Pursuit and evasion at low Reynolds number

The modern study of pursuit and evasion dates at least as far back as the 18th century, when Bouguer determined the pursuit course of a pirate ship chasing a merchant vessel. Pursuit and evasion in a viscous fluid, however, introduces numerous additional complexities - first among them, the flow field generated by a pursuer can either aid or infinitely hamper its attempt to capture its prey. We will discuss time-optimal pursuit strategies at the micron scale. For a pursuer which imposes a stresslet on the surrounding environment, using Pontryagin's Minimum Principle we identify a two-state optimal control - the pursuer's optimal strategy switches discontinuously upon arrival at a critical ratio involving the pursuer's speed and its distance from the evader. A fixed obstacle is then introduced, which affects the dynamics in non-trivial ways. We investigate the pursuer's strategies to bypass the obstacle and the resulting paths, using both analytical and numerical methods.