The cyclodimerisation of 3-methyl-2-butenenitrile

3-Methyl-2-butenenitrile (1) cyclodimerised on treatment with lithium diisopropylamide in dimethoxyethane at temperatures between ?78°C and 0°C to 3-amino-4-cyano-1,5,5-trimethyl-1,3-cyclohexadiene (2) the structure of which was established by acid hydrolysis to the known 4-cyano-1,5,5-trimethyl-1-cyclohexene-3-one (3).     

Solid-state polymerization of vinylpyridine coordination compounds

A survey of the solid-state polymerizability of 2- and 4-vinylpyridine (Vpy) complexes of divalent cobalt, nickel, copper, and zinc chlorides has been carried out. The influence of metal ion, ligand, coordination stereochemistry, and crystal structure is discussed. The tetrahedral modification of the complex Co(4-Vpy)₂Cl₂ has been found to undergo a particularly facile thermal polymerization below its melting point to yield high molecular weight poly-4-vinylpyridine. The polymer is shown to be conventional atactic head-to-tail poly-4-vinylpyridine. Thermogravimetric methods and optical microscopy have been used to study the thermal polymerization of single crystals of the complex. Results indicate a diffusion-controlled mechanism in which defective regions in the crystal act as nuclei for the polymerization.     

Conical parametric scattering of a single extraordinary beam in BaTiO3 crystal

In this paper, the parametric scattering of a single extraordinary polarized beam of laser in BaTiO₃ photorefractive crystal has been investigated experimentally and theoretically. The resulting pattern consists of beam fanning, isotropic ring, and anisotropic one. Among all parts of scattering pattern, isotropic ring has not been studied as much as beam fanning and anisotropic ring, and there still are some differences in reports about it. Therefore, the study has mainly focused on this part. In this experimental configuration, isotropic ring is just visible in positive angles although the other parts of parametric scattering pattern can be visible from behind and in front of the crystal. In addition to steady state pattern in forward and backward directions, its transient behavior with the rotation of crystal has been studied. The results of experiments have been analyzed carefully, and their theoretical explanations have been presented based on the standard theory of parametric scattering in photorefractive crystals. It has been shown that this configuration corresponds to the so called parametric B-process scattering.     

Distributional Modes for Scalar Field Quantization

We propose a mode-sum formalism for the quantization of the scalar field based on distributional modes, which are naturally associated with a slight modification of the standard plane-wave modes. We show that this formalism leads to the standard Rindler temperature result, and that these modes can be canonically defined on any Cauchy surface.     

Controlling the electrophoretic mobility of single-walled carbon nanotubes: a comparison of theory and experiment

The electrophoretic mobilities of single-walled carbon nanotubes (SWNTs) in agarose gels subjected to negatively charged covalent functionalization and noncovalent anionic surfactant adsorption are compared using a simplified hydrodynamic model. Net charges are calculated on the basis of estimated friction coefficients for cylindrical rodlike particles. The effects of functionalization with negatively charged 4-hydroxybenzene diazonium and anionic sodium cholate are quantified and compared with model predictions. The adsorption of Na+ counterions into the nonionic surfactant layer adsorbed on SWNTs (Triton-X-405) is shown to induce a positive charge and reverse the mobility under select conditions. This effect has not been identified or quantified for nanoparticle systems and may be important in the processing of these systems.     

On the zeros of complex Van Vleck polynomials

Polynomial solutions to the generalized Lamé equation, the Stieltjes polynomials, and the associated Van Vleck polynomials, have been studied extensively in the case of real number parameters. In the complex case, relatively little is known. Numerical investigations of the location of the zeros of the Stieltjes and Van Vleck polynomials in special cases reveal intriguing patterns in the complex case, suggestive of a deeper structure. In this article we report on these investigations, with the main result being a proof of a theorem confirming that the zeros of the Van Vleck polynomials lie on special line segments in the case of the complex generalized Lamé equation having three free parameters. Furthermore, as a result of this proposition, we are able to obtain in this case a strengthening of a classical result of Heine on the number of possible Van Vleck polynomials associated with a given Stieltjes polynomial.     

Evaluation of self-consistent polycrystal plasticity models for magnesium alloy AZ31B sheet

Various self-consistent polycrystal plasticity models for hexagonal close packed (HCP) polycrystals are evaluated by studying the deformation behavior of magnesium alloy AZ31B sheet under different uniaxial strain paths. In all employed polycrystal plasticity models both slip and twinning contribute to plastic deformation. The material parameters for the various models are fitted to experimental uniaxial tension and compression along the rolling direction (RD) and then used to predict uniaxial tension and compression along the traverse direction (TD) and uniaxial compression in the normal direction (ND). An assessment of the predictive capability of the polycrystal plasticity models is made based on comparisons of the predicted and experimental stress responses and R values. It is found that, among the models examined, the self-consistent models with grain interaction stiffness halfway between those of the limiting Secant (stiff) and Tangent (compliant) approximations give the best results. Among the available options, the Affine self-consistent scheme results in the best overall performance. Furthermore, it is demonstrated that the R values under uniaxial tension and compression within the sheet plane show a strong dependence on imposed strain. This suggests that developing anisotropic yield functions using measured R values must account for the strain dependence.