Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Gibbs”

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 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2008

Hybrid Gibbs Sampling and MCMC for CMB Analysis at Small Angular Scales

A) Gibbs Sampling has now been validated as an efficient, statistically exact, and practically useful method for "low-L" (as demonstrated on WMAP temperature polarization data). B) We are extending Gibbs sampling to directly propagate uncertainties in both foreground and instrument models to total uncertainty in cosmological parameters for the entire range of angular scales relevant for Planck. C) Made possible by inclusion of foreground model parameters in Gibbs sampling and hybrid MCMC and Gibbs sampling for the low signal to noise (high-L) regime. D) Future items to be included in the Bayesian framework include: 1) Integration with Hybrid Likelihood (or posterior) code for cosmological parameters; 2) Include other uncertainties in instrumental systematics? (I.e. beam uncertainties, noise estimation, calibration errors, other).

Gibbs sampling↗
NASA NTRS1992

Gibbs free energy of reactions involving SiC, Si3N4, H2, and H2O as a function of temperature and pressure

Silicon carbide and silicon nitride are considered for application as structural materials and coating in advanced propulsion systems including nuclear thermal. Three-dimensional Gibbs free energy were constructed for reactions involving these materials in H2 and H2/H2O. Free energy plots are functions of temperature and pressure. Calculations used the definition of Gibbs free energy where the spontaneity of reactions is calculated as a function of temperature and pressure. Silicon carbide decomposes to Si and CH4 in pure H2 and forms a SiO2 scale in a wet atmosphere. Silicon nitride remains stable under all conditions. There was no apparent difference in reaction thermodynamics between ideal and Van der Waals treatment of gaseous species.

Isham, M. A.↗
NASA NTRS1979

Direct measurements of the Gibbs free energy of OH using a CW tunable laser

The paper describes an absorption measurement for determining the Gibbs free energy of OH generated in a mixture of water and oxygen vapor. These measurements afford a direct verification of the accuracy of thermochemical data of H2O at high temperatures and pressures. The results indicate that values for the heat capacity of H2O obtained through numerical computations are correct within an experimental uncertainty of 0.15 cal/mole K.

Killinger, D. K.↗
NASA NTRS1986

Gibbs vector kinematics and inverse dynamics for decoupled spacecraft attitude maneuvers

By use of Gibbs vectors as kinematic variables, multi-axial spacecraft equations of rotational motion are shown to be globally and rationally feedback-equivalent to a set of unconstrained and decoupled harmonic oscillators, driven by generalized acceleration commands. Advantages over alternative formulations with Euler angles and quaternions are pointed out.

Dwyer, T. A. W., III↗
NASA NTRS1990

Elimination of Gibbs' phenomena from error analysis of finite element results

This paper is one of a series on error analysis and correction of finite element solutions for plates and shells. The error analysis in the earlier papers used half-range double Fourier sine series for numerical harmonic analysis. The half-range formulas are simple to apply, but they can be inaccurate near the ends of the ranges of the independent variables. The Gibbs' phenomenon exhibited by half-range sine series in one independent variable has a two-dimensional analog; a classic example is the Navier solution in a double half-range sine series for the simply supported plate under a uniform load. A simple change of variables is introduced in the paper to improve the accuracy of the double Fourier sine series without adding complexity to the numerical analysis. The change of variables is applied to the problem of approximating a transverse load that is tabulated on a rectangular grid. A solution based on the change of variables is compared with results from the Navier solution for the simply supported plate problem and finite element results for the same problem.

Thurston, Gaylen A.↗
NASA NTRS1992

On the Gibbs phenomenon 1: Recovering exponential accuracy from the Fourier partial sum of a non-periodic analytic function

It is well known that the Fourier series of an analytic or periodic function, truncated after 2N+1 terms, converges exponentially with N, even in the maximum norm, although the function is still analytic. This is known as the Gibbs phenomenon. Here, we show that the first 2N+1 Fourier coefficients contain enough information about the function, so that an exponentially convergent approximation (in the maximum norm) can be constructed.

Gottlieb, David↗
NASA NTRS1992

Gibbs free energy difference between the undercooled liquid and the beta phase of a Ti-Cr alloy

The heat of fusion and the specific heats of the solid and liquid have been experimentally determined for a Ti60Cr40 alloy. The data are used to evaluate the Gibbs free energy difference, delta-G, between the liquid and the beta phase as a function of temperature to verify a reported spontaneous vitrification (SV) of the beta phase in Ti-Cr alloys. The results show that SV of an undistorted beta phase in the Ti60Cr40 alloy at 873 K is not feasible because delta-G is positive at the temperature. However, delta-G may become negative with additional excess free energy to the beta phase in the form of defects.

Ohsaka, K.↗
NASA NTRS1993

Gibbs free-energy difference between the glass and crystalline phases of a Ni-Zr alloy

The heats of eutectic melting and devitrification, and the specific heats of the crystalline, glass, and liquid phases have been measured for a Ni24Zr76 alloy. The data are used to calculate the Gibbs free-energy difference, Delta G(AC), between the real glass and the crystal on an assumption that the liquid-glass transition is second order. The result shows that Delta G(AC) continuously increases as the temperature decreases in contrast to the ideal glass case where Delta G(AC) is assumed to be independent of temperature.

Ohsaka, K.↗
NASA NTRS1993

On the Gibbs phenomenon 3: Recovering exponential accuracy in a sub-interval from a spectral partial sum of a piecewise analytic function

The investigation of overcoming Gibbs phenomenon was continued, i.e., obtaining exponential accuracy at all points including at the discontinuities themselves, from the knowledge of a spectral partial sum of a discontinuous but piecewise analytic function. It was shown that if we are given the first N expansion coefficients of an L(sub 2) function f(x) in terms of either the trigonometrical polynomials or the Chebyshev or Legendre polynomials, an exponentially convergent approximation to the point values of f(x) in any sub-interval in which it is analytic can be constructed.

Gottlieb, David↗
NASA NTRS1994

On the Gibbs phenomenon 4: Recovering exponential accuracy in a sub-interval from a Gegenbauer partial sum of a piecewise analytic function

We continue our investigation of overcoming Gibbs phenomenon, i.e., to obtain exponential accuracy at all points (including at the discontinuities themselves), from the knowledge of a spectral partial sum of a discontinuous but piecewise analytic function. We show that if we are given the first N Gegenbauer expansion coefficients, based on the Gegenbauer polynomials C(sub k)(sup mu)(x) with the weight function (1 - x(exp 2))(exp mu - 1/2) for any constant mu is greater than or equal to 0, of an L(sub 1) function f(x), we can construct an exponentially convergent approximation to the point values of f(x) in any subinterval in which the function is analytic. The proof covers the cases of Chebyshev or Legendre partial sums, which are most common in applications.

Gottlieb, David↗
NASA NTRS2003

Gibbs-Thomson Law for Singular Step Segments: Thermodynamics Versus Kinetics

Classical Burton-Cabrera-Frank theory presumes that thermal fluctuations are so fast that at any time density of kinks on a step is comparable with the reciprocal intermolecular distance, so that the step rate is about isotropic within the crystal plane. Such azimuthal isotropy is, however, often not the case: Kink density may be much lower. In particular, it was recently found on the (010) face of orthorhombic lysozyme that interkink distance may exceed 500-600 intermolecular distances. Under such conditions, Gibbs-Thomson law (GTL) may not be applicable: On a straight step segment between two corners, communication between the comers occurs exclusively by kink exchange. Annihilation between kinks of opposite sign generated at the comers results in the grain in step energy entering GTL. If the step segment length l much greater than D/v, where D and v are the kink diffusivity and propagation rate, respectively, the opposite kinks have practically no chance to annihilate and GTL is not applicable. The opposite condition of the GTL applicability, l much less than D/v, is equivalent to the requirement that relative supersaturation Delta(sub mu)/kT much less than alpha/l, where alpha is molecular size. Thus, GTL may be applied to a segment of 10(exp 3)alpha approx. 3 x 10(exp -5)cm approx 0.3 micron only if supersaturation is less than 0.1%, while practically used driving forces for crystallization are much larger. Relationships alternative to the GTL for different, but low, kink density have been discussed. They confirm experimental evidences that the Burton-Cabrera-Frank theory of spiral growth is growth rates twice as low as compared to the observed figures. Also, application of GTL results in unrealistic step energy while suggested kinetic law give reasonable figures.

Chernov, A. A.↗
NASA NTRS1994

On the Gibbs phenomenon 5: Recovering exponential accuracy from collocation point values of a piecewise analytic function

The paper presents a method to recover exponential accuracy at all points (including at the discontinuities themselves), from the knowledge of an approximation to the interpolation polynomial (or trigonometrical polynomial). We show that if we are given the collocation point values (or a highly accurate approximation) at the Gauss or Gauss-Lobatto points, we can reconstruct a uniform exponentially convergent approximation to the function f(x) in any sub-interval of analyticity. The proof covers the cases of Fourier, Chebyshev, Legendre, and more general Gegenbauer collocation methods.

Gottlieb, David↗
NASA NTRS2004

Steps in Solution Growth: Revised Gibbs-Thomson Law, Turbulence and Morphological Stability

Two groups of new phenomena revealed by AFM and high resolution optical interferometry on crystal faces growing from solutions will be discussed. 1. Spacing between strongly polygonized spiral steps with low less than 10(exp -2) kink density on lysozyme and K- biphtalate do not follow the Burton-cabrera-Frank theory. The critical length of the yet immobile first Short step segment adjacent to a pinning defect (dislocation, stacking fault) is many times longer than that following from the step free energy. The low-kink density steps are typical of many growth conditions and materials, including low temperature gas phase epitaxy and MBE. 2. The step bunching pattern on the approx. 1 cm long { 110) KDP face growing from the turbulent solution flow (Re (triple bonds) 10(exp 4), solution flow rate approx. 1 m/s) suggests that the step bunch height does not increase infinitely as the bunch path on the crystal face rises, as is usually observed on large KDP crystals. The mechanism controlling the maximal bunch width and height is based on the drag of the solution depleted by the step bunch down thc solution stream. It includes splitting, coagulation and interlacing of bunches

Chernov, A. A.↗
NASA NTRS1985

Sigma Filter

The GLA Fourth-Order model is needed to smooth the topography. This is to remove the Gibbs phenomenon. The Gibbs phenomenon occurs whenever we truncate a Fourier Series. The Sigma factors were introduced to reduce the Gibbs phenomenon. It is found that the smooth Fourier series is nothing but the original Fourier series with its coefficients multiplied by corresponding sigma factors. This operator can be applied many times to obtain high order sigma filtered field and is easily applicable using FFT. It is found that this filter is beneficial in deriving the topography.

Balgovind, R. C.↗