After an MISG there is time to reflect. I will report briefly on the follow up to two problems that we have worked on.
Crack Repair:
It has been found that thin elastically weak spray on liners stabilise walls and reduce rock blast in mining tunnels. Why? The explanation seems to be that the stress field singularity at a crack tip is strongly altered by a weak elastic filler, so cracks in the walls are less likely to extend.
Boundary Tracing:
Using known exact solutions to partial differential equations new domains can be constructed along which prescribed boundary conditions are satisfied. Most notably this technique has been used to extract a large class of new exact solutions to the non-linear Laplace Young equation (of importance in capillarity) including domains with corners and rough boundaries. The technique has also been used on Poisson's, Helmholtz, and constant curvature equation examples. The technique is one that may be useful for handling modelling problems with awkward/interesting geometry.