Probes for narcotic receptor-mediated phenomena. 33. Construction of a strained trans-5,6-ring system by displacement of a nitro-activated aromatic fluorine. synthesis of the penultimate oxide-bridged phenylmorphans

The synthesis of the ortho- and para-e isomers in the oxide-bridged 5-phenylmorphan series of rigid tetracyclic compounds was accomplished via rac-5-(2-fluoro-5-nitrophenyl)-2-methyl-2-azabicyclo[3.3.1]nonan-9beta-ol ((+/-)-10), an intermediate containing an aromatic nitro-activated fluorine atom. The fluorine atom was used as the leaving group for the formation of the strained tetracyclic trans-fused 5,6-ring system in rac-(1alpha,4aalpha,9aalpha)-1,3,4,9a-tetrahydro-2-methyl-6-nitro-2H-1,4a-propanobenzofuro[2,3-c]pyridine ((+/-)-11), although preference for cis ring fusion during the formation of tricyclic tetra- and hexahydrodibenzofurans has been well-documented. Single-crystal X-ray crystallographic study of the desired para-e isomer ((+/-)-2), as well as of two intermediates in its synthesis, provided assurance of the correct structures. The e-isomers are among the last of the 12 oxide-bridged 5-phenylmorphans to be synthesized. We envisioned the syntheses of these rigid, tetracyclic compounds in order to determine the three-dimensional pattern of a ligand that would enable interaction with opioid receptors as agonists or antagonists.     

Discontinuous boundary implementation for the shallow water equations

Quasi‐bubble finite element approximations to the shallow water equations are investigated focusing on implementations of the surface elevation boundary condition. We first demonstrate by numerical results that the conventional implementation of the boundary condition degrades the accuracy of the velocity solution. It is also shown that the degraded velocity leads to a critical instability if the advection term is present in the momentum equation. Then we propose an alternative implementation for the boundary condition. We refer to this alternative implementation as a discontinuous boundary (DB) implementation because it introduces at each boundary node two independent mass–flux values that result in a discontinuity at the boundary. Numerical results show that the proposed DB implementation is consistent, stabilizes the quasi‐bubble scheme, and leads to second‐order accuracy at the surface elevation specified boundary. Copyright © 2004 John Wiley & Sons, Ltd.     

Modelling of self-aligned total internal reflection waveguide mirrors: an interlaboratory comparison

Results of modelling of light propagation in 45° self-aligned total internal reflection rib waveguide mirrors on InP substrate are compared. Six laboratories participated in the comparison with the following six modelling methods: the standard fast-Fouriertransform beam propagation method (BPM), the standard finite-difference (FD) BPM using the Crank-Nicholson scheme (two laboratories), the FD-BPM with the correction for the slowly varying envelope approximation, the method of lines, the eigenmode expansion and propagation method, and a simple method based on the field overlap. All the laboratories used the effective-index method to reduce the three-dimensional problem to two dimensions. The differences among the results obtained by different methods are briefly discussed and qualitatively compared to measured values.     

Development of the direct stress solution technique for three-dimensional hydrodynamic models using finite elements

Velocity varies rapidly near sheared boundaries. Therefore in many practical fluid problems it can be inefficient to solve discrete equations with velocity as the dependent variable. Conversely, shear stress varies slowly near sheared boundaries, suggesting that it may be well suited for use as the dependent variable in discrete equations. This paper describes a formulation of the internal mode equations for a three-dimensional hydrodynamic model using shear stress as the dependent variable. The resulting direct stress solution (DSS), coupled with a spatial discretization using linear finite elements, yields a system matrix that can be set up and solved with the efficiency of a banded matrix with bandwidth 8. If the eddy viscosity distribution is assumed to be piecewise linear over the depth (with an arbitrary number of time-varying segments), the recovery of velocity from stress can be easily accomplished in closed form, thereby avoiding any difficulty resulting from the logarithmic singularity in the velocity profile that occurs at a boundary. Results from tidal and wind-driven test cases with realistic boundary layers are used to demonstrate the accuracy and computational advantages of a DSS formulation versus a standard velocity-based formulation.     

A solution for the vertical variation of stress,rather than velocity,in a three-dimensional circulation model

A simple technique is presented that allows a numerical solution to be sought for the vertical variation of shear stress as a substitute for the vertical variation of velocity in a three-dimensional hydrodynamic model. In its most general form the direct stress solution (DSS) method depends only upon the validity of an eddy viscosity relation between the shear stress and the vertical gradient of velocity. The rationale for preferring a numerical solution for shear stress to one for velocity is that shear stress tends to vary more slowly over the vertical than velocity, particularly near boundaries. Consequently, a numerical solution can be obtained much more efficiently for shear stress than for velocity. When needed, the velocity profile can be recovered from the stress profile by solving a one-dimensional integral equation over the vertical. For most practical problems this equation can be solved in closed form. Comparisons are presented between the DSS technique, the standard velocity solution technique and analytical solutions for wind-driven circulation in an unstratified, closed, rectangular channel governed by the linear equations of motion. In no case was the computational effort required by the velocity solution competitive with the DSS when a physically realistic boundary layer was included. The DSS technique should be particularly beneficial in numerical models of relatively shallow water bodies in which the bottom and surface boundary layers occupy a significant portion of the water column.     

Synthesis of rac-(1R,4aR,9aR)-2-methyl-1,3,4,9a-tetrahydro-2H-1,4a-propanobenzofuro[2,3-c]pyridin-6-ol. An unusual double rearrangement leading to the ortho- and para-f oxide-bridged phenylmorphan isomers

In an attempt to obtain the para-f isomer, rac-(1R,4aR,9aR)-2-methyl-1,3,4,9a-tetrahydro-2H-1,4a-propanobenzofuro[2,3-c]pyridin-6-ol, via mesylation of an intermediate 9[small alpha]-hydroxyphenylmorphan, we obtained, instead, a rearranged chloro compound with a 5-membered nitrogen ring, 7-chloro-3a-(2,5-dimethoxyphenyl)-1-methyl-octahydroindole. This indole underwent a second rearrangement to give us the desired para-f isomer. The structures of the intermediate indole and the final product were unequivocally established by X-ray crystallography. A resynthesis of the known rac-(1R,4aR,9aR)-2-methyl-1,3,4,9a-tetrahydro-2H-1,4a-propanobenzofuro[2,3-c]pyridin-8-ol, the ortho-f isomer, was achieved using the reaction conditions for the para-f isomer, as well as under Mitsunobu reaction conditions where, unusually, the oxide-bridge ring in the 5-phenylmorphan was closed to obtain the desired product. The synthesis of the para-f isomer adds an additional compound to those oxide-bridged phenylmorphans that were initially visualized and synthesized; the establishment of the structure and configuration of 8 of the theoretically possible 12 racemates has now been achieved. The X-ray crystallographic structure analysis of the para-f isomer provides essential data that will be needed to establish the configuration of a ligand necessary to interact with an opioid receptor.     

Coupling methods between finite element–based Boussinesq‐type wave and particle‐based free‐surface flow models

We develop one‐way coupling methods between a Boussinesq‐type wave model based on the discontinuous Galerkin finite element method and a free‐surface flow model based on a mesh‐free particle method to strike a balance between accuracy and computational cost. In our proposed model, computation of the wave model in the global domain is conducted first, and the nonconstant velocity profiles in the vertical direction are reproduced by using its results. Computation of the free‐surface flow is performed in a local domain included within the global domain with interface boundaries that move along the reproduced velocity field in a Lagrangian fashion. To represent the moving interfaces, we used a polygon wall boundary model for mesh‐free particle methods. Verification and validation tests of our proposed model are performed, and results obtained by the model are compared with theoretical values and experimental results to show its accuracy and applicability.     

Chemistry of (+)-aromadendrene. Part 6: Rearrangement reactions of ledene, isoledene and their epoxides

The chemistry of (+)-ledene and (−)-isoledene, both easily available from (+)-aromadendrene has been investigated. Reactions at the double bond of ledene take place preferably from the β-side. Under acidic conditions its C7-C8 β-epoxide and β-diol preferably react via carbocations, which are initially formed at C8. Rearrangement takes place to compounds with cubebane and cadinane skeletons. The reaction pattern of isoledene and its α-epoxide, under acidic conditions, is governed by the easy formation of an intermediate α-cyclopropylcarbinyl carbocation. Further reactions lead to products in which the C2-C3 bond of the cyclopropane ring is broken to give compounds with a guaiane skeleton. Guaiane-type dienes and unsaturated cyclic ethers are the final products of these rearrangements. Several derivatives of these compounds have been prepared.     

Optical deflection tomography with the phase-shifting schlieren

We present a new optical deflection tomography method that takes advantage of the phase-shifting schlieren. The reconstruction algorithm is based on filtered backprojection. The instrument is well adapted for three-dimensional imaging of spatially sparse objects exhibiting large refractive index variations. It achieves a 35 μm resolution with a 3 mm depth of field. Its performance is illustrated with a bundle of fibers immersed in a matching index solution.     

Synthesis of chiral methyl-branched linear pheromones starting from (+)-aromadendrene. Part 7

Ethyl (7S)-10-hydroxy-7-methyldecanoate (4), a linear methyl-branched intermediate with its chiral center at C7, and with two different functional groups at the ends of the chain, has been synthesized from (+)-aromadendrene in nine steps. A Baeyer-Villiger oxidation and a Grob fragmentation are the key reactions in this transformation. Intermediate 4 has been applied in the synthesis of three linear methyl-branched pheromones, (i) (R)-10-methyl-2-tridecanone, the active pheromone of the southern corn rootworm Diabrotica undecimpunctata howardi Barber, (ii) (S)-9-methylnonadecane, one of the sex pheromones of the cotton leafworm Alabama argillacea, and (iii) (meso)-13,23-dimethylpentatriacontane, the sex pheromone of the tse tse fly Glossina pallidipes.