Potential PhD topicsPattern formation and equivariant bifurcation theoryMany physical, chemical and biological systems spontaneously develop patterns when driven hard enough. Many pattern formation problems can be analysed using equivariant bifurcation theory, but there are still many experimentally observed patterns that cannot yet be explained within this framework. Examples include quasipatterns and spatially modulated two-dimensional patterns. PhD projects would examine these kinds of patterns with an aim to developing new theory.
Nonlinear dynamics: symmetries and chaosGlobal bifurcations are often responsible for creating chaotic dynamics in dissipative differential equations. Much of the complicated behaviour exhibited by chaotic systems can be explained by constructing maps (usually one-dimensional) that are valid near such a bifurcation. The presence of symmetry makes the analysis more difficult, and introduces the possibility of new types of phenomena: synchronisation, cycling chaos, and blow-out bifurcations. PhD projects would study these phenomena in cases where symmetry requires the use of higher-dimensional maps to describe the dynamics.
Astrophysical fluid dynamics: magnetoconvection and dynamics of sunspotsMagnetic fields influence the dynamics of convection in many astrophysical bodies. For example, sunspots are dark because magnetic fields suppress convective heat transport. Unexplained issues in understanding magnetic features on the sun include: the spontaneous separation of convection into magnetised and unmagnetised regions; the structure of the filamentary penumbra; the structure of subsurface flows. PhD projects would study these phenomena primarily using numerical techniques.
Please contact me if you'd like further information on potential PhD projects, or go to the Departmental web page for details on how to apply for admission. I encourage students to become independent thinkers as they develop a thesis, with the goal that the work be publishable. I enjoy self-motivated, thorough and dedicated students. In turn, you can expect my supervision to be structured and involved. I am prompt with answering questions and open to meet with students as the need arises.
A full list of PhD topics in the Department of Applied Mathematics can be found here. |