Research

PhD Thesis

My thesis concerns the study of pattern formation with a conservation law.  The presence of a conserved quantity gives rise to a large-scale mode which must be considered in addition to the pattern-forming modes - this gives rise to a range of new stability behaviours.

In my thesis, the influence of a conserved mode is considered in three scenarios:

  • A generic oscillatory bifurcation
  • Vibrated granular layers
  • Faraday waves (vibrated fluid layers)

A PDF version can be downloaded from the eTheses archive of the University of Nottingham.

There are also three publications based on work done during my PhD:

The complex Ginzburg-Landau equation

The complex Ginzburg-Landau equation is one of the most studied in nonlinear physics, and can be used to describe a disparate array of phenomena.  This tutorial provides an introductory overview of the equation, reviewing both its history and applications.  Movies and images are used to illustrate the many behaviours possible.

» Tutorial: The complex Ginzburg-Landau equation

This tutorial was constructed for the DSWeb competition 2005, part of the SIAM Conference on Applications of Dynamical Systems, Snowbird, Utah.  The tutorial won second prize.

Thesis files in LaTeX

Getting your thesis to format correctly and look good using LaTeX can be tricky.  Many a happy hour of my PhD was spent trawling USENET message boards for LaTeX and PDF hacks to produce the perfect thesis template.

To share some of my hard work, I have boiled down all my LaTeX experience into a tutorial, which includes a number of templates.

» Tutorial: Thesis files in LaTeX