Complex Systems Science

Lattice statistics

A number of concepts from lattice statistical mechanics have proved influential in thinking about the science of complex systems. These include:

emergence, where a collective system shows properties that are not inherent in the components
power-law (fractal) scaling relations connecting different physical quantities
universality: the property of different systems having the same scaling laws

In addition, a strong theme of complex systems studies in contingency: the sensitive dependence on prior events. The mathematical analysis of chaos shows that such sensitive dependence can arise in quite simple systems. My projects related to lattice statistics are:

stochastic cellular automata (MORE).
population Monte Carlo, using techniques from statistical physics to analyse global change (MORE).
New applications in the Finite Lattice Method of series expansion. - surface effects, Kosterlitz-Thouless transitions.

Data assimilation in the study of complex systems

One of my ongoing research interests is the role of data assimilation as a way of analysing complex systems. This is suggested by the experience of the weather services analysing a complex system several times a day. The concept is that analysing complex systems as an inverse problem, with observations as boundary conditions might take the place of the archetypal reductionist approach of controlled experiment in systems where controlled experiment is not possible. Some expansion of these initial thoughts is given in CSIRO Atmospheric Research, technical paper 62 (pdf file).

A new project related to data assimilation is the developement of automatic differentiation through operator overlaoding in C++.

Links

CSIRO Complex Systems Science website.

Other

Some of my suggestions (and a few anti-suggestions) of books on (and related to) complex systems science are listed, extending an earlier list on the CSIRO Complex Systems Science website.

Disclaimer

This page, its contents and style, are the responsibility of the author and do not represent the views, policies or opinions of The University of Melbourne.

Ian Enting: last change 5/7/05.