A research and academic program on** Fluid Dynamical Systems** has been introduced by Rui A. P. Perdigão in 2015, entailing his recently developed generalised class of dynamical systems beyond the classical ergodic stochastic-deterministic paradigms. Rui’s advances have brought out a unified mathematical physics of complexity and fluids, advancing nonlinear statistical physics, analytical mechanics, functional analysis, theoretical thermodynamics, information theory and differential geometry in a unified framework.

Academically, these advances are already being delivered into Rui Perdigão’s graduate course of Fluid Dynamical Systems. Since its inception, the course has been held by Rui himself at TU Wien, Austria. Following international invitations, Rui’s course became available in condensed form through international courses, workshops and seminar series booked in advance through the Meteoceanics Doctoral School on Complexity, which is also chaired by Rui Perdigão.

The general course program encompasses a brief review on fluid dynamics and physics of complexity, then progressing to an in-depth presentation of the recent fundamental contributions from the coordinator shaping this field beyond the realms of both fluid mechanics and dynamical systems. In this sense, Fluid Dynamical systems are neither to be confused with fluid mechanics nor with dynamical systems approaches to fluid flow.

The scientific relevance of Fluid Dynamical Systems ranges across the dynamics and predictability of complex systems beyond the classical notion of a fluid: from quantum electrohydrodynamics to the coevolutionary earth system and astrophysical dynamical systems, shedding fundamental mechanisms and governing principles across spatiotemporal scales. These applications are thoroughly explored in the course as well.

Special relevance arises from its central role in providing fundamental physical understanding and dynamic predictability to critical phenomena such as extreme events, including “black swan” behaviour unforeseen from past data records and from the ensemble of possibilities spun by classical dynamical system theories. Course participants are taken on a journey to unveil hidden predictability in seemingly unpredictable phenomena.

Mathematical applications are also explored, ranging from advancing the kinematic geometry of space-time manifolds to the non-local differential geometry of fractal structures, and providing a more fundamental analytical background to probability theory, nonlinear statistics and information theory, including in far-from-equilibrium and non-ergodic coevolutionary settings in nonlinear statistical physics following recent advances by Rui Perdigão.

Engineering applications covered in the course include dynamic model design and decision support in the wake of environmental hazards and fluid-structure interaction challenges in a coevolutionary world. Moreover, they include structural-functional design and traffic optimisation for telecommunication and transportation networks.

A promotional poster for the course is presented below:

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