Grid‐free surface vorticity method applied to flow induced vibration of flexible cylinders

In order to study cross flow induced vibration of heat exchanger tube bundles, a new fluid–structure interaction model based on surface vorticity method is proposed. With this model, the vibration of a flexible cylinder is simulated at Re=2.67 × 10⁴, the computational results of the cylinder response, the fluid force, the vibration frequency, and the vorticity map are presented. The numerical results reproduce the amplitude‐limiting and non‐linear (lock‐in) characteristics of flow‐induced vibration. The maximum vibration amplitude as well as its corresponding lock‐in frequency is in good agreement with experimental results. The amplitude of vibration can be as high as 0.88D for the case investigated. As vibration amplitude increases, the amplitude of the lift force also increases. With enhancement of vibration amplitude, the vortex pattern in the near wake changes significantly. This fluid–structure interaction model is further applied to simulate flow‐induced vibration of two tandem cylinders and two side‐by‐side cylinders at similar Reynolds number. Promising and reasonable results and predictions are obtained. It is hopeful that with this relatively simple and computer time saving method, flow induced vibration of a large number of flexible tube bundles can be successfully simulated. Copyright © 2004 John Wiley & Sons, Ltd.     

Divinylsiloxane‐bisbenzocyclobutene‐based polymer modified with polystyrene–polybutadiene–polystyrene triblock copolymers

Divinylsiloxane‐bisbenzocyclobutene (DVS‐bisBCB) polymer has very low dielectric constant and dissipation factor, good thermal stability, and high chemical resistance. The fracture toughness of the thermoset polymer is moderate due to its high crosslink density. A thermoplastic elastomer, polystyrene–polybutadiene–polystyrene triblock copolymer, was incorporated into the matrix to enhance its toughness. The cured thermoset matrix showed different morphology when the elastomer was added to the B‐staged prepolymer or when the elastomer was B‐staged with the DVS‐bisBCB monomer. Small and uniformly distributed elastomer domains were detected by transmission electron micrographs (TEM) in the former case, but TEM did not detect a separate domain in the latter case. A high percentage of the polystyrene–polybutadiene–polystyrene triblock copolymer could be incorporated into the DVS‐bisBCB thermoset matrix by B‐staging the triblock copolymer with the BCB monomer. The elastomer increased the fracture toughness of DVS‐bisBCB polymer as indicated by enhanced elongation at break and increased K1c values obtained by the modified edge‐lift‐off test. Elastomer modified DVS‐bisBCB maintained excellent electrical properties, high T_g and good thermal stability, but showed higher coefficient of linear thermal expansion values. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1591–1599, 2006     

Extendible elements of the alternating groups

An element σ of A_n, the Alternating group of degree n, is extendible in S_n, the Symmetric group of degree n, if there exists a subgroup H of S_n but not A_n whose intersection with A_n is the cyclic group generated by σ. A simple number-theoretic criterion, in terms of the cycle-decomposition, for an element of A_n to be extendible in S_n is given here.     

A theoretical study of the sulphonium cation SH+3

Ab initio Hartree—Fock calculations with STO-3G functions have been performed to determine the structure (1.371 Å and 95.33°) of SH⁺₃ and the proton affinity (≈196 kcal/mol) of H₂S. Inclusion of a sulphur 3d function in the basis has been found essential to give a better geometry of SH⁺₃.     

Electron paramagnetic resonance study of partially oriented clay platelets intercalated with copper(II) 1,4,8,11-tetraazacyclotetradecane

Electron paramagnetic resonance (EPR) spectra of powder and oriented films of montmorillonite, hectorite, and saponite intercalated with [Cu(cyclam)](2+) (cyclam = 1,4,8,11-tetraazacyclotetradecane) exhibit three components: an orientation-dependent component without hyperfine features, an orientation-dependent component with hyperfine features, and an orientation-independent component without hyperfine feature. EPR spectra of [Cu(cyclam)](2+)-saponite, which exhibit only two components and the best resolved hyperfine features, were simulated. The spectra indicate that a large portion of the saponite platelets are inclined to the glass surface, although they tend to align with their basal planes parallel to the glass surface. The orientation-dependent spectra could be simulated by introducing a Gaussian distribution with a standard deviation of 20 degrees for the inclination angle. The standard deviation may be used as a disorder parameter for the microcrystals assembled on glass plates. Spectral simulation also shows that the CuN(4) plane of [Cu(cyclam)](2+) is parallel to the clay layers. EPR spectra of some other partially oriented systems are also discussed.     

Über kondensierte Heterocyclen aus β-Isothiocyanatoketonen und Aminoalkoholen bzw. Diaminen

2- and 3-aminoalcohols, o-aminobenzylalcohol, o-hydroxybenzylamine and o-amino(thio)-phenol react with 4-isothiocyanato-4-methyl-2-pentanone (1) to yield derivatives of condensed heterocycles (oxazolopyrimidines7, pyrimidooxazine8, pyrimidobenzoxazines9, 10, pyrimidobenzoxazole11 a and pyrimidobenzothiazole11 c respectively). Ethylenediamine or 1,3-diaminopropane react with1 to yield either imidazo-pyrimidine13 and pyrimidopyrimidine14 respectively or the 1,2-ethylene- and trimethylenebisdihydro-2(1H)-pyrimidinethione15 a, b respectively, according to the molar ratio of the reactants. o-Phenylenediamine gives pyrimidobenzimidazole11 d. 11a undergoes ring cleavage in boiling dimethylformamide followed by methylpyrimidine-pyridine rearrangement to dihydrohydroxyphenylamino-2(1H)-pyridinethione12, while15 a is converted into the bis-4-(ethanediimino)-pyridinthione16.     

Synthesis of an isomer of the germacranolide isoaristolactone

Photocycloadditlon of (+)-isoplperltenone and cyclobutene-1-carboxylic acid gives an adduct which upon reduction with NaCNBH₃ followed by thermolysis yields an isomer of isoaristolactone in an overall yield of 26%.     

Synthesis of Functionalized Spiro[cycloalkanono-2,3'-thiophenes] via Tandem Conjugate Addition-Cyclization of 3-Oxoacid Thioanilides to Nitroalkenes

A convenient method is described for the synthesis of functionalized spiro[cycloalkanono-2,3-thiophenes] by treatment of cyclic 3-oxoacid thioanilides with -nitrostyrenes. Reaction of the obtained products with acetic anhydride yielded the corresponding oxime acetates.     

Über 4-Alkylamino-bzw. 4-Arylamino-5,6-dihydro-2(1H)-pyridinthione

Heating 1-alkyl- or 1-aryldihydro-6-methyl-2(1H)-pyrimidinethiones5, 6 in an inert medium causes rearrangement to 4-alkylamino-(4-arylamino-)-5,6-dihydro-2(1H)-pyridinethiones11, 12, probably via the methylene form29, by thermal heterolysis of the N₁/C₂ bond and exchange of the alkylamino (arylamino) group 1 through the carbon atom of the methylene group 6. The aminodihydropyridinethiones11, which can be regarded as cyclic derivatives of 3-aminothiocrotonamide, react with bistrichlorophenylmalonate under diacylation, and with formaldehyde and primary amines to yield aminodialkylation products of the enamine system, tetrahydro-4-hydroxy-7,7-dimethyl-5-thioxopyrido[4,3-b]pyridine-2(1H)-ones13, 14 and hexahydro-7,7-dimethylpyrido[4,3-d]pyrimidine-5(6H)-thiones18, 19, 21 respectively. H₂O₂ converts11 to the corresponding 4-aminodihydro-2(1H)-pyridones22, which can be reconverted into11 with P₄S₁₀.11 reacts with alkyl halides to 2-alkylthiodihydropyridines23, 24, 25. The mechanism of the methylpyrimidine-pyridine rearrangement is discussed.     

An easy preparation of per- and poly-fluoroalkyl propenyl sulfones

Sodium tridecafluorohexanesulfinate (1a) and sodium 1-chloro-2,2,2-trifluoroethanesulfinate (1b) were prepared by the treatment of 1-iodo-tridecafluorohexane and 1-bromo-1-chloro-2,2,2-trifluoroethane with sodium dithionite in a water-acetonitrile solution. Prolonged reaction of 1a with allyl bromide in DMF afforded tridecafluorohexane 1-propenyl sulfone 2 as the only product in good yield. A similar treatment of 1b gave exclusively 1-chloro-2,2,2-trifluoroethane 3-propenyl sulfone 4. Bromination of 4 followed by dehydrobromination with Et₃N resulted in a mixture of 1-chloro-2,2,2-trifluoroethane 3-bromo-1-propenyl sulfone 6 and 1-chloro-2,2,2-trifluoroethane 2-bromo-3-propenyl sulfone 7, while dehydrobromination with pyridine gave sulfone 6 practically as the only product. α,β-Unsaturated sulfones 2 and 6 were shown to be active dienophiles.