Accurate 3-D finite element simulation of elastic wave propagation with the combination of explicit and implicit time-integration methods

One of the big issues in finite element solutions of wave propagation problems is the presence of spurious high-frequency oscillations that may lead to divergent results at mesh refinement. The paper deals with the extension of the new two-stage time-integration technique developed in our previous papers to the solution of wave propagation problems with explicit time-integration methods.The explicit central difference method is used for accurate time-integration of the semi-discrete system of elastodynamics at the stage of basic computations and allows spurious high-frequency oscillations. To filter these oscillations, pre- or/and post-processing (the filtering stage) is applied using a few time increments of the implicit time-continuous Galerkin method with large numerical dissipation.A special calibration procedure is used for the selection of the minimum necessary amount of numerical dissipation (in terms of a time increment) at the filtering stage. In contrast to existing approaches that use a time-integration method with the same dissipation (or artificial viscosity) for all time increments, the new technique yields accurate and non-oscillatory results for wave propagation problems without interaction between user and computer code. The solutions of 3-D wave propagation and impact problems show the effectiveness of the new approach.     

Evidence for shape-dependent deposition in crossflow microfiltration of microbial cells

Measurements of the mean cell volume and mean cell aspect ratio are reported for suspensions of the polymorphic yeast Kluyveromyces marxianus var. marxianus NRRLy2415 and for cakes of the same microorganism recovered after crossflow microfiltration with a tubular ceramic membrane at fixed trans-membrane pressure and crossflow velocity. The mean cell volume and the mean cell aspect ratio in the cake were determined using image analysis. The mean cell volume was found to be consistently smaller in the cake than in the suspension while tentative evidence was found that the mean cell aspect ratio was also smaller in the cake. Enhanced deposition of less elongated cells is likely to be a consequence of preferential deposition of small cells because, for the microorganism used in this study, the mean cell aspect ratio in a suspension increases with increasing mean cell volume. Close analysis of the data reveals that the mean cell aspect ratio is greater in the cake than would be expected based on the mean cell volume in the suspension, suggesting that the deposition of more elongated cells is favoured over less elongated cells of the same volume.     

Explicit bounds for multidimensional linear recurrences with restricted coefficients

This note employs path counting techniques to extend recent results on bounds for odd order linear recurrences to higher dimensions. The results imply optimal zero-free polydisks for multivariable power series with 0, 1 coefficients. Among the applications is a result that states that the optimal zero-free polydisk has radius approximately 1/(v+1), for large dimensions v.     

On a class of nonzero-sum,linear-quadratic differential games

A class of two-player, nonzero-sum, linear-quadratic differential games is investigated for Nash equilibrium solutions when both players use closed-loop control and when one or both of the players are required to use open-loop control. For three formulations of the game, necessary and sufficient conditions are obtained for a particular strategy set to be a Nash equilibrium strategy set. For a fourth formulation of the game, where both players use open-loop control, necessary and sufficient conditions for the existence of a Nash equilibrium strategy set are developed. Several examples are presented in order to illustrate the differences between this class of differential games and its zero-sum analog.This research was supported by the National Science Foundation under Grant No. GK-3341.     

Temperature dependent hyperfine distributions in Fe-B and Fe-Ni-Si-B glasses

Mössbauer spectra of amorphous Fe_xNi_{80- x} Si₁₀B₁₀ (x=10,50) and Fe₈₀B₂₀ have been taken at 4.2-300K and in 0-6T applied magnetic fields. Detailed analysis shows that the standard deviation of the magnetic hyperfine field σ(B) varies with temperature depending on the iron concentration. For small x the variation is taken as evidence for a break-down of long-range magnetic order. Temperature induced changes in the fluctuations and correlations of the hyperfine parameters are reported. In all cases the isomer shift fluctuations are small compared to those of the first-order electric quadrupole splitting (u); neither are strongly temperature dependent. The correlation <ΔBΔu> is negative and increases with temperature. For Fe₈₀B₂₀, <ΔBΔδ> is positive and increases with temperature, whereas for Fe-Ni-Si-B it is small, negative, and temperature invariant.     

Fine structure inversion of the 3d excited state of sodium

The observed inversion of the fine structure of the excited 3d state of the sodium atom explained as due to a second-order effect between the electrostatic dipole exchange interaction and the magnetic spin-orbit interaction acting on the core 2p electrons.