School of Mathematics

Michael Cates

Michael Cates abstract

Michael Cates, School of Physics, UoE

Phase separation in self-propelled organisms

Micro-organisms such as motile bacteria move persistently along a body axis that gets updated either by sudden changes or gradual angular diffusion. Self-propulsion is a fundamentally non-equilibrium process, yet at large distances such motion is a diffusive random walk. As such, it superficially resembles the Brownian motion of equilibrium colloidal particles suspended in an isothermal fluid. However, if the speed v of self-propulsion varies in space, fundamental differences from equilibrium Brownian motion emerge. Specifically, self-propelled particles tend to accumulate in regions where they move slowly -- a tendency entirely forbidden in thermal equilibrium. Likewise, they can undergo phase separation into dense and dilute fluid regions, even if all interactions are repulsive. This arises when v is a rapidly decreasing function of rho, creating a feedback between slowing-induced accumulation and density-induced slowing. I shall trace the tortuous path from the microscopic dynamics of individual swimmers to a stochastic PDE for their density rho, called active Model B, which exposes some unexpected subtleties of this new type of phase separation.