University of Edinburgh
I am interested in computer simulation of the behaviour of solids.
At very high pressure, even the simple elements can dramatically change character. Semiconductors like silicon become metals. Metals like sodium become insulators. Diatomic gases like hydrogen become molecular crystals and ultimately non-molecular metals. Almost every element undergoes its own distinctive set of changes. My work is to understand how this occurs, by solving the equations of quantum mechanics for the electrons which hold these materials together.
I am also interested in practical applications using the same techniques, in particular designing new and improved steels and titanium alloys. For understanding structural properties it it necessary to simulate assemblages of millions of atoms, and to do this some simplification of the quantum mechanics which allows rapid calculation of forces between atoms is needed. Much of my work concentrates on deriving so-called interatomic potentials which fulfil this role.
I am also interested in complex feedback systems, particularly model based on evolutionary game theory. Many social and environmental problems are extremely complicated, and to model them appears to require huge numbers of parameters to define many effects. Typically these parameters are not known, and worse a "desired" outcome can normally be obtained by judicious choice. . Evolutionary game theory models avoid this fine-tuning by proposing that the world we see is based on successful previous choices, which automatically tune the parameters to give individuals an evolutionary advantage.
I have applied these models to ecologies, population dynamics and economies. Strikingly similar patterns emerge: once it is possible for different regions to behave differently, they do so, and normally oscillate in time. The evolutionarily successful strategy is normally the one which overexploits resources, causing it to expand from it core region, but ultimately collapse. Most models have a healthy, complex, stable regime in which strategies expand and die, to be replaced by others from different parts of the space. Two things can destroy these models - globalization is which one strategy dominates the space, and equality in which the benefits of a successful strategy are disbursed to all. The mathematical logic of this offends my ethical sense (and people don't want to hear it), so I've stopped working on this.
Interests and expertise (Subject groups)