Controlling coastlines while generating power. The Project aims to produce strategies for protecting coasts from storms using farms of wave-energy machines, which also generate electricity. Increasing lengths of coast need protection as the climate changes, but conventional barriers create permanent environmental impacts and are a sunk cost usually borne by the taxpayer. The Project expects to derive a strategy for the setting of each machine in the farm, so that they collectively absorb or refl ....Controlling coastlines while generating power. The Project aims to produce strategies for protecting coasts from storms using farms of wave-energy machines, which also generate electricity. Increasing lengths of coast need protection as the climate changes, but conventional barriers create permanent environmental impacts and are a sunk cost usually borne by the taxpayer. The Project expects to derive a strategy for the setting of each machine in the farm, so that they collectively absorb or reflect damaging waves under severe conditions. Under normal conditions, enough wave energy to sustain environmental processes would pass through. Sales of electricity would help to pay back the capital cost. Outcomes would include reduced coastal-erosion costs and a low-intermittency energy supply.Read moreRead less
Symmetry and geometric partial differential equations. This project aims to develop tools to assist the study of partial differential equations, which are fundamental to our understanding of the physical world. Symmetries of the Laplace equation are fundamental in both finding and interpreting its solutions and can be traced to the conformal symmetries of the underlying space. Only for the most symmetric of spaces, Euclidean space and the sphere, is this correspondence well understood. Using pow ....Symmetry and geometric partial differential equations. This project aims to develop tools to assist the study of partial differential equations, which are fundamental to our understanding of the physical world. Symmetries of the Laplace equation are fundamental in both finding and interpreting its solutions and can be traced to the conformal symmetries of the underlying space. Only for the most symmetric of spaces, Euclidean space and the sphere, is this correspondence well understood. Using powerful geometric tools from conformal geometry, the project will extend this to less symmetric spaces. The knowledge generated from this project will extend to more general geometric contexts providing a concrete setting for the study of the associated natural equations in curved spaces.Read moreRead less