Mathematics and Statistics, University of Strathclyde
Tenure since 2016
Non-autonomous coagulation-fragmentation equations
My research is focussed on non-autonomous coagulation-fragmentation equations. In the natural and industrial world there are many instances in which clusters of particles combine to form larger clusters and fragment into smaller clusters; the evolution of these clusters is described by coagulation-fragmentation equations. Most mathematical investigations into these equations has concentrated on the autonomous version, where the rates at which particles fragment and coalesce are independent of time. However, not a great deal is known about the non-autonomous version of these equations, where the rates depend on time, and it is these equations which I will be researching.
I will be investigating questions about these equations such as: when does a solution exist? When is it unique? What asymptotic behaviour does the solution show?
To study the non-autonomous equations I will be building on the techniques used to study the autonomous equations. In particular I will use the theory of evolution families and evolution semi-groups.
Processes of coagulation and fragmentation arise in many, diverse areas including blood clotting, polymer science, aerosols and astrophysics (e.g. star formation from dust). With regards to the non-autonomous case which I will be studying, there is a particular importance to industrial spray drying processes, where a detailed study of these equations can play a useful role in attempts to improve the production process.
Lyndsay graduated from the University of Strathclyde in June 2016 with a First class honours degree. In her final year The University of Strathclyde awarded her the Astronomical Society of Glasgow Prize which is awarded to the most distinguished student in their final year of a BSc Honours course in maths. She was also awarded the Sir Hermann Bondi Prize, which is awarded annually to a student for excellence in their fourth year research project, and the Gary Roach Prize, which is awarded annually to a student who shows excellence in mathematical analysis.
Her fourth year project was on indefinite inner product spaces and was supervised by Dr Matthias Langer, who is now her PhD supervisor along with Dr Wilson Lamb. She really enjoyed this project and this encouraged her to embark on a PhD.
As an undergraduate she was awarded a BP STEM scholarship and was employed as an undergraduate teaching assistant at Strathclyde University in her third and fourth years of study.