Complex Systems Science
A number of concepts from lattice statistical mechanics have proved influential
in thinking about the science of complex systems. These include:
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:
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
- stochastic cellular automata (MORE).
- population Monte Carlo, using techniques from statistical physics to analyse global change
- 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++.
CSIRO Complex Systems Science website.
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.
This page, its contents and style, are the responsibility of the author
and do not represent the views, policies or opinions of The University
Ian Enting: last change 5/7/05.