Linear response approach to active Brownian particles in time-varying activity fields

Area of Science:

• Soft Matter Physics
• Statistical Mechanics
• Non-equilibrium Systems

Background:

• Active Brownian particles (ABPs) are model systems exhibiting self-propulsion.
• Understanding particle behavior in response to external stimuli is crucial for designing novel materials and processes.
• Previous studies have explored static or simple external fields on ABPs.

Purpose of the Study:

• To theoretically and computationally investigate the response of active Brownian particles to time-varying sinusoidal activity waves in 3D.
• To derive analytical expressions for particle polarization and flux using linear response theory.
• To explore the potential of activity waves for controlling particle mixtures and spatial distribution.

Main Methods:

• Application of the linear response (Green-Kubo) formalism to derive analytical expressions.
• Conducting three-dimensional Langevin dynamics simulations to validate theoretical predictions.
• Analysis of particle fluxes and polarization profiles as a function of particle size and activity levels.

Main Results:

• Fully analytical expressions for torque-free polarization profiles of non-interacting ABPs were derived.
• Activity waves induce particle fluxes that are strongly dependent on particle size.
• The linear response formalism shows high accuracy for small particles (high Brownian motion) or low activity levels.

Conclusions:

• Time-varying activity waves offer a controllable method for manipulating active Brownian particles.
• The derived analytical framework accurately predicts particle behavior under specific conditions.
• This work provides a foundation for using dynamic fields to de-mix particle mixtures or create targeted particle accumulations.