Locking effects in the finite element approximation of elasticity problems

Summary We consider the finite element approximation of the 2D elasticity problem when the Poisson ratiov is close to 0.5. It is well-known that the performance of certain commonly used finite elements deteriorates asv0, a phenomenon calledlocking. We analyze this phenomenon and characterize the strength of the locking androbustness of varioush-version schemes using triangular and rectangular elements. We prove that thep-andh-p versions are free of locking with respect to the error in the energy norm. A generalization of our theory to the 3D problem is also discussed.The work of this author was supported in part by the Office of Naval Research under Naval Research Grant N00014-90-J-1030The work of this author was supported in part by the Air Force Office of Scientific Research, Air Force Systems Command, U.S. Air Force, under grant AFOSR 89-0252     

Solid-state diphotocyclization of iso- and terephthalaldehydes via dihalogen substitution

The supramolecular nonbonded C-H...X interactions between formyl hydrogens and ortho-halogen atoms (Br/Cl) have been exploited to achieve conformational control in the solid state of dimethyl-substituted iso- and terephthaladehydes (1-3) for unprecedented diphotocyclization. It is shown that the dihalogen substitution also contributes to the stability of the benzocyclobutenols relative to their precursor photoenols, so that the solid-state photolysis of dialdehydes 2b, 2c, and 3b leads to diphotocyclization to afford respectable yields of bis-benzocyclobutenols.     

Triphase catalysis. I. Kinetics and mechanism of alkylation of phenylacetonitrile with alkyl halides catalyzed by aqueous naoh and polymer-supported benzyltriethylammonium chloride

The alkylation and cycloalkylation of phenylacetonitrile (PAN) with excess of 1-bromobutane and 1,4-dibromobutane respectively catalyzed by aqueous NaOH and insoluble polystyrene-bound benzyltriethylammonium chloride were studied and the rates depend upon several experimental parameters. The rate of cycloalkylation of PAN is five times faster than the alkylation and the former proceeds even in the absence of the solid catalyst. Both alkylation and cycloalkylation gave higher rates in reverse addition method than in direct addition. Deprotonation of PAN by hydroxide ion takes place without participation of the polymeric catalyst. The electrostatic force between the positive charge on the nitrogen atom of catalyst and carbanion is responsible for alkylation of active nitrile with polystyrene-bound phase-transfer catalyst. The rates of both the reactions increase with increased stirring speed, ring substitution, hydroxide ion concentration and catalyst amount and decrease with increased particle size and the degree of cross-linking of the polymer. Apparent activation energies for the reactions were calculated. The kinetic results are discussed in terms of mass transfer and a combination of intraparticle diffusion and intrinsic reactivity limitations of the rates.     

Cationic carbohydroxylation of alkenes and alkynes using the cation pool method

The reactions of an N-acyliminium ion pool with alkenes and alkynes gave gamma-amino alcohols and beta-amino carbonyl compounds, respectively, after treatment with H(2)O/Et(3)N. The present reaction serves as an efficient method for cationic carbohydroxylation of alkenes and alkynes. When vinyltrimethylsilane was used as an alkene, the reaction was highly diastereoselective and served as an access to an enantiomerically pure alpha-silyl-gamma-amino alcohol. [reaction: see text]     

A Highly stereospecific and efficient synthesis of homopentafluoro- phenylalanine

A short and efficient synthesis of homopentafluorophenylalanine (6) from oxazolidine aldehyde 1 in 57% overall yield and in > 98% ee is described. The enantiomeric excess of the product was determined by 19F NMR analysis of the coupling product derived from 5 and L-Ser(O-t-Bu)-OCH3, by comparison to a dipeptide obtained from racemic 5.     

Sequential Pd/Ru-catalysed allenylation/olefin metathesis/1,3-dipolar cycloaddition route to novel heterocycles

A novel sequential palladium/ruthenium-catalysed four component process is described involving carbonylation of an aryl/heteroaryl iodide followed by allenylation to generate (π-allyl) palladium species which are intercepted by nitrogen nucleophiles to afford 1,6-dienes. Subsequent Ring-Closing Metathesis (RCM) affords C-acyl-N-heterocycles in good yield. These heterocycles proved to be active dipolarophiles in sequential and cascade 1,3-dipolar cycloaddition reactions (1,3-DC) as exemplified by reactions with nitrones and azomethine ylides.     

X=Y-ZH Systems as potential 1,3-dipoles : Part 13. Prototropic generation of azomethine imines from hydrazones

Hydrazones of aldehydes and ketones undergo intermolecular cycloaddition to electronegative olefins via azomethine imines, formed by a formal 1,2-prototropic shift, in low to moderate yield on heating in xylene or ethanol. In some instances the reaction is diverted to give products derived (at least formally) from an ene reaction. Similar intramolecular cycloadditions occur with unactivated terminal alkenes and alkynes.     

One-electron oxidation of toluidine blue. A pulse radiolysis study

The one-electron oxidation of toluidine blue by specific oxidising radicals such as Cl ₂ ⁻ , Tl(II), N₃, Br ₂ ⁻ etc. has been studied by employing the pulse radiolysis technique. The Br ₂ ⁻ radical was found to be less efficient in oxidising toluidine blue as compared to Cl ₂ ⁻ ., Tl⁺² and N₃. The semioxidised species exhibited only onepK _a indicating the presence of two conjugate acid-base forms whose spectral and kinetic features were evaluated. Reaction of OH radicals with the dye gave rise to a transient species which exhibited spectral and kinetic features different from that of the semioxidised species indicating that the mode of reaction of OH is different.     

In situ fabricated porous filters for microsystems

Porous filters were fabricated inside a microchannel using emulsion photo-polymerization. The porosity of the filter is dependent on the composition of the pre-polymer mixture. The morphology and flow resistance of four filters with varying water and cross-linker concentrations was studied. The porous filter was used to separate samples, such as whole blood to cell/serum components, based on size. The efficiency of cell/serum separation by the porous filter was tested by performing a glucose-6-phosphate dehydrogenase assay and was found to be comparable to separation by centrifuge. The porous filter thus mimics the functionality of the centrifuge, with the added benefits of no power requirements and ability to handle small sample volumes.     

An investigation on visible luminescence of Ho activated LBTAF glasses

Different concentrations of Ho³⁺-doped lead borate titanate aluminum fluoride (LBTAFHo) glasses with chemical composition of PbO-H₃BO₃-TiO₂-AlF₃-Ho₂O₃ were prepared by the melt quenching method. The spectral properties were investigated using the absorption, emission and decay measurements. The experimental oscillator strengths were calculated from the area under the absorption bands. Applying Judd-Ofelt theory, the intensity parameters (Ω_{λ=2, 4, 6}) were calculated, by the least square fit approach from which the radiative transition rates, luminescence branching ratios and radiative decay times were determined. The photoluminescence spectra revealed the quenching of luminescence intensity beyond 1.0 mol% of Ho³⁺ ion concentration. To investigate the luminescence potentiality of ⁵F₄→⁵I₈ emission level, the effective bandwidth and the stimulated emission cross-section were determined. The quenching in experimental decay time is attributed to the resonance energy transfer among the excited Ho³⁺ ions.