Lok Hang (Lachlan) Kan
University of Waterloo | 3A BSc Student, Hon. Physics
Research Assistant at CFD and Turbulence modelling Laboratory, University of Waterloo
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Welcome to the Projects Portfolio!
Welcome to the Projects Portfolio!
Hi! I'm Lachlan, welcome to my projects portfolio! This site documents my computational projects across areas of physics, including fluid dynamics, quantum physics, astrophysics, condensed matter physics, geophysics, and more. Most of my projects involve developing a solver from first principles to investigate a chosen phenomenon, and validating my model against known results and benchmarks. My projects range from relatively small simulations to full custom solvers, and are organised on the pages of this site. For each project, I also produce visualisations that showcase the beauty of physics to a wide audience on instagram (@lachlanphys).
Hi! I'm Lachlan, welcome to my projects portfolio! This site documents my computational projects across areas of physics, including fluid dynamics, quantum physics, astrophysics, condensed matter physics, geophysics, and more. Most of my projects involve developing a solver from first principles to investigate a chosen phenomenon, and validating my model against known results and benchmarks. My projects range from relatively small simulations to full custom solvers, and are organised on the pages of this site. For each project, I also produce visualisations that showcase the beauty of physics to a wide audience on instagram (@lachlanphys).
Image of paper by Y. Suzuki et. al., 2019. Actual simulation result visuals coming soon
Quantum Computational Fluid Dynamics
Quantum Computational Fluid Dynamics
Supervised by Prof. F.S. Lien | Quantum Computing. Fluid Dynamics
How can we apply quantum computational algorithms to fluid dynamical problems?
Transform Burgers' equation approximately into a series of coupled ordinary integral equations using the method of lines
Using Quantum Amplitude Estimation without Phase Estimation (Suzuki et al., 2019), implement an integration scheme applicable to the equations
This project is done as part of my research assistantship at the University of Waterloo CFD and Turbulence modelling Laboratory
Project Date: Sept 2026 (2nd co-op term, Year 3) - In progress
Instabilities in Boussinesq Fluids
Instabilities in Boussinesq Fluids
Fluid Dynamics. Geophysics
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 from scratch
Enforced incompressibility using an FFT-based spectral divergence cleaner
Base Navier-Stokes solver benchmarked against Taylor-Green Vortex with <2% error in energy decay rate.
Project Date: Apr 2025 (Year 2)
Dark Matter Halo Structures
Dark Matter Halo Structures
Many Body Classical Mechanics
How are particles inside of a dark matter halos arranged?
Simulated large scale dark matter halo formation using the Barnes-Hut Algorithm from scratch
Vectorised Verlet integration at node level enables fast evolution of 500k+ particles
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 (ear 2)
Vortex Behaviour in Bose-Einstein Condensates
Vortex Behaviour in Bose-Einstein Condensates
Condensed Matter Physics. Fluid Mechanics
How can Bose-Einstein Condensate form vortices, and how do they behave?
Developed a numerical solver for the Gross-Pitaevskii Equation under an optical trap from scratch
Used 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)
Thermalisation and Recurrence of the Fermi-Pasta-Ulam Problem
Thermalisation and Recurrence of the Fermi-Pasta-Ulam Problem
Nonlinear Many Body Classical Mechanics. Information Theory.
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
Benchmarked against original recurrence time (Fermi et. al, 1955) within 3.5% error
Project Date: Aug 2025 (Summer of Year 1)
Ferromagnetism and the Ising Model
Ferromagnetism and the Ising Model
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)
The Greatest Neutron Star
The Greatest Neutron Star
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)
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