Geometric multigrid for an implicit-time immersed boundary method

The immersed boundary (IB) method is an approach to fluid-structure interaction that uses Lagrangian variables to describe the deformations and resulting forces of the structure and Eulerian variables to describe the motion and forces of the fluid. Explicit time stepping schemes for the IB method require solvers only for Eulerian equations, for which fast Cartesian grid solution methods are available. Such methods are relatively straightforward to develop and are widely used in practice but often require very small time steps to maintain stability. Implicit-time IB methods permit the stable use of large time steps, but efficient implementations of such methods require significantly more complex solvers that effectively treat both Lagrangian and Eulerian variables simultaneously. Several different approaches to solving the coupled Lagrangian-Eulerian equations have been proposed, but a complete understanding of this problem is still emerging. This paper presents a geometric multigrid method for an implicit-time discretization of the IB equations. This multigrid scheme uses a generalization of box relaxation that is shown to handle problems in which the physical stiffness of the structure is very large. Numerical examples are provided to illustrate the effectiveness and efficiency of the algorithms described herein. These tests show that using multigrid as a preconditioner for a Krylov method yields improvements in both robustness and efficiency as compared to using multigrid as a solver. They also demonstrate that with a time step 100–1000 times larger than that permitted by an explicit IB method, the multigrid-preconditioned implicit IB method is approximately 50–200 times more efficient than the explicit method.     

Crystal plasticity simulations of microstructure-induced uncertainty in strain concentration near voids in brass

The uncertainty in mechanical response near a cylindrical hole in polycrystalline alpha brass was simulated as a function of variations in the crystallographic orientations of the grains near the hole. A total of 4 hole sizes were examined, including the case of a microstructure without a hole, and 45 simulations were performed for each case (yielding 180 simulations total) to acquire statistical data. For a hole larger than the grain size, the deformation resembles the homogenous solution but with perturbations due to the local microstructural environment. For a hole approximately equal to or smaller than the grain size, the deformation deviates substantially from the continuum behaviour, and depends strongly on the local microstructural environment surrounding the hole. Each population of simulations was analysed statistically to determine the effect of micro structural variability on strain localization near each of the four defect sizes. The coefficient of variation in the maximum plastic strain around microstructure-scale holes is about 37%, and the largest values of plastic strain are about twice those in the absence of microstructure. These results have significant implications for analyses of the margin of failure due to defects of this class (e.g. voids or small bolt holes).     

SYNTHESIS OF 1,3-THIAZANE-2,4-DIONE AND 2-THIO-5,6-DIHYDROURACIL AND THEIR DERIVATIVES

Abstract

1,3-Thiazane-2,4-diones and 2-thio-5,6-dihydrouracils belong to biologically interesting groups of compounds. The 5-ethyl-6-phenyl derivative (Dolitrone) of the former has shown marked activity as an intravenous general anaesthetic. Several derivatives of 2-thio-5,6-dihydrouracil have been reported to possess antitubercular and antithyroid activity. In the present study these two groups of compounds have been synthesised from common starting materials, namely, different α,β-unsaturated acids and thiourea.     

A regioselective etherification of pyridoxine via an ortho-pyridinone methide intermediate

The catalyst-free, regioselective synthesis of 4′-O-substituted pyridoxine derivatives under solventless conditions is described. The methodology relies on the highly regioselective formation of the ortho-pyridinone methide from pyridoxine and subsequent oxa-Michael addition of alcohol nucleophiles. This methodology provides good to excellent yields for primary and secondary alcohols and moderate yields for tertiary alcohols.     

A Sequential Tensile Method for Rapid Characterization of Extreme-value Behavior in Microfabricated Materials

A high-throughput sequential tensile test method has been developed to characterize the fracture strength distribution of microfabricated polycrystalline silicon, the primary structural material used in microelectromechanical systems (MEMS). The resulting dataset of over 1,000 microtensile tests reveals subtle extreme-value behavior in the tails of the distribution, demonstrating that the common two-parameter Weibull distribution is inferior to a three-parameter Weibull model. The results suggest the existence of a cut-off or threshold stress (1.446 GPa for this particular material) below which tensile failure will not occur. The existence of a cut-off stress suggests that the material’s flaw size distribution and toughness distribution are both also bounded. From an application perspective, the cut-off stress provides a statistically-sound basis for reliable design. While the sequential method is demonstrated here for tensile strength distributions in polycrystalline silicon MEMS, the technique could be extended to a wide range of mechanical tests (bending strength, elastic modulus, fracture toughness, creep, etc.) for both microsystem and conventional materials.     

Nanoscale anisotropic plastic deformation in single crystal aragonite

The nanoscale anisotropic elastic-plastic behavior of single-crystal aragonite is studied using nanoindentation and tapping mode atomic force microscopy imaging. Force-depth curves coaxial to the axis exhibited load plateaus indicative of dislocation nucleation events. Plasticity on distinct slip systems was evident in residual topographic impressions where four pileup lobes were present after indentation with a conospherical probe and distinct, protruding slip bands were present after indentation with a Berkovich pyramidal probe. A finite element crystal plasticity model revealed the governing roles of the {110}<001>slip system family, as well as the (100)[010], (100)[001], (010)[100], (010)[001], (001)[100] and (001)[010] systems.     

Experimental limit on optical-photon coupling to light neutral scalar bosons

We report on the first results of a sensitive search for scalar coupling of photons to a light neutral boson in the mass range of approximately 1.0 meV (milli-electron volts) and coupling strength greater than 10(-6) GeV(-1) using optical photons. This was a photon regeneration experiment using the "light shining through a wall" technique in which laser light was passed through a strong magnetic field upstream of an optical beam dump; regenerated laser light was then searched for downstream of a second magnetic field region optically shielded from the former. Our results show no evidence for scalar coupling in this region of parameter space.     

Acoustic modeling of American English /r/

Recent advances in physiological data collection methods have made it possible to test the accuracy of predictions against speaker-specific vocal tracts and acoustic patterns. Vocal tract dimensions for /r/ derived via magnetic-resonance imaging (MRI) for two speakers of American English [Alwan, Narayanan, and Haker, J. Acoust. Soc. Am. 101, 1078-1089 (1997)] were used to construct models of the acoustics of /r/. Because previous models have not sufficiently accounted for the very low F3 characteristic of /r/, the aim was to match formant frequencies predicted by the models to the full range of formant frequency values produced by the speakers in recordings of real words containing /r/. In one set of experiments, area functions derived from MRI data were used to argue that the Perturbation Theory of tube acoustics cannot adequately account for /r/, primarily because predicted locations did not match speakers' actual constriction locations. Different models of the acoustics of /r/ were tested using the Maeda computer simulation program [Maeda, Speech Commun. 1, 199-299 (1982)]; the supralingual vocal-tract dimensions reported in Alwan et al. were found to be adequate at predicting only the highest of attested F3 values. By using (1) a recently developed adaptation of the Maeda model that incorporates the sublingual space as a side branch from the front cavity, and by including (2) the sublingual space as an increment to the dimensions of the front cavity, the mid-to-low values of the speakers' F3 range were matched. Finally, a simple tube model with dimensions derived from MRI data was developed to account for cavity affiliations. This confirmed F3 as a front cavity resonance, and variations in F1, F2, and F4 as arising from mid- and back-cavity geometries. Possible trading relations for F3 lowering based on different acoustic mechanisms for extending the front cavity are also proposed.