Cross-curriculum applications of mathematics

In Australia applications of mathematics in other curriculum contexts are located within the jurisdiction of mathematics courses. That is mathematics reaches out, but the applications are decided by mathematics personnel rather than designed in collaboration with subject experts from other areas. This may be achieved either by school-based decision making, or by means of a common application or investigation set at a state level. Examples from both approaches are provided in the paper. Tertiary mathematicians support the introduction of applications, but university training of applied mathematicians has not as yet linked closely with the increased emphasis introduced at secondary level.     

Quantum Dot Versus Quantum Well Semiconductor Optical Amplifiers for Subpicosecond Pulse Amplification

The performance of quantum well and quantum dot semiconductor optical amplifiers was theoretically investigated. The effects on subpicosecond pulse propagation due to gain and refractive index dispersion, calculated using a microscopic polarization equation and a reduced wave equation in the linear regime including the background refractive index dispersion, were used in the comparison. In particular, the spectral shift and phase modulation imposed on the pulse were compared. It is shown that quantum dot amplifiers suffer comparable spectral shifts to the quantum well amplifier, strong linear frequency chirp and large pulse broadening. In quantum dot amplifiers with small inhomogeneous broadening, similar pulse break-up is shown as that calculated for the quantum well amplifier. In quantum dot amplifiers with large inhomogeneous broadening, the background refractive index dispersion makes the linear frequency chirp the dominant feature. In the light of our calculations, the advantages and disadvantages of quantum dot and quantum well amplifiers are discussed.     

Cooperative sulfate binding by metal salt extractants containing 3-dialkylaminomethylsalicylaldimine units

The pH-dependence of simultaneous metal- and sulfate-loading of simple salen derivatives demonstrates the feasibility of their application as extractants for recovery of base metals from the leaching of sulfidic ores. The efficacy of the ligands depends on the templating of the sulfate binding site by the attendant metal ion.     

A study of the complexation and extraction of Cu(II) sulfate and Ni(II) sulfate by N3O2-donor macrocycles

Comparative solvent extraction (water/chloroform) studies of Ni(II) and Cu(II) employing a dinonyl-substituted N3O2-donor macrocycle (L2) as extractant have been undertaken from sulfate, chloride, nitrate and acetate-containing aqueous media. Contrary to expectations, efficient extraction of both metal sulfates was observed, the degree of extraction being comparable (or slightly enhanced) relative to that observed for each of the other anionic systems. X-Ray diffraction studies of [NiL1(H2O)3]SO4 x 4H2O and [CuL1(H2O)]SO4 x 6.67 H2O (where L1 is the unsubstituted derivative of L2) show that each complex occurs as a hydrogen-bonded 'cluster', with the sulfate anions involved in hydrogen bonded networks that incorporate ligand amine protons and water molecules; in the copper complex, which adopts a dimeric arrangement, simultaneous sulfate binding to a copper site is also present. In each complex the macrocyclic ligand fails to coordinate via its ether oxygen donors but instead is arranged so that the metal ion and sulfate anions are somewhat shielded hydrophobically from the exterior of the complex cluster assembly.     

Photon emission induced by elastic exciton-carrier scattering in semiconductor quantum wells

We present a study of the elastic exciton-electron (X-e⁻) and exciton-hole (X-h) scattering processes in semiconductor quantum wells, including fermion exchange effects. The balance between the exciton and the free carrier populations within the electron-hole plasma is discussed in terms of ionization degree in the nondegenerate regime. Assuming a two-dimensional Coulomb potential statically screened by the free carrier gas, we apply the variable phase method to obtain the excitonic wavefunctions, which we use to calculate the 1s exciton-free carrier matrix elements that describe the scattering of excitons into the light cone where they can radiatively recombine. The photon emission rates due to the carrierassisted exciton recombination in semiconductor quantum-wells (QWs) at room temperature and in a low density regime are obtained from Fermi’s golden rule, and studied for mid-gap and wide-gap materials. The quantitative comparison of the direct and exchange terms of the scattering matrix elements shows that fermion exchange is the dominant mechanism of the exciton-carrier scattering process. This is confirmed by our analysis of the rates of photon emission induced by electron-assisted and hole-assisted exciton recombinations.