A combination of biological population dynamics and thin-film fluid flow and wetting dynamics will be used. The student may concentrate on the development of computational thin film fluid flow methods or on more fundamental mathematical analyses of existing continuum models. A further option is available to construct discrete representations of the continuum models that are more suitable for the analysis of complex spatial patterns. M. A. Bees, P. Andresen, E. Mosekilde and M. Giskov. The interaction of thin-film flow, bacterial swarming and cell differentiation in colonies of Serratia liquefaciens.
Solitary waves are an important class of waves in the oceanic environment.
Gap solitary waves are a curious new class of solitary waves that have only recently been discovered and involve the interaction between two distinct types of solitary waves. By reformulating wave equations as dynamical systems in the space variable, solitary waves can be characterised as homoclinic orbits. The project will consist of three parts. The first part is to determine the dynamical systems aspects of gap solitary waves. The second part of the project is to then study the connection between the homoclinic orbits found in part one and the gap solitary waves found in model PDEs such as coupled KdV equations.