Computer Science Projects

Voronoi Visualiser

This was my 2003 second-year computer science project with Greg Priday to generate and visualise Voronoi diagrams and Delaunay triangulations, written in C++ and OpenGL with the WxWidgets UI library.

I implemented 2D O(N log N) divide-and-conquer algorithms for the Delaunay triangulation that I then converted into a Voronoi diagram, and just got an O(N⁴) algorithm for 3D Delaunay triangulation working, but no 3D Voronoi diagram. [source code archive]

BigNum Pi Calculator in MIPS Assembly

We were asked to write anything in MIPS32 assembly for the SPIM emulator, and so of course I picked something really hard - a calculator of Pi to ten thousand decimal places. I used a series expansion of the faster-converging form of the Gregory-Leibniz series for pi and used decimal bignums with one decimal digit per byte. [source code]

Physics Projects

Angular correlation of gamma-rays emitted by Sodium-22

In 2004, my 3rd year of university, each of us performed an independent experimental project in nuclear physics, and I chose to replicate the test of the prediction by nuclear theory that that sodium-22 undergoes beta+ decay, which results in back-to-back gamma rays when the emitted positron annihilates an electron.

I set up an experiment to measure the time difference between gamma rays detected by two scintillators, from which I could calculate the frequency of simultaneous detections. I used trigonometry to predict the frequency of such events as a function of angle between the two detectors, and experimentally confirmed the predicted curve.

Applied Mathematics Projects

Collision of Soliton Solutions to the Non-Linear Schrodinger Equation

In this final-year assignment I simulated the collision of soliton solutions of the cubic-quintic Schrodinger equation, which models short light pulses in optic fibres of higher-order refractive index. I used the split-step method and explored the effects of varying the strength of nonlinearity and the soliton velocity.

Solutions of the Massive Thirring Model

This was a helluva difficult final-year assignment, to find solutions to the Massive Thirring Model. The Thirring model is an exactly solvable quantum field theory which describes the self-interactions of a Dirac field in two dimensions, describing neutrinos. The massive Thirring model would describes electrons, protons and other massive fermions. If the Thirring model is an accurate reflection of reality, it would imply that sub-atomic particles are solitons (standing waves), that mass is a field energy, and that particles interact as a consequence of their topology. Years later I found a 1975 paper on soliton solutions of the massive Thirring model and the original paper by Walter E. Thirring

Finite difference simulation and asymptotic expansion

In which I analysed the model for Gaussian initial conditions using a finite differences scheme. The model is stable for small initial conditions, but develops exponentially growing oscillatory insta­bilities for larger ones. Growth in what should be a conserved quantity reliably indicates the presence of instability. An asymptotic expansion of the solution to the linearised equation is a qualitatively good approximation to the system's long­term behaviour under small initial conditions.

Soliton solutions to the Massive Thirring Model

The massive Thirring model equations have Lorentz-invariant travelling soliton solutions. Working at first with the stationary case, the Thirring model equation can be written as two complex ODE's. Using polar decomposition, I reduced the four equations in four real-valued unknowns to reduced to one ODE and evaluated it in terms of hyperbolic functions. I then used the finite differences scheme to model the behaviour of the soliton solution.

My solution has an error such that the resulting wave is not a true soliton, which was discovered and corrected by Michael Ben-Yosef a couple years later in his version of the assignment.