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Results for “approximation theory”

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 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
NASA NTRS2016

Passive Rocket Diffuser Theory: A Re-Examination of Minimum Second Throat Size

Second-throat diffusers serve to isolate rocket engines from the effects of ambient back pressure during testing without using active control systems. Among the most critical design parameters is the relative area of the diffuser throat to that of the nozzle throat. A smaller second throat is generally desirable because it decreases the stagnation-to-ambient pressure ratio the diffuser requires for nominal operation. There is a limit, however. Below a certain size, the second throat can cause pressure buildup within the diffuser and prevent it from reaching the start condition that protects the nozzle from side-load damage. This paper presents a method for improved estimation of the minimum second throat area which enables diffuser start. The new 3-zone model uses traditional quasi-one-dimensional compressible flow theory to approximate the structure of two distinct diffuser flow fields observed in Computational Fluid Dynamics (CFD) simulations and combines them to provide a less-conservative estimate of the second throat size limit. It is unique among second throat sizing methods in that it accounts for all major conical nozzle and second throat diffuser design parameters within its limits of application. The performance of the 3-zone method is compared to the historical normal shock and force balance methods, and verified against a large number of CFD simulations at specific heat ratios of 1.4 and 1.25. Validation is left as future work, and the model is currently intended to function only as a first-order design tool.

Jones, Daniel R.↗
NASA NTRS1986

Approximation methods in gravitational-radiation theory

The observation of gravitational-radiation damping in the binary pulsar PSR 1913 + 16 and the ongoing experimental search for gravitational waves of extraterrestrial origin have made the theory of gravitational radiation an active branch of classical general relativity. In calculations of gravitational radiation, approximation methods play a crucial role. Recent developments are summarized in two areas in which approximations are important: (a) the quadrupole approxiamtion, which determines the energy flux and the radiation reaction forces in weak-field, slow-motion, source-within-the-near-zone systems such as the binary pulsar; and (b) the normal modes of oscillation of black holes, where the Wentzel-Kramers-Brillouin approximation gives accurate estimates of the complex frequencies of the modes.

Will, C. M.↗
NASA NTRS1972

On the first-excursion probability in stationary narrow-band random vibration. II.

The first-excursion probability of a stationary narrow-band Gaussian process with mean zero has been studied. Within the framework of point process approach, series approximations derived from the theory of random points and approximations based on the maximum entropy principle have been developed. With the aid of numerical examples, merits of the approximations proposed previously as well as of those developed in this paper have been compared. The results indicate that the maximum entropy principle has not produced satisfactory approximations but the approximation based on nonapproaching random points is found to be the best among all the approximations proposed herein. A conclusion drawn from the present and the previous studies is that the point process approach produces a number of useful approximations for the first-excursion probability, particularly those based on the concepts of the Markov process, the clump-size, and the nonapproaching random points.

Yang, J.-N.↗
NASA NTRS1982

Relativistic perturbations on the motion and tracking of the LAGEOS satellite

The modifications to Geodyn to substitute the Einstein gravitational theory for Newtonian gravitation are described. This results in modifications to both the satellite equations of motion and to the modeling of satellite tracking measurements. Since the Newtonian theory is a very close approximation to the Einstein theory (or general theory of relativity), observable deviations from Newtonian theory are small, and the applicable equations of motion or observation equations can be formulated so that they differ only by small terms which are denoted as relativistic perturbations. In the implementation of the Einstein theory in an orbital data reduction program, station coordinates and satellite coordinates which resemble the normal Cartesian coordinates are considered.

Martin, C. F.↗
NASA NTRS1987

Approximation of discrete-time LQG compensators for distributed systems with boundary input and unbounded measurement

The approximation of optimal discrete-time linear quadratic Gaussian (LQG) compensators for distributed parameter control systems with boundary input and unbounded measurement is considered. The approach applies to a wide range of problems that can be formulated in a state space on which both the discrete-time input and output operators are continuous. Approximating compensators are obtained via application of the LQG theory and associated approximation results for infinite dimensional discrete-time control systems with bounded input and output. Numerical results for spline and modal based approximation schemes used to compute optimal compensators for a one dimensional heat equation with either Neumann or Dirichlet boundary control and pointwise measurement of temperature are presented and discussed.

Gibson, J. S.↗
NASA NTRS1988

Approximation of discrete-time LQG compensators for distributed systems with boundary input and unbounded measurement

The approximation of optimal discrete-time linear quadratic Gaussian (LQG) compensators for distributed parameter control systems with boundary input and unbounded measurement is considered. The approach applies to a wide range of problems that can be formulated in a state space on which both the discrete-time input and output operators are continuous. Approximating compensators are obtained via application of the LQG theory and associated approximation results for infinite dimensional discrete-time control systems with bounded input and output. Numerical results for spline and modal based approximation schemes used to compute optimal compensators for a one-dimensional heat equation with either Neumann or Dirichlet boundary control and pointwise measurement of temperature are presented and discussed.

Gibson, J. S.↗
NASA NTRS1988

Modeling and control of flexible structures

This monograph presents integrated modeling and controller design methods for flexible structures. The controllers, or compensators, developed are optimal in the linear-quadratic-Gaussian sense. The performance objectives, sensor and actuator locations and external disturbances influence both the construction of the model and the design of the finite dimensional compensator. The modeling and controller design procedures are carried out in parallel to ensure compatibility of these two aspects of the design problem. Model reduction techniques are introduced to keep both the model order and the controller order as small as possible. A linear distributed, or infinite dimensional, model is the theoretical basis for most of the text, but finite dimensional models arising from both lumped-mass and finite element approximations also play an important role. A central purpose of the approach here is to approximate an optimal infinite dimensional controller with an implementable finite dimensional compensator. Both convergence theory and numerical approximation methods are given. Simple examples are used to illustrate the theory.

Gibson, J. S.↗
NASA NTRS1975

Development of a stratospheric and mesospheric microwave temperature sounder experiment

A passive microwave spectrometer system for measuring global atmospheric temperature profiles from 0-75 km altitude was developed and analyzed. The system utilizes 12 channels near the 5 mm wavelength oxygen absorption band and is designed to provide global coverage by scanning perpendicular to the orbital track of a polar orbiting satellite. A significant improvement in the accuracy of theoretical atmospheric microwave transmittance functions was achieved through the development of a first-order approximation to overlapping line theory for the oxygen molecule. This approximation is particularly important in the troposphere and lower stratosphere where pressure-broadening blends nearby lines. Ground-based and aircraft observations of several resonances of stratospheric oxygen generally support the theory. The 23, 25, 29, and 31 atmospheric oxygen lines were measured and the frequencies of several such oxygen lines were measured with improved precision. The polarization and Zeeman splitting of the atmospheric 27 line was also observed.

Staelin, D. H.↗
NASA NTRS1984

On the detection of underwater bottom topography by imaging radars

A theoretical model which explains basic properties of radar imaging of underwater bottom topography in tidal channels is presented. The surface roughness modulation is described by weak hydrodynamic interaction theory in the relaxation time approximation. In contrast to previous theories on short wave modulation by long ocean waves, a different approximation is used to describe short wave modulation by tidal flow over underwater bottom topography. The modulation depth is proportional to the relaxation time of the Bragg waves. The large modulation of radar reflectivity observed in SEASAT-SAR imagery of sand banks in the Southern Bight of the North Sea are explained by assuming that the relaxation time of 34 cm Bragg waves is of the order of 30-40 seconds.

Alpers, W.↗
NASA NTRS1985

The determination of physical and dynamical parameters of Pluto/Charon and binary asteroids by least-square formation of a matched filter for a time series of images. I - The operational theory

A theory is derived for the determination of the masses, radii, and orbital elements of the Pluto/Charon, or similar, system based on the prediction of an image distribution over space and time and its comparison with observation. The comparison may be ultimately through the theory of least squares or the application of a matched filter to the observations as a three-dimensional signal stream at an initial or intermediate state. The theory is an approximation correct to fifth order in the diameters of celestial bodies. The theory of astronomical seeing that is used is based on Kolmogorov turbulence in the long-exposure limit. The images must be photometric. Linear tracking errors that can be removed are preferable to either automatic or manual guiding, in the collection of candidate observations.

Wildey, R. L.↗
NASA NTRS1992

Theory of magnetohydrodynamic waves - The WKB approximation revisited

The present paper revisits the derivation of the WKB approximation for small-amplitude magnetohydrodynamic waves, allowing for possible spatial variation of the background entropy. The equation of variation of wave amplitude is rederived; it is a bilinear equation which, it turns out, can be recast in the action conservation form. It is shown that this action conservation equation is in fact equivalent to the action conservation law obtained from Lagrangian treatments.

Barnes, Aaron↗
DOE OSTI2024

A new “gold standard”: Perturbative triples corrections in unitary coupled cluster theory and prospects for quantum computing

A major difficulty in quantum simulation is the adequate treatment of a large collection of entangled particles, synonymous with electron correlation in electronic structure theory, with coupled cluster (CC) theory being the leading framework for dealing with this problem. Augmenting computationally affordable low-rank approximations in CC theory with a perturbative account of higher-rank excitations is a tractable and effective way of accounting for the missing electron correlation in those approximations. This is perhaps best exemplified by the “gold standard” CCSD(T) method, which bolsters the baseline CCSD with the effects of triple excitations using considerations from many-body perturbation theory (MBPT). Despite this established success, such a synergy between MBPT and the unitary analog of CC theory (UCC) has not been explored. In this work, we propose a similar approach wherein converged UCCSD amplitudes are leveraged to evaluate energy corrections associated with triple excitations, leading to the UCCSD[T] method. In terms of quantum computing, this correction represents an entirely classical post-processing step that improves the energy estimate by accounting for triple excitation effects without necessitating new quantum algorithm developments or increasing demand for quantum resources. The rationale behind this choice is shown to be rigorous by studying the properties of finite-order UCC energy functionals, and our efforts do not support the addition of the fifth-order contributions as in the (T) correction. We assess the performance of these approaches on a collection of small molecules and demonstrate the benefits of harnessing the inherent synergy between MBPT and UCC theories.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1989

The role of repair in the survival of mammalian cells from heavy ion irradiation - Approximation to the ideal case of target theory

Experiments are discussed in which the cell-cycle dependency of the repair deficiency of the S/S variant of the L5178Y murine leukemic lymphoblast was examined by treatment with the heavy ions, Ne-20, Si-28, Ar-40, Fe-56, and Nb-93. Evidence from those studies provide support for the notion that as the linear energy transfer of the incident radiation increases the ability of the S/S cell to repair radiation damage decreases until it is eliminated around 500 keV/micron. In the region of the latter linear energy transfer value, the behavior of the S/S cell approximates the ideal case of target theory where post-irradiation metabolism does not influence cell survival.

Lett, J. T.↗
NASA NTRS1992

Validation of three-dimensional incompressible spatial direct numerical simulation code: A comparison with linear stability and parabolic stability equation theories for boundary-layer transition on a flat plate

Spatially evolving instabilities in a boundary layer on a flat plate are computed by direct numerical simulation (DNS) of the incompressible Navier-Stokes equations. In a truncated physical domain, a nonstaggered mesh is used for the grid. A Chebyshev-collocation method is used normal to the wall; finite difference and compact difference methods are used in the streamwise direction; and a Fourier series is used in the spanwise direction. For time stepping, implicit Crank-Nicolson and explicit Runge-Kutta schemes are used to the time-splitting method. The influence-matrix technique is used to solve the pressure equation. At the outflow boundary, the buffer-domain technique is used to prevent convective wave reflection or upstream propagation of information from the boundary. Results of the DNS are compared with those from both linear stability theory (LST) and parabolized stability equation (PSE) theory. Computed disturbance amplitudes and phases are in very good agreement with those of LST (for small inflow disturbance amplitudes). A measure of the sensitivity of the inflow condition is demonstrated with both LST and PSE theory used to approximate inflows. Although the DNS numerics are very different than those of PSE theory, the results are in good agreement. A small discrepancy in the results that does occur is likely a result of the variation in PSE boundary condition treatment in the far field. Finally, a small-amplitude wave triad is forced at the inflow, and simulation results are compared with those of LST. Again, very good agreement is found between DNS and LST results for the 3-D simulations, the implication being that the disturbance amplitudes are sufficiently small that nonlinear interactions are negligible.

Joslin, Ronald D.↗
NASA NTRS2003

On the Applicability of High-frequency Approximations to Lilley's Equation

Three forms of the high-frequency asymptotic Green's function for Lilley's equation are reviewed and compared to the exact solution over wide range of Strouhal numbers. The asymmetric approximation, which applies to sources away form the jet axis, and the quasi-symmetric approximation, which is arrived at by making a near-axis source assumption, are both obtained for parallel round jets from a formal Fourier-transform solution. The ray-theory solution, which is the only high-frequency approximation that can be applied to more general mean flows, follows from a WKB ansatz and is shown to be closely related to the asymmetric approximation. The comparisons show that the best overall prediction of the exact Green's function is given by the asymmetric approximation which remains accurate down to a Strouhal number of 1/2. The close relationship between the asymmetric and ray-theory approximations suggests that the high-frequency asymptotic Green's function for more general mean flows would be similarly successful.

Wundrow, David W.↗