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NASA NTRS1981

On a fourth order accurate implicit finite difference scheme for hyperbolic conservation laws. I - Nonstiff strongly dynamic problems

An implicit finite difference method of fourth order accuracy in space and time is introduced for the numerical solution of one-dimensional systems of hyperbolic conservation laws. The basic form of the method is a two-level scheme which is unconditionally stable and nondissipative. The scheme uses only three mesh points at level t and three mesh points at level t + delta t. The dissipative version of the basic method given is conditionally stable under the CFL (Courant-Friedrichs-Lewy) condition. This version is particularly useful for the numerical solution of problems with strong but nonstiff dynamic features, where the CFL restriction is reasonable on accuracy grounds. Numerical results are provided to illustrate properties of the proposed method.

Harten, A.↗

NASA NTRS1976

Time-dependent perturbation of a two-state quantum system by a sinusoidal field

Different methods for solving the 'two-level problem' are discussed, namely, the problem of what happens to a material system having only two nondegenerate energy levels when it is perturbed by an electromagnetic field that varies with time in a monochromatic sinusoidal fashion. The various methods discussed include: (1) the Sen Gupta technique using nondegenerate Rayleigh-Schroedinger perturbation theory, (2) the Salwen-Winter-Shirley partitioning perturbation technique, (3) the Shirley and series degenerate Rayleigh-Schroedinger expansion, (4) the degenerate Rayleigh-Schroedinger technique for considering high frequency fields, and (5) the singular perturbation expansion technique.

Dion, D. R.↗

NASA NTRS1975

Drive-train dynamics technology - State-of-the-art and design of a test facility for advanced development

A program for the development and verification of drive-train dynamic technology is described along with its basis and the results expected from it. A central feature of this program is a drive-train test facility designed for the testing and development of advanced drive-train components, including shaft systems, dampers, and couplings. Previous efforts in designing flexible dynamic drive-train systems are reviewed, and the present state of the art is briefly summarized. The design of the test facility is discussed with major attention given to the formulation of the test-rig concept, dynamic scaling of model shafts, and the specification of design parameters. Specific efforts envisioned for the test facility are briefly noted, including evaluations of supercritical test shafts, stability thresholds for various sources and types of instabilities that can exist in shaft systems, effects of structural flexibility on the dynamic performance of dampers, and methods for vibration control in two-level and three-level flexible shaft systems.

Badgley, R. H.↗

NASA NTRS1982

Control systems synthesis for a large flexible space antenna

The problem of control systems synthesis is considered for controlling the rigid-body attitude and elastic motion of a large deployable space-based antenna. Two methods for control systems synthesis are considered. The first method utilizes the stability and robustness properties of the controller consisting of torque actuators and collocated attitude and rate sensors. The second method is based on the linear-quadratic-Gaussian (LQG) control theory. A combination of the two methods, which results in a two-level hierarchical control system, is also briefly discussed. The performance of the controllers is analyzed by computing the variances of pointing errors, feed misalignment errors and surface contour errors in the presence of sensor and actuator noise.

Joshi, S. M.↗

NASA NTRS1976

Laser induced fluorescence applied to turbulent reacting flows

The saturated fluorescence method makes use of the great simplifications which occur when under conditions of intense radiation the excitation process becomes saturated. A description is presented of the saturated fluorescence method, taking into account rate equations and saturation, radiative transfer, the two-level system, a multilevel system, and measurements under saturation conditions. The detectability limits of the method are investigated. Fluorescence trapping is found to place an upper limit on the number density of the fluorescing species that can be measured without signal loss. Turbulence places time and spatial constraints on the measurements, but otherwise poses no difficulties. Saturated laser induced fluorescence spectroscopy appears to be a most promising method for measuring species concentrations in flames.

Daily, J. W.↗

NASA NTRS1977

Composite methods for hyperbolic equations

A composite approximation procedure combining the properties of the Lax-Wendroff and leapfrog algorithms is proposed for solving hyperbolic equations. For a one-dimensional equation, a three-step approximation consisting of a two-step Richtmeyer method followed by a leapfrog step is considered. This is a two-level scheme, so all difficulties, including storage requirements, associated with the three-level leapfrog are eliminated. For two-dimensional problems a generalization of the preceding method is used consisting of a rotated Richtmeyer method followed by a modified leapfrog step. It is found that the composite schemes are effective in reducing oscillations and nonlinear instabilities that affect the leapfrog method. The dissipation in the composite schemes is much less than in the Richtmeyer algorithm, and hence can be used for long term integrations.

Turkel, E.↗

NASA NTRS1984

An improved computational approach for multilevel optimum design

A penalty-function algorithm employing Newton's method with approximate second derivatives (Haftka and Starnes, 1980) is developed for two-level hierarchical design optimization problems. The difficulties posed by discontinuous behavior in typical multilevel problems are explained and illustrated for the case of a three-bar truss; the algorithm is formulated; and its advantages are demonstrated in the problem of a portal framework having three beams (described by six cross-section parameters), subjected to two loading conditions, and to be constructed in six different materials for comparison. The final design parameters are listed in a table.

Haftka, R. T.↗

NASA NTRS1983

Structural optimization by multilevel decomposition

The application of formal optimization techniques to the design of large engineering structures such as aircraft is presently hindered in connection with the large number of design variables involved. According to an approach which attempts to overcome the difficulties, the problem is broken up into several smaller subproblems. This approach has, however, weaknesses which may prevent a determination of the minimum structural weight. Schmit and Ramanathan (1973) have developed a method, which is designed to incorporate control of the material distribution among the finite elements of an assembled structure for a two-level optimization. However, the optimization schemes considered would not be suitable to optimization schemes considered would not be suitable to multidisciplinary optimization of large engineering systems. Sobieszczanski-Sobieski (1982) proposed a method for decomposing a large multidisciplinary optimization problem into a number of small subproblems. The present investigation is concerned with the implementation of this method.

Sobieszczanski-Sobieski, J.↗

NASA NTRS1979

An explicit algorithm for a fluid approach to nonlinear optics propagation using splitting and rezoning techniques

The paper presents a three-dimensional analysis of the nonlinear light matter interaction in a hydrodynamic context. It is reported that the resulting equations are a generalization of the Navier-Stokes equations subjected to an internal potential which depends solely upon the fluid density. In addition, three numerical approaches are presented to solve the governing equations using an extension of McCormack predict-corrector scheme. These are a uniform grid, a dynamic rezoned grid, and a splitting technique. It is concluded that the use of adaptive mapping and splitting techniques with McCormack two-level predictor-corrector scheme results in an efficient and reliable code whose storage requirements are modest compared with other second order methods of equal accuracy.

Mattar, F. P.↗

NASA NTRS1975

Electron and proton damage coefficients in low-resistivity silicon

The electron and proton damage coefficients for low resistivity p-type boron-doped silicon were determined from minority-carrier lifetime measurements on bulk material and diffusion length measurements on solar cells. The bulk samples were irradiated with electrons at three energy levels (0.5, 1.5, and 2.5 MeV) using a Dynamitron. Lifetime measurements were made with a steady-state photoconductivity apparatus, and comparison measurements of diffusion length were obtained using the steady-state surface photovoltage method (Goodman, 1961). The diffusion-length damage coefficients increased with decreasing resistivity for boron-doped silicon; this dependence can be qualitatively accounted for using a two-level Hall-Shockley-Read model. The damage coefficients for solar cells were larger than for their bulk-material counterparts. The damage coefficient was apparently independent of the dislocation density in the 0.1 ohm-cm bulk samples and solar cells investigated.

Srour, J. R.↗

NASA NTRS1972

Techniques for control of long-term reliability of complex integrated circuits. I - Reliability assurance by test vehicle qualification.

Development of an alternate approach to the conventional methods of reliability assurance for large-scale integrated circuits. The product treated is a large-scale T squared L array designed for space applications. The concept used is that of qualification of product by evaluation of the basic processing used in fabricating the product, providing an insight into its potential reliability. Test vehicles are described which enable evaluation of device characteristics, surface condition, and various parameters of the two-level metallization system used. Evaluation of these test vehicles is performed on a lot qualification basis, with the lot consisting of one wafer. Assembled test vehicles are evaluated by high temperature stress at 300 C for short time durations. Stressing at these temperatures provides a rapid method of evaluation and permits a go/no go decision to be made on the wafer lot in a timely fashion.

Van Vonno, N. W.↗

NASA NTRS1982

A January angular momentum balance in the OSU two-level atmospheric general circulation model

The present investigation is concerned with an analysis of the atmospheric angular momentum balance, based on the simulation data of the Oregon State University two-level atmospheric general circulation model (AGCM). An attempt is also made to gain an understanding of the involved processes. Preliminary results on the angular momentum and mass balance in the AGCM are shown. The basic equations are examined, and questions of turbulent momentum transfer are investigated. The methods of analysis are discussed, taking into account time-averaged balance equations, time and longitude-averaged balance equations, mean meridional circulation, the mean meridional balance of relative angular momentum, and standing and transient components of motion.

Kim, J.-W.↗

NASA NTRS1980

A two-level controller design approach for large space structures

A controller design approach is proposed for large space structures (LSS) using an Annular Momentum Control Device (AMCD). The controller consists of a primary attitude controller and a secondary or modal damping enhancement controller. It is proved that the LSS/AMCD system using the proposed damping enhancement controller is stable in the sense of Lyapunov regardless of the number of modes in the model and without the necessity of precise knowledge of the modal frequencies and mode shapes. Numerical results obtained for the secondary controller design for a large thin flat plate indicate that the proposed method can yield satisfactory damping enhancement with small weight penalty.

Joshi, S. M.↗

NASA NTRS1982

Sensitivity of the boundary layer energy fluxes to forcing parameters in a simple climate model

Winter and summer surface temperatures and time-averaged boundary layer energy fluxes are calculated by utilizing the Saltzman-Ashe parameterization for boundary layer fluxes in a two-level static model. The results are found to agree with observed patterns. Within the framework of this simple model, sensitivity analyses of the time-averaged boundary layer energy fluxes are conducted. Based on these results some of the forcing parameters (such as the subsurface temperature, cloud cover, surface albedo, etc.) are arranged in a hierarchical order of importance. A generalized method of sensitivity analysis is also suggested.

Rao, M. S.↗

NASA NTRS1972

Design of automata theory of cubical complexes with applications to diagnosis and algorithmic description

The following problems are considered: (1) methods for development of logic design together with algorithms, so that it is possible to compute a test for any failure in the logic design, if such a test exists, and developing algorithms and heuristics for the purpose of minimizing the computation for tests; and (2) a method of design of logic for ultra LSI (large scale integration). It was discovered that the so-called quantum calculus can be extended to render it possible: (1) to describe the functional behavior of a mechanism component by component, and (2) to compute tests for failures, in the mechanism, using the diagnosis algorithm. The development of an algorithm for the multioutput two-level minimization problem is presented and the program MIN 360 was written for this algorithm. The program has options of mode (exact minimum or various approximations), cost function, cost bound, etc., providing flexibility.

Roth, J. P.↗

NASA NTRS1982

Minimum mass sizing of a large low-aspect ratio airframe for flutter-free performance

A procedure for sizing an airframe for flutter-free performance is demonstrated on a large, flexible supersonic transport aircraft. The procedure is based on using a two-level reduced basis or modal technique for reducing the computational cost of performing the repetitive flutter analyses. The supersonic transport aircraft exhibits complex dynamic behavior, has a well-known flutter problem and requires a large finite-element model to predict the vibratory and flutter response. Flutter-free designs are produced with small mass increases relative to the wing structural weight and aircraft payload. In view of the ability of the resizing procedure to handle this supersonic transport configuration, it seems likely that the method could be used for many other aircraft.

Greene, W. H.↗

NASA NTRS1980

Collisional redistribution of radiation. I - The density matrix

As a first step in deriving accurate, calculable expressions for collisional redistribution of radiation, valid outside the impact regime a method for calculating an accurate binary-collision density operator for an atom in the presence of a driving field and perturbers is presented. Projection-operator techniques to establish first the precise validity of the Markoff approximation for radiative relaxation are used. Using the same techniques, it is shown how the collisional-relaxation problem may be analyzed in a practical manner outside the Markoff approximation. The effect of correlations between radiative and collisional events is included in a consistent way and the physical implications of these correlation effects are demonstrated for a simple example, the two-level atom with nondegenerate levels.

Burnett, K.↗

NASA NTRS1977

Departures of the electron energy distribution from a Maxwellian in hydrogen. I - Formulation and solution of the electron kinetic equation. II - Consequences

The problem of calculating the steady-state free-electron energy distribution in a hydrogen gas is considered in order to study departures of that distribution from a Maxwellian at sufficiently low degrees of ionization. A model kinetic equation is formulated and solved analytically for the one-particle electron distribution function in a steady-state partially ionized hydrogen gas, and it is shown that the formal solution can be accurately approximated by using the WKB method. The solutions obtained indicate that the high-energy tail of the distribution is susceptible to distortion by imbalanced inelastic collisions for ionization fractions not exceeding about 0.1 and that such departures from a Maxwellian can lead to significant changes in the collisional excitation and ionization rates of ground-state hydrogen atoms. Expressions for the electron-hydrogen collision rates are derived which explicitly display their dependence on the hydrogen departure coefficients. The results are applied in order to compare self-consistent predictions with those based on the a priori assumption of a Maxwellian distribution for models of the thermal ionization equilibrium of hydrogen in the optically thin limit, spectral-line formation by a gas consisting of two-level atoms, and radiative transfer in finite slabs by a gas of four-level hydrogen atoms.

Shoub, E. C.↗