Numerical solution of finite geometry boundary-value problems in nonlinear magnetoelasticity

This paper provides examples of the numerical solution of boundary-value problems in nonlinear magnetoelasticity involving finite geometry based on the theoretical framework developed by Dorfmann and co-workers. Specifically, using a prototype constitutive model for isotropic magnetoelasticity, we consider two two-dimensional problems for a block with rectangular cross-section and of infinite extent in the third direction. In the first problem the deformation induced in the block by the application of a uniform magnetic field far from the block and normal to its larger faces without mechanical load is examined, while in the second problem the same magnetic field is applied in conjunction with a shearing deformation produced by in-plane shear stresses on its larger faces. For each problem the distribution of the magnetic field throughout the block and the surrounding space is illustrated graphically, along with the corresponding deformation of the block. The rapidly (in space) changing magnitude of the magnetic field in the neighbourhood of the faces of the block is highlighted.     

Synthesis and Evaluation of Conformationally Restricted N4-Tetradentate Ligands for Implementation in An(III)/Ln(III) Separations

The previous literature demonstrates that donor atoms softer than oxygen are effective for separating trivalent lanthanides (Ln(III)) from trivalent actinides (An(III)) (Nash, K.L., in: Gschneider, K.A. Jr., et al. (eds.) Handbook on the Physics and Chemistry of Rare Earths, vol. 18—Lanthanides/Actinides Chemistry, pp. 197–238. Elsevier Science, Amsterdam, 1994). It has also been shown that ligands that “restrict” their donor groups in a favorable geometry, appropriate to the steric demands of the cation, have an increased binding affinity. A series of tetradentate nitrogen containing ligands have been synthesized with increased steric “limits”. The pK _a values for these ligands have been determined using potentiometric titration methods and the formation of the colored copper(II) complex has been used as a method to determine ligand partitioning between the organic and aqueous phases. The results for the 2-methylpyridyl-substituted amine ligands are encouraging, but the results for the 2-methylpyridyl-substituted diimines indicate that these ligands are unsuitable for implementation in a solvent extraction system due to hydrolysis.     

A study of the atmospherically important reactions of dimethylsulfide (DMS) with I2 and ICl using infrared matrix isolation spectroscopy and electronic structure calculations

The reactions of dimethylsulfide (DMS) with molecular iodine (I(2)) and iodine monochloride (ICl) have been studied by infrared matrix isolation spectroscopy by co-condensation of the reagents in an inert gas matrix. Molecular adducts of DMS + I(2) and DMS + ICl have also been prepared using standard synthetic methods. The vapour above each of these adducts trapped in an inert gas matrix gave the same infrared spectrum as that recorded for the corresponding co-condensation reaction. In each case, the infrared spectrum has been interpreted in terms of a van der Waals adduct, DMS?:?I(2) and DMS?:?ICl, with the aid of infrared spectra computed for their minimum energy structures at the MP2 level. Computed relative energies of minima and transition states on the potential energy surfaces of these reactions were used to understand why they do not proceed further than the reactant complexes DMS?:?I(2) and DMS?:?ICl. The main findings of this research are compared with results obtained earlier for the DMS + Cl(2) and DMS + Br(2) reactions, and the atmospheric implications of the conclusions are also considered.     

Luminescent lanthanoid complexes of a tetrazole-functionalised calix[4]arene

p-t-Butylcalix[4]arene functionalised at the lower rim with two tetrazole moieties is found to be a useful receptor for lanthanoid cations. The luminescence of the resulting complexes can be controlled by addition of base, with emission achieved in the visible and infrared regions.     

Counter-intuitive results in acousto-elasticity

We present examples of body wave and surface wave propagation in deformed solids where the slowest and the fastest waves do not travel along the directions of least and greatest stretch, respectively. These results run counter to commonly accepted theory, practice, and implementation of the principles of acousto-elasticity in initially isotropic solids. For instance, we find that in nickel and steel the fastest waves are along the direction of greatest compression, not greatest extension (and vice-versa for the slowest waves), as soon as those solids are deformed. Further, we find that when some materials are subject to a small-but-finite deformation, other extrema of wave speeds appear in non-principal directions. Examples include nickel, steel, polystyrene, and a certain hydrogel. The existence of these “oblique”, non-principal extremal waves complicates the protocols for the non-destructive determination of the directions of extreme strains.     

Nonlinear electroelastostatics: a variational framework

Different formulations of the constitutive laws and governing equations for nonlinear electroelastic solids are reviewed and two new variational principles for electroelastostatics are introduced. One is based on use of the electrostatic scalar potential and one on the vector potential, combined with the deformation function. In each case Lagrangian forms of the electric variables are used. Their connections with several formulations of nonlinear electroelasticity in the literature are established and some differences highlighted.      

Nonlinear electroelastostatics: a variational framework

Different formulations of the constitutive laws and governing equations for nonlinear electroelastic solids are reviewed and two new variational principles for electroelastostatics are introduced. One is based on use of the electrostatic scalar potential and one on the vector potential, combined with the deformation function. In each case Lagrangian forms of the electric variables are used. Their connections with several formulations of nonlinear electroelasticity in the literature are established and some differences highlighted.     

Some solutions for a compressible isotropic elastic material

In this article we obtain closed-form solutions for the combined inflation and axial shear of an elastic tube in respect of the compressible isotropic elastic material introduced by Levinson and Burgess. Several other boundary-value problems are also examined, including the bending of a rectangular block and straightening of a cylindrical sector, both coupled with stretching and shearing, and an axially varying twist deformation. Some of the solutions appear in closed form, others are expressible in terms of elliptic functions.