My research activities are in the statistical mechanics of disordered and non-equilibrium systems and random matrices. Most of my research is analytical, but supported where appropriate by numerical simulations.
Statistical mechanics is the branch of theoretical physics that attempts to explain, by starting at the level of atoms, molecules or other small particles, the behaviour of systems where a large number of these particles interact. In other words, it attempts to move from the microscopic rules, such as the way in which molecules in a gas "collide" with one another, to macroscopic quantities such as pressure or temperature. The subject area itself is really just a collection of theoretical techniques rather than a unified theory and can be applied to any situation in which one is interested in collective behaviour, from population dynamics, through solids, liquids and gases to traffic flow, financial markets and social science.
Much progress has been made in understanding the equilibrium statistical mechanics of pure, perfect, non-random solids, liquids and gases. Many mathematical and theoretical physicists have now moved on to study the equilibrium statistical mechanics of random systems such as spin glasses, other random magnets or electron systems. These models, which describe the effect of flaws or defects in a particular material, exhibit a much richer behaviour, with more exotic phase transitions and glassy (slow) kinetic behaviour.
The other major theme in this research area is the study of non-equilibrium systems. These are systems in which the major variables in the system change with time and never assume a steady state value. We have been involved in the study of a number of non-equilibrium phenomena, including deposition, coagulation, fragmentation, growth and aggregation. We have been applying some ideas from non-equilibrium statistical mechanics to study complex adaptive systems, which can be used to model buying and selling in a market, and herding in financial markets. Herding is believed to be the phenomenon that underlies the fat tails in the distribution of returns (profits) observed on short time scales for many stocks, shares and market indices. More recently, we have been studying both scale free and small world networks, systems made up of vertices and edges, using the techniques of statistical mechanics.
I have active research links with the Institute Josef Stefan, Ljubljana, the University of Havana, University of Wroclaw, Poland, Seoul National University, Boston University and Cambridge University.
I have compiled a list of my recent publications and I am always happy to receive enquiries about my research activities, particularly from potential collaborators, students or postdocs. For potential postgraduate research students, the Brunel University application form is available online. There is a short version of my cv here.
Here is a picture of our successful TQA team, and a few terrifying shots of the evidence in the baseroom, as well as some photos of more enjoyable times at the Econophysics conference, Dublin, July 1999, in the Yellow Mountains in China in 2000 and at ICCS in Krakow in 2004. Here is a picture of my friends in Havana.
This is a photograph of the group of people that sat near my brother and I during Portugal versus USA, Uruguay versus Senegal, Brazil versus Costa Rica and Spain versus Ireland at the 2002 World Cup Finals in Korea. Finally, for fans of great football everywhere, Paul Evans' goal from the half-way-line for Brentford in the game against Preston North End on 25 September 1999. See if you can see me in the New Road stand.I have compiled a list of links that I find useful.
Last updated 10 July 2004
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