The Hamiltonian of the Ising model in one-, two- and three-dimensions has been analysed using unitary transformations and combinatorics. We have been able to obtain closed formulas for the eigenvalues of the Ising Hamiltonian for an arbitrary number of dimensions and sites. Although the solution...

Reducing greenhouse gas emissions without reducing economic growth requires advances in technology (which reduce the emissions intensity of industrial production) and/or policy measures to promote structural change (which shift the composition of production in favour of less polluting...

In his recent book "Dog Days", Garnaut (2013) argues that the Australian economy faces significant economic challenges, with a risk that just as the investment phase of the mining boom ends, Australia will be entering an economic environment characterised by declining terms of trade, a rising...

We compare three methods of estimating the duration, or half-life, of how well each method works with the data aggregated over different time intervals. In contrast with the existing theory on the, so called, data interval bias, our experiments are based upon realistic advertising schedules. Our...

A second quantised operator approach has been used to calculate formulae for one-body fractional parentage coefficients (fpc) for a system of many spinless bosons. A number of examples have been discussed and compared with some of those already calculated by a different technique when used to...

A method is described for calculating crystal fields for rare-earth ions in non-magnetic hosts. Screening is included by performing a Bohm-Pines-like unitary transformation on the starting Hamiltonian which contains kinetic-energy and Coulombic energies of electrons in the presence of fixed...

The equivalent operator method has been extended and applied to anisotropic intersite electron-electron interactions between a central paramagnetic ion and its ligand neighbours. The relativistic character of both the interaction operator, in Breit-Pauli form, as well as the electronic...

The cyto-architecture of eukaryotic cells contains self-assembled long cylinder-like structures called microtubules (MTs) which play an important role in a number of cellular activities such as cell division, motility, information processing and intracellular transport. In this paper we present...

The Gross–Pitaevskii régime of a Bose–Einstein condensate is investigated using a fully non-linear approach. The confining potential first adopted is that of a linear ramp. An infinite class of new analytical solutions of this linear ramp potential approximation to the Gross–Pitaevskii...