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Results for “phase space methods”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2022

Numerical phase space optics methods and applications to the analysis of fiber coupling efficiency in atmospheric turbulence

A fundamental requirement of free-space optical communication is the ability to efficiently couple atmospherically distorted light from a telescope to a detector. A numerical method is presented for modeling fiber-based receiver performance in atmospheric conditions based on phase space optics which does not rely on Monte Carlo methods. This method is employed to analyze the waveguide insertion loss and optimal coupling geometry in atmospheric conditions for step-index fibers, graded-index fibers, and photonic lanterns with and without tilt compensation and central obscurations in the telescope.

free-space optical communication↗
NASA NTRSDate not supplied

Numerical phase space optics methods and applications to the analysis of fiber coupling efficiency in atmospheric turbulence

A fundamental requirement of free-space optical communication is the ability to efficiently couple atmospherically distorted light from a telescope to a detector. A numerical method is presented for modeling fiber-based receiver performance in atmospheric conditions based on phase space optics which does not rely on Monte Carlo methods. This method is employed to analyze the waveguide insertion loss and optimal coupling geometry in atmospheric conditions for step-index fibers, graded-index fibers, and photonic lanterns with and without tilt compensation and central obscurations in the telescope.

free-space optical communication↗
NASA NTRS1972

The application of the phase space time evolution method to electron shielding

A computer technique for treating the motion of charged and neutral particles and called the phase space time evolution method was developed. This technique employs the computer's bookkeeping capacity to keep track of the time development of a phase space distribution of particles. This method was applied to a study of the penetration of electrons. A 1 MeV beam of electrons normally incident on a semi-infinite slab of aluminum was used. Results of the calculation were compared with Monte Carlo calculations and experimental results. Time-dependent PSTE electron penetration results for the same problem are presented.

Cordaro, M. C.↗
NASA NTRS1995

A comparison of two algorithms for simulating collisionless systems

Two completely different simulation algorithms are compared by applying them to the same stellar dynamical problems: one is a self-consistent field (SCF) method for solving Poisson's equation and the other is a phase-space method for integrating the collisionless Boltzmann equation. We consider simulations of spherical stellar systems which are initially far from equilibrium and relax to their final states by gravitational collapse. The initial conditions consist of either uniform-density spheres or nonequilibrium models having Plummer density profiles, in which velocity dispersions are assigned according to given virial ratios. If a few tens of radial expansion terms with hundreds of thousands of particles are used in the SCF code, excellent agreement is found between the results it generates and those obtained with the phase-space solver, provided that a sufficiently large number of grid cells are employed with the latter. These findings imply that for simulating collisionless systmes over many dynamical times, the SCF approach based on sampling phase space is competitive with the approach treating phase space as a continuous fluid. The results of our tests make it possible to estimate the number of particles and basis functions required in situations like those modeled. Limitations of the SCF method and the choice of an optimal set of basis functions are also discussed.

Hozumi, Shunsuke↗
NASA NTRS1991

Convection of ion cyclotron waves to ion-heating regions

Results are presented on calculations of the convection, to lower altitudes, of low-frequency ion cyclotron waves generated in the central plasma sheet. In the calculations, ion cyclotron waves generated in the equatorial plane by a proton temperature anisotropy are considered, and the computed growth rates are used to create a model wave distribution. Spectral densities are then mapped along the magnetic field lines, using phase space methods of Ronnmark and Larsson (1988). It was found that, even in the absence of growth associated with a plasma instability, the electric fields of ion cyclotron emissions from the equatorial region will increase substantially as the waves propagate to higher latitudes. It is shown that ion cyclotron waves propagating down the field lines may contribute to the waves observed together with ion conics.

Ronnmark, Kjell↗
NASA NTRS1979

The classical solution of a definite integral occurring in the satellite theory in the extended phase space

A method of integrating the functions defined by Scheifele and Graf (1974), arising in the elimination of time from the arguments of satellite theory using Delaunay elements in the extended phase space, is proposed. By repeated applications of an identity of Stiefel and Scheifele (1971), neglecting certain terms, and assuming a solution in the form of a product of Bessel functions, a solution expanded in the eccentricity is obtained.

Bond, V. R.↗
NASA NTRS1983

Computations of two-phase supersonic nozzle flows by a space-marching method

A practical method for efficiently analyzing the two-phase flow field in the supersonic region of an axisymmetric rocket nozzle is presented. The governing hyperbolic equations for the gas- and particle-phases are simultaneously integrated downstream using a space-marching procedure. Both one- and two-phase flow computations are performed for the JPL axisymmetric nozzle. The results show the nonequilibrium effects which are due to the existence of particles in the flow. The comparisons with the experimental data and other numerical solutions are made to examine the accuracy of the present method.

Fujii, K.↗
NASA NTRS1973

Certain characteristics and capture regions of nonlinear vibrating systems

Free vibrations of a system and vibrations which are multiples of them in frequency are discussed. The corresponding periodic forced vibrations of the type n/m (n is the number of periods of disturbance between periods of movement and m is the number of periods of movement in one period of disturbance), generated by a harmonic or close to harmonic disturbance, are propagated close to the corresponding curves of the free vibrations and their frequency multiples. It has been proposed that investigation of transitional modes of motion and capture regions be carried out by precise methods in phase space, with the least number of coordinates. Thus, for example, for nonautonomous second order equations (for example, the Duffing equations), in place of three variables (coordinates, velocity, phases), it is proposed to use two: velocity during transition of the coordinate through zero and phase.

Ragulskene, V. L.↗
NASA NTRS1989

Simulation of collisional transport processes and the stability of planetary rings

The utility of the phase-space fluid method for the study of planetary ring dynamics is presently demonstrated through the numerical solution of a model kinetic equation for a flattened Keplerian disk. Attention is given to ringlets composed of single-sized particles, as well as to ringlets composed of two different-sized particles; in the latter case, the ringlets evolve in such a way that the lighter particles are confined by the heavier ones. The results obtained indicate that some natural process may sharpen the optical depth profile of edges even without an external forcing mechanism, and that intermediate optical depths are dynamically preferred in some cases.

Brophy, Thomas G.↗
NASA NTRS1990

A phase-space fluid simulation of a two-component narrow planetary ring - Particle size segregation, edge formation, and spreading rates

The Krook kinetic equation for identical planetary ring particles is presently generalized for the case of two-component systems, and the equations are numerically solved on the basis of Brophy and Esposito's (1989) phase-space CFD method. Attention is given to the simulation results obtained for a two-component narrow ring, in which the large particles are eight times as massive as the small particles. This ring's unconstrained edge dynamics are resolved by the simulation, and are found to exhibit a sharpening that would not have been expected in single-component rings.

Brophy, Thomas G.↗
NASA NTRS2002

Parametric Identification of Nonlinear Dynamical Systems

In this project, we looked at the application of harmonic balancing as a tool for identifying parameters (HBID) in a nonlinear dynamical systems with chaotic responses. The main idea is to balance the harmonics of periodic orbits extracted from measurements of each coordinate during a chaotic response. The periodic orbits are taken to be approximate solutions to the differential equations that model the system, the form of the differential equations being known, but with unknown parameters to be identified. Below we summarize the main points addressed in this work. The details of the work are attached as drafts of papers, and a thesis, in the appendix. Our study involved the following three parts: (1) Application of the harmonic balance to a simulation case in which the differential equation model has known form for its nonlinear terms, in contrast to a differential equation model which has either power series or interpolating functions to represent the nonlinear terms. We chose a pendulum, which has sinusoidal nonlinearities; (2) Application of the harmonic balance to an experimental system with known nonlinear forms. We chose a double pendulum, for which chaotic response were easily generated. Thus we confronted a two-degree-of-freedom system, which brought forth challenging issues; (3) A study of alternative reconstruction methods. The reconstruction of the phase space is necessary for the extraction of periodic orbits from the chaotic responses, which is needed in this work. Also, characterization of a nonlinear system is done in the reconstructed phase space. Such characterizations are needed to compare models with experiments. Finally, some nonlinear prediction methods can be applied in the reconstructed phase space. We developed two reconstruction methods that may be considered if the common method (method of delays) is not applicable.

Feeny, Brian↗
NASA NTRS2003

The Statistical Mechanics of Ideal MHD Turbulence

Turbulence is a universal, nonlinear phenomenon found in all energetic fluid and plasma motion. In particular. understanding magneto hydrodynamic (MHD) turbulence and incorporating its effects in the computation and prediction of the flow of ionized gases in space, for example, are great challenges that must be met if such computations and predictions are to be meaningful. Although a general solution to the "problem of turbulence" does not exist in closed form, numerical integrations allow us to explore the phase space of solutions for both ideal and dissipative flows. For homogeneous, incompressible turbulence, Fourier methods are appropriate, and phase space is defined by the Fourier coefficients of the physical fields. In the case of ideal MHD flows, a fairly robust statistical mechanics has been developed, in which the symmetry and ergodic properties of phase space is understood. A discussion of these properties will illuminate our principal discovery: Coherent structure and randomness co-exist in ideal MHD turbulence. For dissipative flows, as opposed to ideal flows, progress beyond the dimensional analysis of Kolmogorov has been difficult. Here, some possible future directions that draw on the ideal results will also be discussed. Our conclusion will be that while ideal turbulence is now well understood, real turbulence still presents great challenges.

Shebalin, John V.↗
NASA NTRS1997

Nonlinear Behavior of a Typical Airfoil Section with Control Surface Freeplay: A Numerical and Experimental Study

A three degree-of-freedom aeroelastic typical section with control surface freeplay is modeled theoretically as a system of piecewise linear state-space models. The system response is determined by time marching of the governing equations using a standard Runge-Kutta algorithm in conjunction with Henon's method for integrating a system of equations to a prescribed surface of phase space section. Henon's method is used to locate the "switching points" accurately and efficiently as the system moves from one linear region into another. An experimental model which closely approximates the three degree-of-freedom, typical section in two-dimensional, incompressible flow has been created to validate the theoretical model. Consideration is given to modeling realistically the structural damping present in the experimental system. The effect of the freeplay on the system response is examined numerically and experimentally. The development of the state-space model offers a low-order, computationally efficient means of modeling fully the freeplay nonlinearity and may offer advantages in future research which will investigate the effects of freeplay on the control of flutter in the typical section.

Conner, M. D.↗
NASA NTRS1981

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.↗
NASA NTRS1984

On the use of parametric differentiation to predict weak shock waves

The method of parametric differentiation is shown to be an effective means to transform both the time-linearized and the fully nonlinear transonic small disturbance potential flow equations to a linear system of equations. The globally linearized equations are then solved in phase space by finite difference methods and integral equation methods. The predicted birth, growth, and motion of weak shock waves in two-dimensional transonic flows are compared with existing theory and experiment.

Harris, W. L.↗