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NASA NTRS1995

Structural design using equilibrium programming formulations

Solutions to increasingly larger structural optimization problems are desired. However, computational resources are strained to meet this need. New methods will be required to solve increasingly larger problems. The present approaches to solving large-scale problems involve approximations for the constraints of structural optimization problems and/or decomposition of the problem into multiple subproblems that can be solved in parallel. An area of game theory, equilibrium programming (also known as noncooperative game theory), can be used to unify these existing approaches from a theoretical point of view (considering the existence and optimality of solutions), and be used as a framework for the development of new methods for solving large-scale optimization problems. Equilibrium programming theory is described, and existing design techniques such as fully stressed design and constraint approximations are shown to fit within its framework. Two new structural design formulations are also derived. The first new formulation is another approximation technique which is a general updating scheme for the sensitivity derivatives of design constraints. The second new formulation uses a substructure-based decomposition of the structure for analysis and sensitivity calculations. Significant computational benefits of the new formulations compared with a conventional method are demonstrated.

Scotti, Stephen J.↗

NASA NTRS1994

Physical processes in eclipsing pulsars: Eclipse mechanisms and diagnostics

We investigate how the radio emission of a pulsar interacts with plasma derived from a stellar companion. Various physical mechanisms that can cause radio pulse eclipse are discussed, and predictions are made for the polarization properties of the emergent radio wave. We consider eclipses by a wind from the stellar companion, by a stellar magnetosphere, or by material entrained in the pulsar wind. Eclipses due to refraction require either a relatively high plasma density or a sharp edge to the plasma distribution. The conditions that must prevail for free-free absorption to be effective in eclipsing a radio beam are also outlined. Pulse smearing may be important at higher frequencies; related eclipse mechanisms include pulse spreading due to a rapidly changing electron column, and scattering by Langmuir turbulence. The high brightness temperature radio beam can generate its own plasma turbulence via a number of nonlinear parametric instabilities, such as the instability associated with stimulated Raman scattering. When the plasma turbulence is heavily damped, the radio bean can still undergo induced Compton scattering. Stimulated scattering effects such as these are very sensitive to the presence of narrow-band substructure in the pulsar radio emission. Finally, we consider the possibility that plasma derived from a stellar companion may mix with the relativistic pulsar wind and cause cyclotron absorption at low radio frequencies. Even if the cyclotron optical depth is small, fluctuations in the emergent polarization of the radio beam on the timescale of a few seconds are a very sensitive probe of the spatial structure of the magnetic field in the pulsar wind. The current observational properties of two known eclipsing pulsar systems, PSR 1957+20 and PSR 1744-24A, are used to construct tentative eclipse models. The favored model for PSR 1957+20 is cyclotron or synchrotron absorption by plasma embedded in the pulsar wind combined with pulse smearing at high frequency, and the favored model for PSR 1744-24A is backscattering off plasma turbulence generated by the stimulated Raman scattering parametric instability. Pulsar eclipses promise to provide a good diagnostic of pulsar winds and possible of the pulse emission mechanism.

Thompson, C.↗

NASA NTRS1994

Cold dark matter. 1: The formation of dark halos

We use numerical simulations of critically closed cold dark matter (CDM) models to study the effects of numerical resolution on observable quantities. We study simulations with up to 256(exp 3) particles using the particle-mesh (PM) method and with up to 144(exp 3) particles using the adaptive particle-particle-mesh (P3M) method. Comparisons of galaxy halo distributions are made among the various simulations. We also compare distributions with observations, and we explore methods for identifying halos, including a new algorithm that finds all particles within closed contours of the smoothed density field surrounding a peak. The simulated halos show more substructure than predicted by the Press-Schechter theory. We are able to rule out all omega = 1 CDM models for linear amplitude sigma(sub 8) greater than or approximately = 0.5 because the simulations produce too many massive halos compared with the observations. The simulations also produce too many low-mass halos. The distribution of halos characterized by their circular velocities for the P3M simulations is in reasonable agreement with the observations for 150 km/s less than or = V(sub circ) less than or = 350 km/s.

Gelb, James M.↗

NASA NTRS1994

Synthesized spectra of turbulent clouds

A comparison has been made of the velocity structure of non-star-forming dense molecular clouds and the output of a 512(exp 3) hydrodynamic code for compressible gas displaying features of turbulence. A remarkable similarity exists between the interstellar line profiles and the velocity profiles found by integrating, with an optically thin assumption, through subsections of the simulation. This similarity is in terms of both the structure of individual spectra, showing skewness, multiple peaks, and wings, and also the variations of the spectra from point to point. It is possible to see the origin of the various velocity substructures and how they correlate with regions of high density and velocity divergence, or regions of high vorticity, by deprojecting individual spectra of the simulation. It is found that the interstellar medium spectra are best represented by the epoch of the simulation in which the energy spectrum is essentially Kolmogorov-like and initially developed shocks have been largely converted into vorticity structures. Further, it is found that the vorticity peaks ascribed to intermittency contribute to the non-Gaussian features and wings of the line profile, but at an intensity level that is weak compared to the contribution of the bulk of the flow.

Falgarone, E.↗

NASA NTRS1994

Hubble Space Telescope imaging of super-star clusters in NGC 1569 and NGC 1705

We examine the structural properties of three super-star clusters in the nearby, H I-rich galaxies NGC 1569 and NGC 1705. The clusters, which have total absolute V magnitudes between -13.3 and -14.1, appear to be point sources on ground-based images but are partially resolved in new images obtained with the Hubble Space Telescope (HST) Planetary Camera. From deconvolved V- and I-band images we find that the three clusters have very compact cores with extended halos that are partially resolved into individual stars. Using new distances to the galaxies derived from color-magnitude diagrams for field stars, we find that the half-light radii are 2.2-3.4 pc. The cluster in NGC 1705 is barely resolved in the HST images. The clusters in NGC 1569, on the other hand, show significant substructure in their cores and ellipticities that are comparable to the flattenings seen in young clusters in the Large Magellanic Cloud (LMC). The clusters show internal (V-I) color gradients. The properties of these clusters are similar to R136, the core of the luminous star-forming complex 30 Doradus in the LMC, except that R136 has a lower luminosity and central surface brightness. The half-light surface brightness of the brightest cluster (NGC 1569 A) is 1.3 x 10(exp 6) L(sub v) solar/ sq cm, which is over 65 times higher than R136 and 1200 times higher than the mean rich LMC star cluster other than R136 after allowing for aging effects. The next brightest clusters in each of these galaxies are greater than or = 2 mag fainter. Thus, the super-star clusters represent an extreme but uncommon mode of star formation. In terms of luminosity and size, they appear to be good analogs of young globular clusters.

O'Connell, Robert W.↗

NASA NTRS1994

The dynamical evolution of poor clusters of galaxies: Growth and properties of the first-ranked galaxy

We report N-body simulations of the dynamical evolution of isolated clusters of 50 galaxies containing a dark matter component that comprises 90% of the cluster mass. For our adopted physical scaling, the line-of-sight velocity dispersion of the cluster is 310 km/s and the initial core radius is 250 kpc. Our results are applicable to (1) present-day poor clusters, (2) the small systems that may have merged to produce present-day rich clusters, and (3) virialized subclumps within larger systems, in between major substructure merger events. We have evolved a total of 10 cluster models, using N = 40,000 particles per model. The models are fully self-consistent in that each galaxy is represented as an extended structure containing many particles and the gravitational potential arises from the particles alone. Dark matter is apportioned between the galaxy halos and a smoothly distributed common group halo, the intracluster background (ICB). The percentage of cluster mass initially in the ICB, Beta, is chosen to be 50, 75, or 90. Increasing Beta has the effect of removing mass from dark halos around galaxies and distributing it throughout the cluster. The initial conditions were constructed by randomly sampling a King distribution with W(sub 0) = 6. The galaxies are also King models; the masses of the galaxies follow a Schechter distribution function.

Bode, Paul W.↗

NASA NTRS1993

Symposium on Parallel Computational Methods for Large-scale Structural Analysis and Design, 2nd, Norfolk, VA, US

Computing speed is leaping forward by several orders of magnitude each decade. Engineers and scientists gathered at a NASA Langley symposium to discuss these exciting trends as they apply to parallel computational methods for large-scale structural analysis and design. Among the topics discussed were: large-scale static analysis; dynamic, transient, and thermal analysis; domain decomposition (substructuring); and nonlinear and numerical methods.

Storaasli, Olaf O.↗

NASA NTRS1993

Space station static and dynamic analyses using parallel methods

Algorithms for high-performance parallel computers are applied to perform static analyses of large-scale Space Station finite-element models (FEMs). Several parallel-vector algorithms under development at NASA Langley are assessed. Sparse matrix solvers were found to be more efficient than banded symmetric or iterative solvers for the static analysis of large-scale applications. In addition, new sparse and 'out-of-core' solvers were found superior to substructure (superelement) techniques which require significant additional cost and time to perform static condensation during global FEM matrix generation as well as the subsequent recovery and expansion. A method to extend the fast parallel static solution techniques to reduce the computation time for dynamic analysis is also described. The resulting static and dynamic algorithms offer design economy for preliminary multidisciplinary design optimization and FEM validation against test modes. The algorithms are being optimized for parallel computers to solve one-million degrees-of-freedom (DOF) FEMs. The high-performance computers at NASA afforded effective software development, testing, efficient and accurate solution with timely system response and graphical interpretation of results rarely found in industry. Based on the author's experience, similar cooperation between industry and government should be encouraged for similar large-scale projects in the future.

Gupta, V.↗

NASA NTRS1993

Fast structural design and analysis via hybrid domain decomposition on massively parallel processors

A hybrid domain decomposition framework for static, transient and eigen finite element analyses of structural mechanics problems is presented. Its basic ingredients include physical substructuring and /or automatic mesh partitioning, mapping algorithms, 'gluing' approximations for fast design modifications and evaluations, and fast direct and preconditioned iterative solvers for local and interface subproblems. The overall methodology is illustrated with the structural design of a solar viewing payload that is scheduled to fly in March 1993. This payload has been entirely designed and validated by a group of undergraduate students at the University of Colorado using the proposed hybrid domain decomposition approach on a massively parallel processor. Performance results are reported on the CRAY Y-MP/8 and the iPSC-860/64 Touchstone systems, which represent both extreme parallel architectures. The hybrid domain decomposition methodology is shown to outperform leading solution algorithms and to exhibit an excellent parallel scalability.

Farhat, Charbel↗

NASA NTRS1994

1919+479: Big WAT in a poor cluster

New x-ray, optical, and redshift data are presented for the cluster of galaxies associated with the giant, 1 Mpc diameter, wide-angle tailed (WAT) radio galaxy 1919+479. The ROSAT Position-Sensitive Proportional Counter (PSPC) pointed observation shows an x-ray peak on the WAT and elongated diffuse emission tracing the galaxy distribution. In addition, an asymmetric extension of emission exists between the tails of the WAT. The fitting of a Raymond-Smith thermal model to the x-ray spectra suggests an approximately = 2 keV temperature intracluster medium (ICM). The cooling time and irregular morphology rule out a cluster-wide cooling flow. The x-ray luminosity and temperature are consistent with the velocity dispersion, 480 km/s, estimated from 31 galaxy velocities. However, this velocity distribution is significantly non-Gaussian, which along with the x-ray morphology, suggests incomplete virialization in the cluster. Substructure analysis does not reveal significant clumping in the velocities/positions; but, the spatial distribution of galaxies is very elongated. Also, the cD galaxy producing the WAT does not have a significant radial peculiar velocity with respect to the cluster centroid. These characteristics are consistent with a merger scenario in which a subcluster has crossed the cluster core in the plane of the sky and has dispersed. We compare this cluster with the post-merger cluster Abell 2634 (Pinkney et al., 1993), containing the prototype WAT, and with a recent N-Body/Hydro simulation of merging clusters. The similarities indicate that the cluster 1919+479 may be the poor extreme of a class of clusters in which the bulk motion in the ICM, caused by a subcluster merger, in shaping the central WAT.

Pinkney, Jason↗

NASA NTRS1995

Hubble Space Telescope imaging of a radio-quiet galaxy at redshift z = 3.4

We have observed with the Wide Field/Planetary Camera (WF/PC) on the Hubble Space Telescope (HST) a radio-quiet Ly alpha-emitting galaxy at redshift z = 3.428 (G2 below). The images probe the rest-frame UV light around 1250 A with an angular resolution of approx. = 0.1 sec, corresponding to 1.4 h(exp -1, sub 50) kpc at redshift z = 3.4 (in this Letter we use q(sub 0) = 0 and H(sub 0) = 50 h(exp -1, sub 50) km/s/Mpc). The light profile of the central approx. 10h(exp -1, sub 50) kpc region is well fitted by an r(exp 1/4) law with r(sub e) approx. = 1.3 h(exp -1, sub 50) kpc, suggesting a dynamically relaxed state. The outer regions are characterized by the presence of substructures, such as an elongated formation and low surface brightness nebulosities. The isophotal analysis shows no evidence of an active galactic nuclei (AGN)-like unresolved source in the center. The structural properties of G2 are consistent with a dynamically hot stellar system observed during an early phase of star formation, very likely the progenitor of an elliptical or the bulge of a spiral galaxy.

Giavalisco, Mauro↗

NASA NTRS1993

The X-ray structure of nearby galaxy clusters

The combination of the large effective area and the very low internal background of the ROSAT Position Sensitive Proportional Counter provides an extremely sensitive instrument for the study of diffuse X-ray sources. In this paper we review new results on the X-ray structure of nearby clusters as measured with ROSAT. Substructure is a common feature in these objects. Such structure provides evidence that clusters have formed relatively recently through mergers of relatively large subunits. This behavior is predicted by hierarchical formation theories in a dense universe.

Henry, J. P.↗

NASA NTRS1995

The spatial distribution, kinematics, and dynamics of the galaxies in the region of Abell 2634 and 2666

A total of 663 galaxies with known redshifts in a 12 deg x 12 deg field centered on A2634, including 211 new measurements, are used to study in detail the structure of the region. In it we find six main galaxy concentrations: the nearby clusters A2634 and A2666, two groups in the vicinity of A2634, and two distant clusters at approximately 18,000 (A2622) and approximately 37,000 km/s seen in projection near the core of A2634. For A2634, the most richly sampled of those concentrations, we are able to apply strict cluster membership criteria. Two samples - one containing 200 galaxies within 2 deg from the cluster center and a second, magnitude-limited, of 118 galaxies within the central half degree - are used to examine the structure, kinematics, dynamics, and morphological segregation of the cluster. We show that early type galaxies appear to be a relaxed system, while the spiral population eschews the center of the cluster and exhibits both a multimodal velocity distribution and a much larger velocity dispersion that the ellipticals. We propose that the spiral galaxies of A2634 represent a dynamically young cluster population. For the galaxy component of A2634, we find no evidence of significant substructure in the central regions. We also conclude that the adoption of lenient membership criteria that ignore the dynamical complexity of A2634 are unlikely to be responsible for the conflicting results reported on the motion of this cluster with respect ot the CMB. The kinematical and dynamical analysis is extended to A2634's close companion, A2666, and the two distant background clusters.

Scodeggio, Marco↗

NASA NTRS1995

Predictions of thermal buckling strengths of hypersonic aircraft sandwich panels using minimum potential energy and finite element methods

Thermal buckling characteristics of hypersonic aircraft sandwich panels of various aspect ratios were investigated. The panel is fastened at its four edges to the substructures under four different edge conditions and is subjected to uniform temperature loading. Minimum potential energy theory and finite element methods were used to calculate the panel buckling temperatures. The two methods gave fairly close buckling temperatures. However, the finite element method gave slightly lower buckling temperatures than those given by the minimum potential energy theory. The reasons for this slight discrepancy in eigensolutions are discussed in detail. In addition, the effect of eigenshifting on the eigenvalue convergence rate is discussed.

Ko, William L.↗

NASA NTRS1995

Parallelized modelling and solution scheme for hierarchically scaled simulations

This two-part paper presents the results of a benchmarked analytical-numerical investigation into the operational characteristics of a unified parallel processing strategy for implicit fluid mechanics formulations. This hierarchical poly tree (HPT) strategy is based on multilevel substructural decomposition. The Tree morphology is chosen to minimize memory, communications and computational effort. The methodology is general enough to apply to existing finite difference (FD), finite element (FEM), finite volume (FV) or spectral element (SE) based computer programs without an extensive rewrite of code. In addition to finding large reductions in memory, communications, and computational effort associated with a parallel computing environment, substantial reductions are generated in the sequential mode of application. Such improvements grow with increasing problem size. Along with a theoretical development of general 2-D and 3-D HPT, several techniques for expanding the problem size that the current generation of computers are capable of solving, are presented and discussed. Among these techniques are several interpolative reduction methods. It was found that by combining several of these techniques that a relatively small interpolative reduction resulted in substantial performance gains. Several other unique features/benefits are discussed in this paper. Along with Part 1's theoretical development, Part 2 presents a numerical approach to the HPT along with four prototype CFD applications. These demonstrate the potential of the HPT strategy.

Padovan, Joe↗

NASA NTRS1996

Domain Decomposition Algorithms for First-Order System Least Squares Methods

Least squares methods based on first-order systems have been recently proposed and analyzed for second-order elliptic equations and systems. They produce symmetric and positive definite discrete systems by using standard finite element spaces, which are not required to satisfy the inf-sup condition. In this paper, several domain decomposition algorithms for these first-order least squares methods are studied. Some representative overlapping and substructuring algorithms are considered in their additive and multiplicative variants. The theoretical and numerical results obtained show that the classical convergence bounds (on the iteration operator) for standard Galerkin discretizations are also valid for least squares methods.

Pavarino, Luca F.↗

NASA NTRS1993

The Mid-Infrared Transmission Spectra of Antarctic Ureilites

The mid-infrared (4000-450 1/cm; 2.5-22.2 micron) transmission spectra of seven Antarctic ureilites and 10 Antarctic H-5 ordinary chondrites are presented. The ureilite spectra show a number of absorption bands, the strongest of which is a wide, complex feature centered near 1000 1/cm (10 micron) due to Si-O stretching vibrations in silicates. The profiles and positions of the substructure in this feature indicate that Mg-rich olivines and pyroxenes are the main silicates responsible. The relative abundances of these two minerals, as inferred from the spectra, show substantial variation from meteorite to meteorite, but generally indicate olivine is the most abundant (olivine:pyroxene = 60:40 to 95:5). Both the predominance of olivine and the variable olivine-to-pyroxene ratio are consistent with the known composition and heterogeneity of ureilites. The H-5 ordinary chondrites spanned a range of weathering classes and were used to provide a means of addressing the extent to which the ureilite spectra may have been altered by weathering processes. It was found that, while weathering of these meteorites produces some weak bands due to the formation of small amounts of carbonates and hydrates, the profile of the main silicate feature has been little affected by Antarctic exposure in the meteorites studied here. The mid-infrared ureilite spectra provide an additional means of testing potential asteroidal parent bodies for the ureilites. At present, the best candidates include the subset of S-type asteroids having low albedos and weak absorption features in the near infrared.

Sandford, Scott A.↗

NASA NTRS1997

Thermostructural Behavior of a Hypersonic Aircraft Sandwich Panel Subjected to Heating on One Side

Thermostructural analysis was performed on a heated titanium honeycomb-core sandwich panel. The sandwich panel was supported at its four edges with spar-like substructures that acted as heat sinks, which are generally not considered in the classical analysis. One side of the panel was heated to high temperature to simulate aerodynamic heating during hypersonic flight. Two types of surface heating were considered: (1) flat-temperature profile, which ignores the effect of edge heat sinks, and (2) dome-shaped-temperature profile, which approximates the actual surface temperature distribution associated with the existence of edge heat sinks. The finite-element method was used to calculate the deformation field and thermal stress distributions in the face sheets and core of the sandwich panel. The detailed thermal stress distributions in the sandwich panel are presented, and critical stress regions are identified. The study shows how the magnitudes of those critical stresses and their locations change with different heating and edge conditions. This technical report presents comprehensive, three-dimensional graphical displays of thermal stress distributions in every part of a titanium honeycomb-core sandwich panel subjected to hypersonic heating on one side. The plots offer quick visualization of the structural response of the panel and are very useful for hot structures designers to identify the critical stress regions.

Ko, William L.↗