Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “N-Th”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1974

Optimal compensator structure for linear time-invariant plant with inaccessible states

The problem is considered of designing an optimal linear time-invariant dynamic compensator for the regulation of an n-th order linear time-invariant plant with m independent outputs. The initial plant state is characterized by its first and second moments, and the cost is usual quadratic infinite-time penalty on the state and control, averaged over the initial plant and compensator states. The compensator is based on a minimal-order Luenberger observer and consequently has fixed dimension n-m. Necessary and sufficient conditions are derived for optimality of the compensator gains. The optimal compensator is shown to be unique if the plant has a particular canonical form, and, in general, for any arbitrary plant, the class of all optimal compensators is precisely determined.

Blanvillain, P. J. P.↗
NASA NTRS1974

Degenerate RS perturbation theory

A concise, systematic procedure is given for determining the Rayleigh-Schroedinger energies and wave functions of degenerate states to arbitrarily high orders even when the degeneracies of the various states are resolved in arbitrary orders. The procedure is expressed in terms of an iterative cycle in which the energy through the (2n + 1)-th order is expressed in terms of the partially determined wave function through the n-th order. Both a direct and an operator derivation are given. The two approaches are equivalent and can be transcribed into each other. The direct approach deals with the wave functions (without the use of formal operators) and has the advantage that it resembles the usual treatment of nondegenerate perturbations and maintains close contact with the basic physics. In the operator approach, the wave functions are expressed in terms of infinite-order operators which are determined by the successive resolution of the space of the zeroth-order functions.

Hirschfelder, J. O.↗
NASA NTRS1974

Interplanetary diffusion coefficients for cosmic rays

Information on the cosmic-ray diffusion coefficient, kappa, derived from near-earth observations of the solar modulation of galactic electron fluxes and from the near-earth power spectra of the interplanetary magnetic field, has been used to study the heliocentric radial dependence of kappa, and to derive limits on the spatial extent of the solar modulation region. Representing kappa, as a separable function of radius r and rigidity, and assumming kappa(r) proportional to r to the n-th power, we can place a limit on the power law exponent, n not greater than 1.2. The distance of the modulation boundary is a function of n, and, e.g., for n = 0, falls into the range of 6-25 AU.

Cummings, A. C.↗
NASA NTRS1978

Convective heat transfer during dendritic solidification

Experiments on succinonitrile are described in which the dependence of dendritic growth velocity is studied as a function of orientation with respect to gravity. Growth rate measurements were carried out at a relatively small supercooling, requiring high specimen purity as well as extreme thermal stability and precision temperature measurement. The normalized growth velocity showed a dependence on orientation described by the ratio of observed growth velocity to that expected for convection-free growth being equal to 3.52 times the n-th power of Cos half the orientation angle, where n lies between 0.5 and 0.75.

Glicksman, M. E.↗
NASA NTRS1978

Time transformations and Cowell's method

The precise numerical integration of Cowell's equations of satellite motion is frequently performed with an independent variable s defined by an equation of the form dt = cr to the n-th power ds, where t represents time, r the radial distance from the center of attraction, c is a constant, and n is a parameter. This has been primarily motivated by the 'uniformizing' effects of such a transformation resulting in desirable 'analytic' stepsize control for elliptical orbits. This report discusses the 'proper' choice of the parameter n defining the independent variable s for various types of orbits and perturbation models, and develops a criterion for its selection.

Velez, C. E.↗
NASA NTRS1978

Abundances and spectra for cosmic-ray nuclei from lithium to iron for 2 to 150 GeV per nucleon

Measurements of primary cosmic-ray composition and energy spectra made with a balloon-borne superconducting magnetic spectrometer are described. Results for both 6.7 g/sq cm equivalent vertical atmospheric depth and the top of the atmosphere are presented for the absolute and relative integral abundances, the differential energy spectra, and the spectral indices for cosmic-ray nuclei from Li to Fe and energies of 2 to 50 GeV/n. It is found that propagation effects can explain essentially all the elemental abundances, that the abundances of Li, Be, and B for rigidities below 10 GV/c are consistent with an energy-independent mean interstellar path length of 4.5 + or - 0.5 g/sq cm for the 'leaky box' propagation model, that the abundances of all elements above 10 GV/c are consistent with a path length that decreases as the inverse n-th power of rigidity, and that n equals 0.6 (+0.4, -0.3) for the simplest assumptions made in fitting the source spectra.

Orth, C. D.↗
NASA NTRS1986

Analysis of the harmonic gyrotron traveling wave amplifier

A single nonlinear differential equation is derived for describing the spatial evolution of the wave field in a gyrotron amplifier on the cylindrical guide geometry. The equation is then used to determine the efficiencies and the optimized interaction lengths for gyrotron operated with TE sub N1 modes at the N-th cyclotron harmonic. The equation offers a significant advantage in simplifying numerical work in comparison with the brute force particle simulation approach. The efficiencies of the harmonic operations by using a hollow beam decrease quickly with increasing harmonic number, but are enhanced by using an axis-encircling beam instead.

Kuo, S. P.↗
NASA NTRS1991

Lunar regolith densification

Core tube samples of the lunar regolith obtained during the Apollo missions showed a rapid increase in the density of the regolith with depth. Various hypotheses have been proposed for the possible cause of this phenomenon, including the densification of the loose regolith material by repeated shaking from the seismic tremors which have been found to occur at regular monthly intervals when the moon and earth are closest to one another. A test bed was designed to study regolith densification. This test bed uses Minnesota Lunar Simulant (MLS) to conduct shaking experiments in the geotechnical centrifuge with an inflight shake table system. By reproducing realistic in-situ regolith properties, the experiment also serves to test penetrator concepts. The shake table system was designed and used for simulation experiments to study effects of earthquakes on terrestrial soil structures. It is mounted on a 15 g-ton geotechnical centrifuge in which the self-weight induced stresses are replicated by testing an n-th scale model in a gravity field which is n times larger than Earth's gravity. A similar concept applies when dealing with lunar prototypes, where the gravity ratio required for proper simulation of lunar gravity effects is that between the centrifugal acceleration and the lunar gravity. Records of lunar seismic tremors, or moonquakes, were obtained. While these records are being prepared for use as the input data to drive the shake table system, records from the El Centro earthquake of 1940 are being used to perform preliminary tests, using a soil container which was previously used for earthquake studies. This container has a laminar construction, with the layers free to slide on each other, so that the soil motion during the simulated earthquake will not be constrained by the otherwise rigid boundaries. The soil model is prepared by pluviating the MLS from a hopper into the laminar container to a depth of 6 in. The container is mounted on the shake table and the centrifuge is operated to generate an acceleration of 10 times Earth's gravity or 60 times the lunar gravity, thus simulating a lunar regolith thickness of 30 ft. The shake table is then operated using the scaled 'moonquake' as the input motion. One or more model moonquakes are used in each experiment, after which the soil is analyzed for its density profile with depth. This is accomplished by removing from the soil bed a column of soil contained within a thin rubber sleeve which has been previously embedded vertically in the soil during pluviation. This column of soil is transferred to a gamma ray device, in which the gamma ray transmission transversely through the soil is measured and compared with standard calibration samples. In this manner, the density profile can be determined. Preliminary results to date are encouraging, and the Center plans to study the effects of duration of shaking, intensity of the shaking motion, and the frequency of the motion.

Ko, Hon-Yim↗
NASA NTRS1990

An efficient design sensitivity analysis of eigenvectors

Subspace iteration has been a major advance in solving large eigen problems when only a subset of eigen-pairs is required. The essence of this method is a transformation from displacement coordinates of an n-th order eigensystem to generalized coordinates of a smaller q-th order. The eigenvalue problem is then solved in the reduced space. The method was first developed by Clint and Jennings for real symmetric systems and was then called 'simultaneous iteration'. The success of the method prompted further research along this line and there have been many improved algorithms developed. This approach has been widely used by structural engineers for extracting the most useful natural frequencies and mode shapes of large-scale dynamic systems. This paper exploits into a new direction which is in the form of iterative process for simultaneously calculating eigenvector derivatives of many eigenvectors with respect to multi-variables. The method fully uses all the available information from preceding eigenvalue solution and, thus, effectively economizes computational efforts. It iterates through two equations derived from the first variation of the two fundamental equations used in subspace iteration method. There is no expensive large matrix decomposition required and the process converges to acceptable solution in a finite number of iterations. Therefore, the procedure increases its efficiency superiority over the others as the system size or the number of interested eigenvectors become larger and larger.

Ting, T.↗
NASA NTRS1993

Estimating the instabilities of N clocks by means of comparison measurements

The estimation of individual instabilities of N clocks, compared by measuring the differences of their readings, is considered without assuming a priori any hypotheses on their uncorrelation. Instabilities of the N clocks are described by a complete (non-diagonal) N x N covariance matrix R. Only differences of clock readings are available in order to estimate R. Statistical processing of these data allows one to calculate the (N-1)x(N-l) covariance matrix S of the differences relative to the N-th(reference) clock. By analyzing the relationships tying R and S, several pieces of information can be inferred and, in particular, the conditions for the validity of the uncorrelation hypothesis are established. The estimation of R from S is not unique: in any case R must be positive definite. A theorem states that R is positive definite if and only if its determinant is positive. Nevertheless infinitely many acceptable choices of R still fulfill the condition of positive definiteness. This paper shows that, by increasing the number N of compared clocks, the amount of arbitrariness in estimating R is reduced. The analysis of some experimental data illustrates the capability of the method.

Premoli, Amedeo↗
NASA NTRS1993

On the spline-based wavelet differentiation matrix

The differentiation matrix for a spline-based wavelet basis is constructed. Given an n-th order spline basis it is proved that the differentiation matrix is accurate of order 2n + 2 when periodic boundary conditions are assumed. This high accuracy, or superconvergence, is lost when the boundary conditions are no longer periodic. Furthermore, it is shown that spline-based bases generate a class of compact finite difference schemes.

Jameson, Leland↗
NASA NTRS1994

A distributed planning concept for Space Station payload operations

The complex and diverse nature of the payload operations to be performed on the Space Station requires a robust and flexible planning approach. The planning approach for Space Station payload operations must support the phased development of the Space Station, as well as the geographically distributed users of the Space Station. To date, the planning approach for manned operations in space has been one of centralized planning to the n-th degree of detail. This approach, while valid for short duration flights, incurs high operations costs and is not conducive to long duration Space Station operations. The Space Station payload operations planning concept must reduce operations costs, accommodate phased station development, support distributed users, and provide flexibility. One way to meet these objectives is to distribute the planning functions across a hierarchy of payload planning organizations based on their particular needs and expertise. This paper presents a planning concept which satisfies all phases of the development of the Space Station (manned Shuttle flights, unmanned Station operations, and permanent manned operations), and the migration from centralized to distributed planning functions. Identified in this paper are the payload planning functions which can be distributed and the process by which these functions are performed.

Hagopian, Jeff↗
NASA NTRS1996

Finding New Math Identities by Computer

Recently a number of interesting new mathematical identities have been discovered by means of numerical searches on high performance computers, using some newly discovered algorithms. These include the following: pi = ((sup oo)(sub k=0))(Sigma) (1 / 16) (sup k) ((4 / 8k+1) - (2 / 8k+4) - (1 / 8k+5) - (1 / 8k+6)) and ((17 pi(exp 4)) / 360) = ((sup oo)(sub k=1))(Sigma) (1 + (1/2) + (1/3) + ... + (1/k))(exp 2) k(exp -2), zeta(3, 1, 3, 1, ..., 3, 1) = (2 pi(exp 4m) / (4m+2)! where m = number of (3,1) pairs. and where zeta(n1,n2,...,nr) = (sub k1 (is greater than) k2 (is greater than) ... (is greater than) kr)(Sigma) (1 / (k1 (sup n1) k2 (sup n2) ... kr (sup nr). The first identity is remarkable in that it permits one to compute the n-th binary or hexadecimal digit of pu directly, without computing any of the previous digits, and without using multiple precision arithmetic. Recently the ten billionth hexadecimal digit of pi was computed using this formula. The third identity has connections to quantum field theory. (The first and second of these been formally established; the third is affirmed by numerical evidence only.) The background and results of this work will be described, including an overview of the algorithms and computer techniques used in these studies.

Bailey, David H.↗
NASA NTRS2019

Efficient method for approximating nonlinear dynamics: applications to uncertainty propagation and estimation

High-order Taylor series expansions can be used to model nonlinear dynamics at the cost of integrating a large set of variational equations to obtain high-order state-transition tensors (STTs). This paper presents an innovative technique for approximating the high-order STTs that reduces significantly the computational cost by retaining only the dominant secular terms. We propagate the low-order partial derivatives of Kepler’s equation, which only requires the integration of six additional equations to extend an n-th order approximation to order (n + 1). The approximation stems from the Lindstedt-Poincare procedure and exploits the stability properties of orbital motion. Since the method makes no dynamical assumptions, it can accommodate any source of orbital perturbations. We show how the approximation of the second-order STT significantly increases the accuracy of the linear method for uncertainty propagation with only a small computational overhead. Finally, we derive a high-order approximate extended Kalman filter that implements the proposed approximation of the STT and improves the performance of linear filters. Examples of application with different perturbation sources include the heliocentric orbit of an asteroid, an orbiter around Europa, and an Earth-orbiting satellite.

Park, Ryan S↗
DOE OSTI2025

Implementation of fuel management multi-cycle optimization capabilities in RAVEN optimization framework

Optimization in nuclear fuel-management assists the core reload engineer with finding optimal out-of-core and in-core strategies. RAVEN is INL’s open source software that is equipped with fuel-management optimization capabilities including single-cycle, single- and multi-objective optimization of pressurized water reactors (PWRs) loading patterns (LP) of a fresh core using genetic algorithm (GA) and non-dominated sorting genetic algorithm (NSGA-II). In practice, however, medium and long term planning of fuel-management needs a multi-cycle approach, where the history and availability of fuel assemblies is considered in the optimization process. In this paper, we present a description of an initial expansion of RAVEN fuel-management optimization capabilities for a multi-cycle optimization framework. N-th cycle optimization capabilities that account for the unique history of recycled fuel assembly in the core were added. The multi-cycle optimization approach taken is formulated as a cycle-wise optimization problem where out-of-core decisions are used to onset each cycle optimization. Out-of-core decisions are managed externally to the in-core optimization by a fuel inventory management module. A proof-of-concept optimization problem is also presented.

42 - ENGINEERING↗
DOE OSTI2020

Materials Data on Th2N3 by Materials Project

Th2N3 crystallizes in the trigonal P-3m1 space group. The structure is three-dimensional. Th4+ is bonded in a 7-coordinate geometry to seven N+2.67- atoms. There are a spread of Th–N bond distances ranging from 2.36–2.73 Å. There are two inequivalent N+2.67- sites. In the first N+2.67- site, N+2.67- is bonded to six equivalent Th4+ atoms to form NTh6 octahedra that share corners with twelve equivalent NTh4 tetrahedra, edges with six equivalent NTh6 octahedra, and edges with six equivalent NTh4 tetrahedra. In the second N+2.67- site, N+2.67- is bonded to four equivalent Th4+ atoms to form NTh4 tetrahedra that share corners with six equivalent NTh6 octahedra, corners with six equivalent NTh4 tetrahedra, edges with three equivalent NTh6 octahedra, and edges with three equivalent NTh4 tetrahedra. The corner-sharing octahedra tilt angles range from 17–56°.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Materials Data on Th3N4 by Materials Project

Th3N4 crystallizes in the trigonal R-3m space group. The structure is three-dimensional. there are two inequivalent Th4+ sites. In the first Th4+ site, Th4+ is bonded to six equivalent N3- atoms to form edge-sharing ThN6 octahedra. All Th–N bond lengths are 2.54 Å. In the second Th4+ site, Th4+ is bonded in a 7-coordinate geometry to seven N3- atoms. There are a spread of Th–N bond distances ranging from 2.32–2.91 Å. There are two inequivalent N3- sites. In the first N3- site, N3- is bonded to six Th4+ atoms to form distorted NTh6 octahedra that share corners with three equivalent NTh6 octahedra, corners with six equivalent NTh4 tetrahedra, edges with nine equivalent NTh6 octahedra, and edges with three equivalent NTh4 tetrahedra. The corner-sharing octahedral tilt angles are 0°. In the second N3- site, N3- is bonded to four equivalent Th4+ atoms to form NTh4 tetrahedra that share corners with six equivalent NTh6 octahedra, corners with six equivalent NTh4 tetrahedra, edges with three equivalent NTh6 octahedra, and edges with three equivalent NTh4 tetrahedra. The corner-sharing octahedra tilt angles range from 25–50°.

36 MATERIALS SCIENCE↗