# PhD Progress Seminar

## 1:00 pm — 1:20 pm

## Thursday, 28^{th} May 2020

We have two progress seminars on Thursday 28th May. The first is Benjamin Maldon at 1pm. Ben is working with Natalie Thamwattana. The second is Neil Dizon at 2pm. Neil is working with Jeff Hogan. Both talks will be about 20 minutes long followed by questions, and we'll have a break between the two. As you can see from the abstracts, the topics may be of interest across our school. Everyone is most welcome - please come along!

**Email carma@newcastle.edu.au for the Zoom link for this talk.**

# Benjamin Maldon

(The University of Newcastle)
*Mathematical Modelling of Dye-Sensitized Solar Cells*

Dye-Sensitized Solar Cells (DSSCs) have remained a viable source of renewable energy since their introduction in 1991 for their novel choice of materials. In particular, the substitution of a high-purity Silicon semiconductor for a nanoporous Titanium Dioxide greatly lowers production costs. Mathematical modelling for DSSCs must account for the electrochemical nature of DSSCs over the traditional models inherited from Shockley's work in the 1940s. Though the literature has developed a diffusion model for this purpose, there is sparse mathematical treatment in this area. The objective of this thesis is to provide mathematical insight with the goals of increasing our understanding of DSSCs and maximising their efficiency. In addition to providing new analytical solutions for linear diffusion models, we also apply Lie symmetry analysis to the nonlinear diffusion model and develop a new fractional diffusion equation based on subdiffusion equations derived from random-walk simulations.