Cecilie graduated with an MMath from Oxford University in 2020. She increasingly specialised in applied mathematics and particularly in dynamical systems and finished by writing a dissertation exploring the pattern forming behaviour of the Swift Hohenberg equation, using a combination of analytical and numerical methods. Outside of Maths, Cecilie enjoys orienteering and running.

Research project title:
Hybrid asymptotic-numerical schemes for exponentially small selection mechanisms

Supervisor(s):
Phil Trinh, Paul Milewski

Project description:
This project considers the asymptotic analysis of differential equations in some singular limit, say ɛ → 0, and where an eigenvalue, say λ, exhibits a selection mechanism. In some cases, this yields a countably infinite sequence, λ1 < λ2 < λ3 < . . .. However, within a number of such open problems, the mechanism determining the sequence as ɛ → 0 is governed by exponentially small terms beyond-all-orders. This project will study open problems related to selection mechanisms in potential flow. First we are considering the open problem related to the selection mechanism determining the angle of separation in the falling jet/rising bubble problem. Later we hope to resolve such selection mechanisms for several other related open challenges in fluid and continuum mechanics.