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At least 19 records

Multivariable Hermite polynomials and phase-space dynamics

The phase-space approach to classical and quantum systems demands for advanced analytical tools. Such an approach characterizes the evolution of a physical system through a set of variables, reducing to the canonically conjugate variables in the classical limit. It often happens that phase-space distributions can be written in terms of quadratic forms involving the above quoted variables. A significant analytical tool to treat these problems may come from the generalized many-variables Hermite polynomials, defined on quadratic forms in R(exp n). They form an orthonormal system in many dimensions and seem the natural tool to treat the harmonic oscillator dynamics in phase-space. In this contribution we discuss the properties of these polynomials and present some applications to physical problems.

Dattoli, G.

A simple nonlinear model for the return to isotropy in turbulence

A quadratic nonlinear generalization of the linear Rotta model for the slow pressure-strain correlation of turbulence is developed. The model is shown to satisfy realizability and to give rise to no stable non-trivial equilibrium solutions for the anisotropy tensor in the case of vanishing mean velocity gradients. The absence of stable non-trivial equilibrium solutions is a necessary condition to ensure that the model predicts a return to isotropy for all relaxational turbulent flows. Both the phase space dynamics and the temporal behavior of the model are examined and compared against experimental data for the return to isotropy problem. It is demonstrated that the quadratic model successfully captures the experimental trends which clearly exhibit nonlinear behavior. Direct comparisons are also made with the predictions of the Rotta model and the Lumley model.

Sarkar, Sutanu

A simple nonlinear model for the return to isotropy in turbulence

A quadratic nonlinear generalization of the linear Rotta model for the slow pressure-strain correlation of turbulence is developed. The model is shown to satisfy realizability and to give rise to no stable nontrivial equilibrium solutions for the anisotropy tensor in the case of vanishing mean velocity gradients. The absence of stable nontrivial equilibrium solutions is a necessary condition to ensure that the model predicts a return to isotropy for all relaxational turbulent flows. Both the phase space dynamics and the temporal behavior of the model are examined and compared against experimental data for the return to isotropy problem. It is demonstrated that the quadratic model successfully captures the experimental trends which clearly exhibit nonlinear behavior. Direct comparisons are also made with the predictions of the Rotta model and the Lumley model.

Sarkar, Sutanu

Proposed dynamic phase difference method for the detection of tile debonding from the space shuttle orbiter

A noncontracting, semi-global, dynamic technique was developed for detecting loose tiles on the space shuttle orbiter. In laboratory tests on a single tile, the substrate was excited into lateral motion at a constant frequency and amplitude of 2g. The phase relationship between the motions of tile and substrate was examined by noncontacting probes in order to relate the dynamic properties of the tile SIP system to its fatigue history; by a visual technique using a stroboscope and split screen video monitor for practical application in the field. When the substrate is excited at an appropriate frequency (between 30 and 60 Hz), a good tile moves in phase and a loose tile out of phase with the substrate. The out of phase motion is readily observable in the form of a "beat" between the tile and a reference marker on the substrate.

Zuckerwar, A. J.

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.

Cometary orbital evolution in the outer planetary region

Numerical integrations of fictitious objects are carried out in order to elucidate the dynamical behavior of potential short-period comets when they move in orbits at distances from the Sun comparable to those of Uranus and Neptune. As in the case of observed short-period comets, close encounters with the planets play a major role for the orbital evolution, and this is especially true for encounters with initial orbits nearly tangent to that of the planet. A comparison with integrations in which the planetary masses are larger by a factor 10 shows that, in the latter case, the orbital evolution is greatly accelerated, but the dynamical paths in phase space followed by the comets are altered.

Manara, Allesandro

Nonlinear dynamics of the magnetosphere and space weather

The solar wind-magnetosphere system exhibits coherence on the global scale and such behavior can arise from nonlinearity on the dynamics. The observational time series data were used together with phase space reconstruction techniques to analyze the magnetospheric dynamics. Analysis of the solar wind, auroral electrojet and Dst indices showed low dimensionality of the dynamics and accurate prediction can be made with an input/output model. The predictability of the magnetosphere in spite of the apparent complexity arises from its dynamical synchronism with the solar wind. The electrodynamic coupling between different regions of the magnetosphere yields its coherent, low dimensional behavior. The data from multiple satellites and ground stations can be used to develop a spatio-temporal model that identifies the coupling between different regions. These nonlinear dynamical models provide space weather forecasting capabilities.

Sharma, A. Surjalal

Space Shuttle Atmospheric ascent flight dynamics

The atmospheric ascent flight phase of the mated composite booster and orbiter is discussed. The composite recoverable space shuttle booster and orbiter exhibits unique flight control characteristics. This uniqueness results from large lifting surfaces and aerodynamic and structural assymetrics. An effective load relief technique reduces aerodynamic loads on both the booster and the orbiter. Reducing aerodynamic loads permits decreasing the structural weight of the lifting and stabilizing surfaces. An orbiter payload penalty is caused by trajectory deviations resulting from load relief. However, the net effect of an effective load relief technique is an increase in payload capability. Atmospheric launch dynamics investigations have been carried out for different configuration types, which include expendable, straight wing, delta wing, and ballistic recoverable boosters.

Patha, J. T.

On trajectory generation for flexible space crane: Inverse dynamics analysis by LATDYN

For future in-space construction facility, one or more space cranes capable of manipulating and positioning large and massive spacecraft components will be needed. Inverse dynamics was extensively studied as a basis for trajectory generation and control of robot manipulators. The focus here is on trajectory generation in the gross-motion phase of space crane operation. Inverse dynamics of the flexible crane body is much more complex and intricate as compared with rigid robot link. To model and solve the space crane's inverse dynamics problem, LATDYN program which employs a three-dimensional finite element formulation for the multibody truss-type structures will be used. The formulation is oriented toward a joint dominated structure which is suitable for the proposed space crane concept. To track a planned trajectory, procedures will be developed to obtain the actuation profile and dynamics envelope which are pertinent to the design and performance requirements of the space crane concept.

Chen, G.-S.

Why HOC+ is detectable in interstellar clouds: the rate of the reaction between HOC+ and H2

The recent confirmation by Ziurys and Apponi of the detection of HOC+ toward Sgr B2 (OH), and their identification of the ion in Orion-KL and several other sources show that HOC+ is far more abundant than predicted by previous ion-molecule models. In these models, the reaction HOC(+) + H2 --> HCO(+) + H2 is assumed to rapidly destroy HOC+, based on the results of a prior calculation. We have recalculated the rate of this reaction as a function of temperature using a new ab initio potential surface and a phase space approach to the dynamics which includes tunneling. The newly calculated rate is small (< or = 1 x 10(-10) cm3 s-1) at temperatures under 100 K.

Non-NASA Center

Phase-space-Lagrangian action principle and the generalized K-X theorem

The covariant coupled equations for plasma dynamics and the Maxwell field are expressed as a phase-space-Lagrangian action principle. The linear interaction is transformed to the bilinear beat Hamiltonian by a gauge-invariant Lagrangian Lie transform. The result yields the generalized linear susceptibility directly.

Kaufman, Allan N.

Gas Phase Effects on Slosh Dynamics

Gas phase effects on slosh dynamics were quantified using computational fluid dynamics (CFD) simulation for a range of propellant and ullage gas combinations. Historical slosh modeling using potential flow solutions typically neglects gas phase effects. Regardless, the results have been shown to compare well with slosh ground tests typically performed with water and air at standard temperature and pressure. CFD analysis reveals that as the liquid-to-gas density ratio decreases, slosh dynamics change due to the relative increase in gas inertia and thus influence on liquid motion. The result is a profound impact on slosh dynamics over certain parameter spaces particularly for liquid hydrogen. Gas phase effects on slosh dynamics should be considered in slosh models especially for liquid hydrogen propellant tanks.

Jacob M Brodnick