Diffusion of active chiral particles
Abstract
The diffusion of chiral active Brownian particles in threedimensional space is studied analytically, by consideration of the corresponding FokkerPlanck equation for the probability density of finding a particle at position x and moving along the direction v ̂ 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 differentialrecurrence 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 meansquared 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 a uniformly distributed random axis, evidence is found of the socalled effect "anomalous, yet Brownian, diffusion," for which particles follow a nonGaussian distribution for the positions yet the meansquared displacement is a linear function of time.
 Publication:

Physical Review E
 Pub Date:
 December 2016
 DOI:
 10.1103/PhysRevE.94.062120
 arXiv:
 arXiv:1611.06324
 Bibcode:
 2016PhRvE..94f2120S
 Keywords:

 Condensed Matter  Statistical Mechanics
 EPrint:
 To appear in Physical Review E, 21 pages, 8 Figs