Research
Publications
The Three-Body Problem is far from fully solved despite centuries of effort. The restricted Euler Problem is a special case in which two bodies are fixed in place, resulting in two Poisson-commuting conserved quantities, allowing the system to be fully integrable by the Liouville–Arnold theorem. We analysed the restricted Euler problem using an order-4 symplectic integrator, which conserves the Hamiltonian. We used this integrator to simulate the restricted Euler problem and recovered known orbits from the literature.
Hong Kong Observatory internship (summer 2026)
During my summer internship at the Hong Kong Observatory I worked on estimating the intensity and central pressure of tropical cyclones from machine-learning weather forecasts. These models now forecast storm tracks well but tend to underestimate how strong storms are. A first-author paper is submitted, and I will link it here once the preprint is public.
Computational statistical physics (2026): the 3D Heisenberg model
My final project for Computational Statistical Physics at ETH Zürich, which received full marks: a Monte Carlo study of the three-dimensional classical Heisenberg model, measuring the critical temperature and five critical exponents with Metropolis and Wolff cluster simulations on lattices up to 256³ spins, all within 1σ of the 3D O(3) universality class.
Semester project (2026): tropical cyclone potential intensity
A semester project in the Atmospheric Physics group at ETH Zürich, supervised by Prof. Ulrike Lohmann and Dr Bernhard Enz. Using the ERA5 ensemble reanalysis over the western tropical Atlantic, I looked at how the potential intensity of tropical cyclones depends on the spatial and temporal resolution of its inputs.
Background and interactive figures
Summer research project (2025): synchronisation in 2D turbulence
I studied the synchronisation of small scales in two-dimensional turbulence driven by Kolmogorov forcing, using JAX-CFD, and checked my code against results in the literature. I am now extending the theory to include Coriolis effects on the beta-plane. The work is supervised by Dr Jacob Page, with assistance from Dr Dmitriy Zhigunov.
Summer research project (2024): the three-body problem
An eight-week project in the School of Physics and Astronomy, University of Edinburgh, supervised by Prof. Jenni Smillie.
The project had two aims: to reproduce and visualise important orbits of the three-body problem, and to understand two landmark theoretical results, Chenciner and Montgomery’s proof that the figure-eight orbit exists and the convergence of Sundman’s series. I wrote symplectic integrators up to fourth order, used them to study the Lagrange, figure-eight and Broucke–Hadjidemetriou–Hénon orbits and Euler’s problem of two fixed centres, and ended with a search for new well-behaved orbits.
Research log
I kept a public log while the project ran. It starts from first simulations and works up to the existence proof of the figure-eight orbit:
- Plotting and Visualising the Three-Body Problem 24 Jun 2024
- Symplectic Integrators 25 Jun 2024
- Ellipses and the Two-Body Problem 27 Jun 2024
- Problem of Two Fixed Centres (Part I) 28 Jun 2024
- Understanding and Visualising the Shape Sphere 4 Jul 2024
- Problem of Two Fixed Centres (Part II) 9 Jul 2024
- Sundman's Power Series Solution to the Three-Body Problem (Part I) 12 Jul 2024
- Sundman's Power Series Solution to the Three-Body Problem (Part II) 16 Jul 2024
- Proving the Figure-Eight Orbit Exists: Action Minimisation on the Shape Sphere 17 Jul 2024
- Classifying and Finding New Possible Orbits (Part I) 22 Jul 2024
- Problem of Two Fixed Centres (Part III) 26 Jul 2024
Background: Overview of the two-body problem.
Group project: pendulum models for liquid slosh
Henry Yip, Patrick Truong, Gregory Barbanel and Abdullah Fouzuddeen, with the support of the Edinburgh Scientific Researchers Association.
Starting from a published single-pendulum model of liquid slosh in packaging machines, we proposed a multi-pendulum (discrete) model and a continuous model based on a forced string, to capture the shape of the liquid surface rather than just its tilt. Summary · Poster (PDF)
Notes and talks
- Introduction to LaTeX: slides and handout (2022)
- PHYS08050 Introductory Astrophysics notes (PDF)
- Dark Energy and the Big Rip: a short expository article (2022)