Diffusion of active chiral particles

Abstract

The diffusion of chiral active Brownian particles in three-dimensional space is studied analytically, by consideration of the corresponding Fokker-Planck equation for the probability density of finding a particle at position x and moving along the directionv at time t, and numerically, by the use of Langevin dynamics simulations. The analysis is focused on the marginal probability density of finding a particle at a given location and at a given time (independently of its direction of motion), which is found from an infinite hierarchy of differential-recurrence relations for the coefficients that appear in the multipole expansion of the probability distribution which contains the whole kinematic information. This approach allows the explicit calculation of the time dependence of the mean squared displacement and the time dependence of the kurtosis of the marginal probability distribution, quantities from which the effective diffusion coefficient and the "shape" of the positions distribution are examined. Oscillations between two characteristic values were found in the time evolution of the kurtosis, namely, between the value that corresponds to a Gaussian and the one that corresponds to a distribution of spherical shell shape. In the case of an ensemble of particles, each one rotating around an uniformly-distributed random axis, it is found evidence of the so called effect "anomalous, yet Brownian, diffusion", for which particles follow a non-Gaussian distribution for the positions yet the mean squared displacement is a linear function of time.PACS numbers: 02.50.-r 05.40.-a 05.10.Gg

Intermediate scattering function of an anisotropic Brownian circle swimmer

“…In particular, we have evaluated the non-Gaussian parameter, which displays oscillations at intermediate times mirroring the interplay of circular swimming motion and rotational diffusion of these active agents. This non-monotonic behavior has also been observed in computer simulations of chiral particles in 3D, subject to isotropic translational diffusion [51]. Similar to the non-Gaussian parameter of three dimensional anisotropic particles [41], it is positive for short times reflecting the anisotropic diffusion and approaches zero for long times.…”

Helical paths, gravitaxis, and separation phenomena for mass-anisotropic self-propelling colloids: Experiment versus theory

“…Here the general trajectory shape is a helix 26,42 which has no transient regime and an orientation that depends on the initial particle orientation (see Fig. 2e).…”

Activity induced synchronization: Mutual flocking and chiral self-sorting

“…Despite the common occurrence of such active oscillators both in nature, e.g. microorganisms [28][29][30][31][32] or cell-components [33][34][35], and in the world of synthetic microswimmers [36][37][38][39][40][41][42][43], their generic large-scale synchronization behavior remains surprisingly unclear: (i) In active matter, previous stud-FIG. 1: (a) Phase diagram of active oscillators comprising the mutual flocking phase induced by activity-induced synchronization: Lines and symbols show analytical predictions and simulation for the phase boundaries (red symbols for two species, black ones for a normal frequency distribution) using two different densities (ρ0 = 10, 20 shown in black crosses and squares).…”