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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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

Reflecting Solutions of High Order Elliptic Differential Equations in Two Independent Variables Across Analytic Arcs

Consideration is given specifically to sixth order elliptic partial differential equations in two independent real variables x, y such that the coefficients of the highest order terms are real constants. It is assumed that the differential operator has distinct characteristics and that it can be factored as a product of second order operators. By analytically continuing into the complex domain and using the complex characteristic coordinates of the differential equation, it is shown that its solutions, u, may be reflected across analytic arcs on which u satisfies certain analytic boundary conditions. Moreover, a method is given whereby one can determine a region into which the solution is extensible. It is seen that this region of reflection is dependent on the original domain of difinition of the solution, the arc and the coefficients of the highest order terms of the equation and not on any sufficiently small quantities; i.e., the reflection is global in nature. The method employed may be applied to similar differential equations of order 2n.

Carleton, O.↗
NASA NTRS1981

Canonical orbital elements in terms of an arbitrary independent variable

Within the framework of the Hamiltonian mechanics in the extended phase space, a set of canonical elements of the Delaunay type is developed in terms of an arbitary independent angular variable. Application to the four classical anomalies - eccentric, true, elliptic, and mean - is presented. Particular attention is given to the generalized time equation and its conjugate energy equation.

Bond, V. R.↗
NASA NTRS1995

An all-at-once reduced Hessian SQP scheme for aerodynamic design optimization

This paper introduces a computational scheme for solving a class of aerodynamic design problems that can be posed as nonlinear equality constrained optimizations. The scheme treats the flow and design variables as independent variables, and solves the constrained optimization problem via reduced Hessian successive quadratic programming. It updates the design and flow variables simultaneously at each iteration and allows flow variables to be infeasible before convergence. The solution of an adjoint flow equation is never needed. In addition, a range space basis is chosen so that in a certain sense the 'cross term' ignored in reduced Hessian SQP methods is minimized. Numerical results for a nozzle design using the quasi-one-dimensional Euler equations show that this scheme is computationally efficient and robust. The computational cost of a typical nozzle design is only a fraction more than that of the corresponding analysis flow calculation. Superlinear convergence is also observed, which agrees with the theoretical properties of this scheme. All optimal solutions are obtained by starting far away from the final solution.

Feng, Dan↗
NASA NTRS1997

Annual Sea Level Variability Induced by Changes in Sea Ice Extent and Accumulation on Ice Sheets: An Assessment Based on Remotely Sensed Data

Changes of mean annual net accumulation at the surface on the grounded ice sheets of East Antarctica, West Antarctica, and Greenland in response to variations in sea ice extent are estimated using grid-point values 100 km apart. The data bases are assembled principally by bilinear interpolation of remotely sensed brightness temperature (Nimbus-5 ESMR, Nimbus-7 SMMR), surface temperature (Nimbus-7 THIR), and surface elevation (ERS-1 radar altimeter). These data, complemented by field data where remotely sensed data are not available, are used in multivariate analyses in which mean annual accumulation (derived from firn emissivity) is the dependent variable; the independent variables are latitude, surface elevation, mean annual surface temperature, and mean annual distance to open ocean (as a source of energy and moisture). The last is the shortest distance measured between a grid point and the mean annual position of the 10% sea ice concentration boundary, and is used as an index of changes in sea ice extent as well as of mean concentration. Stepwise correlation analyses indicate that variations in sea ice extent of +/-50 km would lead to changes in accumulation inversely of +/-4% on East Antarctica, +/- 10% on West Antarctica, and +4% on Greenland. These results are compared with those obtained in a previous study using visually interpolated values from contoured compilations of field data; they substantiate the findings for the Antarctic ice sheets (+/-4% on East Antarctica, +/-9% in West Antarctica), and suggest a reduction by one half of the probable change of accumulation on Greenland (from +/-8%). The results also suggest a reduction of the combined contribution to sea level variability to +/- 0.19 mm/a (from +/- 0.22 mm/a).

Zwally, H. J.↗
NASA NTRS1981

A general time element for orbit integration in Cartesian coordinates

Two techniques are discussed for increasing the accuracy of the numerical integration of eccentric orbits in Cartesian coordinates. One involves the use of an independent variable different from time; this increases the efficiency of the numerical integration. The other uses a time element, which reduces the in-track error. A general expression is given of a time element valid for an arbitrary independent variable. It is pointed out that this time element makes it possible to switch the independent variable merely by applying a scaling factor; there is no need to change the differential equations of the motion. Eccentric, true, and elliptic anomalies are used as independent variables in the case of a transfer orbit for a geosynchronous orbit. The elliptic anomaly is shown to perform much better than the other classical anomalies.

Janin, G.↗
NASA NTRS1977

Optimization of confinement in a toroidal plasma subject to strong radial electric fields

The toroidal ring of plasma contained in the NASA Lewis Bumpy Torus facility may be biased to positive or negative potentials approaching 50 kV by applying dc voltages of the respective polarity to 12 or fewer midplane electrode rings. The radial electric fields, which are responsible for raising the ions to high energies by E x B/B-squared drift, then point out of or into the plasma. A preliminary report is given on the identification and optimization of independent variables which affect the ion density and confinement time in the Bumpy Torus plasma. The independent variables include the polarity, position, and number of the midplane electrode rings, the method of gas injection, and the polarity and strength of a weak vertical magnetic field. Some characteristic data taken under conditions where most of the independent variables were optimized are presented. The highest value of the electron number density on the plasma axis is 3.2 trillion per cu cm, the highest ion heating efficiency is 47%, and the longest particle containment time is 2.0 msec.

Roth, J. R.↗
NASA NTRS1977

Optimization of confinement in a toroidal plasma subject to strong radial electric fields

A preliminary report on the identification and optimization of independent variables which affect the ion density and confinement time in a bumpy torus plasma is presented. The independent variables include the polarity, position, and number of the midplane electrode rings, the method of gas injection, and the polarity and strength of a weak vertical magnetic field. Some characteristic data taken under condition when most of the independent variables were optimized are presented. The highest value of the electron number density on the plasma axis is 3.2 x 10 to the 12th power/cc, the highest ion heating efficiency is 47 percent, and the longest particle containment time is 2.0 milliseconds.

Roth, J. R.↗
NASA NTRS1974

A computer graphics display and data compression technique

The computer program discussed is intended for the graphical presentation of a general dependent variable X that is a function of two independent variables, U and V. The required input to the program is the variation of the dependent variable with one of the independent variables for various fixed values of the other. The computer program is named CRP, and the output is provided by the SD 4060 plotter. Program CRP is an extremely flexible program that offers the user a wide variety of options. The dependent variable may be presented in either a linear or a logarithmic manner. Automatic centering of the plot is provided in the ordinate direction, and the abscissa is scaled automatically for a logarithmic plot. A description of the carpet plot technique is given along with the coordinates system used in the program. Various aspects of the program logic are discussed and detailed documentation of the data card format is presented.

Teague, M. J.↗
NASA NTRS1971

Correlation of irradiation data using activation fluences and irradiation temperature.

Nil-ductility transition temperature data for A302-B ferritic steel were analyzed by using multiple regression. Four independent variables were used - i.e., specimen temperature during irradiation, and time-integrated specific activations (activation fluences) of fast-, intermediate-, and thermal-neutron detectors. The results of these analyses were predictive equations having the increase in transition temperature as the dependent variable. For a reference point, a similar analysis was also performed using the flux integral above 1 MeV and the irradiation temperature as independent variables. Also, the effect of excluding irradiation temperature from these analyses was studied. The results of the analyses showed that excellent correlation was achieved by using activation fluences and irradiation temperature as the independent variables. Irradiation temperature was found to account for from 29 to 46% of the data variability depending on the model used.

Lynch, J. H.↗
NASA NTRS1986

On the Lagrangian Method for Steady and Unsteady Flow

A new and general Lagrangian formulation of fluid motion is given in which the independent variables are three material functions and a Lagrangian time, which differs for different fluid particles and is distinct from the Eulerian time. For steady flow it requires only three independent variables - the Lagrangian time and two stream functions - in contrast with the conventional Lagrangian formulation which apparently still requires four independent variables for describing a steady flow. This places the Lagrangian formulation for steady flow on the same footing as the Eulerian. For unsteady flow, the new formulation includes the conventional formulation as a special case when the Lagrangian time is identified with the Eulerian time and when the material functions are taken to be the fluid particle's position at some given time. The distinction between the Lagrangian and Eulerian time, however, is found useful in applications, e.g., to problems involving a free boundary.

Hui, W. H.↗
NASA NTRS2000

Improved Quality in Aerospace Testing Through the Modern Design of Experiments

This paper illustrates how, in the presence of systematic error, the quality of an experimental result can be influenced by the order in which the independent variables are set. It is suggested that in typical experimental circumstances in which systematic errors are significant, the common practice of organizing the set point order of independent variables to maximize data acquisition rate results in a test matrix that fails to produce the highest quality research result. With some care to match the volume of data required to satisfy inference error risk tolerances, it is possible to accept a lower rate of data acquisition and still produce results of higher technical quality (lower experimental error) with less cost and in less time than conventional test procedures, simply by optimizing the sequence in which independent variable levels are set.

DeLoach, R.↗
NASA NTRS1990

Modeling and synthesis of multicomputer interconnection networks

The type of interconnection network employed has a profound effect on the performance of a multicomputer and multiprocessor design. Adequate models are needed to aid in the design and development of interconnection networks. A novel modeling approach using statistical and optimization techniques is described. This method represents an attempt to compare diverse interconnection network designs in a way that allows not only the best of existing designs to be identified but to suggest other, perhaps hybrid, networks that may offer better performance. Stepwise linear regression is used to develop a polynomial surface representation of performance in a (k+1) space with a total of k quantitative and qualitative independent variables describing graph-theoretic characteristics such as size, average degree, diameter, radius, girth, node-connectivity, edge-connectivity, minimum dominating set size, and maximum number of prime node and edge cutsets. Dependent variables used to measure performance are average message delay and the ratio of message completion rate to network connection cost. Response Surface Methodology (RSM) optimizes a response variable from a polynomial function of several independent variables. Steepest ascent path may also be used to approach optimum points.

Standley, Hilda M.↗
NASA NTRS1974

Investigation of highly efficient satellite solution methods

Methods for analyzing the stability of satellites are discussed. The subjects considered are: (1) time elements, (2) stabilization by external energy corrections, and (3) long term global solutions for the synchronous satellite. A set of canonical two-body elements referred to as Delaunay-similar elements is presented. In contrast to the classical Delaunay theory which has time as the independent variable, the D-S theory uses an independent variable which is a generalized true anomaly. The numerical integration of the canonical perturbation equations of these elements is developed.

Nacozy, P. E.↗