This is the main advantage of such ‘mean field’ models. They are known not to describe fluctuations very well, so various quantities, such as size distributions of clusters, are not described accurately. In current research, using fast computational techniques such as ‘Kinetic Monte Carlo’ (KMC), the early stages can be simulated on moderate size lattices. These KMC ‘experiments’ using the same assumptions can then be used to check whether mean field treatments work for a particular quantity. The CSSS seminar on April 15th is by one of the leaders in this area, Dr Steve Bales (Sandia, Livermore). This will be a good chance to compare these different approaches.
The emergence of computer simulation as a third way between experiment and theory is clearly a growth area of our time. To make progress in this area, one has to start with the simplest models, and stick with them until they are really understood. You need to beware generating more heat than light, and in particular of generating special cases which may or may not be of real interest. Simulations can however be very illuminating, and may suggest inputs for simple models that one hadn’t thought of. Animations are immediately appealing, and if Spielberg can do it, why shouldn’t we? The problem lies only in the subsequent claims for correspondence with reality; then a measure of self-discipline is needed, both from the lecturer/writer and the listener/reader.
