Specific Skills: Fluid Dynamics. Geophysics. Divergence Cleaning.

How do instabilities form and evolve in the turbulent waters of the ocean? 

• Developed a solver for 3D incompressible Navier-Stokes equations under the Boussinesq approximation

• Discretisation customisable between finite differences and spectral methods 

• Incompressibility is maintained using an FFT based spectral divergence cleaner

• Solver is benchmarked against Taylor-Green Vortex with maximum error of 2% in energy decay rate.  

Project Date: Mar 2025 (Year 2)

Specific Skills: Many Body Classical Mechanics. Data Structures and Recursion. 

How are particles inside of a dark matter halos arranged? 

• Implements the Barnes-Hut algorithm for the  a high performance N-body simulation

• Strategic use of vectorisation to quickly evolve 200k+ particles via Verlet scheme 

• Initial conditions generated by Metropolis Monte-Carlo from any custom distribution 

• Tracks Virial factor and fits results against known density profiles upon Virialisation

Project Date: Feb 2025 (Year 2)

Specific Skills: Condensed Matter Physics. Fluid Mechanics. Signal Processing. 

How can Bose-Einstein Condensate form vortices, and how do they behave?

• Developed a numerical solver for the Gross-Pitaevskii Equation under optical trap 

• Utilise Strang Splitting with FFT spectral methods for accuracy and numerical stability

• Initial wavefunction obtained by perturbing a ground state with a vortex 

• Ground state obtained by propagating imaginary time through GPE. 

Project Date: Sept 2025 (Year 2)

Specific Skills: Nonlinear Classical Mechanics. Information Theory.  Signal Processing. 

Can a series of nonlinear springs-coupled masses ever thermalise?

• Numerically solved Hamilton's equations for the FPU system using SymPy

• Applied Discrete Sine Transform to obtain Modal spectra and spectral energies 

• Quantified thermalisation progress using Shannon Entropy

• Solver benchmarked against original recurrence time (Fermi et. al, 1955) with error of 3.5%

Project Date: Aug 2025 (Summer of Year 1) 

Specific Skills: Condensed Matter Physics. Electromagnetic, Statistical and Quantum Mechanics. 

At what temperature do ferromagnets lose their magnetisation? 

• Numerically evolved 2D grid of spins through Metropolis Monte Carlo 

• Solver accurately predicts stable spin configurations, energetics, magnetisations, and more.

• Curie point for 2D lattice predicted to within 3% error of Onsager's 1944 solution. 

Project Date: Jul 2025 (Summer of Year 1) 

Specific Skills: Classical, Statistical, Quantum, Relativistic and Nuclear Mechanics. 

Is there a maximum mass to Neutron Stars? 

• Developed a numerical solver for the Tolman-Oppenheimer-Volkov (TOV) equations using Runge-Kutta 4 (RK4)

• Researched gravitational, quantum, nuclear and relativistic effects in Neutron Stars 

• Mass of the most massive neutron star predicted to within 0.2 solar masses compared to current observations  

Project Date: May 2025 (Summer of Year 1)