A novel method for automated grid generation of ice shapes for local‐flow analysis

Modelling a complex geometry, such as ice roughness, plays a key role for the computational flow analysis over rough surfaces. This paper presents two enhancement ideas in modelling roughness geometry for local flow analysis over an aerodynamic surface. The first enhancement is use of the leading‐edge region of an airfoil as a perturbation to the parabola surface. The reasons for using a parabola as the base geometry are: it resembles the airfoil leading edge in the vicinity of its apex and it allows the use of a lower apparent Reynolds number. The second enhancement makes use of the Fourier analysis for modelling complex ice roughness on the leading edge of airfoils. This method of modelling provides an analytical expression, which describes the roughness geometry and the corresponding derivatives. The factors affecting the performance of the Fourier analysis were also investigated. It was shown that the number of sine–cosine terms and the number of control points are of importance. Finally, these enhancements are incorporated into an automated grid generation method over the airfoil ice accretion surface. The validations for both enhancements demonstrate that they can improve the current capability of grid generation and computational flow field analysis around airfoils with ice roughness. Copyright © 2004 John Wiley & Sons, Ltd.     

Palladium-catalyzed synthesis of poly(bromoalkoxy- and bromoalkanoyloxymethylsiloxane)s from poly(hydromethylsiloxane)s

Palladium-catalyzed synthesis of poly(bromoalkoxymethyl- and bromoalkanoyloxymethylsiloxane)s from poly(hydromethylsiloxane)s was studied. Treatment of poly(hydromethylsiloxane)s with mixtures of allyl bromide and cyclic ethers in the presence of a catalytic amount of PdCl₂ gave the corresponding poly[(bromoalkoxy)methylsiloxane]s in good yield. A similar reaction with γ-butyrolactone produced poly[(bromobutanoyloxy)methylsiloxane], although the polymer was highly moisture-sensitive and could not be separated from the reaction mixture. Transformation of the bromoalkoxy unit in the resulting siloxane polymer into an aminoalkoxy group was also examined.     

N-heterocyclic carbene-mediated formal [3+3] annulation of isatin-derived α, β-unsaturated acids: Access to functionalized 3,4′-spirooxindole δ-lactones

An in situ activation of isatin-derived α,β-unsaturated acids 2 for the generation of isatin-derived α,β-unsaturated acyl azoliums II was described. The acyl azoliums II were successfully applied to undergo a formal [3 + 3] annulation with 1,3-dicarbonyl compounds to access functionalized 3,4′-spirooxindole δ-lactones 4. A scale-up synthesis and an enantioselective variant of this protocol were also investigated. The stable and easily prepared acids 2 may be further utilized as promising versatile electrophilic 1,3-synthons for divergent synthesis of spirooxindoles.     

Synthetic study of kosinostatin aglycone: synthesis of BCDE rings using alkoxycarbonylmethylation of diazonaphthoquinone

A synthetic study of kosinostatin aglycone is reported. Synthesis of key intermediate lactone 3, which corresponds to the BCDE ring fragment, was accomplished, and the precursor BCD ring fragment 5 was synthesized via two routes. First, 5 was synthesized from 2,5-dimethoxybenzaldehyde 16 by the combination of typical known transformations including efficient application of non-aqueous OsO₄ oxidation in the presence of PhB(OH)₂. However the synthesis required 15 long steps, and its main difficulty was ortho-alkoxycarbonylmethylation of 1-naphthol. Next we attempted to apply our recently developed alkoxycarbonylmethylation of diazonaphthoquinone for the synthesis of 5, and 5 was successfully synthesized in 9 steps from the same starting compound 16. Finally, 5 was stereoselectively converted to lactone 3 via trifluoroacetic acid-mediated cyclization of the 3,4-epoxycylohexanecarboxylic acid derivative.     

Highly Enantioselective Rhodium(I)‐Catalyzed Carbonyl Carboacylations Initiated by C?C Bond Activation

The lactone motif is ubiquitous in natural products and pharmaceuticals. The Tishchenko disproportionation of two aldehydes, a carbonyl hydroacylation, is an efficient and atom‐economic access to lactones. However, these reaction types are limited to the transfer of a hydride to the accepting carbonyl group. The transfer of alkyl groups enabling the formation of C C bonds during the ester formation would be of significant interest. Reported herein is such asymmetric carbonyl carboacylation of aldehydes and ketones, thus affording complex bicyclic lactones in excellent enantioselectivities. The rhodium(I)‐catalyzed transformation is induced by an enantiotopic C C bond activation of a cyclobutanone and the formed rhodacyclic intermediate reacts with aldehyde or ketone groups to give highly functionalized lactones.     

On the cut‐off phenomenon for the transitivity of randomly generated subgroups

Consider K ≥ 2 independent copies of the random walk on the symmetric group S_N starting from the identity and generated by the products of either independent uniform transpositions or independent uniform neighbor transpositions. At any time $n\in \mathbb{N}$, let G_n be the subgroup of S_N generated by the K positions of the chains. In the uniform transposition model, we prove that there is a cut‐off phenomenon at time N ln(N)/(2K) for the non‐existence of fixed point of G_n and for the transitivity of G_n, thus showing that these properties occur before the chains have reached equilibrium. In the uniform neighbor transposition model, a transition for the non‐existence of a fixed point of G_n appears at time of order $N^{1+\frac{2}{K}}$ (at least for K ≥ 3), but there is no cut‐off phenomenon. In the latter model, we recover a cut‐off phenomenon for the non‐existence of a fixed point at a time proportional to N by allowing the number K to be proportional to ln(N). The main tools of the proofs are spectral analysis and coupling techniques. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2012