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The derivation of gene-transport equations is re-examined. Fisher's assumptions for a sexually reproducing species lead to a Huxley reaction-diffusion equation, with cubic logistic source term for the gene frequency of a mutant advantageous recessive gene. Fisher's equation more accurately represents the spread of an advantaged mutant strain within an asexual species. When the total population density is not uniform, these reaction-diffusion equations take on an additional non-uniform convection term. Cubic source terms of the Huxley or Fitzhugh-Nagumo type allow special nonclassical symmetries. A new exact solution, not of the travelling wave type, and with zero gradient boundary condition, is constructed.

A fluid mechanical model is developed for the filtering mechanism in mussels that enables estimates to be made of the pressure drop through the gill filaments due to (i) the latero-frontal filtering cilia, (ii) the lateral (pumping) cilia and through the non-ciliated zone at the ventral end of the filament. Calculations indicate that the lateral cilia can generate a sufficient pressure change to 'pump' water through the gill filaments. The velocity profile across the filaments indicates that a backflow can occur in the centre of the channel. Normally the latero-frontal cilia would damp out this backflow but in the case when all the cilia are upright, two 'standing' eddies may form at the mouth of the channel, forcing the incoming water to the side.

Line distributions of Stokes flow singularities are used to model the flow around a slender body which is straddling a flat interface between two viscous fluids. Motion of the slender body parallel to the interface and normal to the interface is considered where the axis of symmetry of the slender body is always perpendicular to the undisturbed interface. Asymptotic approximations to the force distributions on the slender body are evaluated and the relative contributions of that part of the slender body in one fluid to the force distribution in the other fluid and of the interface interaction to the force distribution are examined. It is observed that a shielding region exists about the interface which is due to the interaction with that part of the slender body in the other fluid. Finally, for parallel motion, the first order interface deformation is calculated.

A two-layer Newtonian fluid model for muco-ciliary transport in the lung is developed where the viscosity of the upper mucous layer is very much greater than the viscosity of the lower periciliary layer. Theory is presented for both cases when the cilia penetrate, and do not penetrate, the very viscous mucous layer. Calculations suggest that, in normal circumstances, it is not essential for the cilia to penetrate the mucus to provide positive transport. However, it does suggest that there is a weak optimal penetration depth of the cilia of between 10-20% of the cilium length. In the case of high ciliary inactivity (e.g. 90% inactive), penetration of cilia into the mucus is essential for normal transport rates suggesting the mucociliary system may be deliberately overdesigned to cater for a whole range of pathological circumstances.

It is shown that bubbling on wine bottle labels is due to absorption of water from the glue, with subsequent hygroscopic expansion. Contrary to popular belief, most of the glue's water must be lost to the atmosphere rather than to the paper. A simple lubrication model is developed for spreading glue piles in the pressure chamber of the labelling machine. This model predicts a maximum rate for application of labels. Buckling theory shows that the current arrangement of periodic glue strips can indeed accommodate paper expansion. This project provides interesting applications of various areas of undergraduate mathematics, such as trigonometry, Maclaurin series, dimensional analysis, and fluid mechanics. It illustrates that simple mathematical modelling may provide insight into a complicated real-world problem.