Surface and interfacial waves of arbitrary form in isotropic elastic media

A method due to Friedlander of accommodating disturbances of arbitrary form into the theory of surface waves in a semi-infinite isotropic elastic body is extended and shown to yield a simple closed form solution for the displacement field. An analogous treatment of interfacial waves of arbitrary form at a plane contact discontinuity separating different isotropic elastic materials is also given.

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Résumé On développe une méthode, conçue par Friedlander, qui fait entrer les perturbations de forme arbitraire dans la théorie des ondes de surface dans un corps élastique isotropique semi-infini, et on montre qu'elle permet d'obtenir une solution simple et exacte pour le champ de déplacement. Les ondes de forme arbitraire qui existent dans le plan à la frontière de materiaux élastiques isotropiques differents sont traitées de façon analogue.

     

An EXAFS study of dopant substitution in LiNbO3 and LiTaO3

Abstract

We report an EXAFS study of Co and Fe doped LiNbO₃ and LiTaO₃. Our results show that the dopant ions occupy Li sites in both materials.     

Investigation of the superionic behaviour of BaF 2 ( x mol% LaF 3 ) by raman and brillouin scattering and molecular dynamics simulations

High temperature Raman and Brillouin light scattering experiments have been combined with molecular dynamics simulations to provide a comprehensive study of the superionic state of BaF 2 ( x v mol% LaF 3 ) over a particularly wide range of LaF 3 dopant concentrations from x =0 to 50. Room temperature Raman spectra for x =0, 5 and 10 show the usual T 2g symmetry mode at 241 v cm m 1 , but for samples with x =20, 30 and 50 the dominant Raman mode is at higher frequencies and of E g symmetry. The temperature dependence of the Raman line-widths show initial near linear increases followed by substantial increases above temperatures ( T c ) at 1200, 850, 800, 975, 950 and 920 v K for x =0, 5, 10, 20, 30 and 50. In the Brillouin scattering experiments, the acoustic modes respectively related to elastic constants C 11 and C 44 initially showed a quasi-linear decrease in frequency with increasing temperature. Above the same characteristic values of T c , where the Raman line-widths show marked increases, there are substantial decreases in the elastic constant C 11 for all samples with x =0 to 50. Only the doped samples showed significant decreases in C 44 at corresponding values of T c . Molecular dynamics (MD) simulations have been carried out on the same systems. From the calculated mean square displacements, the diffusion coefficients ( D ) of the mobile fluorine ions were calculated as a function of temperature for each of the samples. Substantial increases in the values of D occur above the respective values of T c determined in the light scattering experiments. The MD simulations also provide details of the mechanisms of diffusion of the mobile fluorine ions. The results emphasize the role of motional effects as an explanation of the mechanisms responsible and provide a self-consistent explanation of the dominant processes in the superionic phase of doped fluorites.     

A new proof of Ramanujan’s modular equation relating R(q) with R(q 5)

We give a new proof of Ramanujan’s modular identity relating R(q) with R(q ⁵), where R(q) is the famous Rogers–Ramanujan continued fraction. Our formulation is stronger than those of preceding authors; in particular, we give for the first time identities for the expressions appearing in the numerator and the denominator of Ramanujan’s identity. A related identity for R(q) that has partition-theoretic connections is also proved.     

Two modular equations for squares of the Rogers–Ramanujan functions with applications

Two modular identities of Gordon, McIntosh, and Robins are shown to be connected to the Rogers–Ramanujan continued fraction R(q), and in particular to Ramanujan’s parameter k:=R(q)R ²(q ²). Using this connection, we give new modular relations for R(q), and offer new and uniform proofs of several results of Ramanujan. In particular, we give a new proof of a famous and fundamental modular identity satisfied by the Rogers–Ramanujan continued fraction. We furthermore show that many analogous results hold for Ramanujan’s parameters μ:=R(q)R(q ⁴) and ν:=R ²(q ^1/2)R(q)/R(q ²). New proofs are offered for modular relations connecting R(q) to R(−q), R(q ²), and R(q ⁴), and new relations connecting R(q) at these arguments are offered. Eleven identities for the Rogers–Ramanujan functions are proved, including four new identities.      

Effect of 1‐hexene comonomer on polyethylene particle growth and copolymer chemical composition distribution

An investigation of the polymer particle growth characteristics and polymer molecular weight and composition distributions in ethylene homopolymerization and ethylene/1‐hexene copolymerization has been carried out with a catalyst comprising a zirconocene and methylaluminoxane immobilized on a silica support. The presence of 1‐hexene leads to higher productivity and easier fragmentation of the support during particle growth. Crystallization analysis fractionation and gel permeation chromatography analysis of ethylene/1‐hexene copolymers prepared at different polymerization times reveals a broadening of the chemical composition distribution with increasing polymerization time as a result of the gradual formation of a relatively high‐molecular‐weight, ethylene‐rich fraction. The results are indicative of significant monomer diffusion effects in both homopolymerization and copolymerization. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2883–2890, 2006     

Multistep scattering in the 160 MeV208Pb(α, α′) reaction

New experimental data has been obtained for the²⁰⁸Pb(α, α′) reaction induced by 160 MeV alpha particles, for inelastic scattering to forward angles. We use these data to investigate the applicability of the multistep scattering theory of Feshbach, Kerman, and Koonin for describing this reaction. The mechanism we study, following the work of Gadioli et al. [1], is of the incident alpha particle remaining intact throughout the scattering process, exciting nucleon particle-hole pairs through multistep process. We conclude that this mechanism, combined with compound nucleus decay at low emission energies, can account for much of the observed data. However, there are indications that other processes also contribute at energies above the compound nucleus emission regime, and we outline future theoretical analyses that are needed.