Locomotion strategies employed by unicellular organism are a rich source of inspiration for studying mechanisms for shape control. They are particularly interesting because they are invisible to the naked eye, and offer surprising new solutions to the question of how shape can be controlled.

In recent years, we have studied locomotion and shape control in Euglena gracilis. This unicellular protist is particularly intriguing because it can adopt different motility strategies: swimming by flagellar propulsion, or crawling thanks to large amplitude shape changes of the whole body (a behavior known as metaboly). We will survey our most recent findings within this stream of research.

Superhydrophobic surfaces, formed by air entrapment within the cavities of a hydrophobic solid substrate, offer a promising potential for drag reduction in small-scale flows. It turns out that low-drag configurations are associated with singular limits, which to date have typically been addressed using numerical schemes. I will discuss the application of singular perturbations to several of the canonical problems in the field.