This project consists in the application of stochastic methods to describe the evolution of flows of Newtonian and non-Newtonian fluids (in particular, hemodynamic flows), from theoretical and from the practical point of view. The main goals are twice: 1) Modelling and control the evolution of flows of fluids, by taking into account real world random effects. Here, we hope to establish the well-posedness of some stochastic models for the evolution of complex fluids of differential type, namely second and third grade fluids. In addition, we hope to control and stabilize some flows, as well as to determine stationary statistical solutions. This study intends to contribute to understand and control turbulent flows. 2) To perform Bayesian analysis, by using real data from Hospital Garcia de Orta, to simulate hemodynamic flows in context of hemodialysis. Referring to the sociological relevance, let us mention that hemodialysis is the most prevalent modality of kidney replacement therapy. To perform hemodialysis, it is necessary to create (by surgery) and maintain an appropriate Regional Vascular System, constituted by vessels, arteriovenous fistula and blood flow that support the hemodialysis. The maintenance of such appropriate Regional Vascular System (without or controlled pathologies) is an enormous clinical and economic burden. One of the crucial problem relays on the understanding and control of the turbulence of the hemodynamic flows.
Team: Fernanda Cipriano, Isabel Natário, Adilson Almeida (PhD student), Sílvia Guerra (PhD student).