Effective Hamiltonains and degenerate perturbation theory calculations of the mass spectrum in lattice QCD

Hamiltonian quantum chromodynamics has been formulated on a discrete lattice, in an attempt to calculate the hadronspectrum using strong coupling expansions. Previous attempts have involved including an irrelevant four-fermion interaction term in the Hamiltonian. As well as making the quark content of the zeroth order states the same as that of the simple additive quark model, this term splits the infinite zeroth order degeneracies of the original Hamiltonian. In this paper we calculate the masses of low lying states in the absence of such a term, using an effective Hamiltonian method to solve the degeneracy problem. We discuss the problems of continuing our series to the continuum limit in the presence of level repulsion.     

The non-linear bending of a cantilever beam with shear and longitudinal deformations

A non-linear bending theory for beams is constructed which accommodates shear and longitudinal deformations. Using the theory, an analytical solution for the cantilever beam subject to a compressive load (the elastica) and a series solution for the horizontal cantilever under weight loading are derived. The effects of including shear and longitudinal deformations are found to be negligible for configurations in which the two deformations tend to offset one another—such as at the onset of buckling under a compressive load—but are shown to be significant for certain configurations in which the two deformations are additive—as in some instances of weight loading.     

Studies of the Fermi surface of V3Si by 2D ACAR measurements

We report two-dimensional angular correlation of annihilation radiation (2D ACAR) measurements using positrons in single crystals of V₃Si. Anisotropic structure commensurate with the reciprocal lattice is observed and attributed to the complex Fermi surface (FS). A simple geometrical model for the FS is developed and compared with folded ACAR distributions. The results of a 3D reconstruction are compared with recent band calculations.     

The Search for a Second Sydney Airport: A Dynamic Programming Scheduling Model

A cost-benefit analysis was recently undertaken to assist the Australian Government in the selection of a site for a second Sydney Airport. In order to evaluate sites on a comparable basis, it was necessary to establish, for each possible site, the optimum sequence of developments at both the present airport and the second airport, and the split in the traffic between the two airports. This paper describes a dynamic programming scheduling model developed to carry out this optimisation process for each site.     

Crystal and molecular structures of cis-dichlorobis(trifluorophosphine)bis(triphenylphosphine)ruthenium(II), cis-RuCl2(PF3)2(PPh3)3, and dichloro(2,7-dimethylocta-2,6-diene-1,8-diyl)(trifluorophosphine)ruthenium(IV), RuCl2(PF3)(C10H16)

The first structures of trifluorophosphine complexes of transition metals in an oxidation state greater than +1 are reported.     

Perturbations of subalgebras of type II1 factors

In this paper we consider two von Neumann subalgebras and of a type II₁ factor . For a map φ on , we define

     

Circumferential resonance modes of solid elastic cylinders excited by obliquely incident acoustic waves

When an immersed solid elastic cylinder is insonified by an obliquely incident plane acoustic wave, some of the resonance modes of the cylinder are excited. These modes are directly related to the incidence angle of the insonifying wave. In this paper, the circumferential resonance modes of such immersed elastic cylinders are studied over a large range of incidence angles and frequencies and physical explanations are presented for singular features of the frequency-incidence angle plots. These features include the pairing of one axially guided mode with each transverse whispering gallery mode, the appearance of an anomalous pseudo-Rayleigh in the cylinder at incidence angles greater than the Rayleigh angle, and distortional effects of the longitudinal whispering gallery modes on the entire resonance spectrum of the cylinder. The physical explanations are derived from Resonance Scattering Theory (RST), which is employed to determine the interior displacement field of the cylinder and its dependence on insonification angle.     

Water-compatible molecularly imprinted polymers obtained via high-throughput synthesis and experimental design

A technique allowing high-throughput synthesis and evaluation of molecularly imprinted polymer sorbents at a reduced scale (mini-MIPs) was developed and used for the optimization of MIPs for use in pure aqueous environments. The technique incorporated a 4-port liquid-handling robot for the rapid dispensing of monomers, templates, solvents and initiator into the reaction vessels of a 96-well plate. A library of 80 polymers, each ca. 50 mg, could thus be prepared in 24 h. The MIP rebinding capacity and selectivity could be rapidly assessed in the batch mode by quantifying nonbound fractions in parallel using a UV monochromator plate reader. This allowed a complete evaluation of the binding characteristics of an 80 polymer library in approximately 1 week. With the objective of optimizing a polymer imprinted with the local anaesthetic Bupivacaine for use in pure aqueous systems, a polymer library was prepared by varying the original poly(MAA-co-EDMA) MIP composition. The variable factors were the added amount of the hydrophilic comonomer, 2-hydroxyethyl methacrylate (HEMA), the cross-linking ratio, and the porogen. This optimization resulted in polymers showing high imprinting factors (IF = K(MIP)/K(NIP)) in water as a result, mainly, of reduced binding to the nonimprinted polymer. Normal scale batches of these materials showed strong retention of the template and low nonspecific binding when assessed as chromatographic stationary phases using pure phosphate buffer, pH 7.4, as mobile phase, by equilibrium batch rebinding experiments and as sorbents for extractions of the analyte from blood plasma samples.