On the factorization of secular equations by group theory.
Explicit invariant forms of factor equations for factorization of secular equations by group theory
QUANTUM MECHANICS↗
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A high order accurate finite element algorithm for high Reynolds number flow prediction
A Galerkin-weighted residuals formulation is employed to establish an implicit finite element solution algorithm for generally nonlinear initial-boundary value problems. Solution accuracy, and convergence rate with discretization refinement, are quantized in several error norms, by a systematic study of numerical solutions to several nonlinear parabolic and a hyperbolic partial differential equation characteristic of the equations governing fluid flows. Solutions are generated using selective linear, quadratic and cubic basis functions. Richardson extrapolation is employed to generate a higher-order accurate solution to facilitate isolation of truncation error in all norms. Extension of the mathematical theory underlying accuracy and convergence concepts for linear elliptic equations is predicted for equations characteristic of laminar and turbulent fluid flows at nonmodest Reynolds number. The nondiagonal initial-value matrix structure introduced by the finite element theory is determined intrinsic to improved solution accuracy and convergence. A factored Jacobian iteration algorithm is derived and evaluated to yield a consequential reduction in both computer storage and execution CPU requirements while retaining solution accuracy.
Baker, A. J.↗
The viscoelastic behavior of the principal compliance matrix of a unidirectional graphite/epoxy composite
The time-temperature response of the principal compliances of a unidirectional graphite/epoxy composite was determined. It is shown that two components of the compliance matrix are time and temperature independent and that the compliance matrix is symmetric for the viscoelastic composite. The time-temperature superposition principle is used to determine shift factors which are independent of fiber orientation, for fiber angles that vary from 10 D to 90 D with respect to the load direction.
Morris, D. H.↗
The viscoelastic behavior of the principal compliance matrix of a unidirectional graphite/epoxy composite
A testing program was conducted to determine the time-temperature response of the principal compliances of a unidirectional graphite/epoxy composite. It was shown that the two components of the compliance matrix are time and temperature independent. In addition, the compliance matrix is symmetric for the viscoelastic composite. The time-temperature superposition principle is used to determine shift factors. It was shown that the shift factors are independent of fiber orientation for fiber angles that vary from 10 to 90 deg with respect to the load direction.
Morris, D. H.↗
Impact damage and residual tension strength of a thick graphite/epoxy rocket motor case
Impacters of various masses were dropped from various heights onto thick graphite/epoxy filament-wound cylinders. The cylinders represented filament-wound cases made for the booster motors of the Space Shuttle. Tups of various shapes were affixed to the impacters. Some of the cylinders were filled with inert propellant, and some were empty. The cylinders were impacted numerous times around the circumference and then cut into tension coupons, each containing an impact site. The size of the damage and the residual tension strength were measured. For hemispherical tups, strength was reduced as much as 30 percent by nonvisible damage. The damage consisted of matrix cracking and broken fibers. Analytical methods were used to predict the damage and residual tension strength. A factor of safety to account for nonvisible damage was determined. For corner and rod shaped tups, any damage that resulted in strength loss was readily visible.
Poe, C. C., Jr.↗
Spectral ordering techniques for incomplete LU preconditoners for CG methods
The effectiveness of an incomplete LU (ILU) factorization as a preconditioner for the conjugate gradient method can be highly dependent on the ordering of the matrix rows during its creation. Detailed justification for two heuristics commonly used in matrix ordering for anisotropic problems is given. The bandwidth reduction and weak connection following heuristics are implemented through an ordering method based on eigenvector computations. This spectral ordering is shown to be a good representation of the heuristics. Analysis and test cases in two and three dimensional diffusion problems demonstrate when ordering is important, and when an ILU decomposition will be ordering insensitive. The applicability of the heuristics is thus evaluated and placed on a more rigorous footing.
Clift, Simon S.↗
eddy Users Manual
eddy is a collection of tools - nonlinear solvers, meshing, post-processing, visualization, optimization, etc. - for performing scale-resolving simulations of multi-physics applications. The framework is designed to enable advanced R&D on a variety of topics by leveraging a mature capability for scale resolving simulations, and simultaneously be an appropriate tool for application analysis and support. Currently, eddy is at a relatively low technical readiness level (TRL), and users and developers should maintain appropriate expectations. The technical details behind eddy are outlined in several publications which can be consulted for more information [1–10]. The solvers are built around an unstructured high-order capability, and heavily utilize the tensor product sum-factorization approach for efficiency. The unsteady formulation utilizes a fully implicit space-time approach with a matrix-free Newton- Krylov method. A primitive steady-state solver is available for testing purposes, but is not expected to converge for all but simple verification cases. The Navier-Stokes fluid solvers do not support either RANS or hybrid-RANS capability, only LES and wall-modeled LES approaches. All of the solvers within eddy support three modes of operation: a primal solve of the full nonlinear problem, and two linearization approaches of the primal solve - the ad joint and the tangent solution. Details on how to select and use these three modes are outlined in Sec. 3.
Murman, Scott M.↗
CRRES microelectronic test chip
The JPL CRRES chip was designed and fabricated in 1985 and included in the CRRES MEP. MOSFET Matrix results show the effect of shielding on radiation-induced MOSFET threshold voltage shifts and channel mobility degradation. Shielded (middle board) MOSFETs have a threshold-voltage damage factor that is approximately three orders of magnitude smaller than would be estimated from Co-60 ground tests. Unshielded (outer board) MOSFETs have a threshold-voltage damage factor that would be estimated from Co-60 ground tests. Temperature swings as large as 23 C with a 22.5 orbit periodicity affected the MOSFET data and were removed from the data in order to reveal the radiation effects. This experiment demonstrated the feasibility of characterizing MOSFETs in a matrix, thus reducing the complexity and mass of the experiment.
Lin, Y.-S.↗
Effect of fiber orientation on the fracture toughness of brittle matrix composites
The effective fracture toughness of brittle matrix materials can be increased through the addition of short, poorly bonded fibers which bridge the growing crack. The orientation distribution of the fibers is likely to be biased, and not in an ideal random or aligned state. A micromechanical model is formulated for the postcracking behavior using the force-displacement relation for an arbitrary fiber bridging a crack, the fiber orientation density function, and the fiber location density function. This model is then used to determine an effective traction law for the bridging fibers, as well as the steady state bridging toughness increment. In most cases, the results may be placed in the form of a product of the aligned fiber results times a modifying integrated orientation factor. The frictional shear stress on fiber pull-out is allowed to vary during pull-out, modeling the effects of matrix breakdown, fiber surface smoothing or wear debris accumulation. Results are presented for a variety of representative planar and three-dimensional fiber orientation states.
Jain, L. K.↗
The Mid-Infrared Absorption Spectra of Neutral PAHs in Dense Interstellar Clouds
Polycyclic aromatic hydrocarbons (PAHs) are common throughout the universe and are expected to be present in dense interstellar clouds. In these environments, some P.4Hs may be present in the gas phase, but most should be frozen into ice mantles or adsorbed onto dust grains and their spectral features are expected to be seen in absorption. Here we extend our previous work on the infrared spectral properties of the small PAH naphthalene (C10H8) in several media to include the full mid-infrared laboratory spectra of 11 other PAHs and related aromatic species frozen in H2O ices. These include the molecules 1,2-dihydronaphthalene, anthracene, 9,1O-dihydroanthracene, phenanthrene, pyrene, benzo[e]pyrene, perylene, benzo(k)fluoranthene, pentacene, benzo[ghi]perylene, and coronene. These results demonstrate that PAHs and related molecules, as a class, show the same spectral behaviors as naphthalene when incorporated into H2O-rich matrices. When compared to the spectra of these same molecules isolated in inert matrices (e.g., Ar or N2), the absorption bands produced when they are frozen in H2O matrices are broader (factors of 3-10), show small position shifts in either direction (usually < 4/cm, always < 10/cm), and show variable changes in relative band strengths (typically factors of 1-3). There is no evidence of systematic increases or decreases in the absolute strengths of the bands of these molecules when they are incorporated in H2O matrices. In H2O-rich ices, their absorption bands are relatively insensitive to concentration over the range of 10 < H2O/PAH < 200): The absorption bands of these molecules are also insensitive to temperature over the 10 K < T < 125 K range, although the spectra can show dramatic changes as the ices are warmed through the temperature range in which amorphous H2O ice converts to its cubic and hexagonal crystalline forms (T > 125 Kj. Given the small observed band shifts cause by H2O, the current database of spectra from Ar matrix-isolated neutral PAHs and related molecules should be useful for the search for these species in dense clouds on the basis of observed absorption band positions. Furthermore, these data permit determination of column densities to better than a factor of 3 for PAHs in dense clouds. Column density determination of detected aromatics to better than a factor of 3 will, however, require good knowledge about the nature of the matrix in which the PAH is embedded and laboratory studies of relevant samples.
Bernstein, M. P.↗
A ceramic matrix composite thermal protection system for hypersonic vehicles
The next generation of hypersonic vehicles (NASP, SSTO) that require reusable thermal protection systems will experience acreage surface temperatures in excess of 1100 C. More important, they will experience a more severe physical environment than the Space Shuttle due to non-pristine launching and landing conditions. As a result, maintenance, inspection, and replacement factors must be more thoroughly incorporated into the design of the TPS. To meet these requirements, an advanced thermal protection system was conceived, designated 'TOPHAT'. This system consists of a toughened outer ceramic matrix composite (CMC) attached to a rigid reusable surface insulator (RSI) which is directly bonded to the surface. The objective of this effort was to evaluate this concept in an aeroconvective environment, to determine the effect of impacts to the CMC material, and to compare the results with existing thermal protection systems.
Riccitiello, Salvatore R.↗
Crystallization of bFGF-DNA Aptamer Complexes Using a Sparse Matrix Designed for Protein-Nucleic Acid Complexes
The Sparse Matrix approach for obtaining lead crystallization conditions has proven to be very fruitful for the crystallization of proteins and nucleic acids. Here we report a Sparse Matrix developed specifically for the crystallization of protein-DNA complexes. This method is rapid and economical, typically requiring 2.5 mg of complex to test 48 conditions. The method was originally developed to crystallize basic fibroblast growth factor (bFGF) complexed with DNA sequences identified through in vitro selection, or SELEX, methods. Two DNA aptamers that bind with approximately nanomolar affinity and inhibit the angiogenic properties of bFGF were selected for co-crystallization. The Sparse Matrix produced lead crystallization conditions for both bFGF-DNA complexes.
Cannone, Jaime J.↗
The mechanisms of dispersion strengthening and fracture in Al-based XD(tm) alloys, part 1
The influence of reinforcement size, volume fraction, and matrix deformation behavior on room and elevated temperature strength; the fracture toughness; and the fatigue crack growth rate of metal matrix composites of Al-4(pct)Cu-1.5(pct)Mg with TiB2 were examined. The influence of reinforcement volume fraction was also examined for pure aluminum with TiB2. Higher TiB2 volume fractions increased the tensile yield strength at both room and elevated temperatures, and reduced the elongation to fracture. Tensile tests also indicate that small particles provided a greater increase in strength for a given volume fraction than larger particles, whereas elongation to fracture appeared to be insensitive to reinforcement size. Interparticle spacing appears to be the factor that controls the strength of these alloys, with the exact nature of the dependence relying on the nature of dislocation slip in the matrix (planar vs. diffuse). The isothermal aging response of the precipitation strengthened Al-4(pct)Cu-1.5(pct)Mg alloys was not accelerated by the presence of TiB2. Cold work prior to artificial aging created additional geometrically necessary dislocations which serve as heterogeneous nucleation sites leading to accelerated aging, a finer precipitate size, and an increase in the strength of the alloy.
Aikin, R. M., Jr.↗
Normal and radial impact of composites with embedded penny-shaped cracks
A method is developed for the dynamic stress analysis of a layered composite containing an embedded penny-shaped crack and subjected to normal and radial impact. The material properties of the layers are chosen such that the crack lies in a layer of matrix material while the surrounding material possesses the average elastic properties of a two-phase medium consisting of a large number of fibers embedded in the matrix. Quantitatively, the time-dependent stresses near the crack border can be described by the dynamic stress intensity factors. Their magnitude depends on time, on the material properties of the composite and on the relative size of the crack compared to the composite local geometry. Results obtained show that, for the same material properties and geometry of the composite, the dynamic stress intensity factors for an embedded (penny-shaped) crack reach their peak values within a shorter period of time and with a lower magnitude than the corresponding dynamic stress intensity factors for a through-crack.
Sih, G. C.↗
Interface effects in interlaminar fracture of thermoplastic composites
Mode I interlaminar fracture toughness was determined on a series of unidirectional poly(phenylene oxide)/carbon fiber composites using the double cantilever beam test. Initial toughness for growth of a delamination from an insert depends on fiber type, and ranges from 190 to 440 J/sq m, with intermediate modulus fibers tending to give lower values than high-strain fibers. Low toughness values are attributed to poor fiber-matrix adhesion. As a delamination progress down the beam, fiber bridging increases the apparent toughness by up to a factor of 7, depending on the fiber.
Hinkley, J. A.↗
Role of interfacial thermal barrier in the transverse thermal conductivity of uniaxial SiC fiber-reinforced reaction bonded silicon nitride
The transverse thermal conductivity of reaction-bonded Si3N4 is significantly affected by an interfacial barrier at the interface formed with SiC reinforcing fibers. A comparative study of composites with and without reinforcing-fiber carbon coatings found the coating to reduce effective thermal conductivity by a factor of about 2; this, however, is partially due to a thermal expansion-mismatch gap between fiber and matrix. HIPing of composites with coated fibers led to an enhancement of thermal conductivity via improved interfacial thermal contact and greater grain size and crystallinity of the fibers.
Bhatt, H.↗
Quantifying Uncertainties in the Thermo-Mechanical Properties of Particulate Reinforced Composites
The present paper reports results from a computational simulation of probabilistic particulate reinforced composite behavior. The approach consists use of simplified micromechanics of particulate reinforced composites together with a Fast Probability Integration (FPI) technique. Sample results are presented for a Al/SiC(sub p)(silicon carbide particles in aluminum matrix) composite. The probability density functions for composite moduli, thermal expansion coefficient and thermal conductivities along with their sensitivity factors are computed. The effect of different assumed distributions and the effect of reducing scatter in constituent properties on the thermal expansion coefficient are also evaluated. The variations in the constituent properties that directly effect these composite properties are accounted for by assumed probabilistic distributions. The results show that the present technique provides valuable information about the scatter in composite properties and sensitivity factors, which are useful to test or design engineers.
Mital, Subodh K.↗
Linearized T-Matrix and Mie Scattering Computations
We present a new linearization of T-Matrix and Mie computations for light scattering by non-spherical and spherical particles, respectively. In addition to the usual extinction and scattering cross-sections and the scattering matrix outputs, the linearized models will generate analytical derivatives of these optical properties with respect to the real and imaginary parts of the particle refractive index, and (for non-spherical scatterers) with respect to the ''shape'' parameter (the spheroid aspect ratio, cylinder diameter/height ratio, Chebyshev particle deformation factor). These derivatives are based on the essential linearity of Maxwell's theory. Analytical derivatives are also available for polydisperse particle size distribution parameters such as the mode radius. The T-matrix formulation is based on the NASA Goddard Institute for Space Studies FORTRAN 77 code developed in the 1990s. The linearized scattering codes presented here are in FORTRAN 90 and will be made publicly available.
Analytic linearization↗