Scalability Analysis of Parallel GMRES Implementations

Applications involving large sparse nonsymmetric linear systems encourage parallel implementations of robust iterative solution methods, such as GMRES(k). Two parallel versions of GMRES(k) based on different data distributions and using Householder reflections in the orthogonalization phase, and variations of these which adapt the restart value k, are analyzed with respect to scalability (their ability to maintain fixed efficiency with an increase in problem size and number of processors).A theoretical algorithm-machine model for scalability is derived and validated by experiments on three parallel computers, each with different machine characteristics

Spectra of Maser Radiation from a Turbulent, Circumnuclear Accretion Disk. III. Circular polarization

Calculations are performed for the circular polarization of maser radiation from a turbulent, Keplerian disk that is intended to represent the sub-parsec disk at the nucleus of the galaxy NGC4258. The polarization in the calculations is a result of the Zeeman effect in the regime in which the Zeeman splitting is much less than the spectral linebreadth. Plausible configurations for turbulent magnetic and velocity fields in the disk are created by statistical methods. This turbulence, along with the Keplerian velocity gradients and the blending of the three hyperfine components to form the $6_{16} - 5_{23}$ masing transition of water, are key ingredients in determining the appearance of the polarized spectra that are calculated. These spectra are quite different from the polarized spectra that would be expected for a two-level transition where there is no hyperfine structure. The effect of the hyperfine structure on the polarization is most striking in the calculations for the maser emission that represents the central (or systemic) features of NGC4258. Information about magnetic fields is inferred from observations for polarized maser radiation and bears on the structure of accretion disks.Comment: Latex, uses aastex, eucal, to be published in the Astrophysical Journa

Evaluation of a Multizone Impedance Eduction Method

A computational study is used to evaluate the PyCHE impedance eduction method developed at the NASA Langley Research Center. This method combines an aeroacoustic duct propagation code based on numerical solution to the convected Helmholtz equation with a global optimizer that uses the Differential Evolution algorithm. The efficacy of this method is evaluated with acoustic pressure data simulated to represent that measured with one-zone, two-zone, and three-zone liners mounted in the NASA Langley Grazing Flow Impedance Tube. The PyCHE method has a normalized impedance error of approximately 0.2 for (uniform) one-zone liners with a length of at least 5, and produces quite reasonable results for liners as short as 2. Whereas the impedance of the liner has an effect on eduction accuracy, the amount of attenuation is shown to be the dominant parameter. Similar results are observed for two-zone liners, for which the impedance of each zone is unique. The two-zone results also indicate it is more difficult to accurately educe resistance than reactance, and a zone length of at least 6 (slightly longer than for uniform liners) is needed to limit the normalized error to 0.2. The PyCHE method is also demonstrated to successfully educe the impedances for each zone of a three-zone liner. These results are sufficiently encouraging to warrant the continued usage of the PyCHE impedance eduction method for single and multizone liners

Development of a super ductile diecast Al-Mg-Si alloy

This is the post-print version of the final paper published in Materials Science and Engineering A. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright @ 2012 Elsevier B.V.The super ductile diecast aluminium alloys have been developed particularly for application in automotive body structure. On the basis of the reviewing aluminium alloys currently available, the requirement of diecast aluminium alloys is summarized and the Al-Mg-Si system is focused in the development. The effect of various alloying elements on the microstructure and the mechanical properties, such as yield strength, ultimate tensile strength and elongation is assessed. The optimized composition of the super ductile Al-Mg-Si alloy has been found to be at 5.0-5.5wt% Mg, 1.5-2.0wt% Si, 0.5-0.7wt% Mn, 0.15-0.2wt% Ti with Fe <0.25wt% for the best combination of strength and ductility, which shows 150MPa of yield strength, 300MPa of ultimate tensile strength, and 15% of elongation under as-cast condition. The paint baking hardenability of the optimized alloy is found to be insignificant. Less than a 10% increase in the yield strength was achieved, with a slight decrease in the elongation after aging at 180°C for 30min, which is a simulated process of paint baking. Cu is found to slightly increase the yield strength under the as-cast condition and after the heat treatment, but with a significant reduction in the ductility. Therefore, Cu should be limited in the super ductile aluminium alloy. The microstructure of diecast aluminium alloys at the optimized composition consists of the primary α-Al phase, the α-AlFeMnSi intermetallics and the Al-Mg Si eutectics. There are two types of primary α-Al phase: dendritic or fragmented dendritic α-Al phase solidified in the shot sleeve and globular α-Al particles solidified in the die cavity. The α-AlFeMnSi intermetallics is in the form of compact morphology and with a size of less than 3μm. The eutectic cells are at size of 10μm with a typical lamellar morphology of α-Al phase and Mg Si phase.EPSRC and JLRUK

High Redshift Standard Candles: Predicted Cosmological Constraints

We investigate whether future measurements of high redshift standard candles (HzSCs) will be a powerful probe of dark energy, when compared to other types of planned dark energy measurements. Active galactic nuclei and gamma ray bursts have both been proposed as potential HzSC candidates. Due to their high luminosity, they can be used to probe unexplored regions in the expansion history of the universe. Information from these regions can help constrain the properties of dark energy, and in particular, whether it varies over time. We consider both linear and piecewise parameterizations of the dark energy equation of state, $w(z)$, and assess the optimal redshift distribution a high-redshift standard-candle survey could take to constrain these models. The more general the form of the dark energy equation of state $w(z)$ being tested, the more useful high-redshift standard candles become. For a linear parameterization of $w(z)$, HzSCs give only small improvements over planned supernova and baryon acoustic oscillation measurements; a wide redshift range with many low redshift points is optimal to constrain this linear model. However to constrain a general, and thus potentially more informative, form of $w(z)$, having many HzSCs can significantly improve limits on the nature of dark energy.Comment: Accepted MNRAS, 27 Pages, 15 figures, matches published versio

On the Use of Group Theoretical and Graphical Techniques toward the Solution of the General N-body Problem

Group theoretic and graphical techniques are used to derive the N-body wave function for a system of identical bosons with general interactions through first-order in a perturbation approach. This method is based on the maximal symmetry present at lowest order in a perturbation series in inverse spatial dimensions. The symmetric structure at lowest order has a point group isomorphic with the S_N group, the symmetric group of N particles, and the resulting perturbation expansion of the Hamiltonian is order-by-order invariant under the permutations of the S_N group. This invariance under S_N imposes severe symmetry requirements on the tensor blocks needed at each order in the perturbation series. We show here that these blocks can be decomposed into a basis of binary tensors invariant under S_N. This basis is small (25 terms at first order in the wave function), independent of N, and is derived using graphical techniques. This checks the N^6 scaling of these terms at first order by effectively separating the N scaling problem away from the rest of the physics. The transformation of each binary tensor to the final normal coordinate basis requires the derivation of Clebsch-Gordon coefficients of S_N for arbitrary N. This has been accomplished using the group theory of the symmetric group. This achievement results in an analytic solution for the wave function, exact through first order, that scales as N^0, effectively circumventing intensive numerical work. This solution can be systematically improved with further analytic work by going to yet higher orders in the perturbation series.Comment: This paper was submitted to the Journal of Mathematical physics, and is under revie

A flight investigation of a terminal area navigation and guidance concept for STOL aircraft

A digital avionics system was installed in the CV-340 transport aircraft. Flight tests were made to obtain preliminary performance data in the manual flight director mode using time controlled guidance. These tests provide a basis for selection of terminal area guidance, navigation, and control system concepts for short haul aircraft and for investigating operational procedures

An Investigation, Using Standard Experimental Techniques, to Determine FLCs at Elevated Temperature for Aluminium Alloys

An experimental procedure has been developed for the determination of FLCs at elevated temperatures. The GOM ARGUS system was employed for measuring surface strain based on pre-applied grids (pattern), and limit strains were determined according to the ISO 12004-2:2008 standard. Forming limit curves (FLCs) have been determined for AA5754 under warm forming conditions in an isothermal environment. The tests were carried out at various temperatures up to 300oC and forming speeds ranging from 5 – 300 mm s-1 . Results reveal the significant effect of both temperature and forming speed on FLCs of AA5754. Formability increases with increasing temperature above 200oC. Formability also increases with decreasing speed. The presented FLC results show that the best formability exists at low forming speed and the high temperature end of the warm forming range

Reorientation of quantum Hall stripes within a partially filled Landau level

We investigate the effect of the filling factor on transport anisotropies, known as stripes, in high Landau levels of a two-dimensional electron gas. We find that at certain in-plane magnetic fields, the stripes orientation is sensitive to the filling factor within a given Landau level. This sensitivity gives rise to the emergence of stripes away from half-filling while an orthogonally-oriented, native stripes reside at half-filling. This switching of the anisotropy axes within a single Landau level can be attributed to a strong dependence of the native symmetry breaking potential on the filling factor