NON LINEAR DYNAMICS IN COMPLEX SYSTEMS The research project is made of two main axes in the fields: NON LINEAR PHYSICS and STATISTICAL PHYSICS. 1) COMPLEX CHAOTIC DYNAMICS IN LATTICES The idea is to use chaos theories and statistical approaches to study the dynamics of nonlinear coupled systems, where just a few rigorous results on the dynamics are available when the number of oscillators is large. Recently, systems with both on-site and nearest-neighbour nonlinear force have been studied which are susceptible of applications to physical and biological systems (nonlinear effects in solids, diffusion of adatoms on surfaces, denaturation of DNA, high conductivity in hydrogen bonded systems.... ).
2) LOCALIZATION OF ENERGY IN LATTICES In most of the non linear system, the discreteness is an important ingredient for the dynamics of non linear excitations but also of their creation. We would like to * extend the method, I developed during my thesis, to lattices with different components. * study existence and stability of localized solutions in lattices of 2 and 3 dimensions. * study in higher dimension the new mechanism of localization of energy by collision of breather-like excitations.
For both axes of research, we would like to * predict numerically the behaviors of non linear discrete systems with several coupled degrees of freedom. * elaborate new theoretical approaches to study the modes induced by the non linearity and the discreteness. * apply the results to new problems including non linear coupling of different degrees of freedom: magnetic systems and hydrogen bonded systems.
Both laboratories are members of the same european network "Complexity and chaos" (No ERBCHRXCT940546).