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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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Encoding trade-offs and design toolkits in quantum algorithms for discrete optimization: coloring, routing, scheduling, and other problems

Challenging combinatorial optimization problems are ubiquitous in science and engineering. Several quantum methods for optimization have recently been developed, in different settings including both exact and approximate solvers. Addressing this field of research, this manuscript has three distinct purposes. First, we present an intuitive method for synthesizing and analyzing discrete (i.e., integer-based) optimization problems, wherein the problem and corresponding algorithmic primitives are expressed using a discrete quantum intermediate representation (DQIR) that is encoding-independent. This compact representation often allows for more efficient problem compilation, automated analyses of different encoding choices, easier interpretability, more complex runtime procedures, and richer programmability, as compared to previous approaches, which we demonstrate with a number of examples. Second, we perform numerical studies comparing several qubit encodings; the results exhibit a number of preliminary trends that help guide the choice of encoding for a particular set of hardware and a particular problem and algorithm. Our study includes problems related to graph coloring, the traveling salesperson problem, factory/machine scheduling, financial portfolio rebalancing, and integer linear programming. Third, we design low-depth graph-derived partial mixers (GDPMs) up to 16-level quantum variables, demonstrating that compact (binary) encodings are more amenable to QAOA than previously understood. We expect this toolkit of programming abstractions and low-level building blocks to aid in designing quantum algorithms for discrete combinatorial problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Analysis of Compressibility Effects and Nonlinear Property Variations in a Supercritical CO2 Mixing Layer

Calculations are performed using the large eddy simulation technique to qualitatively assess the effects of fluid compressibility and thermodynamic nonlinearities on the dynamics of a supercritical flow field. Resulting data are also used to interrogate instantaneous subfilter-scale fields, as modeled by the mixed-dynamic Smagorinsky closure and gradient diffusion model. A three-dimensional wall-resolved calculation of a spatially evolving mixing layer composed solely of carbon dioxide is performed. This is followed by a coarse grid calculation to examine model performance as a function of resolution. Theoretical analysis indicates that the partial derivatives of density with respect to pressure and temperature are important modulators of the temperature and pressure field evolution, respectively. Results pertaining to subfilter velocity-velocity and velocity-temperature fields indicate that the models are most stressed in the regions where compressibility and thermo-fluid nonlinearities dominate the physics.

42 ENGINEERING↗
DOE OSTI2016

TURBULENCE-GENERATED PROTON-SCALE STRUCTURES IN THE TERRESTRIAL MAGNETOSHEATH

Recent results of numerical magnetohydrodynamic simulations suggest that in collisionless space plasmas, turbulence can spontaneously generate thin current sheets. These coherent structures can partially explain the intermittency and the non-homogenous distribution of localized plasma heating in turbulence. In this Letter, Cluster multi-point observations are used to investigate the distribution of magnetic field discontinuities and the associated small-scale current sheets in the terrestrial magnetosheath downstream of a quasi-parallel bow shock. It is shown experimentally, for the first time, that the strongest turbulence-generated current sheets occupy the long tails of probability distribution functions associated with extremal values of magnetic field partial derivatives. During the analyzed one-hour time interval, about a hundred strong discontinuities, possibly proton-scale current sheets, were observed.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1963

Orbit prediction accuracy theory

Equations for estimating orbit prediction accuracy theory, with partial derivatives calculated from two-body elliptical orbit theory

ORBIT EQUATION↗
NASA NTRS1967

A user's view of ECAP

Partial derivatives and sensitivity coefficients for options built into computer circuit

ELECTRIC NETWORK↗
NASA NTRS1968

HICOV - Newton-Raphson calculus of variation with automatic transversalities

Computer program generates trajectories that are optimum with respect to payload placed in an earth orbit. It uses a subroutine package which produces the terminal and transversality conditions and their partial derivatives. This program is written in FORTRAN 4 and FORMAC for the IBM 7094 computer.

Heintschel, T. J.↗
NASA NTRS1971

Compensator improvement for a large space vehicle.

This paper presents the theory and a technique for compensator improvement. Several definitions in regard to relative stability are presented along with some frequency response limitations and characteristics of a large space vehicle. A nonlinear programming algorithm for obtaining an improved solution for a strict constraint problem is developed and the necessary partial derivatives for applying the algorithm to compensator improvement are derived. Finally, for illustrating the effectiveness of the algorithm, the frequency response of a large space vehicle is improved.

Mitchell, J. R.↗
NASA NTRS1973

A mesh gradient technique for numerical optimization

A class of successive-improvement optimization methods in which directions of descent are defined in the state space along each trial trajectory are considered. The given problem is first decomposed into two discrete levels by imposing mesh points. Level 1 consists of running optimal subarcs between each successive pair of mesh points. For normal systems, these optimal two-point boundary value problems can be solved by following a routine prescription if the mesh spacing is sufficiently close. A spacing criterion is given. Under appropriate conditions, the criterion value depends only on the coordinates of the mesh points, and its gradient with respect to those coordinates may be defined by interpreting the adjoint variables as partial derivatives of the criterion value function. In level 2, the gradient data is used to generate improvement steps or search directions in the state space which satisfy the boundary values and constraints of the given problem.

Willis, E. A., Jr.↗
NASA NTRS1973

The numerical solution of ordinary differential equations by the Taylor series method

A programming implementation of the Taylor series method is presented for solving ordinary differential equations. The compiler is written in PL/1, and the target language is FORTRAN IV. The reduction of a differential system to rational form is described along with the procedures required for automatic numerical integration. The Taylor method is compared with two other methods for a number of differential equations. Algorithms using the Taylor method to find the zeroes of a given differential equation and to evaluate partial derivatives are presented. An annotated listing of the PL/1 program which performs the reduction and code generation is given. Listings of the FORTRAN routines used by the Taylor series method are included along with a compilation of all the recurrence formulas used to generate the Taylor coefficients for non-rational functions.

Silver, A. H.↗
NASA NTRS1974

Surface fitting three-dimensional bodies

The geometry of general three-dimensional bodies is generated from coordinates of points in several cross sections. Since these points may not be smooth, they are divided into segments and general conic sections are curve fit in a least-squares sense to each segment of a cross section. The conic sections are then blended in the longitudinal direction by fitting parametric cubic-spline curves through coordinate points which define the conic sections in the cross-sectional planes. Both the cross-sectional and longitudinal curves may be modified by specifying particular segments as straight lines and slopes at selected points. Slopes may be continuous or discontinuous and finite or infinite. After a satisfactory surface fit has been obtained, cards may be punched with the data necessary to form a geometry subroutine package for use in other computer programs. At any position on the body, coordinates, slopes and second partial derivatives are calculated. The method is applied to a blunted 70 deg delta wing, and it was found to generate the geometry very well.

Dejarnette, F. R.↗
NASA NTRS1974

A method of revitalizing Sampson's theory of the Galilean satellites

A method is developed by which Sampson's theory of motion of Jupiter's Galilean satellites can be revitalized by use of algebraic manipulation software on a digital computer. The technique seeks (1) to remove algebraic errors existing in the current Sampson theory, (2) to introduce some neglected effects due to solar interactions and the 3-7 commensurability between the outer two satellites, (3) to allow for nonzero amplitude and phase of the libration, (4) to allow future revision of the arbitrary constants of integration, (5) to express the final results as analytic functions of variations in the numerous arbitrary constants of integration and arbitrary parameters, and (6) to provide analytic partial derivatives by means of which the numerical values of coefficients in the expressions for the coordinates can be adjusted. The level of precision desired is one arc second (Jovicentric) for the coordinates (2, 3.3, 5.2, and 9.1 km, respectively, for satellites I through IV).

Lieske, J. H.↗
NASA NTRS1973

Reentry guidance for Space Shuttle

An explicit guidance scheme is outlined which provides the appropriate energy management in order for the shuttle orbiter to reach any location within the required footprint. Considering the orbiter as entering the earth's atmosphere, expressions for the downrange, crossrange, and the time of the termination of the entry phase as functions of the control variables are developed. Performing an order-of-magnitude analysis of the terms in these expressions, only dominant terms are retained. Analytical expressions for the elements of the sensitivity matrix which represents the partial derivatives of the desired range with respect to control variables are formulated. Using the Gauss-Jordan inversion technique, the required change in guidance commands as a function of the deviations in the downrange and crossrange are explicitly computed.

Causey, W.↗
NASA NTRS1974

Prediction of pressure and flow transients in a gaseous bipropellant reaction control rocket engine

An analytic model is developed to predict pressure and flow transients in a gaseous hydrogen-oxygen reaction control rocket engine feed system. The one-dimensional equations of momentum and continuity are reduced by the method of characteristics from partial derivatives to a set of total derivatives which describe the state properties along the feedline. System components, e.g., valves, manifolds, and injectors are represented by pseudo steady-state relations at discrete junctions in the system. Solutions were effected by a FORTRAN IV program on an IBM 360/65. The results indicate the relative effect of manifold volume, combustion lag time, feedline pressure fluctuations, propellant temperature, and feedline length on the chamber pressure transient. The analytical combustion model is verified by good correlation between predicted and observed chamber pressure transients. The developed model enables a rocket designer to vary the design parameters analytically to obtain stable combustion for a particular mode of operation which is prescribed by mission objectives.

Markowsky, J. J.↗
NASA NTRS1975

A numerical method for solving the Navier-Stokes equations with application to shock-boundary layer interactions

A numerical method for solving the compressible form of the unsteady Navier-Stokes equations is described. This method was originally presented in 1970 and has since been modified during the development of computer programs at Ames for implementing models that account for the effects of turbulence in shock-induced separated flows. Although this paper does not describe the turbulence models themselves, a complete description of the basic numerical method is given with emphasis on the choice of a computational mesh for high Reynolds number flows, finite-difference approximations for mixed partial derivatives, extension of the Courant-Friedrichs-Lewy stability condition for viscous flows, mesh boundary conditions, and numerical smoothing for strong shock-wave calculations.

Maccormack, R. W.↗
NASA NTRS1976

A general geometric theory of attitude determination from directional sensing

A general geometric theory of spacecraft attitude determination from external reference direction sensors was presented. Outputs of different sensors are reduced to two kinds of basic directional measurements. Errors in these measurement equations are studied in detail. The partial derivatives of measurements with respect to the spacecraft orbit, the spacecraft attitude, and the error parameters form the basis for all orbit and attitude determination schemes and error analysis programs and are presented in a series of tables. The question of attitude observability is studied with the introduction of a graphical construction which provides a great deal of physical insight. The result is applied to the attitude observability of the IMP-8 spacecraft.

Fang, B. T.↗