MATH 487/488/489: Brendan Harding's Projects
Dynamical systems - Analysis of particle migration in microscope devices
This project gives you the opportunity to study the dynamics of particles suspended in fluid flow through a class of microfluidic devices. In these devices particles migrate against streamlines due to the inertial lift force. You'll learn about the inertial lift force and use some models I have developed to study particle migration in a family of similar device geometries. You'll have the opportunity to develop and apply knowledge of dynamical systems and scientific computing throughout the project.
Fluid mechanics - Analysis of fluid flow through Cornu spiral inspired geometries
This project gives you the opportunity to develop some computational fluid dynamics skills. Specifically, you will study the fluid flow through a variety of geometries inspired by Cornu spirals. These geometries have a curvature that varies smoothly with respect to arc length and you will compare the flow through cross-sections at different points along the main axis with that which occurs in curved duct flow with identical curvature. The goal will be to study how parameters such as the flow rate and rate of curvature change influence the fluid flow.
Numerical analysis - The sparse grid combination technique
Sparse grids are a way to discretise a spatial domain which is significantly cheaper than a regular grid discretisation. You will learn about the sparse grid combination technique, a method for approximating sparse grid solutions, and apply it to the solution of a partial differential equation on a two or three dimensional domain. You will analyse how the smoothness of the initial/boundary conditions impacts on the approximation error.
Fractal transformations are a mapping between the attractors of two iterated function systems (IFSs) constructed via their code spaces. Under appropriate conditions these can be continuous, or even preserve area/volume, while simultaneously changing the fractal dimension of subsets of the domain. You will learn about fractal transformations and study examples constructed via IFSs consisting of three overlapping affine maps on the unit interval.
