Confined active Brownian particles: theoretical description of propulsion-induced accumulation

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 a...

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Bibliographic Details
Published in:New journal of physics 2018-01, Vol.20 (1), p.15001
Main Authors: Das, Shibananda, Gompper, Gerhard, Winkler, Roland G
Format: Article
Language:English
Subjects:
Accumulation
active Brownian particle
active matter
Anharmonicity
Brownian motion
Cartesian coordinates
Computer simulation
Conditional probability
confinement
Diffusion coefficient
Distribution functions
Economic models
Exact solutions
Fokker-Planck equation
Mathematical analysis
microswimmer
Physics
Probability distribution
Probability distribution functions
Propulsion
trapping
Tumbling
Velocity
Velocity distribution
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Summary: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.
ISSN:1367-2630
1367-2630
DOI:10.1088/1367-2630/aa9d4b