Abstract
The stationary-state distribution function of confined active Brownian particles (ABPs) is analyzed by computer simulations and analytical calculations. We consider a radial harmonic as well as an anharmonic confinement potential. In the simulations, the ABP is propelled with a prescribed velocity along a body-fixed direction, which is changing in a diffusive manner. For the analytical approach, the Cartesian components of the propulsion velocity are assumed to change independently; active Ornstein–Uhlenbeck particle (AOUP). This results in very different velocity distribution functions. The analytical solution of the Fokker–Planck equation for an AOUP in a harmonic potential is presented and a conditional distribution function is provided for the radial particle distribution at a given magnitude of the propulsion velocity. This conditional probability distribution facilitates the description of the coupling of the spatial coordinate and propulsion, which yields activity-induced accumulation of particles. For the anharmonic potential, a probability distribution function is derived within the unified colored noise approximation. The comparison of the simulation results with theoretical predictions yields good agreement for large rotational diffusion coefficients, e.g. due to tumbling, even for large propulsion velocities (Péclet numbers). However, we find significant deviations already for moderate Péclet number, when the rotational diffusion coefficient is on the order of the thermal one.
Highlights
The distinct feature of active systems is their autonomous motion powered by an internal energy source or by utilizing energy from their environment [1,2,3,4,5,6,7,8,9]
We have investigated the properties of active Brownian particle (ABP) confined in a radially symmetric potential
The study of ABPs and active Ornstein– Uhlenbeck particle (AOUP) confined in a harmonic potential clearly reveals the strong effect of the condition ∣v∣ = v0 = const. on the stationary-state properties
Summary
This results in very different velocity distribution functions. The analytical solution of the Fokker–Planck equation for an AOUP in a harmonic potential is presented and a conditional distribution function is provided for the radial particle distribution at a given magnitude of the propulsion velocity. This conditional probability distribution facilitates the description of the coupling of the spatial coordinate and propulsion, which yields activity-induced accumulation of particles. The comparison of the simulation results with theoretical predictions yields good agreement for large rotational diffusion coefficients, e.g. due to tumbling, even for large propulsion velocities (Péclet numbers).
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