Hydrodynamic equations for active Brownian particles in the high-persistence regime

Area of Science:

• Physics
• Soft Matter Physics
• Statistical Mechanics

Background:

• Active Brownian particles (ABPs) are model systems for self-propelled entities.
• In regimes of high persistence, polarization emerges as a key dynamical field.
• Existing models may not fully capture the complex dynamics in these regimes.

Purpose of the Study:

• Derive macroscopic equations for density and polarization fields of ABPs in the high persistence regime.
• Investigate the connection between derived equations and motility-induced phase separation (MIPS).
• Explore clustering dynamics and emergent phenomena like damped density waves.

Main Methods:

• Utilized a recently proposed kinetic description for ABPs.
• Derived Navier-Stokes-like equations for density and polarization.
• Employed the Chapman-Enskog method to determine transport coefficients from microscopic dynamics.
• Performed linear stability analysis and numerical simulations in one spatial dimension.

Main Results:

• Successfully derived equations capturing density and polarization dynamics.
• Confirmed that the equations describe the density instability leading to MIPS.
• Numerical solutions revealed clustering, polarized interfaces, domain coarsening, and particle accumulation under gravity.
• Identified damped density wave modes arising from polarization coupling, verified by simulations.
• Found a need for a regularizing pressure term to handle high densities.

Conclusions:

• The derived Navier-Stokes-like equations provide a robust framework for studying ABPs in the high persistence regime.
• The model accurately predicts MIPS and complex clustering behaviors.
• The coupling between density and polarization fields leads to novel dynamic modes, such as damped density waves.