The energies of adsorbed H and D recoiled from tungsten surfaces during bombardment with 3 keV Ne{sup +} at oblique angles of incidence were measured. The energy spectra show structure that extends above the elastic recoil energy. We find that the high-energy structure results from multiple collisions, namely recoil of a H isotope followed by scattering from an adjacent W atom, and vice versa. This scattering assisted recoil process is especially prevalent for H isotopes adsorbed on W, owing to the large mass difference between the scattering partners. Such processes will tend to enhance H isotope recycling from plasma-facing W surfaces and reduce energy transfer to the W substrate.
Two heuristic strategies intended to enhance the performance of the generalized global basis (GGB) method [H. Waisman, J. Fish, R.S. Tuminaro, J. Shadid, The Generalized Global Basis (GGB) method, International Journal for Numerical Methods in Engineering 61(8), 1243-1269] applied to nonlinear systems are presented. The standard GGB accelerates a multigrid scheme by an additional coarse grid correction that filters out slowly converging modes. This correction requires a potentially costly eigen calculation. This paper considers reusing previously computed eigenspace information. The GGB? scheme enriches the prolongation operator with new eigenvectors while the modified method (MGGB) selectively reuses the same prolongation. Both methods use the criteria of principal angles between subspaces spanned between the previous and current prolongation operators. Numerical examples clearly indicate significant time savings in particular for the MGGB scheme.
We consider linear systems arising from the use of the finite element method for solving scalar linear elliptic problems. Our main result is that these linear systems, which are symmetric and positive semidefinite, are well approximated by symmetric diagonally dominant matrices. Our framework for defining matrix approximation is support theory. Significant graph theoretic work has already been developed in the support framework for preconditioners in the diagonally dominant case, and in particular it is known that such systems can be solved with iterative methods in nearly linear time. Thus, our approximation result implies that these graph theoretic techniques can also solve a class of finite element problems in nearly linear time. We show that the support number bounds, which control the number of iterations in the preconditioned iterative solver, depend on mesh quality measures but not on the problem size or shape of the domain.
A family of microporous phases with compositions Na{sub 2}Nb{sub 2-x}Ti{sub x}O{sub 6-x}(OH){sub x} {center_dot} H{sub 2}O (0 {le} x {le} 0.4) transform to Na{sub 2}Nb{sub 2-x}Ti{sub x}O{sub 6-0.5x} perovskites upon heating. In this study, we have measured the enthalpies of formation of the microporous phases and their corresponding perovskites from the constituent oxides and from the elements by drop solution calorimetry in 3Na{sub 2}O {center_dot} 4MoO{sub 3} solvent at 974 K. As Ti/Nb increases, the enthalpies of formation for the microporous phases become less exothermic up to x = {approx}0.2 but then more exothermic thereafter. In contrast, the formation enthalpies for the corresponding perovskites become less exothermic across the series. The energetic disparity between the two series can be attributed to their different mechanisms of ionic substitutions: Nb{sup 5+} + O{sup 2-} {yields} Ti{sup 4+} + OH{sup -} for the microporous phases and Nb{sup 5+} {yields} Ti{sup 4+} + 0.5 V{sub O}** for the perovskites. From the calorimetric data for the two series, the enthalpies of the dehydration reaction, Na{sub 2}Nb{sub 2-x}Ti{sub x}O{sub 6-x}(OH){sub x} {center_dot} H{sub 2}O {yields} Na{sub 2}Nb{sub 2-x}Ti{sub x}O{sub 6-0.5X} + H{sub 2}O, have been derived, and their implications for phase stability at the synthesis conditions are discussed.
Analytic solutions are useful for code verification. Structural vibration codes approximate solutions to the eigenvalue problem for the linear elasticity equations (Navier's equations). Unfortunately the verification method of 'manufactured solutions' does not apply to vibration problems. Verification books (for example [2]) tabulate a few of the lowest modes, but are not useful for computations of large numbers of modes. A closed form solution is presented here for all the eigenvalues and eigenfunctions for a cuboid solid with isotropic material properties. The boundary conditions correspond physically to a greased wall.
We report on unique particle-in-cell simulations to understand the relativistic electron beam thermalization and subsequent heating of highly compressed plasmas. The simulations yield heated core parameters in good agreement with the GEKKO-PW experimental measurements, given reasonable assumptions of laser-to-electron coupling efficiency and the distribution function of laser-produced electrons. The classical range of the hot electrons exceeds the mass density-core diameter product {rho}L by a factor of several. Anomalous stopping appears to be present and is created by the growth and saturation of an electromagnetic filamentation mode that generates a strong back-EMF impeding hot electrons on the injection side of the density maxima.
An empirical model for investigating the behavior of CaCO{sub 3} polymorphs incorporating a shell model for oxygen has been created. The model was constructed by fitting to: the structure of aragonite and calcite; their elastic, static and high-frequency dielectric constants; phonon frequencies at the wave vectors [1/2 0 2] and [0 0 0] of calcite; and vibrational frequencies of the carbonate deformation modes of calcite. The high-pressure phase transition between calcite I and II is observed. The potentials for the CO{sub 3} group were transferred to other carbonates, by refitting the interaction between CO{sub 3} and the cation to both the experimental structures and their bulk modulus, creating a set of potentials for calculating the properties of a wide range of carbonate materials. Defect energies of substitutional cation defects were analyzed for calcite and aragonite phases. The results were rationalized by studying the structure of calcite and aragonite in greater detail.