(473i) Brachistochrone Trajectories for Microorganisms and Artificial Microswimmers

Microorganisms and artificial microswimmers maneuver through their environment to explore, navigate, and harvest energy. In doing so, they may ascend or descend to reach their target. While self-propelling through a fluid, they experience both gravitational and buoyant forces. A central question arises: given two points, what is the fastest path between them? This leads to the problem of determining underwater brachistochrone trajectories for microswimmers operating under low Reynolds number hydrodynamics. The solution depends on the swimmer's shape as well as the balance of competing forces, which influence not only the geometry of the trajectory but also the swimmer’s orientation relative to the path as it travels. A. Nourhani acknowledges support from the National Science Foundation CAREER award, grant number CBET-2238915, and M.-R. Alam acknowledges support from the American Bureau of Shipping.