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At least 163 records · Page 9

A Discontinuous Petrov-Galerkin Methodology for Adaptive Solutions to the Incompressible Navier-Stokes Equations

The discontinuous Petrov-Galerkin methodology with optimal test functions (DPG) of Demkowicz and Gopalakrishnan [18, 20] guarantees the optimality of the solution in an energy norm, and provides several features facilitating adaptive schemes. Whereas Bubnov-Galerkin methods use identical trial and test spaces, Petrov-Galerkin methods allow these function spaces to differ. In DPG, test functions are computed on the fly and are chosen to realize the supremum in the inf-sup condition; the method is equivalent to a minimum residual method. For well-posed problems with sufficiently regular solutions, DPG can be shown to converge at optimal rates—the inf-sup constants governing the convergence are mesh-independent, and of the same order as those governing the continuous problem [48]. DPG also provides an accurate mechanism for measuring the error, and this can be used to drive adaptive mesh refinements. We employ DPG to solve the steady incompressible Navier-Stokes equations in two dimensions, building on previous work on the Stokes equations, and focusing particularly on the usefulness of the approach for automatic adaptivity starting from a coarse mesh. We apply our approach to a manufactured solution due to Kovasznay as well as the lid-driven cavity flow, backward-facing step, and flow past a cylinder problems.

adaptive finite elements↗

27 Al Pulsed Field Gradient, Diffusion–NMR Spectroscopy of Solvation Dynamics and Ion Pairing in Alkaline Aluminate Solutions

Here, pulsed field gradient nuclear magnetic resonance (PFG-NMR) measurements were successfully applied to the 27 Al (I = 5/2) nucleus in concentrated electrolytes to investigate the diffusion of aluminate ions [Al(OH) 4 – ] in simulant high-level nuclear waste (3 M NaOH) between 25 and 85 °C. The temperature-dependent diffusion coefficients obtained from 1 H, 23 Na, and 27 Al PFG-NMR were well fit by a Vogel–Fulcher–Tammann model and a power law equation. Comparison of 27 Al diffusion coefficients of 0.1 M Al(OH) 4 – in ~3 M MOH (where M = Na + , K + , (CH 3 ) 4 N + ) at room temperature varied in agreement with the expected changes in solution viscosity via Stokes–Einstein relationship, confirming that the dominant Al species at these conditions are Al(OH) 4 – monomers. This 27 Al PFG-NMR study extends an established methodology to a previously unexplored nucleus enabling this experimental technique to be leverage for exploring ion transport, speciation, and solution structure in concentrated electrolytes.

Diffusion↗

Magnetic and structural properties of the solid solution CuAl 2(1–x) Ga 2x O 4

CuAl 2 O 4 is a ternary oxide spinel with Cu 2+ ions (s = 1/2) primarily populating the A-site diamond sublattice. The compound is reported to display evidence of spin glass behavior but possess a non-frozen magnetic ground state below the transition temperature. On the other hand, the spinel CuGa 2 O 4 displays spin glass behavior at ~ 2.5 K with Cu 2+ ions more readily tending to the B-site pyrochlore sublattice. Therefore, we investigate the magnetic and structural properties of the solid solution CuAl 2(1-x) Ga 2x O 4 examining the evolution of the magnetic behavior as Al 3+ is replaced with a much larger Ga 3+ ion. Our results show that the Cu 2+ ions tend to migrate from tetrahedral to octahedral sites as the Ga 3+ ion concentration increases, resulting in a concomitant change in the glassy magnetic properties of the solution. Results indicate glassy behavior for much of the solution with a general trend towards decreasing magnetic frustration as the Cu 2+ ion shifts to the B-site. However, the x = 0.1 and 0.2 members of the system do not show glassy behavior down to our measurement limit (1.9 K) suggesting a delayed spin glass transition. We suggest that these two members are additional candidates for investigation to access highly frustrated exotic quantum states.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Perturbation solution of the Navier-Stokes equations and its relation to the Lighthill-Curle solution of aerodynamic sound

The aerodynamic sound described by the Lighthill-Curle solution is reexamined using a method of matched asymptotic expansions. The governing Navier-Stokes equations written in nondimensional form are expanded for a small Mach number. First- and second-order solutions for the pressure field are obtained, and the singular nature of the expansion at large distances is indicated. The nearfield pressure is governed by the Poisson equation, whereas the farfield equations describe a linear wave system in a dissipative medium. The pseudosound is related to the incompressible Reynolds stresses associated with a solenoidal velocity field, the velocity, the pressure perturbation, and their derivatives on the boundaries. A uniformly valid first-order solution for the pressure is obtained. It is shown that viscosity, thermal conductivity, and entropy in the flow do not contribute to the first-order noise generation, while the viscous stress contributes to noise only from some boundaries. The application of the proposed perturbation method to a subsonically moving surface and a hot jet is discussed.

Pan, Y. S.↗

Comparison of uniform perturbation solutions and numerical solutions for some potential flows past slender bodies

Approximate solutions for potential flow past an axisymmetric slender body and past a thin airfoil are calculated using a uniform perturbation method and then compared with either the exact analytical solution or the solution obtained using a purely numerical method. The perturbation method is based upon a representation of the disturbance flow as the superposition of singularities distributed entirely within the body, while the numerical (panel) method is based upon a distribution of singularities on the surface of the body. It is found that the perturbation method provides very good results for small values of the slenderness ratio and for small angles of attack. Moreover, for comparable accuracy, the perturbation method is simpler to implement, requires less computer memory, and generally uses less computation time than the panel method. In particular, the uniform perturbation method yields good resolution near the regions of the leading and trailing edges where other methods fail or require special attention.

Wong, T. C.↗

Solute-Filled Syringe For Formulating Intravenous Solution

Prefilled syringe contains premeasured amount of solute in powder or concentrate form used to deliver solute to sterile interior of large-volume parenteral (LVP) bag. Predetermined amount of sterile water also added to LVP bag through sterilizing filter, and mixed with contents of syringe, yielding sterile intravenous solution of specified concentration.

Owens, Jim↗

Multigrid solution of internal flows using unstructured solution adaptive meshes

This is the final report of the NASA Lewis SBIR Phase 2 Contract Number NAS3-25785, Multigrid Solution of Internal Flows Using Unstructured Solution Adaptive Meshes. The objective of this project, as described in the Statement of Work, is to develop and deliver to NASA a general three-dimensional Navier-Stokes code using unstructured solution-adaptive meshes for accuracy and multigrid techniques for convergence acceleration. The code will primarily be applied, but not necessarily limited, to high speed internal flows in turbomachinery.

Smith, Wayne A.↗

Phase Shift Interferometer and Growth Set Up to Step Pattern Formation During Growth From Solutions. Influence of the Oscillatory solution Flow on Stability

We have assembled an experimental setup based on Michelson interferometry with the growing crystal surface as one of the reflective surfaces. The crystallization part of the device allows optical monitoring of a face of a crystal growing at temperature stable within 0.05 C in a flow of solution of controlled direction and speed. The reference arm of the interferometer contains a liquid crystal element that allows controlled shifts of the phase of the interferograms. We employ an image-processing algorithm, which combines five images with a pi/2 phase difference between each pair of images. The images are transferred to a computer by a camera capable of capturing 60 frames per second. The device allows data collection on surface morphology and kinetics during the face layers growth over a relatively large area (approximately 4 sq. mm) in situ and in real time during growth. The estimated depth resolution of the phase shifting interferometry is approximately 50 Angstroms. The data will be analyzed in order to reveal and monitor step bunching during the growth process. The crystal chosen as a model for study in this work is KH2PO4 (KDP). This optically non-linear material is widely used in frequency doubling applications. There have been a number of studies of the kinetics of KDP crystallization that can serve as a benchmark for our investigations. However, so far, systematic quantitative characteristics of step interaction and bunching are missing. We intend to present our first quantitative results on the onset, initial stages and development of instabilities in moving step trains on vicinal crystal surfaces at varying supersaturation, flow rate, and flow direction. Behavior of a vicinal face growing from solution flowing normal to the steps and periodically changing its direction in time was considered theoretically. It was found that this oscillating flow reduces both stabilization and destabilization effects resulted from the unidirectional solution flow directed up the step stream and down the step stream. This reduction of stabilization and destabilization comes from effective mixing which entangles the phase shifts between the spatially periodic interface perturbation and the concentration wave induced by this perturbation. Numerical results and simplified mixing criterion will be discussed.

Chernov, Alex A.↗

A parametric approach to supersymmetric quantum mechanics in the solution of Schrödinger equation

We study exact solutions of the Schrödinger equation for some potentials. We introduce a parametric approach to supersymmetric quantum mechanics to calculate energy eigenvalues and corresponding wave functions exactly. As an application we solve Schrödinger equation for the generalized Morse potential, modified Hulthen potential, deformed Rosen-Morse potential and Poschl-Teller potential. The method is simple and effective to get the results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Automating crystallographic structure solution and refinement of protein–ligand complexes

A software system for automated protein–ligand crystallography has been implemented in the Phenix suite. This significantly reduces the manual effort required in high-throughput crystallographic studies. High-throughput drug-discovery and mechanistic studies often require the determination of multiple related crystal structures that only differ in the bound ligands, point mutations in the protein sequence and minor conformational changes. If performed manually, solution and refinement requires extensive repetition of the same tasks for each structure. To accelerate this process and minimize manual effort, a pipeline encompassing all stages of ligand building and refinement, starting from integrated and scaled diffraction intensities, has been implemented in Phenix. The resulting system is able to successfully solve and refine large collections of structures in parallel without extensive user intervention prior to the final stages of model completion and validation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Challenges and solutions for the analysis of in situ, in crystallo micro-spectrophotometric data

The particular challenge of the analysis of optical absorption and Raman spectroscopic data measured from protein crystals and how the SLS-APE software toolbox supports scientists in dealing with such data is described. Combining macromolecular crystallography with in crystallo micro-spectrophotometry yields valuable complementary information on the sample, including the redox states of metal cofactors, the identification of bound ligands and the onset and strength of undesired photochemistry, also known as radiation damage. However, the analysis and processing of the resulting data differs significantly from the approaches used for solution spectrophotometric data. The varying size and shape of the sample, together with the suboptimal sample environment, the lack of proper reference signals and the general influence of the X-ray beam on the sample have to be considered and carefully corrected for. In the present article, how to characterize and treat these sample-dependent artefacts in a reproducible manner is discussed and the SLS-APEin situ, in crystallo optical spectroscopy data-analysis toolbox is demonstrated.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Structure of a Hydrated Sulfonatotitanyl(IV) Complex in Aqueous Solution and the Dimethylsulfoxide Solvated Titanyl(IV) Ion in Solution and Solid State

The coordination chemistry of oxotitanium(IV) or titanyl(IV), TiO 2+ , has been studied in solution by X-ray methods. The titanyl(IV) ion hydrolyzes easily in aqueous systems to solid titanium dioxide as long as it is not stabilized through complexation. In this study the structures of the hydrated bissulfatotitanyl(IV) complex and the dimethylsulfoxide (DMSO) solvated titanyl(IV) ions have been determined. In isolated monomeric titanyl complexes titanium(IV) binds strongly to a doubly bound oxo group at ca. 1.64 Å, to four ligands in the equatorial plane almost perpendicular to the Ti=O bond at ca. 2.02 Å, and there is one weakly bound ligand, trans to the Ti=O bond, at ca. 2.22 Å, for oxygen donor ligands; the O=Ti–O eq bond angles are 95°–100°. The structure of the DMSO solvated titanyl(IV) ion in the solid state is maintained in DMSO solution.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗