Generalising geometric microscopic swimming
Microscopic swimmers, like bacteria or algae, exist within viscous fluid environments. The nature of such fluids means that these swimmers are constrained by geometry and must break time symmetry to generate motion. As a result of these conditions the displacement of any swimmer can be written in terms of a path integral over a 'gauge' field. This integral representation is known as the geometric swimming representation and was first introduced by Shapere and Wilczek. Though this technique works well for simple swimmers it can be cumbersome when the swimmers have many modes of deformation or if variables do not commute. In this talk I will introduce the key ideas behind swimming in viscous fluids and the geometric swimming representation. With the aid of some example swimmers, I will then discuss my recent attempts to extend this representation to systems with non-commuting variables and systems with many deformation modes.
Dr Lyndon Koens, Macquarie University