Science and Engineering at The University of Edinburgh

Statistical Physics and Complexity

Staff

Profs. Graeme Ackland, Mike Cates and Martin Evans; Dr. Richard Blythe

About Us

Statistical mechanics is a major theoretical tool we use for the understanding of complex systems. The systems in question include many forms of condensed matter, although we also work on non-traditional areas such as ecosystem dynamics and the jamming of traffic. We have strong links with many of the other research areas within the Institute for Condensed Matter and Complex Systems, in particular, the Computational Materials Physics, Physics of Living Matter and Soft Matter Physics themes.

As in simulation, there has in recent years been a shift away from purely equilibrium problems to working on systems that are out of equilibrium. Here in Edinburgh we conduct a wide programme of fundamental work on model systems which addresses the many novel principles of nonequilibrium physics: for example, true phase transitions can arise even in one dimension. Our work also has direct relevance to a wide range of other disciplines, for example, biology, ecology and linguistics.

Research Interests

Below are some examples of the kinds of physics problem now being addressed by PhD students and others within the group:

Nonequilibrium Phase Transitions

Accessibility note: This is a floating box containing an image and a caption. Figure 1: Water percolating through rock
Caption: Figure 1: Water percolating through rock

Analysis of simple models can reveal important generic principles. For example, within a wide class of models for traffic flow, the vehicles will organize in such a way as to minimize the mean velocity, although each vehicle is driven to maximise its own. Such insights feed into our more phenomenological work on colloidal jamming, etc. One keystone model is called 'Directed Percolation' (DP). Think of water attempting to penetrate a porous rock under gravity. In Figure 1, water is injected at the centre. The left frame shows the network of pores (light solid lines) with those accessible from the injection point (heavy). The right frame shows the flow under gravity. There is a phase transition when the fluid first makes it through the rock. The same mathematics represents many other simple models, e.g. of epidemic spreading.

Networks and Agents in Physics and Ecology

Accessibility note: This is a floating box containing an image and a caption. Figure 2: Desert formation thermogram
Caption: Figure 2: Desert formation thermogram

This work addresses the evolution of interacting objects under nonequilibrium conditions. The objects are often not merely passive but dynamic 'agents': a new science of 'networks' has developed, based on the realization that the web of interaction between agents determines their response to, and effect on, their environment. Evolution can give rise to stable 'emergent phenomena' such as peloton formation in cycle races, or ecosystems adapted to cope with global forcing. In a simple model called 'daisyworld', black and white daisies compete for space on the earth's surface. Figure 2 shows a thermogram for the earth in this model showing formation of a desert (in red). Also shown is 'albedo' (mean reflectivity of the earth's surface, which depends on the vegetation colour).

More information about agents and networks can be found on the NANIA (Novel Approaches to Networks of Interacting Autonomes) website. See in particular the Javascript models that you can play with.

Modelling cultural change

Accessibility note: This is a floating box containing an image and a caption. Figure 3: Simple agent-based model for language change
Caption: Figure 3: Simple agent-based model for language change

Cultural traits (languages, fashions, technologies) change over time through processes of innovation, replication and selection - by evolution, in other words. Is it possible to predict what kinds of innovations will propagate, how far, and how long it will take them to do so? We have used the formation of the New Zealand English language dialect as a testing ground for new ideas, and in particular to see how well modelling paradigms from physics and genetics are suited to the task. We are also examining how fundamental symmetries in quantitative models map on to concepts and theories in language and cultural change. Meanwhile, learning plays a central role in cultural replication, so we're also trying to come up with some theories for how that works both for individuals and in spatially-extended populations too.

See Richard Blythe's website for more information.