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A training program for an equivalent of 270 man-month covering analytic, dynamical systems with few degrees of freedom. The objective of the numerical and experimental methods as well as the physical, mathematical and applied aspects of the subject is proposed. Teaching material, proposal is to develop theoretical, computational and experimental tools for the study of spatially extended systems, which constitute a including electronic material for interactive simulations will be developed and become available throughout the network. Network members will organise particularly relevant class of multi variate dynamical systems from the several workshops and summer schools whose Proceedings will be edited, and standpoint of physical sciences. The following main topics will be addressed.
will prepare reviews on important aspects of nonlinear behaviour of - Fundamental aspects of spatially extended systems: Properties which are spatially extended systems. Special effort will be made to acquaint the uniform in the system size versus those which become well-defined only in young scientists attached to the network laboratories with the activities of the network as a whole.
the infinite size limit; sensitivity to initial conditions in the presence of a continuous spectrum of positive Lyapunov exponents; reduction of the dynamics to a sub manifold of phase space; exact solutions of systems exhibiting nontrivial phase portraits.
- Pattern competition, localised structures and selection: The dynamics of defects and their bifurcations; the role of symmetry groups; diffraction versus diffusion; localised structures in dissipative systems. - Scaling of turbulent fields - A physicist's approach: A systematic field-theoretic approach to turbulence paying special attention to non-perturbative effects; confrontation with recent experiments showing the limitations of current theoretical approaches; numerical simulations of the passive scalar problem in connection with scaling properties. - Statistical approach to spatially extended systems: Study of multi variate Liouville and Frobenius-Perron equations using techniques of statistical mechanics; statistical characterisation of complex spatio-temporal structures; approach to equilibrium of radiation fields coupled to matter in confined regions; theoretical and molecular dynamics studies of the role of dynamical chaos in transport processes. - Expected technological spin-offs: Polymer growth on catalytic surfaces; monitoring and prediction of ecological patterns; signal stabilisation and control; modelling, control and development of diagnostic tools in connection with cardiac arrhythmias, insuline secretion and bone remodelling.

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Bd du Triomphe, Campus de la Plaine CP2

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Participants (8)