Research project P4/08 (Research action P4)
The theme of complexity provides a unifying view of large classes of systems of interest in physical, environmental and life sciences sharing the common feature of exhibiting a great variety of behaviors, from coherent structures to fully developed chaos, as a result of the fundamental mechanism of instability. This confers to them an enhanced sensitivity, highlights the role of probabilistic elements in the evolution and raises the problem of prediction and control. The objective of this research project is to develop a concerted approach encompassing the deterministic and the probabilistic aspects of complex systems and to explore potential applications.
The expertise of the participating laboratories covers statistical mechanics and thermodynamics, nonlinear dynamics, stochastic processes, quantum and mathematical physics as well as atmospheric sciences, where complexity and the issue of prediction are parts of everyday reality. This complementarity and the cross fertilization of the theoretical, numerical and experimental techniques that are developed will allow to address from a novel point of view fundamental questions as well as practical issues of current concern.
The research topics are the following :
-Macroscopic level: thermodynamic aspects; competing bifurcations, defect dynamics and spatio-temporal chaos in reaction-diffusion systems and materials under stress; singularity analysis, integrability and chaos in continuous and discrete dynamic systems.
-Probabilistic approach to complex systems: spectral representation of the evolution operators of probability densities; status of the mean-field description.
-Mesoscopic and microscopic scales: microscopic chaos in statistical mechanics and quantum physics; interference patterns in Bose-Einstein condensates; nonlinear dynamics in low-dimensional and restricted geometry systems; reactive dynamics on cell membranes; non-equilibrium critical phenomena; stochastic resonance; microscopic simulations.
-Prediction and control: error growth in multivariate chaotic systems; predictability of atmospheric fields; neural network and multifractal methods for data assimilation.
-Evolutionary and cognitive processes: learning by examples; immune memory and self-nonself discrimination; cooperative dynamics in group-living organisms.
In the long run, complex systems research is likely to lead to major advances in applied sectors, such as new prediction techniques in atmospheric sciences and building of materials whose mesoscopic structure is tailored to specific purposes. Shorter term applications are also envisaged:
-how to use complex dynamic behaviours to enhance the specificity of a reaction pathway in heterogeneous catalysis;
-hybrid codes combining particle and field representations for computing complex flows;
-detection of complex signals on the basis of stochastic resonance phenomena and noise-induced transitions;
-utilization of collective behaviours in resource management.
