Wavepacket Dynamics on One-Dimensional Harmonic Potentials. An Intuitive Approach to the Understanding of Absorption and Luminescence Spectra

Absorption and luminescence spectra can be used to derive quantitative information about differences in molecular structure between the ground and excited electronic states. Examples illustrate the effect of the harmonic vibrational frequency and the offset of the potential energy minima along one normal coordinate on the observed spectrum. The time-dependent approach to spectroscopy is used, leading to intuitively appealing visual representations.     

Characteristic vertices of weighted trees via perron values

We consider a weighted tree T with algebraic connectivity μ, and characteristic vertex v. We show that μ and its associated eigenvectors can be described in terms of the Perron value and vector of a nonnegative matrix which can be computed from the branches of T at v. The machinery of Perron-Frobenius theory can then be used to characterize Type I and Type II trees in terms of these Perron values, and to show that if we construct a weighted tree by taking two weighted trees and identifying a vertex of one with a vertex of the other, then any characteristic vertex of the new tree lies on the path joining the characteristic vertices of the two old trees.     

Constructably Laplacian integral graphs

A graph is Laplacian integral if the spectrum of its Laplacian matrix consists entirely of integers. We consider the class of constructably Laplacian integral graphs - those graphs that be constructed from an empty graph by adding a sequence of edges in such a way that each time a new edge is added, the resulting graph is Laplacian integral. We characterize the constructably Laplacian integral graphs in terms of certain forbidden vertex-induced subgraphs, and consider the number of nonisomorphic Laplacian integral graphs that can be constructed by adding a suitable edge to a constructably Laplacian integral graph. We also discuss the eigenvalues of constructably Laplacian integral graphs, and identify families of isospectral nonisomorphic graphs within the class.     

Multi-scale characterization of laser speckle patterns

The interaction between coherent monochromatic radiation and scattering medium results in a speckle phenomenon. The purpose of this paper is to present a stochastic approach to characterizing speckle patterns, using the differential equation that formalizes Brownian motion. This stochastic approach is based on a differential method for the approximation of diffusion. This method is validated by the characterization of solutions of latex balls of various concentrations.     

A novel synthetic approach towards 2-guanidinomethyl-4(5)-sulfamoylimidazoles

A library of 2-guanidinomethyl-4(5)-sulfamoylimidazoles was synthesised in a convergent manner by introducing a sulfonyl chloride group via a trianion electrophilic sulfinylation of suitably protected 2-guanidinomethyl imidazoles.     

Australian Sugar Mills Optimise Siding Rosters to Increase Profitability

Increasing cost/price ratios in sugarcane production and the pressure to remain internationally competitive have forced Australian sugar mills to reduce capital and operational costs. Increased utilisation of transport infrastructure through improved rostering of harvesting groups into sugarcane rail and road sidings provides an opportunity to reduce transport and harvesting costs. Generating and maintaining siding rosters manually also requires high labour costs because of the time-consuming effort to simultaneously balance limited capacities in the transportation facilities with costs of harvester movements as well as the social considerations of equity between growers. To address this complex socio-economic issue, participatory research was undertaken with a large sugar milling company in Australia to implement siding rosters that were optimised using a tabu search. This resulted in an original adoption of staff rosters produced using operations research techniques, which substantially reduced the up-front and on-going labour costs of planning and maintaining an effective roster throughout the 2002 harvest season.