Abstract:

In the last 30 years a new and far reaching research activity called Complexity science has developed aiming to establish the theoretical foundations of the study of complex systems. Based on an abundance of experimental results and mathematical models, researchers have started to reveal the intricate structure of complex systems and predict the emergence of new dynamical phenomena.

Within this exciting scientific environment, the main goals of this proposal are:

- To solve mathematical models aimed at analyzing brain dynamics as recorded by EEG and ECoG signals.
- To apply analytical and numerical methods of nonlinear dynamics and statistical physics to study Hamiltonian lattices with a broad range of physical applications.
- To solve differential equations of granular matter dynamics and simulate complex materials of interest to materials science and nanotechnology.

The 7 Work Packages of the proposal deal with mathematical modeling of:

- brain complexity,
- classical mechanics,
- celestial mechanics and nonlinear optics,
- nonlinear dynamics and statistical physics of molecular lattices,
- complex materials with technological applications,
- nonlinear wave equations and
- complex systems in biology and physical chemistry.

The expected results are:

- The mapping of brain activity and information flow among brain areas, analyzing EEG and EcoG signals and the solution of mathematical models, whose predictions can be compared with clinical data.
- The development of mathematical tools to distinguish ordered from chaotic motion, predict and control energy transport in molecular lattices and improve the operation of plasma physics and nonlinear optics experiments.
- The solution of differential equations that describe granular clustering with industrial applications, simulate complex materials with exceptional magnetic and optical properties and model complex processes in physical chemistry and biology such as protein crystallization and the dynamics of double helical DNA structures.

*Mis: 379337*