When are active Brownian particles and run-and-tumble particles equivalent? Consequences for motility-induced phase separation
1 SUPA, School of Physics, University of Edinburgh, JCMB Kings Buildings - Edinburgh EH9 3JZ, UK
2 Universite Paris Diderot, Sorbonne Paris Cité, MSC, UMR 7057 CNRS - F-75205 Paris, France
Received: 26 July 2012
Accepted: 5 January 2013
Active Brownian particles (ABPs, such as self-phoretic colloids) swim at fixed speed v along a body-axis u that rotates by slow angular diffusion. Run-and-tumble particles (RTPs, such as motile bacteria) swim with constant u until a random tumble event suddenly decorrelates the orientation. We show that when the motility parameters depend on density ρ but not on u, the coarse-grained fluctuating hydrodynamics of interacting ABPs and RTPs can be mapped onto each other and are thus strictly equivalent. In both cases, a steeply enough decreasing v(ρ) causes phase separation in dimensions d = 2,3, even when no attractive forces act between the particles. This points to a generic role for motility-induced phase separation in active matter. However, we show that the ABP/RTP equivalence does not automatically extend to the more general case of u-dependent motilities.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 87.10.Mn – Stochastic modeling / 64.75.Jk – Phase separation and segregation in nanoscale systems
© EPLA, 2013