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

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.

Non-Gaussian noise without memory in active matter

“…2(c-d): it is more and more peaked as ντ decreases. This is consistent with previous results for persistent active particles [21,[61][62][63]. For a harmonic obstacle, the distribution is singluar at r = σ for non-Gaussian noise, at variance with the persistent case, and a cusp appears for ντ < 5, reminiscent of the profile under harmonic confinement.…”

Activity induced delocalization and freezing in self-propelled systems

“…We point out that in the potential-free model there are two natural temperatures: the solvent temperature T b = γD t and the effective active temperature T a = µ u 2 = µD a /τ = γD a , where we have defined the effective mass µ = γτ (see below). We fix the value of γ = 1 and inspired to the connection between the AOUP and the ABP model 39 -we also fix the ratio D a /τ = 10 that is the variance of the self-propulsion velocity. This protocol allows us to use a single parameter, τ, to tune the relevance of activity in the system.…”

“…In Sec. 3, we discuss the concept of effective temperature applied to the AOUP system 36,37,39,54 . In particular, we discuss whether to characterize the system it is appropriate to define the effective temperature, T , through the Gibbs density configurational distribution ∝ e −U(r)/T e f f or we need alternative definitions, for instance by identifying T with the average kinetic energy of the particles.…”

Local stress and pressure in an inhomogeneous system of spherical active Brownian particles

“…The damping factor γ R is related to the rotational diffusion coefficient, D R , via γ R = 2D R . Alternatively, the velocity equation of motion of an active Ornstein-Uhlenbeck particle can be considered 38,39 , where aside from the orientation also the magnitude of the propulsion velocity is changing. In any case, the correlation function for the active velocity v v v a i = v 0 e e e i is 25,38 v v v a i (t) · v v v a i (0) = v 2 0 e e e i (t) · e e e i (0) = v 2 0 e −γ R t .…”