Peter Wyper and I are offering final-year projects for third-year BSc and fourth-year MMath students at Durham for the upcoming 2023–24 year.
If you are looking for a visually interesting applied maths project, then maybe one of these projects is for you!
Joint supervision bonus: Peter and I have a term each of research leave in 2023–24, so these projects are supervised by me in Michaelmas, and Peter in Epiphany. You buy one, you get one free!
We are very happy to talk you about the projects and possible directions if you would like to get in touch.
Picking a project supervisor is an important task! If we haven’t met yet, you can read about the sort of research I do on my research page; and on the sort of fun things I like to give talks about on my talks page. Then check out Peter’s research and his very cool fun interests.
Projects I’ve run in previous years can be read about in the archive.
MATH3382 (Project III) 2023–24
Project title
Fractal boundaries of mixed liquids and spreading patterns
Overview
When oil spills in the ocean, it floats to the top in a blob. But as the waves mix the water, the shape of the oil blob gets heavily distorted, often creating swirly, fractal-type patterns:
Similarly, a number of reactions between two chemicals create patterns which move and distort over time.
This project will investigate the fractal nature of these swirls and patterns to see if we can learn something about the nature of turbulent mixing or the nature of these chemical reactions by observing how the fractal number changes under different conditions. We will use the box counting method to measure the ‘fractal-ness’ of evolving boundaries, and will implement it by writing and sourcing Python code.
How we might structure the the project
At the start, we could have something like:
- Finding a fractal image online and running a box counting algorithm on it
- Investigating analytically how liquid boundaries evolve under mixing
- Simulating 2D pattern formation in a reaction–diffusion system
- Learning what fractal scaling can tell us about shapes
Prerequisites
This is an applied maths project where you will have to do some practical coding. You should therefore be confident in programming in Python.
MATH4072 (Project IV) 2023–24
Project title
Falling… with style!
Overview
- What makes paper aeroplanes fly? Why do they not simply flutter down? Which design travels furthest when we throw them off the third floor balcony in the maths department?
- How do you bend it like Beckham? What’s the best tactic for a free kick?
- Are rotor ships the future of energy-efficient ocean travel?
- What shapes do flexible objects make as they fall through water? How stable are they?
All these phenomena rely on modelling the flow of fluid around objects, and considering how that plays with the objects’ centres of mass and stability.
This project will take ideas from Fluid Mechanics III and apply them to interesting shapes and objects, with the target ultimately directed by your interests.
How we might structure the the project
At the start, you could have something like:
- Fluid flow around rigid objects: basic theory for air or for water
- Picking an object + a fluid and seeing what research has already been done
- A spherical object spinning through the air or sedimenting through water
Prerequisites
You need to have taken Fluid Mechanics III to do this project.
This is an applied maths project and there is likely to be some computational work as well as some analytical work. You should be competent with Python, but you do not have to be a numerical analysis expert.