare return map technique. We construct piecewise polynomial maps by coarse-graining the phase-space surface of section into parallelograms and using either only values of the Poincare maps at the vertices or also the gradient information at the nearest neighbors to define a polynomial approximation within each cell. The numerical experiments are in good agreement with both the real symplectic and Poincare maps.

Froeschle, Claude↗

NASA NTRS1992

Temperature anisotropies in a magnetospheric FTE

We present AMPTE UKS data from a well-studied magnetospheric flux transfer event, showing detailed ion phase-space distributions for each region of this layered event. We show that the perpendicular temperature anisotropy maximizes at the center of the event. This is inconsistent with recent suggestions that FTE signatures may result from the spacecraft moving into and then out of the magnetosheath via the plasma depletion layer. We present an explanation for the temperature anisotropy structure in terms of a reconnection model.

Smith, M. F.↗

NASA NTRS1992

Energetic ion phase space densities in Neptune's magnetosphere

Ion phase densities of Neptune are presently ascertained at the first and second adiabatic invariants of charged-particle motion on the basis of an analysis of Voyager 2 measurements. The profiles thus obtained are interpreted as indicative of generally inward radial diffusion, with an energetic ion source near L = 10. Excellent agreement is obtained between inbound and outbound phase-space density profiles at the values of the invariants; this suggests approximately axisymmetric, quasi-stationary radiation belts. The inward diffusing power carried by energetic ions appears adequate for powering Neptune's aurora, if enough of the ions are lost to the Neptune atmosphere.

Cheng, Andrew F.↗

NASA NTRS1992

Quasi-linear velocity space diffusion of heavy cometary pickup ions on bispherical diffusion characteristics

We consider an ion transport equation describing the source, convection, adiabatic acceleration, and quasi-linear velocity diffusion of cometary pickup ions. The equation is solved numerically along solar wind plasma flow lines for the environment of Comet Halley, to obtain distributions at positions on the Giotto spacecraft trajectory which may be compared with observations. We obtain full two-dimensional (pitch angle and velocity) numerical distributions which show pitch angle scattering about the wave scattering centers at +/- V(A), where V(A) is the Alfven wave speed in the solar wind frame. Peak ion phase-space densities approximately follow the bispherical shell geometry. The energy distributions F(v) agree well with Giotto observations at lower v, but in the high-energy tail there is evidence possibly for the first-order Fermi acceleration mechanism taking place in the Comet Halley foreshock region.

Huddleston, D. E.↗

NASA NTRS1993

The telegraph equation in charged particle transport

We present a new derivation of the telegraph equation which modifies its coefficients. First, an infinite order partial differential equation is obtained for the velocity space solid angle-averaged phase-space distribution of particles which underwent at least a few collisions. It is shown that, in the lowest order asymptotic expansion, this equation simplifies to the well-known diffusion equation. The second-order asymptotic expansion for isotropic small-angle scattering results in a modified telegraph equation with a signal propagation speed of v(5/11) exp 1/2 instead of the usual v/3 exp 1/2. Our derivation of a modified telegraph equation follows from an expansion of the Boltzmann equation in the relevant smallness parameters and not from a truncation of an eigenfunction expansion. This equation is consistent with causality. It is shown that, under steady state conditions in a convecting plasma, the telegraph equation may be regarded as a diffusion equation with a modified transport coefficient, which describes a combination of diffusion and cosmic-ray inertia.

Gombosi, T. I.↗