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  • 1985-1989  (8,185)
  • General Chemistry  (5,085)
  • Engineering General  (2,473)
  • Physical Chemistry  (627)
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  • 101
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 2 (1989) 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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  • 102
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The crystal and molecular structures of dimesitylketene (1) and bis(3,5-dibromo-2,4,6-trimethylphenyl)ketene (2), the first free ketenes to be studied by X-ray diffraction, have been determined. The molecules of 1 and 2 have crystallographic C1 and C2 symmetry, respectively, and exist in a propeller conformation. Molecular mechanics calculations of 1 and 2 using a modification of Allinger's new allene parameters reproduce satisfactorily the structural parameters of the ketenes. The torsional angles of the aryl rings in 1 and 2 are similar (ca. 50°) and are regarded as ‘intrinsic’ values for a 1,1-dimesitylvinyl propeller. From the similarity in aryl torsional angles in 1 and 2 it is concluded that the buttressing effects in 2 (if any) are not markedly manifested in the structural parameters of 2.
    Additional Material: 2 Ill.
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  • 103
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 2 (1989), S. 323-330 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Photoreactions of Cr(CO)5(Im) (Im = 1,3-dimethyl-4-imidazolin-2-ylidene) have been investigated by laser flash and continuous photolysis. Quantum yields for the disappearance of Cr(CO)5(Im) in benzene under Ar or CO were very low, although transients observed by laser flash photolysis reacted rapidly with CO. This suggests that photodissociation of the carbene ligand is very minor. The laser flash photolysis at 337 nm in benzene (B) gave a transient (λmax = 630 nm), which converted to the second transient (λmax = 455 nm) within ∼100 ns. The kinetic studies of these transients revealed that the first one is a ‘free’ coordinatively unsaturated species (Cr(CO)4(Im)) and the second one carries a solvent molecule as a ligand (Cr(CO)4(Im)(B)). From the comparison of Cr(CO)4(Im) and Cr(CO)5, apparently lower reactivity of Cr(CO)5 was found to be due to the strong coordination of a solvent molecule. The Im ligand neutralizes the deficit of electron density on Cr. A simple synthesis of Cr(CO)5(Im) was also described.
    Additional Material: 3 Ill.
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  • 104
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 2 (1989), S. 359-362 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The reaction pathway of urea formation by selenium-catalysed carbonylation of secondary amines with carbon monoxide in the presence of oxygen was studied using piperidine as a secondary amine. It was established that selenium reacts with carbon monoxide and piperidine to give carbamoselenoate as an intermediate, which affords biscarbamoyl diselenide by the oxidation with molecular oxygen. Aminolysis of biscarbamoyl diselenide gives the urea derivative, accompanying the regeneration of selenium catalyst.
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  • 105
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 2 (1989), S. 377-382 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The rates of N-methylation of pyridine and its ring-substituted derivatives by trimethyl phosphate were measured in D2O and in CDCl3. Relative rates, together with the solvent activity coefficients of substrates for the transfer form chloroform to water, were used for determining the solvent activity coefficients of the activated complexes for this SN2 reaction. The results indicate early activated complexes for all pyridines, with the most nucleophilic substrate showing the most reactant-like activated complex.
    Additional Material: 2 Tab.
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  • 106
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 2 (1989), S. 389-409 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: A gas-phase experimental investigation of the competition between carbon and oxygen alkylation of a series of cyclic and acyclic enolate ions is described. Perfluoropropylene is shown to react in a characteristic way with oxyanions and carbanions to produce distinctive ionic products. The relative yields of these products formed in reactions with ambident enolate ions provides a measure of their intrinsic carbon vs. oxygen regioselectivity. The results for a series of enolates derived from aldehydes, ketones, esters, amides and related compounds show a wide range of reactivity which is a function of the nature of the central substituent. Most aldehyde and ketone enolates react mainly through oxygen, while enolates with σ-acceptor of π-donor type central substituents react mainly thorugh carbon. Ring-size in cyclic ketone enolates also influences C vs. O regioselectivity, i.e. small-ring enolates react mainly through carbon, while larger ring enolates (C7-C9) react preferentially through oxygen. The enolate reactivity patterns can be generally accounted for by the keto-enol energy differences for the parent carbonyl compounds, although some exceptions are evident. The origins of the highly variable, kinetically determined regioselectivities are discussed.
    Additional Material: 5 Tab.
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  • 107
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 2 (1989), S. 417-424 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Two organometallic reagents, butyllithium in heptane solution and dibutylmercury in the gas phase, have been studied by means of core electron spectroscopy. The property of particular interest was the charge polarization as reflected by the ESCA shifts. In the butyllithium compound the C1s binding energy is shifted to a lower value by 1·8 eV for C-1 (situated closest to the Li+ ion) relative to the heptane solvent carbon. This is due to the anionic character of the C-1. The interpretation of the experiments was supported by comparing the results with ab initio calculations made on geometry-optimized butyllithium, butyl anion and butane.
    Additional Material: 3 Ill.
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  • 108
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 2 (1989), S. 455-466 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Mixtures of bicyclo[3.2.0]hept-2-ene and bicyclo[2.2.1]hept-2-ene, with one isomer labeled with two deuterium atoms, were isomerized in the gas phase at 276 °C. By following the concentration ratios of d0 and d2 versions of bicyclo[2.2.1]hept-2-ene as functions of time one finds that the partitioning of bicyclo[3.2.0]hept-2-ene between the primary products bicyclo[2.2.1]hept-2-ene and cyclopentadiene plus ethene is 2:1. This and earlier stereochemical results permit the calculation of the partitioning of the [3.2.0] olefin between the orbital symmetry allowed [1,3] carbon shift-with-inversion product and several forbidden or non-concerted reaction channels (approximately 1:1) and the stereochemistry of the ethene d2 formed from exo,exo-[6,7-2H2]bicyclo[3.2.0]hept-2-ene directly (1:1 E: Z).
    Additional Material: 2 Ill.
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  • 109
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 2 (1989) 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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  • 110
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The ups and downs, and reasons therein, of the π-complex theory of the mechanism of the benzidine rearrangements, and the possible role of π-complexes in a newer understanding of the rearrangements, are described.
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  • 111
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The principal components factors F1 and F2 in the equation \documentclass{article}\pagestyle{empty}\begin{document}$$ \log K = {\rm BDP}_0 + S_1 F_1 + S_2 F_2 $$\end{document} have been used to obtain S1 and S2 values for sets of hydrogen-bond bases against 32 reference acid/solvent systems. The constants S1 and S2 define an angle θ = tan-1 S2/S1 that is a measure of the electrostatic:covalent bonding ratio in the hydrogen-bond complex. It is shown that θ can vary from 53 (4-fluorophenol in CH2Cl2)to 86 degrees (Ph2NH in CCl4) depending on the reference acid and solvent. This variation in θ can lead to family dependent behaviour in plots of log K for bases against a given reference acid system vs log K for bases against another reference acid system, and precludes the construction of any general scale of hydrogen-bond basicity using log K values. Amongst a quite wide range of reference acid/solvent systems θ varies only from 64 to 73 degrees, and for bases against these reference systems a ‘reasonably general’ scale could be set up. Such a scale could be extended to bases against reference acid/solvent systems outside the 64-73 degree range provided that certain classes of base (e.g. pyridines, alkylamines) were excluded from the additional reference acid/solvent systems.
    Additional Material: 6 Tab.
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  • 112
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 2 (1989), S. 300-322 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Various modifications of the Marcus equation have been applied to the problem of photochemical proton transfer, using available data on general acid-catalyzed photohydration reactions. These include incorporation of asymmetry and tightness parameters, as well as distance variation as a function of exoor endothermicity. The intersecting state model of Formosinho has also been successfully applied to these reactions. The overall conclusion from all of these approaches is that the reactions are characterized by somewhat asymmetric and ‘loose’ transition states, with a small but significant degree of charge development on the in-flight proton at the transition state. Estimates of the intrinsic barriers and work terms place these in the 5-7 kcal and 2-3 kcal ranges respectively. A simple valence bond configuration mixing model leads to similar qualitative conclusions about the nature of the transition states in these reactions.
    Additional Material: 10 Ill.
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  • 113
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The difference in reactivity of small [n]cyclophanes towards CF3CO2H is discussed in terms of charge densities, strain energies and proton affinities. These data are calculated with MNDO and MINDO/3 for para-, meta- and ortho-cyclophanes and for their ipso-protonation products; an attempt is made to transform gas phase ΔHf0 values into liquid phase ΔH0f values. Experimental evidence is presented that the acid catalyzed rearrangement of [5]paracyclophane to its ortho-isomer proceeds via two consecutive 1,2-carbon shifts without deprotonation; intermediate adducts were identified by NMR-spectroscopy. Thus, a gradual shift in reaction pattern in the series [4]-, [5]- and [6]paracyclophane is observed experimentally, in line with the calculational results.
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  • 114
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 2 (1989) 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
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  • 115
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    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 2 (1989), S. 367-376 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The relative rates of hydrogen atom abstraction from a series of twelve saturated cyclic ethers and sulfides were determined at 70°C. The abstracting radical could be generated from bromotrichloromethane both photolytically or by the thermal decomposition of AIBN. The reaction rates did not show a dependence upon method of radical generation. Reaction occurred only at the position adjacent to the heteroatom. The reactivity of the cyclic ethers was in the order C4H8O 〉 C6H12O 〉 C3H6O 〉 C5H10O. This trend would indicate appreciable influence by ring strain, however, the slightly greater reactivity of tetrahydrofuran relative to oxepane suggests a contribution by stereoelectronic factors as well. The reactivity of the cyclic sulfides, which reacted faster than the corresponding ethers, was in the order C4H8S 〉 C5H10S 〉 C6H12S. This would imply little influence of ring strain. The major structural effect would be that of variable electron donating ability of the sulfur atom. The rate of reaction of thietane was also determined. It was found to preferentially undergo SH2 attack at the sulfur atom followed by ring opening rather than hydrogen abstraction. The reactivities of both series of compounds were decreased by the inductive effect of a second heteroatom beta to the reaciton site.
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  • 116
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    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 2 (1989), S. 410-416 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Barriers for group transfers between nucleophiles have been postulated to be lowered when the transferring group can carry a considerable negative charge. Furthermore, anions readily subject to one electron oxidation appear to lead to lower barriers than do those of high oxidation potential. These suggestions are pursued here on the identity reaction ArSe- + ArSeSeAr → ArSeSeAr + ArSe-. Indeed the reaction is very fast, as shown by the appearance of only a single peak in the 77Se-NMR in an acetonitrile solution containing both ArSeNa and ArSeSeAr. The rate constant can be only very roughly estimated at low temperatures and dilute solutions, and is likely diffusion controlled for Ar = phenyl and p-methoxyphenyl. A stable intermediate (ArSe)3-, analogous to Br3-, is indicated, but quantitative stability could not be determined, from either the NMR or the UV spectra. Some properties of 77Se-NMR are discussed.
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  • 117
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    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 2 (1989), S. 425-427 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Distribution between pentane and trifluoromethanesulfonic acid (TFMSA) and carbon-13 NMR measurements showed that benzene and toluene are not protonated to any significant extent in TFMSA. This finding contradicts previous reports, and validates the ranking of superacids based on the extent of benzene protonation.
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  • 118
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: A two-hydron transfer mechanism involving hydron transfers from carbon to nitrogen and from nitrogen to carbon was studied. The rearrangement of 1,3,3-triphenylpropene (1) into 1,1,3-triphenylpropene (2) catalyzed by 2,10-diazabicyclo[4.4.0]dec-1-ene (3) in benzene at 25·00°C was studied by 2H-labeling experiments and kinetic 2H-isotope effects. The synthesis and purification of [6,10-2H2]-2,10-diazabicyclo[4.4.0]dec-1-ene ([6,10-2H2]-3), [3-2H]-1,3,3-triphenylpropene ([3-2H]-1), [3-2H]-1,1,3-triphenylpropene ([3-2H]-2) and [3,3-2H2]-1,1,3-triphenylpropene ([3,3-2H2]-2) together with their precursors are reported. Partial reaction of [3-2H]-1 with [6,10-1H2]-3 gave 42% conversion into product 2, which was shown by 1H NMR to be composed of 88% [3-1H]-2 and 12% [3-2H]-2. Partial reaction of [3-1H]-1 with [6,10-2H2]-3 gave 43% of 2, composed of 73% [3-1H]-2 and 27% [3-2H]-2.These results clearly show that a substantial fraction of the reaction takes place in a bifunctional manner but isotope exchange and/or monofunctionally catalyzed reactions interfere. The following kinetic deuterium isotope effects on the rearrangement 1 → 2 were measured: kHH/kDH = 6·56; kHH/kHD = 1·19; kHH/kDD = 7·08; kHD/kDD = 5·94; and kDH/kDD = 1·08.On the basis of these results, a concerted two-hydron transfer mechanism is excluded. Instead, a stepwise mechanism is favored, in which at first the 3-hydron of 1 is abstracted by 3 yielding an ion pair(s), the carbanion of which in a separate step is then hydronated to yield the product 2.The abstraction of the 3-hydron from 1 might be hydrogen bond assisted. The two hydron transfer transition states are together rate limiting, although they limit the rate to different extents. A detailed mechanistic analysis is presented together with the results of an investigation of the nature of the catalyst. The dimerization constant for 3 was determined by 1H NMR to be 1·67 l mol-1 at 25·0°C. Isotopomer composition was measured by 1H NMR and GLC was used for the separation of the substrate and products. Computer-assisted capillary GLC was used for the kinetics.
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  • 119
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The Kinetics of reactions of phenacyl benzenesulphonates with benzylamines were investigated in methanol at 45·0 °C and the cross-interaction constants λXY, λYZ and βXZ were determined in order to elucidate the transition-state structure. The unusually small magnitude of λXY can only be accounted for by the resonance ‘shunt’ effect of the α-CO group of the phenacyl system. Large |λYZ| values indicate a small degree of bond breaking whereas relatively large |βXZ| values compared with those for the dissociative SN2 reaction indicate a relatively tight transition state for the reactions. Further, the similar magnitudes of βXZ values compared with those of the corresponding aniline nucleophile series suggest a similar transition-state structure for the two armatic amine nucleophile series.
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  • 120
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    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 2 (1989), S. 507-518 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The hydrolysis reactions of N-(2,4,6-trinitrophenyl)piperidine (2) and N-(2,4,6-trinitrophenyl)-morpholine (3) were studied. Two kinetic processes well separated in time are observed in both reactions. The fastest process, which is reversible, leads to the formation of a species of λmax 260 and 410 nm and is attributed to the formation of a σ complex of stoichiometry 1 : 2 due to the addition of a second HO- to the σ complex of 1 : 1 stoichiometry. The slowest process leads quantitatively to picrate ion. The equilibrium constants for the formation of the σ complexes of 1:1 and 1:2 stoichiometries and the rate of formation and decomposition of the latter complex were determined. The kinetic data for the slow process lead to the conclusion that the picrate ion is formed from the attack of HO- on the two σ complexes, confirming previous findings. There are some differences in the calculated rates for 2 and 3 which may be an indication that the elimination of the amine is partially rate determining.
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  • 121
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The rate of decarboxylation of 6-nitrobenzisoxazole-3-carboxylate ion increases sharply with increasing head group size in a series of cetyltrialkylammonium bromides (C16H33NR3Br: R = Me, CTABr; R = Et, CTEABr; R = n - Pr, CTPABr; R = n - Bu, CTBABr) with rate enhancements of 102 (CTABr) and 2·8 × 103 (CTBABr). Micellized tetradecylquinuclidinium bromide and hexadecyl-N-methylmorpholinium bromide are slightly better catalysts than CTABr, as is 1,3-bis(N-cetyl-N,N-dimethylamino)propane dibromide, but p-octyloxybenzyltrialkylammonium bromides (alkyl = Me, n - Bu) are less effective than the corresponding CTA+ surfactants. These differences in catalytic efficiency depend on the head group structure and the extent to which the cationic head groups become less accessible to water rather than the overall micellar structure.
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  • 122
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: 1H, 13C, 15N and 17O NMR chemical shifts, 1JNH and 1JCH coupling constants and line widths (Δν1/2) of the 14N and 17O resonance lines were determined for 2-pyrrolidinone neat and for several 2-pyrrolidinone-solvent systems. The 17O NMR chemical shift of 2-pyrrolidinone was clearly most sensitive to the solvent effects, but changes with the solvent were also observable in the 13C (C=O) and 15N NMR chemical shifts, the 1JNH coupling constants and especially the line widths of the 14N and 17O resonance lines. In general, the results reflected a hydrogen bonding effect between the oxygen atom of 2-pyrrolidinone and the proton-donating solvents and a weak molecular interaction of the NH proton of 2-pyrrolidinone with the proton-accepting solvents. The results are compared with the NMR data for the corresponding binary mixtures of 1-ethyl-2-pyrrolidinone.
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  • 123
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    Journal of Physical Organic Chemistry 2 (1989), S. 580-584 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Rate constants were determined for the combination reactions of a series of cation radicals derived from substituted anthracenes with acetate, p-nitrobenzoate, trifluoroacetate, nitrate and perchlorate ions. Rate constants, depending on the identities of the cation radicals and the nucleophiles, ranging from about 200 to 2 × 1010 1 mol-1 s-1 were observed in acetonitrile at 293 K. The key steps in the reaction are (1) reversible complex formation between the anion and the cation radical followed by (2) irreversible bond formation \documentclass{article}\pagestyle{empty}\begin{document}$$ \begin{array}{*{20}c} {\rm{Ar}^{ + \cdot } + \rm{X}^ - \rightleftharpoons {{\rm{Ar}^{ + \cdot } } \mathord{\left/ {\vphantom {{\rm{Ar}^{ + \cdot } } {\rm{X}^ - }}} \right. \kern-\nulldelimiterspace} {\rm{X}^ - }}} &&&&& {(1)} \\ {{{\rm{Ar}^{ + \cdot } } \mathord{\left/ {\vphantom {{\rm{Ar}^{ + \cdot } } {\rm{X}^ - }}} \right. \kern-\nulldelimiterspace} {\rm{X}^ - }} \to \rm{Ar}^ \cdot - \rm{X}} &&&&& {(2)} \\ \end{array} $$\end{document}.The preliminary results show that cation radical-anionic nucleophile reactions can be very facile. The cation radicals of 9-nitro- and 9-cyanoanthracene are particularly reactive, giving rise to rate constants close to the diffusion-controlled limit with all anionic nucleophile studied and even react moderately rapidly with perchlorate ion. The reaction with perchlorate ion can be compared to the behavior of stable carbenium ions that coexist with the anion in solution and in crystalline salts.
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  • 124
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    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 2 (1989), S. 611-622 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The solvent effect on two SN2 reactions was evaluated by discrete, continuum and discrete-continuum models. The potential energy profiles were found to change dramatically on introduction of the solvent effect. The double-well shape which characterizes the F- + CH3F → FCH3 + F- reaction in the gas phase becomes unimodal when the solvent is introduced, in good agreement with experimental data. The solvation parameters are found to intervene in the reaction coordinate. Recent Monte Carlo and molecular dynamics calculations are discussed.
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  • 125
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    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 2 (1989), S. 631-645 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The kinetics of the aromatic nucleophilic substitution (SNAr) reactions of 1,2-dinitrobenzene (1,2-DNB) with butylamine (BA) and piperidine (PIP) were investigated as a function of the amine concentration and temperature, in chloroform, ethyl acetate, tetrahydrofuran (THF), acetonitrile (ACN), dimethylformamide (DMF), dimethyl sulphoxide (DMSO). benzene, toluene, chlorobenzene and diisopropyl ether.In the set of solvents consisting of ethyl acetate, THF, ACN, DMF and DMSO, neither reaction is catalysed (kA = k1). The sequence and range of reactivity for BA and PIP are similar in these solvents. These results indicate that reactions in which nitro in the leaving group behave differently from SNAr reactions with other leaving groups, such as halogens or alkoxy groups, since an intramolecular hydrogen bond may be expected between the leaving nitro group and the ammonium H of the nucleophiles. The correlations of the rate coefficients obtained with Taft and Kamlet's solvatochromic method support these conclusions.On the other hand, these reactions show mild acceleration with relatively non-polar solvents such as the aromatics and diisopropyl ether. The donor properties of these solvents and experiments with solvent mixtures suggest the formation of electron donor-acceptor complexes between them and 1,2-DNB. Hence the preferential solvation of 1,2-DNB by the donor solvent accounts for the mechanism observed.
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  • 126
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    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 2 (1989), S. 281-299 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Mechanisms of the hydrolysis of urea have been investigated using the MNDO and AMI methods. All geometries were fully optimized and the transition states were characterized by calculating force constants. The results showed that: (i) The unimolecular decomposition process via the direct intramolecular proton transfer is preferred to both the A1 and the bimolecular nucleophilic attack by water, in agreement with the experimental results of Shaw et al. in the low acidity medium. (ii) The diprotonated form of urea exists as an equilibrium species, which undergoes the A2 type hydrolysis more favorably than the monoprotonated form, as Moodie et al. found in the intermediate acidity medium. (iii) The A2 hydrolysis of the monoprotonated form is very similar to those of acetamide and methyl carbamate. (iv) As the number of the solvate water molecules increases, the activation barrier for the A2 process of the monoprotonated form increases while that for the unimolecular decomposition of the free base form decreases, indicating a possibility of the barrier height reversal in the bulk solvent in favor of the latter process, thus accommodating all the experimentally found trends in the urea hydrolysis. The A1 mechanisms involving six-membered ring type intermediates can be ruled out as untenable since no such equilibrium species was obtained by both the MNDO and AM1 calculations.
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  • 127
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    Keywords: Organic Chemistry ; Physical Chemistry
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    Topics: Chemistry and Pharmacology , Physics
    Notes: The spectroscopic evidence for the predominance of the equatorial conformers in the title compounds was confirmed by the study of derivatives containing counterpoise substituents, and by chemical equilibration of anancomeric models. ΔG27o°C [P(O)Ph2] ≳ 3·2 kcal/mol was determined in the dioxane, and ΔG55o°C [P(O)Ph2] = 1·42 ± 0·12 kcal/mol in the oxathiane. It follows then that the strong anomeric interaction observed previously in S—C—P segments does not show up in the six-membered heterocycles 2 and 7, which contain O—C—P moieties. This may be due to an inherent inability of oxygen to act as an electron donor to the axial P(O)Ph2 substituent, or to a dominant repulsive steric interaction in the axial conformers.
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  • 128
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: An excellent linear correlation of oxygen-17 substituent chemical shifts (SCS) for twelve α, α, α-trifluoroacetophenones with single σ+ constants, δ = 24·6σ+ + 556·3 (correlation coefficient 0·998) has been observed. However, from this plot, an SCS of 34·3 ppm for 1,1,1-trifluoroacetone will give a corresponding σ+ (γ+) value of 1·44 for a methyl group, which is not in agreement with 0·63-0·79 obtained from solvolytic rate data.
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  • 129
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    Journal of Physical Organic Chemistry 2 (1989), S. 383-388 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Norbornadiene, isolated in argon, xenon and nitrogen matrices at 20 K, was irradiated with UV light. Characterized by UV-VIS-IR absorption spectroscopy the photoproduct, representing a single species, was assigned to quadricyclane. This result is compared with the literature data on photochemistry of norbornadiene in the gas and liquid phase. The role of the rigid matrix environment on selectivity of the photochemical reaction is discussed.
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  • 130
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    Journal of Physical Organic Chemistry 2 (1989) 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
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  • 131
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    Journal of Physical Organic Chemistry 2 (1989), S. 448-454 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The interaction between pyridoxal-5′-phosphate (PLP) and pyridoxamine-5′-phosphate (PMP) was studied by d.c. and differential pulse polarography. Two reduction waves (or two peaks) were observed. The first wave corresponds to the reduction of the adduct and the second to the reduction of free PLP. The behaviour was similar in analogous Schiff bases. The effects of pH, PMP concentration and the capillary characteristics were studied. The apparent formation constant as a function of the pH was calculated. Thermodynamic parameters were estimated at pH 7 and 0 · 1 M ionic strength. The polarographic and kinetic results show that the overall electrode process appears to be irreversible in a basic medium.
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  • 132
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    Journal of Physical Organic Chemistry 2 (1989), S. 476-483 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Dipole moments of para-substituted benzoyl chlorides and bromides, partly measured in benzene and partly recalculated from elderly literature, were analysed in terms of bond moments and additional contributions expressing the conjugation. Although the gross moments are similar, their decomposition yields different pictures for acyl chlorides and bromides. Only in the latter can significant electron transfer from the halogen be observed. On the other hand, conjugation with the benzene nucleus is strong in both aromatic acyl chlorides and bromides, but stronger in chlorides. There is agreement with the evidence from some other physical quantities but not from all.
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  • 133
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    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Benzyl cations, free of counter ions, have been generated from the nuclear decay of tritium atoms contained exclusively in the side-chain of multi-labelled toluene and allowed to react in competition experiments with benzene and toluene. The aromatic substitution was studied in both the gaseous and liquid phase, employing pure aromatics or aromatics dissolved in n-hexane, carbon tetrachloride and nitromethane as the reaction medium. In the gaseous systems, at 20 Torr total pressure, High meta substitution of toluene indicates extensive isomerization of the excited intermediates, while the increase of the kT/kB value in the Presence of NH3 suggests that selective transalkylation competes with proton transfer to ammonia from the benzyl cation adducts with benzene, but not with toluene. High positional and low substrate selectivities were measured in solution, the decrease in kT/kB (from 2·8 to 1·7) in the different solvents being accompanied by an increase in the o/2p ratio. Competition experiments between benzene and methanol indicate that the reaction is not diffusion controlled. The influence of the reaction medium on the substrate selectivity is explained by postulating the formation of a cation-solvent adduct, where the solvent molecule undergoes displacement by the substrate. Positional selectivity would be controlled in a subsequent step.
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  • 134
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    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The basic hydrolysis of 2,4-dinitrochlorobenzene (DNCB) and 2,4-dinitrofluorobenzene (DNFB) was studied in the presence of β-cyclodextrin (CDOH) and in the presence of hydroxy-functionalized micelles containing either a primary hydroxy group [hexadecyl-2-hydroxyethyldimethylammonium bromide (CHEDAB)] or a secondary hydroxy group [headecyl-2-hydroxypropyldimethylammonium bromide (CHPDAB) and 2-hydroxyhexadecyltrimethylammonium bromide (2-OHCTAB)].In all systems a biphasic reaction was observed. The first phase consisted of a competition between the additive (either micelle or cyclodextrin) and hydroxide ion for the aromatic substrate, and the second phase consisted of the hydrolysis of the trapped aryl micellar or cyclodextryl ether.The percentage of trapping of the aromatic substrate by the cyclodextrin was similar to that found for reactions in the hydroxy-functionalized micelles (CHPDAB and 2-OHCTAB) which contained secondary hydroxy groups. The relative rates of reaction for DNFB and for DNCB, i.e. F/Cl rate ratios, in the presence of CDOH were similar to those obtained in the presence of 2-OHCTAB but less than that obtained in the presence of CHEDAB. These results support the assumption that in CDOH the secondary hydroxy groups of C-2 or C-3 are involved in covalent bond formation with the aromatic substrate rather than the primary hydroxy group of C-6. All the reactions studied proceed much more slowly in the presence of CDOH than in the presence of the hydroxy-functionalized micelles. This may reflect a catalytic effect of the positively charged surface present in the micelles but not in the cyclodextrin.
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  • 135
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Using the solvatochromic indicator method, a scale of solvent hydrogen-bond basicity, β1 (General), has been set up using a series of double regression equations, \documentclass{article}\pagestyle{empty}\begin{document}$$ \nu = \nu _0 + s\pi _1^* + b\beta _1 $$\end{document} for 11 aniline-type indicators. A similar solvent scale, β1 (Special), has been constructed by the homomorphic comparison method using only results by Laurence et al. on the indicators 4-nitroaniline and 4-nitro-N,N-dimethylaniline. Results are available from our previous work on a general solute scale, β2H, and we have also obtained a special solute scale, β2 (pKHB) from available log K values for hydrogen-bond complexation of bases with 4-fluorophenol in CCl4. However, the two solute β2 scales are virtually identical.It is shown that there is a general connection between β1(General) and β2H, with r = 0·9775 and s.d. = 0·05 for 32 compounds, and between β1(Special) and β2H, with r = 0·9776 and s.d. = 0·06 for the same 32 compounds. The latter correlation over 60 compounds yields r = 0·9684 and s.d. = 0·07. However, there are so many compounds in these regressions for which the differences in the solvent and solute β values are larger than the total expected error of 0·07 units that the use of β1 to predict β2 or vice versa is a very hazardous procedure. About 70 new β1 values obtained by the double regression method are also reported.
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  • 136
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    Journal of Physical Organic Chemistry 2 (1989), S. 573-579 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The MM2 force field has been extended so that calculations may be carried out on siloxanes. The parameters chosen give a good fit to available experimental data.
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  • 137
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    Journal of Physical Organic Chemistry 2 (1989), S. 602-610 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: In order to assist in the interpretation of the D5h molecular structure of [45] (1,2,3,4,5)ferrocenophane (1) obtained from x-ray crystallographic analysis, a hypothetical hydrocarbon C30H40 (2) was derived from 1 by removing the iron atom and subjected to geometry optimization by molecular mechanics. A stable D5 conformer was found for 2, which has a g+ g- g+ helical bridge conformation and a ring-ring distance almost identical with that in 1 and ferrocene itself. Optimization of a perhydrogenated hydrocarbon model gave a highly strained C1 structure.
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  • 138
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    Journal of Physical Organic Chemistry 2 (1989), S. 623-630 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Photolysis of dichlorodiphenylmethane in glassy 2-methyltetrahydrofuran at 77 K results in the formation of diphenylcarbene and the diphenylchloromethyl radical, which were detected by their fluorescence emission and excitation spectra. The relative yields of the carbene and biradical are shown to vary dramatically as a function of photolysis time. The photolability of the diphenylchloromethyl radical is also demonstrated. These results were interpreted in terms of a two-step mechanism, in which the diphenylchloromethyl radical is an intermediate in the formation of diphenylcarbene.
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  • 139
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The formation of a σ-like complex by reaction between 1,3,5-trinitrobenzene and 1,8-diazabicyclo [5.4.0]-undec-7-ene was investigated in toluene at various temperatures. The kinetic data showed autocatalytic behaviour. Inspection of the reaction mixtures at zero reaction time indicated the presence of an equilibrium preceding the attack of the nucleophile, affording a molecular complex (substrate-nucleophile) which is responsible for the observed kinetic features. The present and the previous data led to the conclusion that the catalytic behaviours usually observed in SNAr reactions (in apolar solvents with amines as nucleophiles) are better explained by the presence of substrate-catalyst interactions than by catalysis on departure of the proton and leaving group from the zwitterionic intermediate.
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  • 140
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    Journal of Physical Organic Chemistry 2 (1989), S. 187-204 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Reaction products of bifunctional chain molecules with structure X—(CH2)n—Y may critically depend on the chain length n. When the chain length is short (n ≤ 5), reaction products particular to an intramolecular reaction can be dominant, while a process corresponding to an intermolecular reaction between X—CH3 and H3C—Y may take place for higher homologues having large n (≥10). The reaction switching dependent on n is explained in terms of the encounter probability for both end groups (X and Y) with conformations pertinent to product formation. The reaction switching of this sort is discussed on the basis of a reactivity profile recorded as a function of the chain length. Similar reactivity profiles have been observed for thermal Friedel-Crafts cyclization and photo-Smiles rearrangement/photoredox reaction. It is anticipated that the magic methylene chain length of 7 may give rise to an appreciable decrease in reaction yields (e.g. ‘difficulty in medium-sized ring closure’) or an anomalous switching of reaction pathways due to chain length effects.
    Additional Material: 8 Ill.
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  • 141
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    Journal of Physical Organic Chemistry 2 (1989), S. 214-224 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The solvolysis of 21 different 3- or 17-androstanyl tosylates or chlorides with halogen, hydroxy or oxo substituents in 17- or 3-position shows rate constant variations in hexafluoro isopropanol of up to 6·3 with regular differences for epimeric substituents. Similar variations ae seen over a distance of ∼10 Å in 13C-NMR shifts at C-17-ones of androstan-17-ones with varied halogen substituents in C-3, whereas the shielding observed at other distant carbon atoms excludes significant through bond effects. It is shown how, on the basis of suitable Coulomb-type equations and of force field minimized geometries, both the stability variation of carbocationic transition states and the carbonyl group polarization are predictable by linear electric field effects, using the same parametrization.
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  • 142
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    Journal of Physical Organic Chemistry 2 (1989), S. 263-270 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Reactivity of dialkyl 2-(dimethylamino)ethyl phosphates, (RO)2P(O)OCH2CH2NMe2 (R = Me, PhCH2) was studied in aqueous solutions. Depending on the initial substrate's concentration, reaction can involve the unimolecular fragmentation to N,N-dimethylaziridinium dialkylphosphate, or the bimolecular isomerization to the zwitterionic derivative. The latter reaction proceeds via two consecutive SN2 steps and involves the formation of two ionic intermediates which were synthesized independently and allowed to react to give the zwitterionic product. Rate constants for the isomerization of the dimethyl ester (R = Me), as well as rate constant for the reaction between the corresponding intermediates have been determined, and the reactivity of the dimethyl ester has been compared with that of the dibenzyl derivative.
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  • 143
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    Journal of Physical Organic Chemistry 2 (1989), S. 531-539 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Acid-catalysed condensation of resorcinol with aromatic aldehydes results in 2,8,14,20-tetrasubstitued calix[4] areneoctols. Sixteen compounds of this type containing different aromatic substituents were synthesized. The ring closure step, under the conditions of the reaction, is a reversible process. Four configurations are possible for every constitution, viz. cccc, cctt, ccct and ctct, but only cccc and cctt were formed in detectable amounts. In seven cases the thermodynamically more stable cccc isomers (1a-5a, 7a, 8a) and also the kinetically controlled cctt isomers (1b-5b, 7b, 8b) could be isolated. The configurations of the compounds were assigned by temperature-dependent 1H NMR analysis. The conformational motions of the macrocyclic ring permit only the cccc isomers to show coalescence for the signals of the aromatic Hb protons. The coalescence temperature was determined for isomers 1a (ΔG384≠ = 83·5 kJmol-1) and 3a (ΔG369≠ = 83·7 kJ mol-1). For steric reasons the ‘chair-chair’ conformers B and the ‘quasi-boat-chair’ conformers F are favoured. 1H and 13C NMR shifts show that compounds 1a-5a and 1b-5b have a quasi-axial arrangement of the aromatic substituents, whereas 6-9 have a quasi-equatorial arrangement of the substituents.
    Additional Material: 5 Ill.
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  • 144
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    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: ΔG, ΔH and TΔS of transfer of 25 aliphatic and aromatic solutes from 2,2,4-trimethylpentane to aqueous buffer (pH 7) at 298 K have been examined in terms of intrinsic volumes and the solvatochromic parameters π*, δ, β and α of the pure solutes Correlations of the form \documentclass{article}\pagestyle{empty}\begin{document}$$ XYZ = XYZ_0 + {{mV_{\rm I} } \mathord{\left/ {\vphantom {{mV_{\rm I} } {100}}} \right. \kern-\nulldelimiterspace} {100}} + s\pi ^* + d\delta + d\beta + a\alpha $$\end{document} indicate that the thermodynamic quantities of transfer are unequally affected by solute properties; most notably, for aromatic solutes the cavity term mVI/100 is a principal (unfavorable) factor affecting TΔS, but has little effect on ΔH. Transfer to water is favored by increasing solute π* (dipolarity-polarizability), β (H-bond basicity) and α (H-bond acidity), because water has greater dipolarity, H-bond acidity and H-bond basicity than trimethylpentane. Hydrogen bonding contributes exothermically to ΔH, but unfavorably to TΔS, as would be expected from a loss of transitional entropy. Correlations of ΔG, ΔH and TΔS with solute VI/100, β, α, μ2 and polarizability function [(n2 - 1)/(n2 + 2)] give closely comparable results.
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  • 145
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    Journal of Physical Organic Chemistry 2 (1989) 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
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  • 146
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    Journal of Physical Organic Chemistry 2 (1989), S. 585-601 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Triarylaminium salts smoothly catalyze the cyclopropanation of dienes, styrenes and tetrasubstituted alkenes by ethyl diazoacetate. The reactions are regioselective and, in the case of additions to conjugated dienes, cyclopropane-periselective. A cation radical chain mechanism involving carbene transfer from ethyl diazoacetate to a substrate cation radical is proposed.
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  • 147
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    Journal of Physical Organic Chemistry 2 (1989), S. 646-652 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Using a series of equations connecting experimental and theoretical values, it is possible to discuss the origin of the N-methylation effect in azoles dissolved in water and dimethyl sulphoxide. The existence in the azoles studied of a linear relationship between the gas → solution transfer enthalpies and the charge on the pyrrole hydrogen atom demonstrated the fundamental importance of the loss of an active centre for solvation. For the imidazole-N-methylimidazole pair, the complete thermochemical cycle has been determined, allowing the apparent lack of an effect of N-methylation on the basicity in solution to be discussed.
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  • 148
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    Journal of Physical Organic Chemistry 2 (1989), S. 660-671 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The kinetics of the oxidation of seven substituted ethanols by sodium N-bromobenzenesulphonamide or bromamine-B (BAB) in the presence of HCl was studied at 45 °C. The rate shows a first-order dependence on [BAB]0 and is fractional in [alcohol]0, [H+] and [Cl-]. Ionic strength variations, addition of benzenesulphonamide reaction product and variation of dielectric constant of the medium have no effect on the rate. The solvent isotope effect kH2O′/kD2O′ ≈ 0·97. The rates do not correlate satisfactorily with Taft's substituent constants. Activation parameters ΔH≠, ΔS≠, ΔG≠ and log A were calculated by studying the reaction at different temperatures (308-323 K). It was found that ΔH≠ and ΔS≠ are linearly related and an isokinetic relationship is observed with isokinetic temperature β = 393 K, indicating enthalpy as a controlling factor.
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  • 149
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    International Journal for Numerical Methods in Fluids 9 (1989) 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 150
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 23-41 
    ISSN: 0271-2091
    Keywords: Momentum transport ; Turbulent mixing layers ; Discrete vortex method ; Time-dependent momentum fluctuations ; Comparison with experiments ; Large-scale structures ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The turbulent momentum transport phenomena in a two-dimensional mixing layer are investigated numerically by a discrete vortex method. The numerical model and calculations are verified through a comparison with existing numerical simulations and experimental measurements. The main emphasis is placed on the exploration of the detailed time-dependent instantaneous local momentum fluctuations and on the comparison of numerical results with available experimental measurements. The current simulations confirm qualitatively the various trends in the turbulent momentum flux and fluctuating components of the velocity in the mixing layer found with several experimental results. The study shows that similarity exists in turbulent momentum quantities along the axial direction of the mixing layer. The calculations also show a definite correlation between the passage of a large-scale structure and a burst in the turbulent momentum flux. The probability density functions of the fluctuating quantities are shown to be mostly Gaussian-like, with only a few exceptions.
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  • 151
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 99-112 
    ISSN: 0271-2091
    Keywords: Mixed and penalty FEM ; Navier-Stokes equations ; Round-off and ill conditioning ; Pressure discretization ; Coupled flow ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: It is generally accepted that mixed and penalty finite element methods can routinely solve the incompressible Navier-Stokes equations. This paper shows by means of simple examples that problems can arise even for the simpler Stokes equations. The causes of the problem fall in either of two categories: round-off and ill conditioning, or a poor choice of pressure discretization. Nonsensical solutions can be obtained. Computation of the discrete divergence of the flow field is a simple and powerful tool to diagnose such conditions. In the first part of the paper several simple techniques for minimizing the effect of round-off are reviewed. In the second part it is shown that, for coupled flow problems, care must be exercised in the choice of the pressure approximation. A unified treatment of various observations by different workers is presented. This should prove useful for general users of the finite element method.
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  • 152
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 59-73 
    ISSN: 0271-2091
    Keywords: Steady Euler equations ; Transonic flows ; Multigrid methods ; Boundary conditions ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Steady 2D Euler flow computations have been performed for a wind tunnel section, designed for research on transonic shock wave-boundary layer interaction. For the discretization of the steady Euler equations, an upwind finite volume technique has been applied. The solution method used is collective, symmetric point Gauss-Seidel relaxation, accelerated by non-linear multigrid. Initial finest grid solutions have been obtained by nested iteration. Automatic grid adaptation has been applied for obtaining sharp shocks. An indication is given of the mathematical quality of four different boundary conditions for the outlet flow. Two transonic flow solutions with shock are presented: a choked and a non-choked flow. Both flow solutions show good shock capturing. A comparison is made with experimental results.
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  • 153
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 167-183 
    ISSN: 0271-2091
    Keywords: Axisymmetric turbulent flow ; Combustors ; Diffusers ; Navier-Stokes equations k-∊ model ; Zonal grid ; Finite differences ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Numerical studies of turbulent flow in an axisymmetric 45° expansion combustor and bifurcated diffuser are presented. The Navier-Stokes equations incorporating a k-∊ model were solved in a non-orthogonal curvillinear co-ordinate system. A zonal grid method, wherein the flow field was divided into several subsections, was developed. This approach permitted different computational schemes to be used in the various zones. In addition, grid generation was made a more simple task. However, treatment of the zonal boundaries required special handling. Boundary overlap and interpolating techniques were used and an adjustment of the flow variables was required to assure conservation of mass flux. Three finite differencing methods - hybrid, quadratic upwind and skew upwind - were used to represent the convection terms. Results were compared with existing experimental data. In general, good agreement between predicted and measured values was obtained.
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  • 154
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 213-233 
    ISSN: 0271-2091
    Keywords: Preconditioning ; Conjugate gradients ; Non-symmetric matrices ; Finite elements ; Convective transport ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Preconditioning techniques based on incomplete Gaussian elimination for large, sparse, non-symmetric matrix systems are described. A certain level of fill-in may be specified in the incomplete factorizations. All methods considered may be applied to matrices with arbitrary sparsity patterns, for instance those associated with the general preprocessor algorithms or adaptive mesh techniques. The preconditioners have been combined with five conjugate gradient-like methods and tested on finite element discretized scalar convection-diffusion equations in 2D and 3D. It is found from numerical experiments that an amount of fill-in corresponding to about 50% of the number of original non-zero matrix entries is the optimal choice for this class of preconditioners. The preconditioners show almost no sensitivity to grid distortion. In problems with significantly variable coefficients or anisotropy the preconditioners stabilize the basic iterative schemes in addition to reducing the computational work substantially, mostly by more than 90%. The modified preconditioning technique, where fill-in is added on the main diagonal, performs in general better than the standard incomplete LU factorization, but is inferior to the latter in 3D problems and for matrix systems with complicated sparsity patterns.
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  • 155
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 374-374 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 156
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 427-452 
    ISSN: 0271-2091
    Keywords: Navier-Stokes equations ; Spectral method ; Chebyshev polynomials ; Convection ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A Chebyshev collocation method for solving the unsteady two-dimensional Navier-Stokes equations in vorticity-streamfunction variables is presented and discussed. The discretization in time is obtained through a class of semi-implicit finite difference schemes. Thus at each time cycle the problem reduces to a Stokes-type problem which is solved by means of the influence matrix technique leading to the solution of Helmholtz-type equations with Dirichlet boundary conditions. Theoretical results on the stability of the method are given. Then a matrix diagonalization procedure for solving the algebraic system resulting from the Chebyshev collocation approximation of the Helmholtz equation is developed and its accuracy is tested. Numerical results are given for the Stokes and the Navier-Stokes equations. Finally the method is applied to a double-diffusive convection problem concerning the stability of a fluid stratified by salinity and heated from below.
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  • 157
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 325-340 
    ISSN: 0271-2091
    Keywords: Semidirect methods ; Finite difference formulation ; Robust solutions ; Navier-Stokes and energy equations ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Semidirect solution techniques can be an effective alternative to the more conventional iterative approaches used in many finite difference methods. This paper summarizes several semidirect techniques which generally have not been applied to the Navier-Stokes and energy equations in finite difference form. The methods presented use both successive substitution and Jacobian-based updates as well as two variations of Broyden's full matrix update. A hybrid method is also presented, as is a norm-reducing search technique that can be used to enhance the convergence characteristics of any semidirect approach. These methods have been compared with the well known iterative methods SIMPLE and SIMPLER. The comparison was performed on the natural convection and driven cavity problems. The semidirect methods proved to be reliably convergent without the need for a priori specification of variable under-relaxation factors, which was necessary with the iterative methods. Natural convection and driven cavity solutions have been readily obtained with the proposed methods for Rayleigh and Reynolds numbers up to 109 and 106 respectively. Of the semidirect techniques, the hybrid approach was the most robust. From an arbitrary zero initial guess this method was able to obtain a solution to the natural convection problem for Rayleigh numbers three orders of magnitude larger than was possible with the Newton-Raphson update. The computational effort required by the semidirect methods is comparable to that required by the iterative methods; however, the memory requirements can be significantly greater.
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  • 158
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 1051-1055 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 159
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 1059-1072 
    ISSN: 0271-2091
    Keywords: Viscoelastic flow ; Leonov model ; Convective integration ; Finite element method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The finite element method is used to find the elastic strain (and thus the stress) for given velocity fields of the Leonov model fluid. With a simple linearization technique and the Galerkin formulation, the quasi-linear coupled first-order hyperbolic differential equations together with a non-linear equality constraint are solved over the entire domain based on a weighted residual scheme. The proposed numerical scheme has yielded efficient and accurate convective integrations for both the planar channel and the diverging radial flows for the Leonov model fluid. Only the strain in the inflow plane is required to be prescribed as the boundary conditions. In application, it can be conveniently incorporated in an existing finite element algorithm to simulate the Leonov viscoelastic fluid flow with more complex geometry in which the velocity field is not known a priori and an iterative procedure is needed.
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  • 160
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 741-745 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 161
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 747-761 
    ISSN: 0271-2091
    Keywords: Navier-Stokes solutions ; Shock wave/boundary layer interactions ; Newton's iteration ; Upwind differencings ; Symmetric line relaxation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The objective of the paper is twofold. First we describe an upwind/central differencing method for solving the steady Navier-Stokes equations. The symmetric line relaxation method is used to solve the resulting algebraic system to achieve high computational efficiency. The grid spacings used in the calculations are determined from the triple-deck theory, in terms of Mach and Reynolds numbers and other flow parameters. Thus the accuracy of the numerical solutions is improved by comparing them with experimental, analytical and other computational results. Secondly we proceed to study numerically the shock wave/boundary layer interactions in detail, with special attention given to the flow separation. The concept of free interaction is confirmed. Although the separated region varies with Mach and Reynolds numbers, we find that the transverse velocity component behind the incident shock, which has not been identified heretofore, is also an important parameter. A small change of this quantity is sufficient to eliminate the flow separation entirely.
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  • 162
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 865-869 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 163
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 891-920 
    ISSN: 0271-2091
    Keywords: Transient flows ; Oscillating aerofoil ; Dynamic stall ; Navier-Stokes equations ; Finite differences ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Unsteady viscous flow around a large-amplitude and high-frequency oscillating aerofoil is examined in this paper by numerical simulation and experimental visualization. The numerical method is based on the combination of a fourth-order Hermitian finite difference scheme for the stream function equation and a classical second-order scheme to solve the vorticity transport equation. Experiments are carried out by a traditional visualization method using solid tracers suspended in water. The comparison between numerical and experimental results is found to be satisfactory. Time evolutions of the flow structure are presented for Reynolds numbers of 3 × 103 and 104. The influence of the amplitude and frequency of the oscillating motion on the dynamic stall is analysed.
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  • 164
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 1302-1304 
    ISSN: 0271-2091
    Keywords: Incompressible flow ; Clebsch potentials ; Three-dimensional ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A recent paper by W. Zijl, which reformulated the Navier-Stokes and Boussinesq equations in terms of Clebsch potentials, has an error that greatly reduces the generality of the results. Some other recent efforts to use such potentials in fluid and plasma dynamics are briefly discussed.
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  • 165
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 1299-1301 
    ISSN: 0271-2091
    Keywords: Navier-Stokes equation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: In a recent paper a generalized potential flow theory and its application to the solution of the Navier-Stokes equation are developed.1 The purpose of this comment is to show that the analysis presented in that paper is in general not correct. We note that the theoretical development of Reference 1 is in fact an extension - although not cited - of some work first done by Hawthorne for steady inviscid flow.2 Hawthorne's solution is correct, and his analysis, which we briefly describe, provides a useful introduction to this note.
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  • 166
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 1307-1319 
    ISSN: 0271-2091
    Keywords: Peaceman-Rachford ADI method ; SOR method ; Oseen approximation ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The Navier-Stokes equations, which are the governing equations for a steady, viscous, incompressible fluid rotating about the z-axis with angular velocity ω, are linearized using the Oseen approximation. Two parameters, namely the Reynolds number Re = Ua/v and Reω = 2ωa2/v (the Reynolds number w.r.t. rotation), enter the linearized equations. These equations are solved by the Peaceman-Rachford ADI method and the resulting algebraic equations are solved by the SOR method. Streamlines are plotted and compared with the Oseen solution for the non-rotating case. The magnitude of the vorticity vector with increasing θ is also plotted.
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  • 167
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 1381-1394 
    ISSN: 0271-2091
    Keywords: Heat exchangers ; Crossflow ; Tube bundle ; Nusselt number ; Streamfunction/vorticity ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A numerical scheme is developed to predict the heat transfer and pressure drop coefficients in flow through rigid tube bundles. The scheme uses the Galerkin finite element technique. The conservation equations for laminar steady-state flow are cast in the form of streamfunction and vorticity equations. A Picard iteration method is used for the solution of the resulting system of non-linear algebraic equations. Results for the heat transfer and pressure drop coefficients are obtained for tube arrays of pitch ratios of 1·5 and 2·0. Very good agreement of the present results and experimental data obtained in the past is observed up to Reynolds numbers of 1000. It is also observed that the results of the present method show better agreement with the experimental data and that they are applicable for higher Reynolds numbers than results of other studies.
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  • 168
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 1269-1283 
    ISSN: 0271-2091
    Keywords: Euler equations ; Real gases ; Local parametrization of the equation of state ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An efficient algorithm is presented for the solution of the Euler equations of gas dynamics with a general convex equation of state. The scheme is based on solving linearized Riemann problems approximately, and in more than one dimension incorporates operator splitting. In particular, only one function evaluation in each computational cell is required by using a local parametrization of the equation of state. The scheme is applied to two standard test problems in gas dynamics for some specimen equations of state.
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  • 169
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 1221-1234 
    ISSN: 0271-2091
    Keywords: Biharmonic equation ; Stokes flow ; Simple layer potential ; Method of fundamental solutions ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A novel formulation of the method of fundamental solutions for the numerical solution of plane biharmonic problems, based on the simple layer potential representation of Fichera, is presented. The applicability and accuracy of the method are demonstrated by examining its performance on a set of practical problems arising in Stokes fluid flow.
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  • 170
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 1487-1501 
    ISSN: 0271-2091
    Keywords: Viscoelastic fluid ; Polymer flow ; Velocity correction method ; Two-step explicit scheme ; Pressure boundary condition ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The effects of non-Newtonian behaviour of a fluid and unsteadiness on flow in a channel with non-uniform cross-section have been investigated. The rheological behaviour of the fluid is assumed to be described by the constitutive equation of a viscoelastic fluid obeying the Oldroyd-B model. The finite element method is used to analyse the flow. The novel features of the present method are the adoption of the velocity correction technique for the momentum equations and of the two-step explicit scheme for the extra stress equations. This approach makes the computational scheme simple in algorithmic structure, which therefore implies that the present technique is capable of handling large-scale problems. The scheme is completed by the introduction of balancing tensor diffusivity (wherever necessary) in the momentum equations. It is important to mention that the proper boundary condition for pressure (at the outlet) has been developed to solve the pressure Poisson equation, and then the results for velocity, pressure and extra stress fields have been computed for different values of the Weissenberg number, viscosity due to elasticity, etc. Finally, it is pertinent to point out that the present numerical scheme, along with the proper boundary condition for pressure developed here, demonstrates its versatility and suitability for analysing the unsteady flow of viscoelastic fluid through a channel with non-uniform cross-section.
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  • 171
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    International Journal for Numerical Methods in Fluids 9 (1989), S. 1539-1542 
    ISSN: 0271-2091
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
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  • 172
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    International Journal for Numerical Methods in Engineering 27 (1989), S. 145-152 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A two-dimensional finite difference alternating direction implicit (ADI) scheme numerical model to solve the vertically integrated form of the non-linear hydrodynamics equations and convection-diffusion equation has been developed for the description of tide flow and pollutant transport in Taipong Bay, China. Computer software for the modelling is well designed to reduce storage and costs of computation. The computed results agree quite well with the observations available. The tidal level, tidal current, residual current and organic pollution in the bay are discussed based on the computed results and observed data. Applications for the environmental problems along the coast of the bay are also mentioned briefly.
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  • 173
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    International Journal for Numerical Methods in Engineering 27 (1989), S. 195-213 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Consolidation problems associated with foundations for off-shore structures are described and analysed using the finite element method. The structure itself and the soft underlying soil are modelled by finite elements with different constitutive relationships for each. Interfacial behaviour between the two is simulated by six-noded elements, with a hyperbolic stress-strain relationship.Having modelled the soil-structure system behaviour during the consolidation stage, a soil-structure interaction analysis is then carried out for both shallow and deep foundations. Other important factors, such as the redistribution of stresses in the structure itself which have resulted from differential settlements, will also be investigated.
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  • 174
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    International Journal for Numerical Methods in Engineering 27 (1989), S. 271-283 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Damage generally refers to the more or less gradual development of micro-voids and micro-cracks. Damage mechanics is the modelling of these phenomena on a structural analysis scale. In this paper we first recall the non-linear behaviour models we have developed to model composite laminates. Then we present two examples of implementations of such models in a structural analysis code in order to simulate the inner-failure of a structure, or to study delamination initiation.
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  • 175
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    International Journal for Numerical Methods in Engineering 27 (1989), S. 299-321 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The stiffness matrix of a beam made of composite superconductor elements is derived. The effects of friction between conductors through the insulation layers are taken into account. Furthermore, the effects of strand transposition of the wires, already studied by the authors, are included in the model.Some applications of the proposed approach to superconductor layouts proposed for the NET (Next European Torus) toroidal and poloidal field coils are shown. These indicate that the effects of slip are not negligible and should be taken into account in a more reliable structural analysis of the coil system. Parametric studies with varying width and heights of the insulation layer have been also carried out and the corresponding diagrams are shown here.
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  • 176
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    International Journal for Numerical Methods in Engineering 27 (1989), S. 383-401 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A review is given of recent advances in two aspects of the numerical simulation of the buckling and postbuckling responses of composite structures. The first aspect is exploiting non-traditional symmetries exhibited by composite structures; and strategies for reducing the size of the model and the cost of the buckling and postbuckling analyses in the presence of symmetry-breaking conditions (e.g. asymmetry of the material, geometry, and/or loading). The second aspect pertains to the prediction of onset of local delamination in the postbuckling range and accurate determination of transverse shear stresses in the structure. The accuracy and effectiveness of the strategies developed are demonstrated by means of a numerical example.
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    International Journal for Numerical Methods in Engineering 27 (1989), S. 453-453 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 178
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    International Journal for Numerical Methods in Engineering 27 (1989) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 179
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    International Journal for Numerical Methods in Engineering 27 (1989), S. 501-522 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We used a conjugate gradient type method, with preconditioning, to solve the sparse linear systems arising from the discretization of PDEs. With such methods, the main obstacles for complete vectorization have been the preconditioning calculation and its application step within the iteration: for the matrices obtained using 5- or 9-point discretization operators, some well known existing preconditionings (like ILU) require a block-recursive procedure which prevents vectorization. Preconditioners based on nested incomplete factorization, which require the calculation of approximate inverses of tridiagonal matrices, allow complete vectorization of the application step. We present a formulation of such a preconditioning, using a Frobenius norm minimization to calculate the inverses, which also allows complete vectorization of the inverses' calculation, thus making the iterative solver completely vectorizable. Numerical experiments show that the method is robust over a range of symmetric and non-symmetric problems, and up to 4 times faster than other existing methods, such as ILU, depending on the computer and compiler being used. We also show the importance of diagonal scaling used in conjunction with other preconditionings and present some theoretical results concerning the approximate inverses of tridiagonal matrices, calculated using the Frobenius norm minimization.
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  • 180
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    International Journal for Numerical Methods in Engineering 27 (1989), S. 571-588 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: ITPACK 2C14 is a package of seven iterative algorithms for solving sparse linear systems represented by Au = b, where A is symmetric and positive definite or mildly non-symmetric. This paper describes the techniques used to vectorize the iterative algorithms in the ITPACK 2C package for the Cyber 205 and Cray X-MP vector computers. The resulting package was named ITPACKV 2C.15 The basic iterative methods in ITPACK 2C are described in terms of matrix-vector multiplications and forward and backward solutions, and the techniques used in the vectorization of these and other computational kernels are given. Results of experiments using ITPACK 2C and ITPACKV 2C are given, including a comparison of megaflop rates and timings for two model problems.
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    International Journal for Numerical Methods in Engineering 27 (1989), S. 589-608 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: NSPCG is the most recent research-oriented software package developed as part of the ITPACK Project at the Center for Numerical Analysis of The University of Texas at Austin. It is designed to solve large sparse systems of linear equations by a variety of different non-symmetric preconditioned conjugate gradient methods. Several different sparse data storage schemes are available for storing the coefficient matrix of the linear system. Matrices with a wide range of structures from highly structured to completely unstructured can be accommodated. To limit memory requirements, the accelerators in the package can be called directly with the matrix stored in a user-defined sparse data storage format (for example, from a particular application) by supplying some user-written routines for certain matrix-vector operations.The main entry point into the package is through a single subroutine call. The various methods are accessed by using a particular naming convention for the first two parameters that in turn selects a preconditioner, an accelerator and a data storage scheme. Some of the basic preconditioners that are available are Jacobi, Incomplete LU Decomposition and Symmetric Successive Overrelaxation as well as block preconditioners. The user can select from a large collection of accelerators such as Conjugate Gradient (CG), Chebyshev (SI, for semi-iterative), Generalized Minimal Residual (GMRES), Biconjugate Gradient Squared (BCGS) and many others. The package is modular so that almost any accelerator can be used with almost any preconditioner. One of the main purposes for the development of the package was to provide a common modular structure for research on iterative methods. The entire package is written in Fortran 77 with vectorization in mind for applications on supercomputers.
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  • 182
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 1-11 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The numerical integration of the rate equation of an elastic-plastic material is considered. Special attention is focused on the discretization via the fully implicit backward Euler method in the small strain case with linear elasticity and the yield function a general quadratic in stress space. Here the calculation of the plastic (Lagrange) multiplier reduces to the computation of the smallest positive root of a polynomial in one variable. Explicit formulae are given for some special cases.
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  • 183
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 145-154 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Based on purely kinematical considerations the possibility of inextensional bending is introduced to isoparametric curved C° elements, which, otherwise, are plagued by severe membrane (and shear) locking. The analysis is restricted to arches and axisymmetric deformations of shells, i.e. kinematically two-dimensional problems. The results show exceptionally good accuracy. High reliability of the approach is guaranteed by absence of spurious kinematic modes on the element level, which complements its ability to bend inextensionally (in the case of arches).
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  • 184
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 193-209 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A phase increment method is introduced to construct the response curves for the damped Duffing oscillator in primary, superharmonic, and subharmonic resonances. Non-linear parameters can be arbitrarily large. The algorithm is numerically stable. All resonance response curves are constructed in a unified manner. Closed loop curves are obtained in subharmonic resonances as opposed to open ended ones predicted by the perturbation method. Higher order resonances are constructed without difficulties. Loops are also observed in superharmonic resonances when non-linearity is not small.
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  • 185
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 241-244 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 186
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 1485-1485 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 187
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 1487-1504 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The presented work addresses the relationships between optimal sampling points, reduced integration and geometric distortion with the objective of estimating errors in terms of those considerations. Isoparametric quadratic plane and solid elements are used as a vehicle for the study. Geometric distortion measures and evaluation conditions, based on convergence requirements, are first defined in terms of the polynomial orders of the geometry and applied strain. Using these, the concept of optimal stress sampling, already established for undistorted elements, is extended to distorted geometry and shown to be effective over a range of geometries and strains. Errors in the strain-displacement relationship and numerical integration of the strains are used to estimate the total response error and to rationalize the connection between optimal stress points and reduced integration. Enhanced convergence, by extension to the representation of linear strains in elements with quadratic geometry, is identified as the main advantage of reduced integration. The applicability of the proposed, and other, distortion parameters to vetting of element geometry and error prediction is discussed.
    Additional Material: 7 Ill.
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  • 188
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 1567-1576 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the Part I companion paper, various PCG (preconditioned conjugate gradient) strategies for solving the first order time dependent problem Mu̇ + Ku = f were compared. In all cases M was assumed to be the consistent ‘mass’ matrix arising out of conventional finite element semi-discretization of the partial differential equation, and not its lumped approximation. In the present paper, similar PCG strategies are applied to the second order time dependent problem Mü + Cu̇ + Ku = f. Again consistent M and C can be retained. Various global and element level preconditioners are compared and optimized.
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  • 189
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 1645-1660 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This article presents a shooting-type numerical procedure for the analysis of a planar, continuous and flexible member where the material is permitted to unload and reload plastically. A kinematic type of strainhardening rule is employed, and large displacements, large rotations and general cross section shapes are admitted. Though numerical and semi-analytical solutions exist in the literature for specific problems where the internal and external loads increase monotonically (see, for example, References 1-4), little attention has been paid to problems where these loads (specifically internal loads) are permitted to decrease or reverse direction. In the present work a comparison is made with the solution to one such problem found in the literature, and the solution to four additional problems is given to show the versatility and usefulness of the method.
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  • 190
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 980-980 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 191
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 1041-1060 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A decomposition technique for alternative loading conditions in the integrated optimal structural design is developed. The method, called the move coordination, consists of partitioning the large structural optimization problem into a set of smaller coupled subproblems. In each subproblem only one loading condition is considered and the subproblems are solved in a parallel cyclic way. The coupling among the subproblems is accomplished through the introduction of coordinating constraints between each subproblem. These constraints ensure that the final design is the same and feasible for all subproblems. The method developed is illustrated by two examples of member sizing of truss structures using the integrated optimal design formulation and geometric programming. The method presents the advantage of reducing the size of the optimization problem as well as the computer processing time. The method is also suitable for implementation on computers using parallel processing.
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 1023-1040 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An operator-splitting algorithm for the two-dimensional convection-dispersion-reaction equation is developed. The flow domain is discretized into triangular elements which are fixed in time. The governing equation is split into three successive initial value problems: a pure convection problem, a pure dispersion problem and a pure reaction problem. For the pure convection problem, solutions are found by the method of characteristics. The solution algorithm involves tracing the characteristic lines backwards in time from a vertex of an element to an interior point. A cubic polynomial is used to interpolate the concentration and its derivatives on an element. For the pure dispersion problem, an explicit finite element algorithm is employed. Analytical solutions are obtained for the pure reaction problem. The treatment of the boundary conditions is also discussed. Several numerical examples are presented. Numerical results agree well with analytical solutions. Because cubic polynomials are used in the interpolation, very little numerical damping and oscillation are introduced, even for the pure convection problem.
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  • 193
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 1115-1129 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The NONSS method for numerically integrating time-dependent constitutive equations requires evaluation of the partial derivatives of the constitutive equations. A numerical method for evaluating these partial derivatives has been developed, thus avoiding the cumbersome task of analytically re-deriving the partial derivatives when improvements to the constitutive model are evaluated. This method is based upon the adaptive finite-difference algorithm published by Stepleman and Winarsky. Modifications of their algorithm are described that allow its efficient use within an extended version of NONSS, called NONSS-ND.Using the MATMOD constitutive equations, the capabilities of NONSS-ND are demonstrated by comparing the results of a wide variety of deformation simulations with those of NONSS, for which the derivatives are computed from analytical solutions. The numerical differentiation within NONSS-ND is shown to be sufficiently accurate for use in integrating time-dependent constitutive equations, but results in a 30-100 per cent increase in computation time. Multi-element structural calculations are therefore found to be uneconomical, but NONSS-ND is well suited for testing alternative constitutive models owing to its accuracy and its general applicability to highly non-linear systems of differential equations.
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  • 194
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    International Journal for Numerical Methods in Engineering 27 (1989), S. 361-382 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finite element models of the continuum-based theories and two-dimensional plate/shell theories used in the analysis of composite laminates are reviewed. The classical and shear deformation theories up to the third-order are presented in a single theory. Results of linear and non-linear bending, natural vibration and stability of composite laminates are presented for various boundary conditions and lamination schemes. Computational modelling issues related to composite laminates, such as locking, symmetry considerations, boundary conditions, and geometric non-linearity effects on displacements, buckling loads and frequencies are discussed. It is shown that the use of quarter plate models can introduce significant errors into the solution of certain laminates, the non-linear effects are important even at small ratio of the transverse deflection to the thickness of antisymmetric laminates with pinned edges, and that the conventional eigenvalue approach for the determination of buckling loads of composite laminates can be overly conservative.
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  • 195
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 1265-1282 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A dynamic programming (DP) method is presented for analysis of statically determinate and indeterminate bridges subjected to moving loads such as those specified by the American Association of State Highway and Transportation Officials (AASHTO) specifications. These loads consist of uniform lane loading, two-axle truck loading and two-axle truck plus one-axle semitrailer loading. The solution of the DP problem is based on the use of influence line diagrams and extremum functions. Recurrence formulae have been developed for various types of AASHTO live loads. The procedure presented in this article is quite general and can be applied to any type of structures with linear behaviour and any type of moving loads. Six examples are presented: a simply-supported beam, a simply-supported Pratt truss, an arch bridge, a continuous Pratt truss, a continuous frame and a cable-stayed bridge.
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    International Journal for Numerical Methods in Engineering 27 (1989), S. 547-557 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The Successive Overrelaxation (SOR) and the Cyclic Chebyshev Semi-Iterative (CCSI) methods are considered for solving the non-symmetric linear systems Ax = b when A has the form \documentclass{article}\pagestyle{empty}\begin{document}$$ {\bf A} = \left({\begin{array}{*{20}c} {{\bf D}_1} & {\bf F} \\ {-{\bf F}^{\rm T}} & {{\bf D}_{\rm 2}}\\ \end{array}} \right) $$\end{document} with D1 and D2 symmetric positive definite (SPD).The D1/2-norms of both methods are determined and it is shown that, though the SOR method is better based on the spectral radius, the CCSI scheme is far better than SOR according to the D1/2-norm.
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    International Journal for Numerical Methods in Engineering 27 (1989), S. 623-635 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 9 Ill.
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  • 198
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    International Journal for Numerical Methods in Engineering 28 (1989) 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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  • 199
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 13-25 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this work, a modal solution method for transient heat conduction utilizing a co-ordinate transformation matrix generated by the Lanczos algorithm is presented. The special characteristics of this co-ordinate transformation are also discussed. The comparisons made in the NASA Insulation Test problem analysis shown that this approach is more cost-effective than direct solutions, without loss of accuracy.
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    International Journal for Numerical Methods in Engineering 28 (1989), S. 95-108 
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An efficient method is developed for sensitivity analysis in shape optimization of axisymmetric structures. The technique of isoparametric mapping is used to generate the finite element mesh from a small set of master elements and master nodes. Co-ordinates of selected master nodes are used as design variables. Shape function values of master elements at derived finite element nodes obtained during the isoparametric mapping process are utilized to calculate the gradients of weight and response of the structures with respect to the design variables. Analytic formulations of the gradients are developed for sensitivity analysis of axisymmetric structures. An optimization procedure using a sequential linear programming method is applied to effectively utilize the calculated gradients. Numerical examples of optimum design of disks subject to thermo-mechanical loadings are presented.
    Additional Material: 3 Ill.
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