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Dynamical systems governing real processes always contain elements characterized by uncertainty or stochasticity. Stochasticity may arise due to incomplete modeling of the governing physical laws, uncertainty in the system parameters, the initial and boundary conditions, and also in the external forcing. The effect of the random components to the responce is often enhanced due to inherent system instabilties, causing distribution of energy to a broadband spectrum of scales both in space and time.
Environmental processes and related engineering applications is a typical class of nonlinear dynamical phenomena presenting strongly transient and stochastic characteristics. These include physical processes such as fluid flows, water waves and transport of tracers (e.g. pollutants or microorganisms) in these flows, but also engineering applications such as energy harvesting devices and structures subjected to environmental loads (e.g. water waves, wind, earthquakes).
In these problems uncertainty evolves dynamically, fully coupled with the system state and in many cases (e.g. in turbulent flows) it becomes equally important. The focus of my research is to study this two-way coupling between stochasticity and system dynamics with ultimate goals the understanding of the fundamental mechanisms governing energy transfer across different temporal and spatial scales in the environmental processes described previously, the development of computationally efficient algorithms describing these processes, and finally the robust optimization and design of engineering configurations that can operate adaptively in these conditions.