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The paper considers the 'ijk forms' of LU and Cholesky factorization on certain parallel computers. This extends an earlier analysis for vector computers. Attention is restricted to local memory systems with processors that may or may not have vector capability. Special attention is given to bus architectures but qualitative analyses are given for other interconnection systems.
This paper gives a detailed exposition of the 'ijk forms' of LU and Choleski factorization. Several aspects of these different organizations are discussed and their properties on vector computers are compared. Extensions of the ijk formalism to other algorithms is also given.
A generalized finite-rate chemistry algorithm with Steger-Warming, Van Leer, and Roe characteristic-based flux splittings is presented in three-dimensional generalized coordinates for the Navier-Stokes equations. Attention is placed on convergence to steady-state solutions with fully coupled chemistry. Time integration schemes including explicit m-stage Runge-Kutta, implicit approximate-factorization, relaxation and LU decomposition are investigated and compared in terms of residual reduction per unit of CPU time. Practical issues such as code vectorization and memory usage on modern supercomputers are discussed.
Lu-doped zirconia (LuDZ) was reported in the 1960s to be a poor oxygen ion conductor. However, we identified this system as worthy of reexamination based on the results of a machine learning-based screen for promising oxygen ion conductors, further supported by a physical argument: because Lu is the heaviest and smallest of the lanthanides, it should offer the possibility of high conductivity due to its high polarizability and size compatibility with the zirconia structure. Here the relationship between dopant concentration and conductivity in the LuDZ system was determined using a high throughput experimental methodology in which spatially resolved conductivity was measured across a compositionally graded film, spanning from Zr 0.93 Lu 0.07 O 1.965 to Zr 0.82 Lu 0.18 O 1.91 . The conductivity broadly peaks with composition at 15 cation % Lu, coinciding with the approximate phase boundary of the fully stabilized cubic phase. The composition-dependent conductivity measurements reveal a surprising increase in activation energy for ion transport with increasing Lu content with no change in this trend at the composition of the conductivity maximum. The pre-exponential factor increases sharply with Lu content, but displays a distinct plateau once the conductivity maximum composition is attained. At 500 °C, the conductivity of Zr 0.85 Lu 0.15 O 1.925 is 2 × 10 –3 S cm –1 , approaching that of optimally doped Sc-stabilized zirconia, which has the highest reported conductivity among zirconia compounds. In comparison to other oxide ion conductors, Lu-stabilized zirconia offers the advantage over ceria of negligible electronic conductivity and is easier to process than (La,Sr)(Ga,Mg)O 3-δ .
This study investigated the correlation between severe plastic deformation and microstructural evolution, along with the corresponding response in the thermoelectric performance. Specifically, severe plastic deformation introduced into intrinsically brittle thermoelectric materials like Bi 2 Te 3 - x Se x leads to microstructural changes ranging from nano- to micro- scales, including phase transformation, phase segregation, and stacking faults. The resultant residual strain and lattice defects in the Bi 2 Te 3-x Se x materials led to engineering of electronic bands, which increases the effective mass of electrons while controlling their concentration, thereby enhancing the power factor.
This investigation provides, for the first time, cyclic strainrange-controlled, thermomechanical fatigue results for the ferritic stainless steel alloy SS409. The alloy has seen extensive application for automotive exhaust system components. The data were generated to calibrate the Total Strain Version of the Strainrange Partitioning (TS-SRP) method for eventual application to the design and durability assessment of automotive exhaust systems. The thermomechanical cyclic lifetime and cyclic stress-strain constitutive behavior for alloy SS409 were measured using bithermal tests cycling between isothermal extremes of 400 and 800 C. Lives ranged up to 10,000 cycles to failure with hold-times of 0.33 to 2.0 minutes. The bithermal fatigue behavior is compared to isothermal, strain-controlled fatigue behavior at both 400 and 800 C. Thermomechanical cycling was found to have a profound detrimental influence on the fatigue failure resistance of SS409 compared to isothermal cycling. Supplementary bithermal cyclic stress-strain constitutive tests with hold-times ranging from 40 seconds up to 1.5 hours were conducted to calibrate the TS-SRP equation for extrapolation to longer lifetime predictions. Observed thermomechanical (bithermal) fatigue lives correlated well with lives calculated using the calibrated TS-SRP equations: 70% of the bithermal fatigue data fall within a factor of 1.2 of calculated life; 85% within a factor of 1.4; and 100% within a factor of 1.8.
Vortex generators within a two-dimensional, external-compression supersonic inlet for Mach 1.6 were investigated to determine their ability to increase total pressure recovery, reduce total pressure distortion, and improve the boundary layer. The vortex generators studied included vanes and ramps. The geometric factors of the vortex generators studied included height, length, spacing, and positions upstream and downstream of the inlet terminal shock. The flow through the inlet was simulated through the computational solution of the steady-state Reynolds-averaged Navier-Stokes equations on multi-block, structured grids. The vortex generators were simulated by either gridding the geometry of the vortex generators or modeling the vortices generated by the vortex generators. The inlet performance was characterized by the inlet total pressure recovery, total pressure distortion, and incompressible shape factor of the boundary-layer at the engine face. The results suggested that downstream vanes reduced the distortion and improved the boundary layer. The height of the vortex generators had the greatest effect of the geometric factors.
A new streamwise upwind algorithm was derived to compute unsteady flow fields with the use of a moving-grid system. The temporally nonconservative LU-ADI (lower-upper-factored, alternating-direction-implicit) method was applied for time marching computations. A comparison of the temporally nonconservative method with a time-conservative implicit upwind method indicates that the solutions are insensitive to the conservative properties of the implicit solvers when practical time steps are used. Using this new method, computations were made for an oscillating wing at a transonic Mach number. The computed results confirm that the present upwind scheme captures the shock motion better than the central-difference scheme based on the beam-warming algorithm. The new upwind option of the code allows larger time-steps and thus is more efficient, even though it requires slightly more computational time per time step than the central-difference option.
New capabilities have been added to a Navier-Stokes solver to perform steady-state simulations more efficiently. The flow solver for solving the Navier-Stokes equations is completely rewritten with a combination of the LU-SGS (Lower-Upper factored Symmetric Gauss-Seidel) implicit method and the modified HLLE (Harten-Lax-van Leer-Einfeldt) upwind scheme. A pseudo-time marching method is used for the directly coupled structural equations to improve overall convergence rates for static aeroelastic analysis. Results are demonstrated for transonic flows over rigid and flexible wings.
Rocket and missile firings from attack helicopters can cause main engine compressor stall. Studies of this phenomenon suggest that the main engine ingests either the plume from the rockets or the rocket blast waves. This creates surges at the inlet face, causing a loss of power in the main engine. The objective of this project is to set-up a computational fluid dynamics (CFD) simulation of the AH-64D Apache Longbow helicopter during a rocket launch, in order to qualitatively study the fluid dynamics of the problem. This project presents a progression of three unsteady Navier-Stokes solutions. The first unsteady solution involves only a rocket launch from its launch canister. The second solution is a launch from a canister mounted on the Apache's wing-pylon assembly. The last solution includes the Apache main engine and fuselage. The computations use a series of structured, overset grid systems, which allow for a rocket moving in a prescribed path. The method implements a Roe upwind scheme with LU-SGS (lower-upper factored symmetric Gauss-Seidel). A rotor pressure disk model approximates the helicopter rotor, while the rocket engine exit properties are applied as a prescribed boundary condition. Although the project is only at the half-way point, the first and second CFD simulations suggest the possibility of pressure wave interference. Sudden surges in pressure occur from two sources: at rocket start-up, and as the rocket leaves the canister. Wave patterns set-up by these sources appear to propagate to the location of the engine inlet. However the simplified geometry simulation with the main engine needs to be performed before coming to a conclusion.
Background: Mainly because of its long half-life and despite its scientific relevance, spectroscopic measurements of 176 Lu forbidden β decays are very limited and lack formulation of shape factors. A direct precise measurement of its Q value is also presently unreported. In addition, the description of forbidden decays provides interesting challenges for nuclear theory. The comparison of precise experimental results with theoretical calculations for these decays can help to test underlying models and can aid the interpretation of data from other experiments. Purpose: Perform the first precision measurements of 176 Lu β-decay spectra and attempt the observation of its electron capture decays, as well as perform the first precision direct measurement of the 176 Lu β-decay Q value. Compare the shape of the precisely determined experimental β spectra to theoretical calculations, and compare the end point energy to that obtained from an independent Q value measurement. Method: Here, the 176 Lu β-decay spectra measurements and the search for electron capture decays were performed with an experimental setup that employed lutetium-containing scintillator crystals and a NaI(Tl) spectrometer for coincidence counting. The β decay Q value was determined via high-precision Penning trap mass spectrometry (PTMS) with the LEBIT facility at the National Superconducting Cyclotron Laboratory. The β-spectrum calculations were performed within the Fermi theory formalism with nuclear structure effects calculated using a shell model approach. Results: Both β transitions of 176 Lu were experimentally observed and corresponding shape factors formulated in their entire energy ranges. The search for electron capture decay branches led to an experimental upper limit of 6.3×10 –6 relative to its β decays. The 176 Lu β-decay and electron capture Q values were measured using PTMS to be 1193.0(6) and 108.9(8) keV, respectively. This enabled precise β end point energies of 596.2(6) and 195.3(6) keV to be determined for the primary and secondary β decays, respectively. The conserved vector current hypothesis was applied to calculate the relativistic vector matrix elements. The β-spectrum shape was shown to significantly depend on the Coulomb displacement energy and on the value of the axial vector coupling constant gA, which was extracted according to different assumptions. Conclusion: The implemented self-scintillation method has provided unmatched observations of 176 Lu, independently validated by the first direct measurements of its β-decay Q value by Penning trap mass spectrometry. Theoretical study of the main β transition led to the extraction of very different effective gA and log10f values, showing that a high-precision description of this transition would require a realistic nuclear structure with nucleus deformation.
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Rare-earth elements (REEs) are 17 elements of the periodic table primarily consisting of lanthanides. In modern society, the usage of REEs is ubiquitous in almost all modern gadgets and therefore efficient recovery and separation of REEs are of high importance. Selective adsorption and chelation of REEs in solid sorbents is a unique and sustainable process for their recovery. In this work, single-stranded oligos with 100 units of thymine were grafted onto carboxylated mesoporous carbon to synthesize a sorbent with phosphorus and oxygen functionalities. Additionally, the sorbent was characterized by X-ray photoelectron spectroscopy, Fourier-transform infrared spectroscopy, and scanning electron microscopy-energy-dispersive X-ray spectroscopy. Three different REEs with varying atomic radii and densities, Lu, Dy, and La, were adsorbed onto the carbon from aqueous solutions. It was observed that the adsorbed amounts increased with the increase in the atomic radius or decrease in the atomic density. Calculation of the distribution coefficients for all the equilibrium adsorption amounts suggested that adsorption is more effective in the lower concentration region. The L 3 -edge X-ray absorption near-edge structure confirmed a 3+ oxidation state of REEs in the adsorbed phase. Extended X-ray absorption fine structure (EXAFS) confirmed the binding of REEs with oxygen functionalities in the adsorbed phase. The radial distribution functions calculated from the EXAFS data suggest a longer RE–O distance for La compared to those for Lu and Dy. The coordination numbers and Debye–Waller factors have typical values of about 8–9 atoms and 0.01–0.02 Å 2 , respectively.
A new method for computing the effect that small changes in the airfoil shape and cascade geometry have on the aeroacoustic and aeroelastic behavior of turbomachinery cascades is presented. The nonlinear unsteady flow is assumed to be composed of a nonlinear steady flow plus a small perturbation unsteady flow that is harmonic in time. First, the full potential equation is used to describe the behavior of the nonlinear mean (steady) flow through a two-dimensional cascade. The small disturbance unsteady flow through the cascade is described by the linearized Euler equations. Using rapid distortion theory, the unsteady velocity is split into a rotational part that contains the vorticity and an irrotational part described by a scalar potential. The unsteady vorticity transport is described analytically in terms of the drift and stream functions computed from the steady flow. Hence, the solution of the linearized Euler equations may be reduced to a single inhomogeneous equation for the unsteady potential. The steady flow and small disturbance unsteady flow equations are discretized using bilinear quadrilateral isoparametric finite elements. The nonlinear mean flow solution and streamline computational grid are computed simultaneously using Newton iteration. At each step of the Newton iteration, LU decomposition is used to solve the resulting set of linear equations. The unsteady flow problem is linear, and is also solved using LU decomposition. Next, a sensitivity analysis is performed to determine the effect small changes in cascade and airfoil geometry have on the mean and unsteady flow fields. The sensitivity analysis makes use of the nominal steady and unsteady flow LU decompositions so that no additional matrices need to be factored. Hence, the present method is computationally very efficient. To demonstrate how the sensitivity analysis may be used to redesign cascades, a compressor is redesigned for improved aeroelastic stability and two different fan exit guide vanes are redesigned for reduced downstream radiated noise. In addition, a framework detailing how the two-dimensional version of the method may be used to redesign three-dimensional geometries is presented.
An implicit scheme for solving the Euler equations is derived and demonstrated. The alternating-direction implicit (ADI) technique is modified, using two implicit-operator factors corresponding to lower-block-diagonal (L) or upper-block-diagonal (U) algebraic systems which can be easily inverted. The resulting LU scheme is implemented in finite-volume mode and applied to 2D subsonic and transonic cascade flows with differing degrees of geometric complexity. The results are presented graphically and found to be in good agreement with those of other numerical and analytical approaches. The LU method is also 2.0-3.4 times faster than ADI, suggesting its value in calculating 3D problems.
The Zintl phase Ca 2 CdSb 2 was found to be dimorphic. Besides the orthorhombic Ca 2 CdSb 2 (-o), here we report on the synthesis, the structural characterization, and the thermoelectric transport properties of its monoclinic form, Ca 2 CdSb 2 (-m), and its Lu-doped variant Ca 2–x Lu x CdSb 2 (x ≈ 0.02). The monoclinic structure exhibits complex structural characteristics and constitutes a new structure type with the non-centrosymmetric space group Cm (Z = 30). The electrical resistivity ρ(T) measured on single crystals of both phases portrays a transition from a semiconductor to a degenerate p-type semiconductor upon doping with Lu and with an attendant change in the Hall carrier concentration nH from 7.15 × 10 18 to 2.30 × 10 19 cm –3 at 300 K. The Seebeck coefficient S(T) of both phases are comparable and indicate a hole-dominated carrier transport mechanism with magnitudes of 133 and 116 μV/K at 600 K for Ca 2 CdSb 2 (-m) and Ca 2–x Lu x CdSb 2 , respectively. The convoluted atomic bonding with an attendant large unit cell volume of ~4365 Å 3 drives a putative low thermal conductivity in these materials resulting in a power factor PF of 1.63 μW/cm K 2 and an estimated thermoelectric figure of merit zT of ~0.5 for Ca 2–x Lu x CdSb 2 at 600 K. Furthermore, differential scanning calorimetry results reveal the stability of these phases up to about 960 K, making them candidates for moderate temperature thermoelectric materials.
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