This project will address problems involving fluid flow and mass transfer in the human body, specifically in the lungs and gut. We are interested in using mathematical models to understand how inhaled particles (allergens, pathogens, drugs) mix and spread through the lung airways, how nutrients are taken up by the intestines, and other similar biomedical problems. These questions require a multi scale modelling approach to deal with the wide range of spatial and temporal scales across which flows occur in the human body. An important technique in this context is reduced order modelling via rational methods from dynamical systems theory, as well as data-driven strategies. 

Webpage: https://sites.google.com/view/jrpicardo

Area: Multiscale modelling, biofluid mechanics, data-driven methods

Prerequisites: To enjoy working on this problem you must seriously want to learn, understand, and apply techniques of multi scale modelling and simulation. By year 2 of your PhD, you will have to be strong in fluid dynamics, theory of ODEs and PDEs, and numerical methods. So a good foundation in these subjects will help. A lot of reading, especially of biomedical literature, will be needed to frame the problems and develop the model.