(a) Biomedical modelling, (b) industrial modelling and (c) social / human interaction modelling are the main thrusts here, with (a), (b) involving a background in the theory of solids and of fluid flows at medium to high Reynolds numbers (fast fluid flows), including the development of corresponding analysis and accurate computational fluid dynamics. The phenomena of interest include interaction, separation, instability, transition and turbulence, especially for slender layers and internal or external motions. The real applications are in industry, such as for food quality, flight safety, in biomedicine, such as for stroke, incontinence, and in atmospheric dynamics, machinery dynamics, engine flows, including in particular air flow past cars, helicopters and hills, water motion past ships, droplets and splashing. Two fundamental examples are to find the rapid flow past a bluff body or past a liquid droplet, at medium to high Reynolds numbers, possibly with flow separation and with transition from laminar to turbulent motion in the boundary layer and detached shear layers. The recent development (c) includes rumour propagation, crime spreading and consumer behaviour.