Non Linear Dynamics, Complexity and Multiscale Phenomena

 

The solar wind - magnetosphere coupling exhibits both global and multiscale characteristics due to the broad range of overlapping space and time scales. The multiscale phenomena have been modeled in terms of many processes such as phase transition, intermittent turbulence, and self-organized criticality. A new theoretical foundation for multiscale processes is developed in terms of fractional kinetics in which the probability densities are described by Fokker-Planck equation with fractional derivatives.      

Dynamics in the solar wind-magnetosphere coupling: The dynamical manifold in 3D
obtained from the cogulated database (left) and globals MHD simulations (right).

 

A collaboration with New York University, funded by National Science Foundation under the Computational and Mathematical Geoscience (CMG), explores the multiscale phenomena in nature. In this project (PI: Dr. Surja Scharma) many approaches based on nonlinear dynamics and chaos, fractional kinetics, nonequilibrium statistical physics and nonlinear time series analysis are used. One of the main topics of research is the long term correlations and its role in extreme events. The systems under study are the large scale open systems in nature (solar wind-magnetosphere interaction), financial markets, and laboratory systems.