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At least 451 records · Page 25

Local Discontinuous Galerkin Methods for Partial Differential Equations with Higher Order Derivatives

In this paper we review the existing and develop new continuous Galerkin methods for solving time dependent partial differential equations with higher order derivatives in one and multiple space dimensions. We review local discontinuous Galerkin methods for convection diffusion equations involving second derivatives and for KdV type equations involving third derivatives. We then develop new local discontinuous Galerkin methods for the time dependent bi-harmonic type equations involving fourth derivatives, and partial differential equations involving fifth derivatives. For these new methods we present correct interface numerical fluxes and prove L(exp 2) stability for general nonlinear problems. Preliminary numerical examples are shown to illustrate these methods. Finally, we present new results on a post-processing technique, originally designed for methods with good negative-order error estimates, on the local discontinuous Galerkin methods applied to equations with higher derivatives. Numerical experiments show that this technique works as well for the new higher derivative cases, in effectively doubling the rate of convergence with negligible additional computational cost, for linear as well as some nonlinear problems, with a local uniform mesh.

Yan, Jue↗

On a model of calculating bond strength

Diffusion bonding is a fabricating process to join the fibers and a matrix together forming a composite. The efficiency of the bonding process depends on temperature, time, and pressure. Based on a simplified pair potential model, an expression for the bond-energy at the fiber-matrix interface is formulated in terms of the above-mentioned three parameters. From this expression and the mean atomic distance, the bond-strength between the fibers and the matrix can be calculated.

Yue, A. S.↗

Estimation of minority carrier diffusion lengths in InP/GaAs solar cells

Minority carrier diffusion length is one of the most important parameters affecting the solar cell performance. An attempt is made to estimate the minority carrier diffusion lengths is the emitter and base of InP/GaAs heteroepitaxial solar cells. The PC-1D computer model was used to simulate the experimental cell results measured at NASA Lewis under AMO (air mass zero) spectrum at 25 C. A 16 nm hole diffusion length in the emitter and a 0.42 micron electron diffusion length in the base gave very good agreement with the I-V curve. The effect of varying minority carrier diffusion lengths on cell short current, open circuit voltage, and efficiency was studied. It is also observed that the front surface recombination velocity has very little influence on the cell performance. The poor output of heteroepitaxial cells is caused primarily by the large number of dislocations generated at the interfaces that propagate through the bulk indium phosphide layers. Cell efficiency as a function of dislocation density was calculated and the effect of improved emitter bulk properties on cell efficiency is presented. It is found that cells with over 16 percent efficiencies should be possible, provided the dislocation density is below 10(exp 6)/sq cm.

Jain, R. K.↗

An Alternative Hypothesis for How Microgravity Improves Macromolecular Crystal Quality

There is a substantial body of experimental evidence, from this and other laboratories, that strongly suggests that for many proteins crystal nucleation and growth is by addition of associated species that are preformed by reversible concentration-driven self association processes in the bulk solution. We have developed a self-association model for the crystal nucleation and growth of the protein chicken egg lysozyme. The model accounts for the obtained crystal symmetry, explains the observed surface structures, and shows the importance of the symmetry obtained by self-association in solution to the process as a whole. This model also offers a possible mechanism for fluid flow effects on the growth process and how microgravity may affect it. While a single lysozyme molecule is relatively small an octamer in the 43 helix configuration (the proposed average sized growth unit) would have a M.W. approx. 115,000 and dimensions of 5.6 x 5.6 x 7.6 nm. Direct AFM measurements of growth unit incorporation indicate that units as wide as 11.2 nm and as long as 11.4 nm (a 24-mer) commonly attach to the crystal. AFM results from Weichmann et al. (Ultramicroscopy 86, 159-166, 2001) suggest that associated species of up to 40-mers in size add to the (101) faces. These measurements reflect the sizes of units that both added and desorbed from the crystal surface. The larger and less isotropic the associated species the more likely that it will be oriented to some degree in a flowing boundary layer, even at the low flow velocities measured about macromolecule crystals. On Earth, concentration gradient driven flow will maintain a high interfacial concentration, i.e., a high level (essentially that of the bulk solution) of solute association at the interface and higher growth rate. Higher growth rates mean an increased probability that misaligned growth units are trapped by subsequent growth layers before they can be desorbed and try again, or that the desorbing species is more likely to be smaller than the adsorbing species. In microgravity the extended diffusive boundary layer will lower the interfacial concentration. This results in a net dissociation of aggregated species that diffuse in from the bulk solution, i.e., smaller associated species, which are more likely able to make multiple attempts to correctly bind, yielding higher quality crystals.

Pusey, Marc↗

NASA Virtual Glovebox (VBX): Emerging Simulation Technology for Space Station Experiment Design, Development, Training and Troubleshooting

The International Space Station demonstrates the greatest capabilities of human ingenuity, international cooperation and technology development. The complexity of this space structure is unprecedented; and training astronaut crews to maintain all its systems, as well as perform a multitude of research experiments, requires the most advanced training tools and techniques. Computer simulation and virtual environments are currently used by astronauts to train for robotic arm manipulations and extravehicular activities; but now, with the latest computer technologies and recent successes in areas of medical simulation, the capability exists to train astronauts for more hands-on research tasks using immersive virtual environments. We have developed a new technology, the Virtual Glovebox (VGX), for simulation of experimental tasks that astronauts will perform aboard the Space Station. The VGX may also be used by crew support teams for design of experiments, testing equipment integration capability and optimizing the procedures astronauts will use. This is done through the 3D, desk-top sized, reach-in virtual environment that can simulate the microgravity environment in space. Additional features of the VGX allow for networking multiple users over the internet and operation of tele-robotic devices through an intuitive user interface. Although the system was developed for astronaut training and assisting support crews, Earth-bound applications, many emphasizing homeland security, have also been identified. Examples include training experts to handle hazardous biological and/or chemical agents in a safe simulation, operation of tele-robotic systems for assessing and diffusing threats such as bombs, and providing remote medical assistance to field personnel through a collaborative virtual environment. Thus, the emerging VGX simulation technology, while developed for space- based applications, can serve a dual use facilitating homeland security here on Earth.

Smith, Jeffrey D.↗

Nonequilibrium Crystal Growth During Laser Annealing of Silicon

The Systematic studies of dopant (Group III, IV, or V) incorporation into silicon as a result of pulsed-laser annealing are reviewed. At low concentrations, dopant profiles measured after laser annealing can be compared to model calculations for redistribution by liquid-phase diffusion in order to determine the interfacial distribution coefficient K('). At high concentrations there is a limit (C sub s) to dopant incorporation into substitutional lattice sites. The mechanisms which limit dopant incorporation are discussed as well as the dependence of K(') and (max) on crystal orientation. Finally, measurements of interface temperatures, temperature profiles, and thermal gradients during rapid solidification are summarized.

White, C. W.↗

Computation of the unsteady facilitated transport of oxygen in hemoglobin

The transport of a reacting permeant diffusing through a thin membrane is extended to more realistic dissociation models. A new nonlinear analysis of the reaction-diffusion equations, using implicit finite-difference methods and direct block solvers, is used to study the limits of linearized and equilibrium theories. Computed curves of molecular oxygen permeating through hemoglobin solution are used to illustrate higher-order reaction models, the effect of concentration boundary layers at the membrane interfaces, and the transient buildup of oxygen flux.

Davis, Sanford↗

Orientation and velocity dependence of the nonequilibrium partition coefficient

Monte Carlo simulations based on a Spin-1 Ising Model for binary alloys have been used to investigate the non-equilibrium partition coefficient (k(sub neq)) as a function of solid-liquid interface velocity and orientation. In simulations of Si with a second component k(sub neq) is greater in the [111] direction than the [100] direction in agreement with experimental results reported by Azlz et al. The simulated partition coefficient scales with the square of the step velocity divided by the diffusion coefficient of the secondary component in the liquid.

Beatty, K. M.↗

Environmental Barrier Coatings Having a YSZ Top Coat

Environmental barrier coatings (EBCs) with a Si bond coat, a yttria-stabilized zirconia (YSZ) top coat, and various intermediate coats were investigated. EBCs were processed by atmospheric pressure plasma spraying. The EBC durability was determined by thermal cycling tests in water vapor at 1300 C and 1400 C, and in air at 1400 C and 1500 C. EBCs with a mullite (3Al2O3 (dot) 2SiO2) + BSAS (1 - xBaO (dot) xSrO (dot) Al2O3 (dot) 2SiO2) intermediate coat were more durable than EBCs with a mullite intermediate coat, while EBCs with a mullite/BSAS duplex intermediate coat resulted in inferior durability. The improvement with a mullite + BSAS intermediate coat was attributed to enhanced compliance of the intermediate coat due to the addition of a low modulus BSAS second phase. Mullite + BSAS/YSZ and BSAS/YSZ interfaces produced a low melting (less than 1400 C) reaction product, which is expected to degrade the EBC performance by increasing the thermal conductivity. EBCs with a mullite + BSAS / graded mullite + YSZ intermediate coat showed the best durability among the EBCs investigated in this study. This improvement was attributed to diffused CTE (Coefficient of Thermal Expansion) mismatch stress and improved chemical stability due to the compositionally graded mullite+YSZ layer.

Lee, Kang N.↗

Li-Doped Ionic Liquid Electrolytes: From Bulk Phase to Interfacial Behavior

Ionic liquids have been proposed as candidate electrolytes for high-energy density, rechargeable batteries. We present an extensive computational analysis supported by experimental comparisons of the bulk and interfacial properties of a representative set of these electrolytes as a function of Li-salt doping. We begin by investigating the bulk electrolyte using quantum chemistry and ab initio molecular dynamics to elucidate the solvation structure of Li(+). MD simulations using the polarizable force field of Borodin and coworkers were then performed, from which we obtain an array of thermodynamic and transport properties. Excellent agreement is found with experiments for diffusion, ionic conductivity, and viscosity. Combining MD simulations with electronic structure computations, we computed the electrochemical window of the electrolytes across a range of Li(+)-doping levels and comment on the role of the liquid environment. Finally, we performed a suite of simulations of these Li-doped electrolytes at ideal electrified interfaces to evaluate the differential capacitance and the equilibrium Li(+) distribution in the double layer. The magnitude of differential capacitance is in good agreement with our experiments and exhibits the characteristic camel-shaped profile. In addition, the simulations reveal Li(+) to be highly localized to the second molecular layer of the double layer, which is supported by additional computations that find this layer to be a free energy minimum with respect to Li(+) translation.

molecular dynamics↗

An investigation of voids formation mechanisms and their effects on freeze and thaw processes of lithium and lithium fluoride

The mechanisms of void formation during the cooldown and freezing of lithium coolant within the primary loop of SP-100 type systems are investigated. These mechanisms are: (1) homogeneous nucleation; (2) heterogeneous nucleation; (3) normal segregation of helium gas dissolved in liquid lithium; and (4) shrinkage of lithium during freezing. To evaluate the void formation potential due to segregation, a numerical scheme that couples the freezing and mass diffusion processes in both the solid and liquid regions is developed. The results indicated that the formation of He bubbles is unlikely by either homogeneous or heterogeneous nucleation during the cooldown process. However, homogeneous nucleation of He bubbles following the segregation of dissolved He in liquid lithium ahead of the solid-liquid interface is likely to occur. Results also show that total volume of He void is insignificant when compared to that of shrinkage voids. In viewing this, the subsequent research focuses on the effects of shrinkage void forming during freezing of lithium on subsequent thaw processes are investigated using a numerical scheme that is based on a single (solid/liquid) cell approach. The cases of lithium-fluoride are also investigated to show the effect of larger volume shrinkage upon freezing on the freeze and thaw processes. Results show that a void forming at the wall appreciably reduces the solid-liquid interface velocity, during both freeze and thaw, and causes a substantial rise in the wall temperature during thaw. However, in the case of Li, the maximum wall temperature was much lower than the melting temperature of PWC-11, which is used as the structure material in the SP-100 system. Hence, it is included that a formation of hot spots is unlikely during the startup or restart of the SP-100 system.

El-Genk, Mohamed S.↗

Mechanisms of voids formation during cooldown and freezing of lithium in SP-100 type systems

The mechanisms of void formation during the cooldown and freezing of lithium coolant within the primary loop of SP-100 type systems are investigated. These mechanisms are: (a) homogeneous nucleation, (b) heterogeneous nucleation, (c) normal segregation of helium gas dissolved in liquid lithium, and (d) shrinkage of lithium during freezing. To evaluate the void formation potential due to segregation, a numerical scheme that couples the freezing and mass diffusion processes in both the solid and liquid regions is developed. The results indicated that the formation of He bubbles is unlikely by either homogeneous or heterogeneous nucleation during the cooldown process. However, homogeneous nucleation of He bubbles following the segregation of dissolved He in liquid Lithium ahead of the solid-liquid interface is likely to occur. Results also show that total volume of He void is insignificant when compared to that of shrinkage voids.

Yang, Jae Y.↗

Numerical modeling of HgCdTe solidification: Effects of phase diagram, double-diffusion convection and microgravity level

A numerical model of HgCdTe solidification was implemented using finite the element code FIDAP. Model verification was done using both experimental data and numerical test problems. The model was used to evaluate possible effects of double-diffusion convection in molten material, and microgravity level on concentration distribution in the solidified HgCdTe. Particular attention was paid to incorporation of HgCdTe phase diagram. It was found, that below a critical microgravity amplitude, the maximum convective velocity in the melt appears virtually independent on the microgravity vector orientation. Good agreement between predicted interface shape and an interface obtained experimentally by quenching was achieved. The results of numerical modeling are presented in the form of video film.

Bune, Andris V.↗

Mission Cycle Life Prediction for C/SiC Composites

The residual strength and life of C/SiC is dominated by carbon interface and fiber oxidation if thermal and mechanical stresses combine with thermal expansion mismatch in a manner such that seal coat and matrix cracks are open to allow oxygen ingress. Under these circumstances life can be predicted by simple oxidation based models based on reaction controlled kinetics at low temperature and gas phase diffusion controlled kinetics at high temperature. Key life governing variables in these models include temperature, applied stress, initial strength, oxygen partial pressure and total pressure. In this paper these models are described and extended to mission cycle life prediction.

Levine, Stanley R.↗

An Investigation of Wave Propagations in Discontinuous Galerkin Method

Analysis of the discontinuous Galerkin method has been carried out for one- and two-dimensional system of hyperbolic equations. Analytical, as well as numerical, properties of wave propagation in a DGM scheme are derived and verified with direct numerical simulations. In addition to a systematic examination of the dissipation and dispersion errors, behaviours of a DG scheme at an interface of two different grid topologies are also studied. Under the same framework, a quantitative discrete analysis of various artificial boundary conditions is also conducted. Progress has been made in numerical boundary condition treatment that is closely related to the application of DGM in aeroacoustics problems. Finally, Fourier analysis of DGM for the Convective diffusion equation has also be studied in connection with the application of DG schemes for the Navier-Stokes equations. This research has resulted in five(5) publications, plus one additional manuscript in preparation, four(4) conference presentations, and three(3) departmental seminars, as summarized in part II. Abstracts of papers are given in part 111 of this report.

Hu, Fang Q.↗

Dendritic Growth Velocity of Ice Crystals

The dendritic growth velocity of ice crystals is measured at undercooling levels between 5-8.5 K using a unique apparatus. The result shows that the measured velocities are smaller that the theoretical prediction based on the thermal diffusion theory with the scalling constant, Q= 0.025, which has been shown to agree with the experimental results at lower undercooling levels between 0.4 -2.5 K.

Dendritic Ice Growth velocity Undercooling Interfa↗

A Reconstruction Approach to High-Order Schemes Including Discontinuous Galerkin for Diffusion

We introduce a new approach to high-order accuracy for the numerical solution of diffusion problems by solving the equations in differential form using a reconstruction technique. The approach has the advantages of simplicity and economy. It results in several new high-order methods including a simplified version of discontinuous Galerkin (DG). It also leads to new definitions of common value and common gradient quantities at each interface shared by the two adjacent cells. In addition, the new approach clarifies the relations among the various choices of new and existing common quantities. Fourier stability and accuracy analyses are carried out for the resulting schemes. Extensions to the case of quadrilateral meshes are obtained via tensor products. For the two-point boundary value problem (steady state), it is shown that these schemes, which include most popular DG methods, yield exact common interface quantities as well as exact cell average solutions for nearly all cases.

Huynh, H. T.↗

Thermocapillary flow and melt/solid interfaces in floating-zone crystal growth under microgravity

Computer simulation of steady-state axisymmetrical heat transfer and fluid flow was conducted to study thermocapillary flow and melt/solid interfaces in floating-zone crystal growth under microgravity. The effects of key variables on the extent of thermocapillary flow in the melt zone, the shapes of melt/solid interfaces and the length of the melt zone were discussed. These variables are: (1) the temperature coefficient of surface tension (or the Marangoni number), (2) the pulling speed (or the Peclet number), (3) the feed rod radius, (4) the ambient temperature distribution, (5) the heat transfer coefficient (or the Biot number), and (6) the thermal diffusivity of the material (or the Prandtl number).

Lan, C. W.↗