Cecilie Andersen
Applied Maths PhD at University of Bath
Oxford University graduate
My research uses combinations of analytical and numerical methods to derive selection laws for eigenvalue problems in fluid mechanics.
About me
I am currently a final year PhD student at the University of Bath as part of the EPSRC funded SAMBa programme (Statistical Applied Maths at Bath). Before this I completed an MMath at the University of Oxford in 2016-2020. My research, supervised by Dr Phil Trinh, focuses on a class of selection problems arising in potential flows in fluid dynamics. I use exponential asymptotics to derive a selection condition for the eigenvalue in the problem. I enjoy combining multiple different analytic and numerical techniques which are required to make progress in these problems. These include exponential asymptotics, numerical solutions of systems of ODEs (in MATLAB), complex analysis, numerical continuation schemes, asymptotic approximations etc.
Research and Teaching
Papers
On the selection of Saffman-Taylor viscous fingers for divergent flow in a wedge (submitted)
Current projects
Saffman-Taylor in a wedge
Rising bubble/Falling jet
Past projects
Integrative Think Tanks (2021-present):
Twice annually our PhD programme holds week-long workshops
where we collaborate with industrial partners to explore a problem from industry. During the week we work in teams with the aim of
formulating the problem in a mathematical way so that it may develop into a future PhD project or research stream with an industrial partner.
Projects I have worked on include: Switching patients to superior treatments during phase 3 of clinical trials (Partner: Roche),
Modelling air pollution in Ulaanbaatar (Partner: National University of Mongolia),
Using machine learning to improve joint scoring in patients with Psoriatic Arthritis (Partner: NHS),
Instability of inverters in a microgrid (Partner: Bath Beacon),
Physical models of river flows including climate effects (Partner: Environmental Agency).
MMath Dissertation (2020):
During the final year of my MMath degree
I wrote a dissertation titled A study of the pattern forming behaviour of the
1D Swift-Hohenberg equation whilst supervised by Dr Priya Subramanian.
Summer research project (2018):
An 8 week summer research project
supervised by Dr Andrey Kormilitzin. I used Machine learning techniques in Python
to investigate a dataset to understand the potential link between certain protein levels and the occurrence of
Alzheimer Disease in patients.
Teaching
I have taught classes for the following undergraduate maths courses:
Multivariable Calculus and differential equations (1st year),
Vectors, vector calculus and mechanics (1st year), Ordinary differential equations and control (2nd year), Numerical
analysis (2nd year), Programming, foundations and connections - Python programming (1st year).
Conferences
During my PhD I have attended numerous conferences and workshops related to my field and presented my work:
Nonlinear Differential Equations and the Stokes Phenomenon:
4-15 September 2023, Okinawa Institute of Science and Technology Graduate University - Japan
Symposium as part of the
TSVP program: Exact asymptotics: From fluid dynamics to quantum geometry. Gave a 30 min online talk titled `Exponential asymptotics for the Saffman-Taylor problem in a wedge'.
SAMBa summer conference:
11-12 July 2023, Bath University
Presented a poster titled
`Exponential asymptotics for Saffman-Taylor in a wedge'. See my poster
here.
Waves and free surface flows: the next twenty years:
15-19 May 2023, Edinburgh University
Gave a 30 min talk titled
`Exponential asymptotics for the Saffman-Taylor problem in a wedge'. Watch my talk
here.
British Applied Maths Colloqium (BAMC):
3-5 April 2023, University of West of England
Gave a 15 min talk titled
`Exponential asymptotics for the Saffman-Taylor problem in a wedge'. This was part of the minisymposium on Water waves and free-surface flows. Received an award for 'Best student talk'.
Applied resurgent asymptotics: summary workshop:
12-16 December 2022, Isaac Newton Institute - Cambridge
Workshop as part of the
programme ARA2: Applicable resurgent asymptotics: towards a universal theory.
Mathematics of beyond all-orders phenomena:
31 October-4 November 2022, Isaac Newton Institute - Cambridge
Workshop as part of the
programme ARA2: Applicable resurgent asymptotics: towards a universal theory. Gave a 30 min talk titled `Challenges in interfacial selection problems with exponential
asymptotics'. Watch my talk here
Physical resurgence: On quantum, gauge and stringy:
12-16 September 2022, Isaac Newton Institute - Cambridge
Workshop as part of the
programme ARA2: Applicable resurgent asymptotics: towards a universal theory.
New directions in water waves: Workshop
25-29 July 2022, Bath University
New directions in water waves: Summer School
18-22 July 2022, Bath University
SAMBa summer conference:
5-6 July 2022, Bath University
Gave a 15 min talk titled
`Selection mechanisms and complex singularities in the falling jet problem'.
British Applied Maths Colloqium (BAMC):
11-13 April 2022, Loughborough University
Gave a 15 min talk titled
`Selection mechanisms and complex singularities in the rising bubble problem'.
Spring school on asymptotic methods and applications:
22-26 March 2021, Isaac Newton Institute - Cambridge
Spring school as part of the
programme ARA1: Applicable resurgent asymptotics: towards a universal theory.
Future plans:
5 week research visit (October-November 2023) to Sydney and Brisbane (Australia) to work with Chris Lustri and Scott McCue
Other
Outside of work I regularly race for Great Britain in orienteering. This is an endurance sport which involves running whilst navigating across a range of terrain types in races ranging from 10-90 minutes in length. My next goal is the 2024 home World Championships in Edinburgh. See my current world ranking here.
Contact me
Email: ca751@bath.ac.uk
Address: 4 West, Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY