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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 109 records · Page 6
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NASA NTRS1993

Explicit least squares system parameter identification for exact differential input/output models

The equation error for a class of systems modeled by input/output differential operator equations has the potential to be integrated exactly, given the input/output data on a finite time interval, thereby opening up the possibility of using an explicit least squares estimation technique for system parameter identification. The paper delineates the class of models for which this is possible and shows how the explicit least squares cost function can be obtained in a way that obviates dealing with unknown initial and boundary conditions. The approach is illustrated by two examples: a second order chemical kinetics model and a third order system of Lorenz equations.

Pearson, A. E.↗
NASA NTRS1993

An automatic multigrid method for the solution of sparse linear systems

An automatic version of the multigrid method for the solution of linear systems arising from the discretization of elliptic PDE's is presented. This version is based on the structure of the algebraic system solely, and does not use the original partial differential operator. Numerical experiments show that for the Poisson equation the rate of convergence of our method is equal to that of classical multigrid methods. Moreover, the method is robust in the sense that its high rate of convergence is conserved for other classes of problems: non-symmetric, hyperbolic (even with closed characteristics) and problems on non-uniform grids. No double discretization or special treatment of sub-domains (e.g. boundaries) is needed. When supplemented with a vector extrapolation method, high rates of convergence are achieved also for anisotropic and discontinuous problems and also for indefinite Helmholtz equations. A new double discretization strategy is proposed for finite and spectral element schemes and is found better than known strategies.

Shapira, Yair↗
NASA NTRS1993

Multigrid methods for a semilinear PDE in the theory of pseudoplastic fluids

We show that by certain transformations the boundary layer equations for the class of non-Newtonian fluids named pseudoplastic can be generalized in the form the vector differential operator(u) + p(x)u(exp -lambda) = 0, where x is a member of the set Omega and Omega is a subset of R(exp n), n is greater than or equal to 1 under the classical conditions for steady flow over a semi-infinite flat plate. We provide a survey of the existence, uniqueness, and analyticity of the solutions for this problem. We also establish numerical solutions in one- and two-dimensional regions using multigrid methods.

Henson, Van Emden↗
NASA NTRS1994

Pseudospectral collocation methods for fourth order differential equations

Collocation schemes are presented for solving linear fourth order differential equations in one and two dimensions. The variational formulation of the model fourth order problem is discretized by approximating the integrals by a Gaussian quadrature rule generalized to include the values of the derivative of the integrand at the boundary points. Collocation schemes are derived which are equivalent to this discrete variational problem. An efficient preconditioner based on a low-order finite difference approximation to the same differential operator is presented. The corresponding multidomain problem is also considered and interface conditions are derived. Pseudospectral approximations which are C1 continuous at the interfaces are used in each subdomain to approximate the solution. The approximations are also shown to be C3 continuous at the interfaces asymptotically. A complete analysis of the collocation scheme for the multidomain problem is provided. The extension of the method to the biharmonic equation in two dimensions is discussed and results are presented for a problem defined in a nonrectangular domain.

Malek, Alaeddin↗
NASA NTRS1995

The large discretization step method for time-dependent partial differential equations

A new method for the acceleration of linear and nonlinear time dependent calculations is presented. It is based on the Large Discretization Step (LDS) approximation, defined in this work, which employs an extended system of low accuracy schemes to approximate a high accuracy discrete approximation to a time dependent differential operator. Error bounds on such approximations are derived. These approximations are efficiently implemented in the LDS methods for linear and nonlinear hyperbolic equations, presented here. In these algorithms the high and low accuracy schemes are interpreted as the same discretization of a time dependent operator on fine and coarse grids, respectively. Thus, a system of correction terms and corresponding equations are derived and solved on the coarse grid to yield the fine grid accuracy. These terms are initialized by visiting the fine grid once in many coarse grid time steps. The resulting methods are very general, simple to implement and may be used to accelerate many existing time marching schemes.

Haras, Zigo↗
NASA NTRS1994

Acoustic instability driven by cosmic-ray streaming

We study the linear stability of compressional waves in a medium through which cosmic rays stream at the Alfven speed due to strong coupling with Alfven waves. Acoustic waves can be driven unstable by the cosmic-ray drift, provided that the streaming speed is sufficiently large compared to the thermal sound speed. Two effects can cause instability: (1) the heating of the thermal gas due to the damping of Alfven waves driven unstable by cosmic-ray streaming; and (2) phase shifts in the cosmic-ray pressure perturbation caused by the combination of cosmic-ray streaming and diffusion. The instability does not depend on the magnitude of the background cosmic-ray pressure gradient, and occurs whether or not cosmic-ray diffusion is important relative to streaming. When the cosmic-ray pressure is small compared to the gas pressure, or cosmic-ray diffusion is strong, the instability manifests itself as a weak overstability of slow magnetosonic waves. Larger cosmic-ray pressure gives rise to new hybrid modes, which can be strongly unstable in the limits of both weak and strong cosmic-ray diffusion and in the presence of thermal conduction. Parts of our analysis parallel earlier work by McKenzie & Webb (which were brought to our attention after this paper was accepted for publication), but our treatment of diffusive effects, thermal conduction, and nonlinearities represent significant extensions. Although the linear growth rate of instability is independent of the background cosmic-ray pressure gradient, the onset of nonlinear eff ects does depend on absolute value of DEL (vector differential operator) P(sub c). At the onset of nonlinearity the fractional amplitude of cosmic-ray pressure perturbations is delta P(sub C)/P(sub C) approximately (kL) (exp -1) much less than 1, where k is the wavenumber and L is the pressure scale height of the unperturbed cosmic rays. We speculate that the instability may lead to a mode of cosmic-ray transport in which plateaus of uniform cosmic-ray pressure are separated by either laminar or turbulent jumps in which the thermal gas is subject to intense heating.

Begelman, Mitchell C.↗
NASA NTRS1994

Three-dimensional currents of electrodynamic tethers obtained from laboratory models

Magnetic probe measurements in three dimensions (greater than 15,000 positions) and time in a large laboratory plasma (n(sub e) greater than or equal to 10(exp 11)/cc, kTe greater than or equal to 1eV, B(sub 0) = 20 G, 1 m diam. x 2.5 m length) reveal the plasma currents J = del(vector differential operator) x B/mu(sub 0) excited by a pulsed (delta-t = 100 ns), stationary, tethered pair of electrodes (approximately equals 1 cm diam., 20 cm spacing perpendicular to B(sub 0)). The plasma currents for a moving, dc-current carrying electrodynamic tether are obtained by a superposition of delayed pulses emitted at successively displaced tether positions. The transient plasma currents are carried by low-frequency whistlers instead of Alfven waves and form a 3D wing structure but no long phantom loop due to cross-field Hall current shunting.

Urrutia, J. M.↗
NASA NTRS1994

Euler potentials of current-free fields expressed in spherical harmonics

Given a magnetic field B = -del(vector differential operator)(sub gamma) with gamma expanded in spherical harmonics, it is shown that analytic Euler potentials may be derived for B if gamma is asymmetrical but contains only the contribution of a single index n. This work generalizes a result for sectorial harmonics with n = m, derived by Willis and Gardiner (1988).

Stern, David P.↗
NASA NTRS1995

The analysis of control trajectories using symbolic and database computing

This final report comprises the formal semi-annual status reports for this grant for the periods June 30-December 31, 1993, January 1-June 30, 1994, and June 1-December 31, 1994. The research supported by this grant is broadly concerned with the symbolic computation, mixed numeric-symbolic computation, and database computation of trajectories of dynamical systems, especially control systems. A review of work during the report period covers: trajectories and approximating series, the Cayley algebra of trees, actions of differential operators, geometrically stable integration algorithms, hybrid systems, trajectory stores, PTool, and other activities. A list of publications written during the report period is attached.

Grossman, Robert↗
NASA NTRS1997

A Nonlinear Programming Perspective on Sensitivity Calculations for Systems Governed by State Equations

This paper discusses the calculation of sensitivities. or derivatives, for optimization problems involving systems governed by differential equations and other state relations. The subject is examined from the point of view of nonlinear programming, beginning with the analytical structure of the first and second derivatives associated with such problems and the relation of these derivatives to implicit differentiation and equality constrained optimization. We also outline an error analysis of the analytical formulae and compare the results with similar results for finite-difference estimates of derivatives. We then attend to an investigation of the nature of the adjoint method and the adjoint equations and their relation to directions of steepest descent. We illustrate the points discussed with an optimization problem in which the variables are the coefficients in a differential operator.

Lewis, Robert Michael↗
NASA NTRS1999

Large Field Visualization with Demand-Driven Calculation

We present a system designed for the interactive definition and visualization of fields derived from large data sets: the Demand-Driven Visualizer (DDV). The system allows the user to write arbitrary expressions to define new fields, and then apply a variety of visualization techniques to the result. Expressions can include differential operators and numerous other built-in functions, ail of which are evaluated at specific field locations completely on demand. The payoff of following a demand-driven design philosophy throughout becomes particularly evident when working with large time-series data, where the costs of eager evaluation alternatives can be prohibitive.

Moran, Patrick J.↗
NASA NTRS2000

Discriminator Stabilized Superconductor/Ferroelectric Thin Film Local Oscillator

A tunable local oscillator with a tunable circuit that includes a resonator and a transistor as an active element for oscillation. Tuning of the circuit is achieved with an externally applied dc bias across coupled lines on the resonator. Preferably the resonator is a high temperature superconductor microstrip ring resonator with integral coupled lines formed over a thin film ferroelectric material. A directional coupler samples the output of the oscillator which is fed into a diplexer for determining whether the oscillator is performing at a desired frequency. The high-pass and lowpass outputs of the diplexer are connected to diodes respectively for inputting the sampled signals into a differential operational amplifier. The amplifier compares the sampled signals and emits an output signal if there is a difference between the resonant and crossover frequencies. Based on the sampled signal, a bias supplied to the ring resonator is either increased or decreased for raising or lowering the resonant frequency by decreasing or increasing, respectively, the dielectric constant of the ferroelectric.

Romanofsky, Robert R.↗
NASA NTRS1988

Charged-particle transport in one dimension

A numerical solution to high-energy charged-particle transport is found by evaluation of the integral equations obtained by inverting the Boltzmann differential operator. An algorithm has been written for either continuous or discrete spectra at the boundary, which allows efficient and accurate evaluation of this rather complicated problem. Present results are compared with analytic solutions based on the perturbation theory.

NASA Discipline Radiation Health↗
NASA NTRS1955

Free-Spinning Characteristics of a 1/24-Scale Model of the Grumman F11F-1 Airplane, TED No. NACA AD 395

An investigation is being conducted in the Langley 20-foot free-spinning tunnel on a 1/24-scale model of the Grumman F11F-1 airplane to determine spin and recovery characteristics and the minimum-size parachute required to satisfactorily terminate the spin in an emergency. Results obtained to date are presented herein. Test results indicate that it may be difficult to obtain an erect or inverted spin on the airplane, but, if a spin is obtained, the spin will be very oscillatory and recovery from the developed erect spin by rudder reversal may not be possible. The lateral controls will have no appreciable effect on recoveries from erect.spins. Recovery from the inverted spin by merely neutralizing the rudder will be satisfactory. After recoveries by rudder reversal and after recoveries from spins without control movement (no spins), the model oftentimes rolled very rapidly about the X-axis. Based on limited preliminary tests made in this investigation to make the model recover satisfactorily, it appears that canards near the nose of the airplane or differentially operated horizontal tails may be utilized to provide rapid recoveries. The parachute test results indicate that an 11-foot-diameter (laid-out-flat) parachute with a drag coefficient of 0.650 (based on the laid- out-flat diameter) and with a towline length equal to the wing span is the minimum-size parachute required to satisfactorily terminate an erect or inverted spin in an emergency.

Bowman, James S., Jr.↗
NASA NTRS2013

An Extension of the Time-Spectral Method to Overset Solvers

Relative motion in the Cartesian or overset framework causes certain spatial nodes to move in and out of the physical domain as they are dynamically blanked by moving solid bodies. This poses a problem for the conventional Time-Spectral approach, which expands the solution at every spatial node into a Fourier series spanning the period of motion. The proposed extension to the Time-Spectral method treats unblanked nodes in the conventional manner but expands the solution at dynamically blanked nodes in a basis of barycentric rational polynomials spanning partitions of contiguously defined temporal intervals. Rational polynomials avoid Runge's phenomenon on the equidistant time samples of these sub-periodic intervals. Fourier- and rational polynomial-based differentiation operators are used in tandem to provide a consistent hybrid Time-Spectral overset scheme capable of handling relative motion. The hybrid scheme is tested with a linear model problem and implemented within NASA's OVERFLOW Reynolds-averaged Navier- Stokes (RANS) solver. The hybrid Time-Spectral solver is then applied to inviscid and turbulent RANS cases of plunging and pitching airfoils and compared to time-accurate and experimental data. A limiter was applied in the turbulent case to avoid undershoots in the undamped turbulent eddy viscosity while maintaining accuracy. The hybrid scheme matches the performance of the conventional Time-Spectral method and converges to the time-accurate results with increased temporal resolution.

Leffell, Joshua Isaac↗
NASA NTRS2021

Extended Stroke and Miniaturized Reverse-Operation DTE Thermal Switches

This paper describes two advanced thermal switches under development that are offshoots of the recently flight-qualified 2500:1 reverse-operation differential thermal expansion (DTE) thermal switch (ROD-TSW). The first is the extended stroke ROD-TSW (ES-ROD-TSW) while the second is the miniaturized ROD-TSW (mini-ROD-TSW). Each employs multiple diametrically nested DTE stages in contrast to the single-stage ROD-TSW. The ES-ROD-TSW employs two stages and a negative CTE material known as Allvar and its main purpose is to extend its stroke for use in non-vacuum planetary environments. The mini-ROD-TSW employs four stages to miniaturize its size for use in compact lunar instruments and rovers. The ES-ROD-TSW was TVAC tested at JPL and its ON/OFF ratio is 13000:1 based on a measured ON conductance of 6.89 W/K and a calculated OFF conductance of 0.00053 W/K. The mini-ROD-TSW is targeted to have an ON conductance of 1.5 W/K and an OFF conductance of 0.0015 W/K, both verified by analysis. Test verification of the mini-ROD-TSW remains to be carried out. The paper will provide design/performance details of each device.

Farmer, Jeffery T.↗