Rokos Awards 2022: New Models for Thermoelastic Instability

Orson Hart (2020) is a third-year Pembroke undergraduate studying Mathematics. Two years into his course, Orson had the opportunity to put some of the theory he had learnt so far into practice with a summer Rokos Internship.

His project built on research which began in the 1960s about the effects of wear and thermal expansion on a system of metal pins which experience friction due to a moving surface.

In 2016 the original model was picked up again and developed to account for physical effects seen in systems such as brakes and clutches. Professor Peter Howell, Orson’s supervisor on the project, has been working on this mathematical model since 2018. Orson’s internship saw him and Professor Howell seek to improve the model by introducing more realistic physical effects.

Orson explains how, as he got to grips with the existing work on the problem and familiarised himself with computational mathematics: “I was able to use the experience and techniques that I learnt from undergraduate courses such as Fourier Series & PDEs, Differential Equations 2, and Complex Analysis.”

Through regular meetings with Professor Howell, Orson explored what new features might be introduced to the model to capture more accurately the behaviour of the physical system. Having introduced a new feature, he used a symbolic manipulation software called Mathematica to investigate the effects. It was a discovery made through this process that led Professor Howell to develop a new theory around the behaviour of the pins. Orson was then able to verify the theory using numerical simulations.

Orson writes: “The Rokos Award Internship allowed me to stay in Oxford for the duration of my project, and facilitated regular meetings with Professor Peter Howell. I was also able to talk with Professor John Ockendon about the problem, and he provided insight and guidance on what possible areas would be useful to explore. My supervisor and I are planning to publish our work in the Journal of the Mechanics and Physics of Solids.”

Read his full report here.

Orson’s internship was funded by the Rokos Internship Scheme which provides full funding for academic summer internships for Pembroke STEM students. Find out more here.