Scaling is an interesting and powerful approach to mathematics. There are many introductory applications ranging from predicting how the period of a pendulum depends on its length to why almost all animals, large and small, can jump about the same height. More sophisticated topics include fractional scaling laws in physics and biology and fractal dimensions. This project would start with dimensional analysis and can go in various directions.

Literature: See, e.g., G.I. Barenblatt “Scaling”, partly available online at: google books

Supervisor: Dr Martin Lavelle