The development of a groove on the surface of a polycrystal where it is intersected by a grain boundary is governed by a fourth-order non-linear partial differential equation. Solutions have been found previously for isotropic and theoretical liquid crystal materials. It was hoped further materials could be modelled using constitutive functions derived from symmetry classification techniques. It was found, however, that only a reduction to third order was possible by finding the point symmetries. Furthermore, higher order terms remained in the boundary conditions.
This was my project for the Master of Mathematics undertaken at the University of Wollongong. It was submitted in 1997. My supervisor was Dr Peter Tritscher.
© Andrew Wright, 1997, 1999