The research described in this dissertation was supported financially by an EPSRC studentship, and it is a great pleasure to be able to thank some of the people who have helped me in various ways, and whose support has been invaluable over the past three years.
My supervisor, Mike Payne, has been a faithful source of wisdom and encouragement throughout, as well as a generous supplier of wine. I am also grateful to Richard Needs and Roger Haydock for stimulating discussions which have helped to broaden my knowledge and understanding of condensed matter physics.
I am indebted to Nicola Marzari for his hospitality and also for pointing out several k-points, not least the concept of the roto-occupations (the ). I also benefitted from discussions with Eric Sandré concerning computational minimisation schemes.
Thanks are due to those who have had the dubious pleasure of sharing offices with me: Murray Jarvis, Duncan Kerr, Yong Mao and Matt Segall have all made life at the Cavendish much more interesting than it would have been on my own.
Ian Bung Bung White has been a continual source of entertainment and diversion, whose initiative in proposing frequent experimental investigations into the aerodynamics of spinning disks and ellipsoids made the days pass much more quickly.
There is insufficient space to thank all my friends at Christ's College and St. Andrew the Great individually, but I value those times spent together which have contributed to making Cambridge a great place to live as well as to work.
Finally, I thank my family for their love and support, without which I would never have got here in the first place.