Complex Systems

Contact: Dr. David Corcoran
Head, Dept. of Physics,
University of Limerick
E-mail: David.Corcoran@ul.ie
Tel. +353-61-202509

State-of-the-art electronic devices, sand and even plate tectonics all share something in common, they are all systems where noise and disorder effects can dominate. Yet despite the Nobel award winning work of de Gennes in 1991" for discovering that methods developed for studying order phenomena in simple systems can be generalized to more complex forms of matter", the application of statistical mechanics to complex out of-equilibrium systems is still today only in the development stage. We therefore investigate a broad spectrum of systems which exhibit what we term disorder dynamics including electromigration in thin metal films, earthquakes, and sheared granular media using experimental and computational modelling techniques (see Fig. 1).

Fig. 1 Complex granular stress chains

By borrowing the tools of statistical mechanics and by focussing explicitly on the role of fluctuations/noise we are developing new approaches in describing, understanding and ultimately predicting complex disordered systems.

A particular area of interest has been exploring the possible mechanism that explains the wide variety of spatial and temporal fractals seen in nature i.e. self-organised criticality.

Fig. 2 Fractal complexity (Mandelbrot Set)

Fractals are known to occur at or near a so-called critical phase transition and in the late 1980s the concept of self-organised criticality gathered rapid popularity, when a simple computer model appeared to automatically generate certain fractal effects. At a critical point there is an infinite size scale and this scale divergence would explain spatial fractal effects. In addition, as there would also be an associated absence of time scale the mechanism would explain the ubiquity of fractal 1/f noise visible in systems from tides to jazz music.

Earthquakes are held by many to be a self-organised critical phenomenon, and earthquake fault lines and earthquake magnitude frequency are typically fractal. We have recently studied the criticality[1] in a well known earthquake model, the so-called Burridge-Knopoff model and demonstrated that rather than self-organisation the system must be tuned to criticality.

[1] "Criticality in the Burridge-Knopoff model", Clancy, I and Corcoran, D., Phys. Rev. E. 71 046124 (2005)

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