The dewetting over a planar substrate of a thin layer of highly viscous fluid under the action of surface tension is considered, with a doubly-nonlinear fourth-order degenerate parabolic equation governing the flow of a power-law fluid. Asymptotic methods are applied to analyse the motion in the shear-thinning, shear-thickening and Newtonian cases, the last of these corresponding mathematically to a critical value of the relevant exponent. In particular, the role played by the local behaviour in the neighbourhood of the contact line is analysed and the dependence of the one-dimensional large-time dewetting behaviour on the fluid's constitutive properties characterised. Stability issues are also touched upon.

Results are presented that demonstrate the effectiveness of using polarization discrimination to improve visibility when imaging in a scattering medium. The study is motivated by the desire to improve visibility depth in turbid environments, such as the sea. Most previous research in this area has concentrated on the active illumination of objects with polarized light. We consider passive or ambient illumination, such as that deriving from sunlight or a cloudy sky. The basis for the improvements in visibility observed is that single scattering by small particles introduces a significant amount of polarization into light at scattering angles near 90 degrees: This light can then be distinguished from light scattered by an object that remains almost completely unpolarized. Results were obtained from a Monte Carlo simulation and from a small-scale experiment in which an object was immersed in a cell filled with polystyrene latex spheres suspended in water. In both cases, the results showed an improvement in contrast and visibility depth for obscuration that was due to Rayleigh particles, but less improvement was obtained for larger scatterers.

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