Abstract

I will describe two biologically inspired systems that can be analyzed using the same hydrodynamic Hamiltonian formalism. The first is ATP synthase proteins, which rotate in a biological membrane. The second is swimming micro-organisms such as bacteria or algae confined to a two-dimensional film. I will show that in both cases, the active systems self-assemble into distinct structural states—the rotating proteins rearrange into a hexagonal lattice, whereas the micro-swimmers evolve into a zig-zag configuration with a particular tilt. While the two systems differ both on the microscopic, local interaction, as well as the emerging, global structure, their dynamics originate from similar geometrical conservation laws applicable to a broad class of fluid flows. Time permitting, I will show experiments and simulations in which the Hamiltonian is perturbed, leading to different and surprising steady-state configurations.