Hyperbolic elements in negatively curved groups

We show that in a negatively curved groupG the conjugacy class of any infinite cyclic subgroup contains a straight element, an elementg with |g ⁿ |=n|g|, and thus the translation number of an element in a negatively curved group is rational with uniformly bounded denominator. We also find an upper bound on the cardinality of a finite normal subgroup.     

A sliding interface method for unsteady unstructured flow simulations

The objective of this work is to develop a sliding interface method for simulations involving relative grid motion that is fast and efficient and involves no grid deformation, remeshing, or hole cutting. The method is implemented into a parallel, node‐centred finite volume, unstructured viscous flow solver. The rotational motion is accomplished by rigidly rotating the subdomain representing the moving component. At the subdomain interface boundary, the faces along the interface are extruded into the adjacent subdomain to create new volume elements forming a one‐cell overlap. These new volume elements are used to compute a flux across the subdomain interface. An interface flux is computed independently for each subdomain. The values of the solution variables and other quantities for the nodes created by the extrusion process are determined by linear interpolation. The extrusion is done so that the interpolation will maintain information as localized as possible. The grid on the interface surface is arbitrary. The boundary between the two subdomains is completely independent from one another; meaning that they do not have to connect in a one‐to‐one manner and no symmetry or pattern restrictions are placed on the grid. A variety of numerical simulations were performed on model problems and large‐scale applications to examine conservation of the interface flux. Overall solution errors were found to be comparable to that for fully connected and fully conservative simulations. Excellent agreement is obtained with theoretical results and results from other solution methodologies. Copyright © 2006 John Wiley & Sons, Ltd.     

Synthesis of (−)-Pinidine via asymmetric,electrophilic enolate hydroxyamination/nitrone reduction

Enantiomerically pure(?)-pinidine ( 1 ) has been synthesized in 18.5% overall yield by a nine-step sequence starting from keto-ester 2 . The key step 5 → 6 involves an asymmetric, electrophilic enolate hydroxyamination. Diastereoselective hydrogenation of nirtone 6 ensures the cis-relation between the substituents at C(2) and C(6) in piperidine 7 .     

An equivalent circuit characterization of power MOSFET accounting for high field and high frequency effects

An equivalent circuit model for analyzing the AC characteristics of power VDMOS transistors is presented. The model accounts for high field and saturation effects. This is achieved by incorporating dependent voltage and current sources in the device model. Results are given for the AC characteristics of a POLYFET F2001 Power VDMOSFET rated with a drain current of 1.4A, power out of 2.5W at 1GHz. The linear, quasi-saturation and saturation regions of the IV characteristics are accounted for in the analysis. The small signal device parasitics are extracted through s-parameter methods. The s-parameter results were used to extract the frequency dependent parasitics including parasitic capacitances, inductances and transconductances.     

Use of computational fluid dynamics simulations for design of a pretreatment screw conveyor reactor

Computational fluid dynamics simulations were employed to compare performance of various designs of a pretreatment screw conveyor reactor. The reactor consisted of a vertical screw used to create cross flow between the upward conveying solids and the downward flow of acid. Simulations were performed with the original screw design and a modified design in which the upper flights of the screw were removed. Results of the simulations show visually that the modified design provided favorable plug flow behavior within the reactor. Pressure drop across the length of the reactor without the upper screws in place was predicted by the simulations to be 5 vs 40 kPa for the original design.     

Spatiotemporal chaos in the Faraday effect

Spatiotemporal chaos in parametrically excited surface waves is compared to fully developed turbulence. Measured correlation functions decay in both space and time. In contrast to turbulence, the inertial range is absent in the Faraday experiment and intermittency is concentrated at a few preferred wavelengths.