Evaluation of massless-spring modeling of suspension-line elasticity during the parachute unfurling process

A general theory on mathematical modeling of elastic parachute suspension lines during the unfurling process was developed. Massless-spring modeling of suspension-line elasticity was evaluated in detail. For this simple model, equations which govern the motion were developed and numerically integrated. The results were compared with flight test data. In most regions, agreement was satisfactory. However, poor agreement was obtained during periods of rapid fluctuations in line tension

A Color-Magnitude Diagram for a Globular Cluster In the Giant Elliptical Galaxy NGC 5128

The Hubble Space Telescope has been used to obtain WFPC2 (V,I) photometry for a large sample of stars in the outer halo of the giant elliptical NGC 5128 (d = 4 Mpc). The globular cluster N5128-C44, at the center of the Planetary Camera field, is well enough resolved to permit the construction of a color-magnitude diagram (CMD) for it which covers the brightest two magnitudes of the giant branch. The CMD is consistent with that of a normal old, moderately low-metallicity ([Fe/H] = -1.30 globular cluster, distinctly more metal-poor than most of the field halo stars at the same projected location (which average [Fe/H] ~ -0.5). This is the most distant globular cluster in which direct color-magnitude photometry has been achieved to date, and the first one belonging to a giant E galaxy.Comment: 12 pages, LaTeX, including 5 postscript figures; submitted to Astronomical Journa

SAGE III aerosol extinction validation in the Arctic winter: comparisons with SAGE II and POAM III

The use of SAGE III multiwavelength aerosol extinction coefficient measurements to infer PSC type is contingent on the robustness of both the extinction magnitude and its spectral variation. Past validation with SAGE II and other similar measurements has shown that the SAGE III extinction coefficient measurements are reliable though the comparisons have been greatly weighted toward measurements made at mid-latitudes. Some aerosol comparisons made in the Arctic winter as a part of SOLVE II suggested that SAGE III values, particularly at longer wavelengths, are too small with the implication that both the magnitude and the wavelength dependence are not reliable. Comparisons with POAM III have also suggested a similar discrepancy. Herein, we use SAGE II data as a common standard for comparison of SAGE III and POAM III measurements in the Arctic winters of 2002/2003 through 2004/2005. During the winter, SAGE II measurements are made infrequently at the same latitudes as these instruments. We have mitigated this problem through the use of potential vorticity as a spatial coordinate and thus greatly increased of the number of coincident events. We find that SAGE II and III extinction coefficient measurements show a high degree of compatibility at both 1020 nm and 450 nm except a 10–20% bias at both wavelengths. In addition, the 452 to 1020 nm extinction ratio shows a consistent bias of ~30% throughout the lower stratosphere. We also find that SAGE II and POAM III are on average consistent though the comparisons show a much higher variability and larger bias than SAGE II/III comparisons. In addition, we find that SAGE II and POAM III data sets are not well correlated at and below 18 km. Overall, we find both the extinction values and the spectral dependence from SAGE III are robust and we find no evidence of a significant defect within the Arctic vortex

Wave spectra of a shoaling wave field: A comparison of experimental and simulated results

Wave profile measurements made from an aircraft crossing the North Carolina continental shelf after passage of Tropical Storm Amy in 1975 are used to compute a series of wave energy spectra for comparison with simulated spectra. Results indicate that the observed wave field experiences refraction and shoaling effects causing statistically significant changes in the spectral density levels. A modeling technique is used to simulate the spectral density levels. Total energy levels of the simulated spectra are within 20 percent of those of the observed wave field. The results represent a successful attempt to theoretically simulate, at oceanic scales, the decay of a wave field which contains significant wave energies from deepwater through shoaling conditions

Multi-color incomplete Cholesky conjugate gradient methods for vector computers

In this research, we are concerned with the solution on vector computers of linear systems of equations, Ax = b, where A is a larger, sparse symmetric positive definite matrix. We solve the system using an iterative method, the incomplete Cholesky conjugate gradient method (ICCG). We apply a multi-color strategy to obtain p-color matrices for which a block-oriented ICCG method is implemented on the CYBER 205. (A p-colored matrix is a matrix which can be partitioned into a pXp block matrix where the diagonal blocks are diagonal matrices). This algorithm, which is based on a no-fill strategy, achieves O(N/p) length vector operations in both the decomposition of A and in the forward and back solves necessary at each iteration of the method. We discuss the natural ordering of the unknowns as an ordering that minimizes the number of diagonals in the matrix and define multi-color orderings in terms of disjoint sets of the unknowns. We give necessary and sufficient conditions to determine which multi-color orderings of the unknowns correpond to p-color matrices. A performance model is given which is used both to predict execution time for ICCG methods and also to compare an ICCG method to conjugate gradient without preconditioning or another ICCG method. Results are given from runs on the CYBER 205 at NASA's Langley Research Center for four model problems

Ince's limits for confluent and double-confluent Heun equations

We find pairs of solutions to a differential equation which is obtained as a special limit of a generalized spheroidal wave equation (this is also known as confluent Heun equation). One solution in each pair is given by a series of hypergeometric functions and converges for any finite value of the independent variable $z$, while the other is given by a series of modified Bessel functions and converges for $|z|>|z_{0}|$, where $z_{0}$ denotes a regular singularity. For short, the preceding limit is called Ince's limit after Ince who have used the same procedure to get the Mathieu equations from the Whittaker-Hill ones. We find as well that, when $z_{0}$ tends to zero, the Ince limit of the generalized spheroidal wave equation turns out to be the Ince limit of a double-confluent Heun equation, for which solutions are provided. Finally, we show that the Schr\"odinger equation for inverse fourth and sixth-power potentials reduces to peculiar cases of the double-confluent Heun equation and its Ince's limit, respectively.Comment: Submitted to Journal of Mathmatical Physic

SAGE III Aerosol Extinction Validation in the Arctic Winter: Comparisons with SAGE II and POAM III

The use of SAGE III multiwavelength aerosol extinction coefficient measurements to infer PSC type is contingent on the robustness of both the extinction magnitude and its spectral variation. Past validation with SAGE II and other similar measurements has shown that the SAGE III extinction coefficient measurements are reliable though the comparisons have been greatly weighted toward measurements made at mid-latitudes. Some aerosol comparisons made in the Arctic winter as a part of SOLVE II suggested that SAGE III values, particularly at longer wavelengths, are too small with the implication that both the magnitude and the wavelength dependence are not reliable. Comparisons with POAM III have also suggested a similar discrepancy. Herein, we use SAGE II data as a common standard for comparison of SAGE III and POAM III measurements in the Arctic winters of 2002/2003 through 2004/2005. During the winter, SAGE II measurements are made infrequently at the same latitudes as these instruments. We have mitigated this problem through the use potential vorticity as a spatial coordinate and thus greatly increased the number of coincident events. We find that SAGE II and III extinction coefficient measurements show a high degree of compatibility at both 1020 nm and 450 nm except a 10-20% bias at both wavelengths. In addition, the 452 to 1020-nm extinction ratio shows a consistent bias of approx. 30% throughout the lower stratosphere. We also find that SAGE II and POAM III are on average consistent though the comparisons show a much higher variability and larger bias than SAGE II/III comparisons. In addition, we find that the two data sets are not well correlated below 18 km. Overall, we find both the extinction values and the spectral dependence from SAGE III are robust and we find no evidence of a significant defect within the Arctic vortex

CSM Testbed Development and Large-Scale Structural Applications

A research activity called Computational Structural Mechanics (CSM) conducted at the NASA Langley Research Center is described. This activity is developing advanced structural analysis and computational methods that exploit high-performance computers. Methods are developed in the framework of the CSM Testbed software system and applied to representative complex structural analysis problems from the aerospace industry. An overview of the CSM Testbed methods development environment is presented and some new numerical methods developed on a CRAY-2 are described. Selected application studies performed on the NAS CRAY-2 are also summarized