On the continuation for variational inequalities depending on an eigenvalue parameter

In this paper we generalize recent theoretical results on the local continuation of parameter-dependent non-linear variational inequalities. The variational inequalities are rather general and describe, for example, the buckling of beams, plates or shells subject to obstacles. Under a technical hypothesis that is satisfied by the simply supported beam, we obtain the existence of a continuation of both the solution and the eigenvalue with respect to a local parameter. A numerical continuation method is presented that easily overcomes turning points. Numerical results are presented for the non-linear beam.     

Quasi-wavelet calculations of sound scattering behind barriers

Quasi-wavelets (QWs) are a representation of turbulence consisting of self-similar, eddy-like structures with random orientations and positions in space. They are used in this paper to calculate the scattering, due to turbulent velocity fluctuations, of sound behind noise barriers as a function of the size and spatial location of the eddies. The sound scattering cross-section for QWs of an individual size class (eddy size) is derived and shown to reproduce results for the von Kármán spectrum when the scattered energies from a continuous distribution of QW sizes are combined. A Bragg resonance condition is derived for the eddy size that scatters most strongly for a given acoustic wavenumber and scattering angle. Results for scattering over barriers show that, for typical barrier conditions, most of the scattered energy originates from eddies in the size range of approximately one-half to twice the size of the eddies responsible for maximum scattering. The results also suggest that scattering over the barrier due to eddies with a line of sight to both the source and receiver is generally significant only for frequencies above several kilohertz, for sources and receivers no more than a few meters below the top of the barrier, and for very turbulent atmospheric conditions.     

Negative luminescence from mid-wave infrared HgCdTe diode arrays

A self-referencing, optical modulation technique was used to measure the negative luminescence efficiencies of an array of mid-wave infrared HgCdTe photodiodes with cutoff wavelength 4.6 μm as a function of sample temperature. The internal efficiency at a wavelength of 4 μm was 93% at 295 K, and nearly independent of temperature in the 240–300 K range. This corresponds to an apparent temperature reduction >50 K at room temperature and >30 K at 240 K. Moreover, the reverse-bias saturation current density was only 0.13 A/cm². The measured transmission and emission spectra were simulated using empirical HgCdTe absorption formulas from the literature.     

Atom transfer radical polymerization of methyl methacrylate by copper(I)‐pyridine‐2‐carboximidate catalysts

Pyridine‐2‐carboximidates [methyl ( 1a ), ethyl ( 1b ), isopropyl ( 1c ), cyclopentyl ( 1d ), cyclohexyl ( 1e ), n‐octyl ( 1f ), and benzyl ( 1g )] were prepared from the reaction of 2‐cyanopyridine with the corresponding alcohols. Cyclopentyl‐substituted 1d was found to be a highly effective ligand for copper‐catalyzed atom transfer radical polymerization (ATRP) of methyl methacrylate (MMA). For example, the observed rate constant for a CuBr/ 1d catalytic system was found to be nearly twice as high as the cyclohexyl‐substituted CuBr/ 1e catalytic system [k_obs = (1.19 vs 0.56) × 10^?4 s^?1). The effects of the solvents, temperature, catalyst/initiator, and solvent/monomer ratio on the ATRP of MMA were studied systematically for the CuBr/ 1d catalytic system. The optimum condition for the ATRP of MMA was found to be a 1:2:1:400 [CuBr]_o/[ 1d ]_o/[ethyl 2‐bromoisobutyrate]_o/[MMA]_o ratio at 60 °C in veratrole solution, which yielded well‐defined poly(MMA) with a narrow molecular weight distribution of 1.14. The catalytically active copper complex 2d was isolated from the reaction of CuBr with 1d . Narrow molecular weight distributions as low as 1.06 were achieved for the CuBr/ 1d catalytic system by employing 10% of the deactivator CuBr₂. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2747–2755, 2004     

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Viscosity,particle size distribution,and structural investigation of tetramethyloxysilane/2‐hydroxyethyl methacrylate sols during the sol–gel process with acid and base catalysts

The tetramethoxysilane (TMOS)/2‐hydroxylethyl methacrylate (HEMA) hybrid gels were synthesized with acid and base catalysts, via the in situ polymerization of HEMA, with and without the cosolvent methanol. With methanol in the TMOS/HEMA sol, the enhanced esterification and depolymerization reactions of the silanols resulted in a slower growth of silica particles. The silica particles that were synthesized with an acid catalyst were less than 40 nm. The thermal resistance of the poly(2‐hydroxyethyl methacrylate) (PHEMA) chains was enhanced by the addition of colloidal silica. The Fourier transform infrared characterizations and the exothermal peaks on the differential scanning calorimetry traces of these hybrid gels indicated chemical hybridization occurring as a result of condensation of the colloid silica and PHEMA at higher temperatures. Hence, the residual weight content of the hybrid gel after its synthesis with the base catalyst was even higher than the content of TMOS in the hybrid sol. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3476–3486, 2004