These patterns can be described by their symmetries and analysed using varied techniques from group theory to the derivation of amplitude equations. Quasipatterns with five- and twelvefold symmetry have been observed in Faraday experiments where a layer of fluid is oscillated up and down, leading to the formation of wave patterns on the fluid surface. It has so far proved very difficult to provide a rigorous analysis of the evolution of quasipatterns. This project would use group theoretic methods to deduce allowable quasipatterns, and to derive amplitude equations describing competition between different types of quasipatterns. Aeolian sand ripples and dunes are formed in the desert or at the seashore by the action of the wind.
Loose sand is picked up by the wind and smashed into the sand bed, sculpting out ripples and dunes.
There is as yet no agreed model for ripple evolution, or indeed for many other phenomena in the field of granular media, so this is a very active area of research. The aim of this project is to provide a unified model of the various interacting modes of sand transport. This project aims to reproduce natural dune shapes in numerical simulations of simple model equations and to compare these shapes with satellite images of desert dunes. Dr P E Hydon Babies who are born very prematurely usually need mechanical help to breathe. However the volume of air used is so small that the conventional theory of breathing does not explain how adequate gas transport can be achieved.