Active Brownian Particles and Run-and-Tumble Particles: a Comparative Study

TL;DR

This paper compares Active Brownian Particles and Run-and-Tumble Particles, revealing their similar steady-state behaviors, differences under external potentials, and the extension of their hydrodynamic equivalence to interacting microscopic models.

Contribution

It provides a detailed comparison of ABPs and RTPs at microscopic and macroscopic levels, including their steady-state distributions and hydrodynamic equivalence with interactions.

Findings

Both models admit an effective equilibrium regime perturbatively.

Particles slow down at high density due to collisions, with unchanged propulsive effort.

Hydrodynamic equivalence extends to microscopic models with repulsive interactions.

Abstract

Active Brownian particles (ABPs) and Run-and-Tumble particles (RTPs) both self-propel at fixed speed $v$ along a body-axis ${\bf u}$ that reorients either through slow angular diffusion (ABPs) or sudden complete randomisation (RTPs). We compare the physics of these two model systems both at microscopic and macroscopic scales. Using exact results for their steady-state distribution in the presence of external potentials, we show that they both admit the same effective equilibrium regime perturbatively that breaks down for stronger external potentials, in a model-dependent way. In the presence of collisional repulsions such particles slow down at high density: their propulsive effort is unchanged, but their average speed along ${\bf u}$ becomes $v(\rho) < v$. A fruitful avenue is then to construct a mean-field description in which particles are ghost-like and have no collisions, but swim at a variable speed $v$ that is an explicit function or functional of the density $\rho$. We give numerical evidence that the recently shown equivalence of the fluctuating hydrodynamics of ABPs and RTPs in this case, which we detail here, extends to microscopic models of ABPs and RTPs interacting with repulsive forces.